Pricing

Transcription

Pricing

journaloffinancialtransformation
Pricing
Services
Real options
Assets
Recipient of the APEX Awards for Publication Excellence 2002-2004
04/2005/#13
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Pricing
Editor
Shahin Shojai, Director of Strategic Research, Capco
Advisory Editors
Predrag Dizdarevic, Partner, Capco
Bill Irving, President, Capco
John Owen, Partner, Capco
Editorial Board
Franklin Allen, Nippon Life Professor of Finance, The Wharton School,
University of Pennsylvania
Joe Anastasio, CEO, Cross Border Exchange, and Partner, Capco
Philippe d’Arvisenet, Group Chief Economist, BNP Paribas
Jacques Attali, Chairman, PlaNet Finance
Rudi Bogni, Former Chief Executive Officer, UBS Private Banking
Bruno Bonati, Strategic Consultant, Bruno Bonati Consulting
David Clark, NED on the board of financial institutions and a former senior
advisor to the FSA
Géry Daeninck, former CEO, Robeco
Douglas W. Diamond, Merton H. Miller Distinguished Service Professor of
Finance, Graduate School of Business, University of Chicago
Elroy Dimson, Professor of Finance, London Business School
Nicholas Economides, Professor of Economics, Leonard N. Stern School of
Business, New York University
Michael Enthoven, Chief Executive Officer, NIB Capital Bank N.V.
José Luis Escrivá, Group Chief Economist, Grupo BBVA
George Feiger, Executive Vice President and Head of Wealth Management,
Zions Bancorporation
Gregorio de Felice, Group Chief Economist, Banca Intesa
Wilfried Hauck, Chief Executive Officer, Allianz Dresdner Asset Management
International GmbH
Thomas Kloet, Senior Executive Vice-President & Chief Operating Officer,
Fimat USA, Inc.
Herwig Langohr, Professor of Finance and Banking, INSEAD
Mitchel Lenson, Global Head of Operations & Technology, Deutsche Bank Group
David Lester, Chief Information Officer, The London Stock Exchange
Donald A. Marchand, Professor of Strategy and Information Management,
IMD and Chairman and President of enterpriseIQ®
Colin Mayer, Peter Moores Professor of Management Studies, Saïd Business
School, Oxford University
Robert J. McGrail, Chairman of the Board, Omgeo
Jeremy Peat, Group Chief Economist, The Royal Bank of Scotland
Jos Schmitt, Partner, Capco
Kate Sullivan, Chief Operating Officer, e-Citi
John Taysom, Founder & Joint CEO, The Reuters Greenhouse Fund
Graham Vickery, Head of Information Economy Unit, OECD
Norbert Walter, Group Chief Economist, Deutsche Bank Group
David Weymouth, Chief Information Officer, Barclays Plc
TABLE OF CONTENTS
NOBEL LAUREATE VIEW
8
The international monetary system
A discussion with Prof. Robert A. Mundell, University Professor of
Economics, Columbia University, and Winner of The Bank of Sweden Prize
in Economic Sciences in Memory of Alfred Nobel 1999
SERVICES
12
Opinion: Pricing traditional vs. alternative asset
management services
Francois-Serge Lhabitant, Head, Investment Research, Kedge Capital, and
Professor of Finance, H.E.C. University of Lausanne, and Professor of
Finance, EDHEC Business School
17
Venture investment contracts as baskets of real options
Didier Cossin, UBS Professor of Finance, IMD
Benoît Leleux, Stephan Schmidheiny Professor of Entrepreneurship and Finance, IMD
Entela Saliasi, FAME and HEC, University of Lausanne
Opinion: Propensity-based pricing
Keith MacDonald, Partner, Capco
Simon Caufield, Managing Director, Nomis Solutions
19
93
103
A real options approach to bankruptcy costs: Evidence from failed
commercial banks during the 1990s
Joseph R. Mason, LeBow College of Business, Drexel University, Wharton Financial
Institutions Center, and Federal Reserve Bank of Philadelphia
Opinion: Pricing outsourcing
Simon Pilkington, Vice President, State Street Corporation
111
22
Opinion: All banks are not alike: Getting out of the
commodity trap
Kuno J. M. Huisman, Consultant, Centre for Quantitative Methods CQM B.V, and
Researcher, Department of Econometrics & Operations Research and CentER,
Tilburg University
Peter M. Kort, Professor, Department of Econometrics & Operations Research and
CentER, Tilburg University, and Professor, Department of Economics, University of
Antwerp
Grzegorz Pawlina, Lecturer, Department of Accounting and Finance, Management
School, Lancaster University
Jacco J.J. Thijssen, Lecturer, Department of Economics, Trinity College Dublin
Reed K. Holden, Founder, Holden Advisors
25
Opinion: Powerful pricing processes: How banks can escape
the profit crisis
Georg Wuebker, Partner, Financial Sevices, Simon-Kucher & Partners
30
Opinion: Market impact: Transaction cost analysis and the
financial markets
Anders Amundson, Managing Director, Elkins/McSherry
35
Measuring trade execution costs from public data
ASSETS
120
124
57
127
Mark Furletti, Payment Cards Center, The Federal Reserve Bank of
Philadelphia
68
131
Opinion: Mergers and acquisitions as a response to
economic change
Bart M. Lambrecht, Professor of Finance, Lancaster University
Management School
77
83
135
139
Pricing default-free fixed rate mortgages: A primer
Patric H. Hendershott, Professor, Aberdeen University
Robert Van Order, Lecturer, University of Pennsylvania
Real options and flexibility
Thomas E. Copeland, Managing Director of Corporate Finance, Monitor
Group, and Senior Lecturer, Sloan School of Management, MIT
Opinion: Impact of seasonality on inflation derivatives pricing
Nabyl Belgrade, Interest Rates Derivatives Research, CDC IXIS CM
Eric Benhamou, Head of Quantitative Interest Rates Derivatives Research,
CDC IXIS CM
Opinion: Valuing real options: Frequently made errors
Pablo Fernández, PricewaterhouseCoopers Professor of Corporate
Finance, IESE Business School - University of Navarra
Opinion: The credit spread puzzle
John Hull, Professor of Finance, Director, Bonham Centre for Finance and Maple
Financial Group Chair in Derivatives and Risk Management, Rotman School of
Management, University of Toronto
Mirela Predescu, PhD. Candidate in Finance, Rotman School of Management,
University of Toronto
Alan White, Peter L. Mitchelson/SIT Investment Associates Foundation Chair in
Investment Strategy and Professor of Finance, Rotman School of Management,
University of Toronto
Opinion: The interaction between real options and financial
hedging in non-financial firms
Tom Aabo, Associate Professor, Aarhus School of Business
Betty J. Simkins, Associate Professor, Department of Finance, Oklahoma
State University
73
Opinion: Is the investor sentiment approach the solution
to the IPO underpricing phenomenon?
Andreas Oehler, Professor of Finance, Bamberg University
Marco Rummer, Ph.D. Student, Teaching and Research Assistant, Department of
Economics and Management, Bamberg University
Peter N. Smith, Professor of Economics and Finance, University of York
Credit card pricing developments and their disclosure
REAL OPTIONS
Opinion: Inflation-induced valuation errors in the stock market
Kevin J. Lansing, Senior Economist, Research Department, Federal Reserve Bank of
San Francisco
Best execution regulation: From orders to markets
Jonathan Macey, Sam Harris Professor of Corporate Law, Corporate
Finance, and Securities Law, Yale Law School
Maureen O’Hara, Robert W. Purcell Professor of Management, Professor
of Finance, Johnson Graduate School of Management, Cornell University
Opinion: Pricing with time-technology and timescapes
Bala R. Subramanian, Associate Professor, DeVry University
Hendrik Bessembinder, A. Blaine Huntsman Presidential Chair in Finance,
David Eccles School of Business, University of Utah
43
Strategic investment under uncertainty: A survey of game
theoretic real options models
151
Efficient pricing of default risk: Different approaches for a
single goal
Damiano Brigo, Head of Credit Models, Banca IMI
Massimo Morini, University of Milan Bicocca
The pricing (r)evolution
Ever since man started to use trading instead of hunting or farming to provide for daily food, mankind has tried
to frame the abstract concept of pricing. At first this was done in an unconventional manner — through barter
— but later, with the invention of money, more sophisticated methods were developed to express value in a way
which allows all parties to a transaction to understand and appreciate the exchange of money for goods or
services. Nowadays it seems that newer, faster, and more reliable methods to calculate prices are invented
every day.
The financial services industry is no exception to this trend, as is outlined in the current issue of the Journal.
The pricing of wholesale and retail financial services changes with each new service or product brought to the
market, and pricing creativity — or should we say confusion — is the menu du jour: offers like ‘basic custody
services are provided for free if you enroll in our securities lending and borrowing program’, or ‘credit cards
with cash back and low interest rates if you sign up today’, or the notorious practice of soft dollars in the
investment industry are all testimonial to the evolution of FSI pricing models.
Correct pricing of financial assets is a complex task, which grows more complex with the degree of sophistication of the asset. Prices for widely traded straightforward instruments are relatively easy to obtain and to
interpret, but as soon as the instrument is unlisted, unconventional, or unknown to the public at large, we start
to lose our sense of ‘fair value’. It is nevertheless a very precise exercise, during which minuscule errors can
make or break a deal. The mutual fund industry is a very sensitive subscriber to this theory: a USD 0.01 error
on a NAV-calculation could cost upwards of a million dollars in missed subscription, or overpaid redemption
fees.
These types of monetary risks explain the constant evolution of newer, faster, more reliable pricing models.
Another reason is regulation: in the United States, the Financial Accounting Standards Board’s plan to
require companies to treat employee stock options as an expense directly affecting issuing companies’ bottom line, has led to the demise of the heretofore favored traditional Black Scholes’ options pricing model —
a true revolution. New and existing binomial models, such as the Cox, Ross, Rubinstein model, allow for
greater flexibility, more accuracy, and less overstating of value, all to the benefit of issuing companies.
I hope you will appreciate the 13th issue of the Journal, which is dedicated to the (r)evolution of pricing in all
its facets. As such it may prove for some of you to be a priceless issue, others may discover that they have
made assumptions in the past which have pricey consequences today. Nevertheless, this issue of the Journal
is a prize in itself.
Rob Heyvaert,
Founder, Chairman and CEO, Capco
Has pricing fully evolved?
Pricing of assets and services has come a long way since the first pricing models were developed. We now have
complex models to price shares, bonds, derivatives, and any combination thereof. However, despite all these
highly developed tools, the valuation of assets still remains far from being totally accurate. The reason, of
course, is that there are far too many unknown variables in our models. What we hope to do in this issue of
the Journal is provide you with a number of the most advanced pricing models and strategies, with the caveat
that while they are the best possible tools available, they are still not totally accurate.
Of course, one of the most complex assets to price are currencies, as they involve a deep understanding of
national economics and international asset and capital flows. Who better to discuss this topic with us than Prof.
Robert Mundell, the recipient of the Nobel Prize in Economics in 1999, and the undisputed world authority on
monetary economics. Prof. Mundell has kindly shared with us some of his views about the world of economics
and currency pricing.
Unlike currency pricing, however, which has had many decades of expert time dedicated to it, the development
of accurate models for pricing financial services is only in its infancy. It is quite remarkable that while we have
spent billions of dollars developing tools to price complex and not so complex products, we have generally
failed to address the pricing of financial services themselves. As in other industries, the correct delivery and
pricing of services can be very effective in distinguishing your capabilities from those of your peers. The articles in the first section of this Journal provide some guidance on the tools available to financial services institutions.
Section two introduces a pricing model that, though available for some time now, has yet to become mainstream. The use of options pricing models to price flexibilities in all types of projects allows us to quantify
behavioral decisions made by the management of most institutions. It also enables us to value the potential
benefits of undertaking a negative NPV project in order to have the capability to take on a very positive NPV
project in the future.
The final section looks at pricing more complex products. Consequently, it is very technical. We cover pricing
models used by the most advanced thinkers in the world of finance. We appreciate that many of our readers
do not deal with this aspect of the industry, but this section does provide a good overview of how we have
advanced in pricing assets.
We hope that you enjoy this rather specialized issue of the Journal and that you continue to support us by
sending us your best ideas.
On behalf of the board of editors
THE NOBEL LAUREATE VIEW
The international monetary system
A discussion with Prof. Robert A. Mundell
Robert A. Mundell, University Professor of Economics, Columbia University,
and Winner of The Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel 1999
We are very honored that Prof. Robert A. Mundell, one of the
cially against the smaller countries. As a result, such instabili-
world’s most respected macro-economists and undoubtedly
ty of exchange rates creates instability in the financial sectors
the leading authority in the field of monetary systems, has
of every country. There are no advantages for services.
kindly taken the time to answer a few questions about the
impact of currencies on the world economy. Below, you will
Q: There has also been a lot of debate about how economic
find the questions posed and the answers kindly provided by
productivity of countries should be compared, whether
Prof. Mundell.
nominal currency rates or PPP should be used. Which one
would you recommend?
Currency and the economy
Q: In recent years we have observed significant fluctuations
Prof. Mundell: Both methods are needed for the two different
of major currencies against each other. Commentators are, of
meanings of productivity. It depends on what you want to use
course, very good at using the same explanation to describe
the productivity measure for.
why a currency has appreciated against another as they do
for its depreciation. What in your opinion are the most impor-
Q: And, doesn’t the fact that the factors used in the evalua-
tant factors that determine currency prices today?
tion of inflation rates across countries are very different
make the whole exercise of evaluating PPP very hard, if not
Prof. Mundell: Exchange rates are determined by supply and
redundant?
demand. The most important factor in affecting supply and
demand is expectations about the future. Under hard fixes,
Prof. Mundell: The relation between PPP’s and exchange rates
such as the gold standard or credible currency board systems,
is not random. There is lots of evidence that the disparities are
or even traditional fixed exchange rate systems, such as the
a function of, i.e., per capita income. I think more theoretical
Bretton Woods arrangements, the expectations are for stabil-
work needs to be done.
ity, and that lets the exchange rate be used as a guide for private-sector planning. Under flexible rates, the main factor in
Q: The dollar has come under a great deal of pressure in
determining expectations is government policy, including cen-
recent years. Economic development, which should be used
tral bank policy, especially with regard to changes in interest
to help it appreciate, is used as a justification that it should
rates and fiscal policy.
fall, since economic growth in the U.S., unlike most countries, is tied to imports, and consequently large trade
Q: In recent years we have experienced very high volatilities
deficits. Where do you see the dollar go from here?
among the major currencies. How do you feel such high
volatilities will impact the purchase of services like banking
Prof. Mundell: I think the dollar will hover around where it is
where differentiation is weak and substitution opportunities
for a while, and then depreciate, but not cataclysmically.
are strong?
World currency
Prof. Mundell: I believe that the arrangement of flexible
Q: You have suggested that if the world had a single curren-
exchange rates between national paper currencies with its
cy — a world currency, as you call it — there could be signifi-
attendant instability and volatility among each of the nearly
cant benefits gained, such as common, or similar, inflation
200 countries of the IMF is an absurd arrangement that is at
and interest rates.
the root of the global macroeconomic problems that we have
today. Apart from its global inefficiency, it discriminates espe-
8 - The
Journal of financial transformation
Prof. Mundell: Yes.
Q: How well do you think the euro has been able to achieve
on whether the products in question are net exports or
similar objectives across Europe?
imports. I believe the increases in prices have been mainly in
exportables, including in this hotel prices, restaurant prices,
Prof. Mundell: Superbly.
etc., bearing in mind that Italy is among the world’s top three
tourist destinations. It means, therefore, that Italy has gained,
Q: Looking at the euro from another perspective, how well
not lost, by the increase in prices. Before the euro, the lira was
has it performed generally?
undervalued on a PPP basis, now it is less undervalued or possibly at ‘par.’
Prof. Mundell: From the perspectives and goals of both
Europe as a whole and each individual country, without excep-
Could it happen in the world economy? The answer is, yes. I
tion, the euro has been an unqualified success. It needs, how-
don’t believe any country would be hurt by it. But they should
ever, to be accompanied by improvements in the financial
be aware of it. Would a world currency joined by China and
structure with euro bills and bonds playing a larger role.
India involve rising prices? I think that given the undervaluation (by the PPP consideration), they would. But India’s prices
Q: I am aware that you are a big fan of the Tuscany region in
are rising fairly briskly staying out.
Italy and I am sure I do not need to inform you just how
much the prices of goods and services have risen since the
Notice, however, that I have not advocated a single currency
arrival of the euro, despite what inflation figures show. Don’t
for the world economy. A common currency yes, but a single
you feel that the same threat could face the establishment
currency no. The latter would not be possible short of a glob-
of a world currency?
al empire or dictatorship.
Prof. Mundell: There is the puzzle that people think prices
Q: Today, we already have three major currencies, and if
have risen since the euro, but it does not show up in the sta-
China and most parts of Asia-Pacific peg their currencies to
tistics. That could mean that people notice the prices that
the yen, or even choose it to replace their own, we could
have risen, but not those that have fallen. I have seen both the
even have three major currency blocks. Would better co-
fall and the rise in prices in Tuscany. But, the most noticeable
ordination of these currencies achieve the same objective
are the rises in prices, because they involve restaurants and
as the world currency or are political pressures too power-
tourist and export goods that would be expected to rise with
ful to maintain such relationships?
the increase in trade brought about by the euro. The evidence
is still anecdotal. But I believe that special effect could be
Prof. Mundell: The possibility of an Asia-Pacific fixed
modeled fairly easily.
exchange rate zone becomes more likely the more the
Americans follow policies that have been called Japan-bash-
There is a general view that the mental conversion of 1936 lire
ing and China-bashing. The tripling of the yen against the dol-
to 1 euro has involved price surges because the conversion
lar from September 1985 to April 1995 ruined the Japanese
ratio is close to 2000. If people are used to paying 30,000 lire
banking system. China wants to avoid a similar problem. So
for a lunch, then why not 30 euros instead of 15 euros? It does
unless the United States accepts the need for global monetary
seem that there has been an escalation of this type.
reform and perhaps a reformation of a Bretton Woods type
system, China and Japan will be pushed into each other’s
Is it harmful? The producers are helped, the consumers are
arms, however reluctantly.
hurt, and the country as a whole benefits or loses depending
9
Q: Can a world currency really help improve international
trade? Would you say that has happened across Europe?
Prof. Mundell: It would be a great benefit to people the world
over and the only losers would be the speculators who thrive
on instability.
Q: Prof. Mundell, thank you very much for giving us this time.
We hope that our readers have benefited from your insight.
10 - The
Services
Pricing traditional vs. alternative asset management services
Propensity-based pricing
Pricing outsourcing
All banks are not alike: Getting out of the commodity trap
Powerful pricing processes: How banks can escape the profit crisis
Market impact: Transaction cost analysis and the financial markets
Pricing traditional vs. alternative
asset management services
Francois-Serge Lhabitant, Head, Investment Research, Kedge Capital,
and Professor of Finance, H.E.C. University of Lausanne, and
Professor of Finance, EDHEC Business School
The past thirty years have witnessed an increased separation
the risk tolerance of the portfolio managers, and their respon-
between the ownership and the control of financial wealth.
siveness to incentives.
The emergence of modern portfolio theory, the increased efficiency of markets, and the growing sophistication of financial
Traditional vs. alternative incentives
instruments have convinced many, if not most, investors to
From a theoretical perspective, incentive contracts may com-
delegate the management of their portfolios to professional
bine three elements, namely, a profit sharing rule (i.e. fee
asset managers and their collective investment vehicles.
structure) to align incentives in terms of returns; a relative
Investment advice is now becoming a commodity.
performance component measured against a benchmark to
monitor performance, make returns comparable, and audit for
Initially, actively managed funds took the lead and intermedi-
common uncertainty; and checks on risk-taking, such as max-
ated much of the consumers’ investments in financial securi-
imum allowable tracking error, reporting requirements, and
ties. However, their dismal average performance simply pro-
constraints on available investment choices.
vided more general evidence of just how difficult it is to beat
the market. It also opened the way for passive strategies and
How are incentive contracts implemented in practice?
indexed funds, which were then perceived as a cost-effective
Surprisingly, the empirical evidence seems to suggest that tra-
way of buying equity market exposure — a strategy that made
ditional and alternative asset managers have taken diametri-
sense in an environment of rapidly rising market valuations.
cally opposed choices. Most traditional investment managers
However, the end of the technology bubble and the subse-
are monitored and evaluated against appropriate style bench-
quent bear market significantly froze the development of
marks, but their compensation is not linked to their relative
passive funds and provoked interest in alternative invest-
performance. Rather, they charge a management fee that is
ments, such as hedge funds and private equity. Since then,
generally expressed as a fixed percentage of the assets of
the number of highly specialized, non-traditional asset man-
their fund. The level of this fee varies depending upon the
agement firms has been growing exponentially. Many of them
complexity of the strategy and the asset class considered, but
are born from the ashes of the failures of mainstream fund
is typically between 1 and 3 percent per annum. Over recent
managers.
years, asset-based fees have been subject to highly competitive pressures and declined. This is not surprising, as investors
Whatever the investment vehicle and investment strategy
have the option of shifting their assets to another asset man-
selected, the delegation of portfolio management activities
ager or investment vehicle as soon as they identify a better
can be seen as a particular case of the principal-agent model
opportunity.
initially introduced in the seminal work of Jensen and
Meckling (1976). Since the costs to wealth owners of monitor-
By contrast, alternative asset managers target an absolute
ing those who are charged with managing their financial hold-
performance, and charge both a management fee (typically
ings are rather large, agency theory’s most basic suggestion is
1% of assets under management) and an incentive fee (typi-
that principals (investors) should compensate the agents
cally 20 percent of profits) based on their fund’s overall per-
(portfolio managers) through incentive contracts in order to
formance. Anecdotal evidence suggests that for most hedge
align their respective interests. The nature and intensity of
funds, the management fee is roughly equal to operating
these incentives should depend upon a series of parameters,
costs1 and the primary compensation is the incentive fee. In
such as the incremental profit generated by an additional unit
most cases, a hurdle rate of return must be exceeded by some
of effort from the manager, the precision with which invest-
multiple and any prior losses must be repaid before the fund
ment performance and risk can be measured and monitored,
manager is eligible to receive any incentive income. Over
1
12 - The
Liang (1999) calculated the average annual management fee for hedge funds to
be 1.36%, with a median of 1%. This base fee proved to be much smaller than total
management fees surveyed from retail mutual funds.
recent years, these fees have risen, particularly those of
strategy that works may continue selling it past the asset
established managers who have been able to create a scarcity
capacity for which it was designed, just because they are
for their fund, which they then use to increase fees and intro-
rewarded essentially on the basis of the size of their assets
duce a lock-up clause.2 On the contrary, with start-up funds in
under management.
the course of raising capital, investors often obtain discounts
on the fees in exchange for early money.
By contrast, performance fees seem to do a better job at aligning the interests of managers (desire for high fees) and
Asset-based fees vs. incentive fees
investors (desire for high excess returns). When subject to a
One may wonder which of the two models, asset-based or
performance fee, a manager will sell his strategy only up to the
incentive fees, is preferable to reduce the agency costs of
asset capacity for which it was designed. Then, he will close his
portfolio management delegation. Fees uniquely based on the
fund to additional investment, as he has stronger incentives for
size of the assets under management offer a small implicit
performance than for asset growth. Adding too much assets
incentive to managers. As the assets in the fund grow, due to
means being forced to put some money into second-best ideas,
capital inflows or the appreciation of the underlying holdings,
and these ideas do not often deliver the kind of returns desired,
the fee collected will grow in tandem. If on the contrary, assets
so asset growth is de-facto limited. At some point, managers
decrease, then the fee collected will be reduced proportion-
may even have to implement net share repurchases. In this
ately. Several empirical academic studies have confirmed the
context, an increase in revenues should essentially come from
positive relationship that exists between a fund’s relative per-
improving the excess returns delivered to investors rather than
formance and subsequent inflow of new investments [Sirri and
by increasing the assets under management. This partially
Tufano (1998)], as well as the fact that some investment funds
explain the relatively small size of hedge funds — about 80% of
voluntarily waive their stated fees in an attempt to boost net
the hedge funds reporting to commercial databases manage
performance and, thereby, to attract additional assets (fee
less than U.S.$100 million of equity capital.
waiving). This suggests that, even though the link between
performance and compensation is not direct, it nevertheless
However, performance fees also have their drawbacks. The
appears to be an important factor in determining fund man-
most important ones are linked to their asymmetric nature,
agers’ behavior. However, we should also note that academic
the manager participates in the upside, but not in the down-
research has evidenced the convex nature of the relationship
side. This corresponds to a potentially perpetual call option
between fund flow and performance. That is, while superior
with a path-dependent payoff — the payoff at any time
relative performance generates an increase in the growth of
depends on the high-water mark, which is related to the max-
assets under management and, in turn, managerial compen-
imum asset value achieved. This option-like payoff structure
sation, there tends to be no symmetric outflow of funds in
may lead to possible adverse incentive effects, because the
response to poor relative performance, at least over the short-
manager simultaneously owns the option and controls its
term. The convex flow/performance relationship creates an
underlying asset (the portfolio), as well as its volatility.
incentive for fund managers to increase risk taking, especially
Therefore, near the end of an evaluation period, some man-
after poor performance. Therefore, the effective incentive of
agers may decide to increase portfolio risk in order to increase
an asset-based fee needs to be carefully assessed on a case-
the value of their option.3 On the contrary, outperforming
by-case basis. However, in the case of skill-based and capacity
managers may attempt to lock-in their positive performance
constrained strategies, asset-based fees may also create a
and dampen portfolio volatility. Alternatively, some fund man-
fiduciary conflict because adding new assets can harm the
agers may also try to improve the return of their portfolios by
interests of existing ones. Managers who have developed a
window dressing them, for example by using stale prices
2 As an illustration, Steve Mandel at Lone Pine Capital can charge half of the performance fee (i.e. 10%) of any gain the fund makes from its low. This 10% performance fee continues until the fund has made up 150% of the drawdown from
the previous high, then the standard 20% fee kicks in again.
3 Carpenter (2000) studies the optimal portfolio strategy of a manager compensated with a convex option-like payoff and proves this is optimal behavior.
13
rather than real market values (or vice-versa) for illiquid stocks
business. It establishes that ‘the law or the fund rules must
or non-traded assets around the end of an evaluation period.
prescribe the remuneration and the expenditure which a man-
Between the lack of agreed-upon standards, different views
agement company is empowered to charge to a unit trust and
about illiquid marks, and moral hazard, valuation can be akin
the method of calculation of such remuneration.’ Therefore,
to numerical quicksand.
legal restrictions to the way companies managing mutual
funds can be compensated for their services, if any, are to be
It is interesting to note that although mutual funds and hedge
found only at the national level. Several countries, such as
funds seem to disagree on what is the best choice between
Spain, France, or the U.K., have left a large degree of latitude
asset-based and performance-based fees for their external
when it comes to portfolio managers deciding on the mecha-
investors, they both agree on their own internal compensation
nism and the value of their compensation. Strikingly, in prac-
structures, which involve asset management firms and indi-
tice, even though it is legally permissible, most mutual fund
vidual fund managers. The compensation of portfolio man-
companies are almost never compensated through incentive
agers tends to be performance-based, with a fixed base salary
contracts. Instead, they are paid a fixed percentage of assets
topped by bonuses based, partially or entirely, on relative per-
under management, and the incentive intensity is set to zero.
formance. This should be kept in mind, as a complete discus-
At the other extreme, hedge funds and other lightly regulated
sion on the incentives facing mutual funds must consider two
private investments companies are primarily charging incen-
layers of agency problems: the agency relationship between
tive fees.
the fund company and the fund investors and the agency relationship between the fund company and fund management
The soft dollar arrangements
[Chevalier and Ellison (1999)].
Our discussion of fees would not be complete if we did not
mention soft dollar brokerage, or simply soft dollars. Soft dol-
The regulatory view
lar brokerage is a popular arrangement between a fund and its
An interesting viewpoint on the question of asset manage-
broker. Basically, the fund manager agrees to place a desig-
ment fees is that of regulators, which varies from one country
nated dollar value of trading commission business with a bro-
to another. In the U.S., for example, mutual funds are regis-
ker over a given period of time. In exchange for this promise,
tered investment companies and they are highly regulated by
the broker provides the manager with research credits equal
the S.E.C. The latter allows performance incentive fees and
to some part, say 50 percent, of the promised commissions.
enables a fund to charge higher fees when it beats a bench-
Rather than rebating these credits back to investors, the man-
mark, so long as it is willing to charge less when it fails to beat
ager keeps them and uses them to buy services and any of the
it. As one could expect, many fund managers are perfectly
large number of broker-approved research products (hard-
happy to sell their funds to the public on the grounds that it
ware, software, subscriptions, databases, etc.) supplied by
can beat the market, but despite the offer, very few of them
third-party research vendors. The broker then pays the man-
are willing to put their own money where their mouths are and
ager’s research bill and simultaneously cancels the appropri-
take the other side of the bet. According to the Lipper data-
ate number of credits from the manager’s soft dollar account.
base, less than 2 percent of the U.S. equity mutual funds apply
From a functional perspective, soft dollars are simply one form
a performance fee.
of bundling research and execution together into a single commission payment. They are unique in allowing research and
14 - The
In Europe, a European Council Directive sets the general legal
execution to be provided by entirely separate firms, thereby
framework within which undertakings for collective invest-
promoting vertical disintegration of the research and execu-
ment in transferable securities (UCITS) may carry on their
tion functions.
Do soft dollars reduce or increase agency costs of delegated
ity brokerage. The threat of termination dramatically increas-
portfolio management? Both views are defendable. On the
es the expected losses to brokers who provide low-quality
one hand, one may argue that soft dollars allow managers to
services, and may therefore perform an effective quality
misappropriate investor’s wealth by churning their portfolios
assuring function.
to subsidize research for which they should pay directly. This,
in turn, generates various inefficiencies, such as the choice of
What makes a good performance fee?
a broker for his willingness to provide research credits rather
Coming back to the main topic of our discussion, at this stage,
than on expected execution quality. At the end of the day,
we may wonder what the necessary characteristics of a good
because brokerage commissions are included in the price
performance fee should be. Ideally, a performance fee should
basis of the underlying security, investors implicitly pay the
be structured to achieve five main objectives. It should reward
underlying research costs. Soft dollars, therefore, subsidize
a proficient manager for excess return earned over the meas-
the manager’s use of research inputs, and in some cases the
urement period, it should control portfolio risk, it should con-
existence or amount of the subsidy is unknown to investors.
tain fair but significant consequences for manager underper-
Thus, portfolio managers shift expenses that are normally
formance, the performance fee agreement should be explicit
shouldered by them onto fund shareholders. But on the other
in its description of the fee structure to eliminate client mis-
hand, one may also argue that soft dollars are aligning the
understandings and properly frame client expectations, and it
interests of asset managers with those of their investors. Fund
should be designed so that there is little economic incentive
managers typically own a very small percentage of their port-
for the manager to grow the assets under management
folio, directly as co-investors or via an annual management
beyond the level at which the performance fees max out. The
fee. If managers were required to pay for all research and exe-
performance fee structure encourages investment firms to
cution out of their own pockets, they would bear a dispropor-
run their strategies at optimal asset levels that permit the
tionate share of the costs of generating portfolio returns in
maximization of dollars of excess return.
relation to the private benefits based on their portfolio share.
Seen in this light, the agency problem faced by portfolio
Are hedge fund fees exaggerated?
investors is that in the absence of agreement, managers will
Throughout the bull market of the 1990s most investors over-
do too little research, identify too few profitable trading oppor-
looked the fees charged by mutual fund companies because
tunities, and execute too few portfolio trades. Thus, soft dollar
returns were so impressive. But times have changed. We are
arrangements allow investors to subsidize investment
now in an era of difficult markets and the level of fees have
research and thereby encourage managers to do more of it,
come under close scrutiny. Many traditional investors who are
which ultimately benefits the portfolio performance.
just beginning to venture into alternative investments find
their levels of fees overwhelming. If the industry standard
Last but not least, soft dollars may also be unique in aligning
seems to be 1 percent for the management fees and 20 per-
the incentives of brokers and managers. When a broker pro-
cent for the performance fee, several funds among the largest
vides soft dollar research credits to a manager, it typically
and top-performing ones are far above that. For instance,
does so in advance of the commission payments it expects
Caxton Corporation which oversees more than U.S.$10 billon
from the manager. But the manager has no legal obligation to
charges 3 percent and 30 percent, while Renaissance’s
trade and may in particular terminate the executing broker
U.S.$6.7 billion Medallion fund charges a 44 percent incentive
relationship with the balance of the soft dollar account unpaid.
fee, more than twice the industry average. Interestingly, both
The broker will then lose a stream of commissions that would
funds are closed to new investors and have returned money to
have included a premium above the cost of providing low-qual-
their existing investors in 2003 in order to be able to maintain
15
positive returns. Of course, only the best performing funds are
ture for asset management? One argument often encoun-
able to dictate conditions like this. Nevertheless, the list of the
tered is that poorly performing managers will be paid less and,
top ten earners in the hedge fund industry is impressive.
therefore, benefit the plan sponsor. On the other hand, man-
According to Institutional Investor, the top 10 managers
agers who perform well will also be paid more. But since the
earned the following sums in 2003 from a combination of
fund earns more, this extra fee will really not cost anything at
their share of the fees generated by the funds they managed
all. Perhaps, proponents contend, the carrot of higher fees and
and the gains on their own capital in the funds: George Soros
the stick of lower ones will make the managers work harder.
of Soros Fund Management, U.S.$750 million, David Tepper of
Appaloosa Management, U.S.$510 million, James Simons of
The objectives of performance fees are to reduce them for flat
Renaissance Technologies, U.S.$500 million, Edward Lampert
and negative performance and to reward managers for posi-
of ESL Investments, U.S.$420 million, Steven Cohen of SAC
tive absolute performance. Structured properly, this makes a
Capital Advisors, U.S.$350 million, Bruce Kovner of Caxton
lot of sense for the investor and the manager if added value is
Associates, U.S.$350 million, Paul Tudor Jones of Tudor
properly identified. Then the client and manager are simply
Investment, U.S.$300 million, Kenneth Griffin of Citadel
entering a profit-sharing plan, and profit sharing is effective in
Investment, U.S.$230 million, Daniel Och of OCH-Ziff Capital
aligning incentives. The problem with performance fees starts
Management, U.S.$150 million, and Leon Cooperman of
when they are not structured properly, that is, if the client is
Omega Advisors, U.S.$145 million.
giving a manager a fee based on something other than added
value (the true alpha). This is not sustainable in the long-run.
Not surprisingly, traditional investors’ first reaction may be to
Nevertheless, many traditional managers are still reluctant to
dismiss the hedge fund industry due to excessive layers of
use performance fees. If the entire industry shifted to per-
fees. Performance fee structures with 25 and 35 percent carry
formance fees, one of the things that might happen is a reduc-
can work out to be tremendous fees, and immediately prompt
tion in fees in general. For instance, if two-thirds of the man-
the question: ‘Does the return justify the fee?’ The answer is
agers underperformed, they would draw one-third of their
twofold. Firstly, outsiders invest in a hedge fund because they
normal fees, while the one-third that outperformed would
believe the manager has an expertise that they can not repli-
draw four-thirds of their normal fees. The industry-wide fees
cate for themselves, or that replication is too costly. This is a
would then be cut by a third. Not surprisingly, at least two
fact to remember when looking at hedge fund fees — you get
thirds of the asset management industry will keep fighting
what you pay for. Secondly, if investors achieve their objec-
such a trend.
tives after expenses, the fees are justified, even if their level
is an especially hard pill to swallow.4 But if a fund delivers
poor performance, it is not worth a low fee; in fact, it is worth
References
no fee at all. Thus, fees should be directly related to provid-
• Carpenter J. N., 2000, “Does option compensation increase managerial risk
appetite?” Journal of Finance, 50, 2311-2331
• Chevalier J. and G. Ellison, 1997, “Risk taking by mutual funds as a response to
incentives,” Journal of Political Economy, 105, 1167-1200
• Goetzmann, M., J. Ingersoll, and S. Ross, 1998, “High water marks,” NBER Working
Paper 6413, National Bureau of Economic Research, Cambridge, MA
• Jensen, M. C., and W. H. Meckling, 1976, “Theory of the firm: Managerial behavior,
agency costs, and ownership structure,” Journal of Financial Economics, 3, 305-360
• Liang B., 1999, “On the performance of hedge funds,” Financial Analysts Journal,
55, 72-85
• Sirri E. R. and P. Tufano, 1998, “Costly search and mutual fund flows,” Journal of
Finance, 53, 1589-1622
ing what the investor wants. Consequently, when evaluating
or selecting an investment fund, the fee charged should not
be the unique determinant. The investment philosophy and
quality and tenure of management are also important considerations, amongst others.
Why so much resistance?
So, in conclusion, are performance-based fees a desirable fea-
16 - The
4 As an illustration, Goetzmann et al. (2001) use an option approach to calculate the
present value of the fees charged by a hedge fund manager and show that the
present value of the incentive fees can be quite high (i.e. for a volatility of 15%,
the fee can be as high as 13% of the assets under management).
Propensity-based pricing
Keith MacDonald, Partner, Capco
Simon Caufield, Managing Director, Nomis Solutions
Financial institutions are now collecting vast amounts of cus-
based price for an unsecured loan is x%, but they may have
tomer data. Spurred on by falling storage costs and more
taken the loan at x% plus 10bp. The rate at which a customer’s
efficient channels, such as the Internet which help automate
demand changes with a change in the underlying price deter-
the process of data gathering and verification, as well as new
mines that customer’s price elasticity. The reality is that cus-
regulations, such as Know Your Customer and anti-money
tomers and segments of customers have different price elas-
laundering, financial institutions are now in possession of a
ticities. For some customers, even small changes in the price
wealth of information about their clients. However, despite
of a given product will translate into large changes in demand
having access to all this information, very little is being done
for that product. Conversely, other customers react minimally
to utilize it effectively to increase revenues.
to changes in price and are price inelastic. Price elasticity is
measured on a sliding scale, with different customers falling
Advances in analytical tools and massive increases in process-
along different points on an elasticity continuum.
ing power are allowing highly sophisticated analytical routines
to be run across the data warehouses, with benefits being
Failure to incorporate customer price elasticity in a pricing
derived in areas such as real time marketing (customized and
decision leads institutions to price sub-optimally, and leads to
targeted propositions) and behavioral risk management.
over- or under-pricing. Traditionally, product marketers
Processing of this type can learn from itself to constantly
focused primarily on the first type of error, and are painfully
improve results.
aware of situations where customers that would have purchased a product at a price lower than the one offered do not
One area being experimented within financial services is
accept the offer, and the sale is lost. However, the second type
propensity-based pricing (PBP). This involves using customer
of error is just as economically inefficient, but usually more
data to maximize revenue based on how much a customer is
difficult to spot. A customer who does accept a product offer,
willing to pay for a product or service, based on understanding
but pays a lower price than he would otherwise have been will-
of their price elasticity. As an approach PBP has existed for
ing to pay, represents lost potential margin.
many years, industries such as telecommunications and business services have been using it to set prices in competitive
If institutions can differentiate customers by their price elas-
bidding situations. In the last couple of years, the same princi-
ticity, across the product range, the potential to tailor prices
ples have been piloted in certain aspects of financial services
and thus optimize revenue would become a reality. Within reg-
with dramatic results.
ulatory constraints, one price need not necessarily fit all.
Principles of propensity-based pricing
Propensity-based pricing manages the trade-off between mar-
Discretionary pricing has been used in financial services since
gin and volume and seeks a pricing solution that optimizes
the services were invented. The power of the bank manager to
revenue. For financial institutions the cycle is iterative and
say yes or no is historical. However, in recent years pricing has
comprises four stages. Firstly, you should segment the market
become more automated, especially with risk-based tools
by creating customer groupings based on common buying
defining acceptable levels of exposure a client handler can
behaviors and other attributes. Secondly, determine segment
introduce. Customer facing roles have in many ways been de-
price sensitivities. If current pricing has created some price
skilled by taking some or all of the risk decision away.
variation, this may be done analytically. If not, create product
campaigns targeting different customers within the same seg-
However, risk-based pricing may not capture the full revenue
ment with different price points. Plot segment-specific
and margin potential. For example, suppose a customer’s risk-
demand curves and price elasticities by accounting for both
17
successful and unsuccessful offers. Thirdly, calculate segment-
develop recommendations for immediate pricing changes to
specific price points, through the combination of price elastic-
drive short-term benefits, and to construct business case and
ity results and product business logic, to identify the price
outline implementation plans for deployment aligned with the
point at which the volume/price trade-off is optimized. Finally,
institution’s business environment and needs.
track, measure, and recalibrate by monitoring results and over
time refining pricing models to reflect both deeper customer
Outputs would include a business case, including outline
segment understanding and changing market conditions.
implementation and systems integration plans, short-term
profit improvement from recommendations for immediate
The product ‘heatmap’
pricing changes, segmentation and pricing models for future
Propensity-based approaches are only effective in certain
use and refinement, and enhanced understanding of how price
product/customer situations. The ideal situation would involve
optimization could operate across the institution.
one or more of the following, a product which is individually
underwritten, such as unsecured lending or general insurance,
Conclusion
quotations made based on specific customer situation, such
While some financial institutions are positioning themselves
as foreign exchange, a competitive bid process, such as
as offering all customers the same price for a product, there
responding to a request for proposal for credit facilities, avail-
are significant benefits to be gained from understanding and
ability of data on offers that were not accepted by customers
applying price sensitivities. Propensity-based pricing is now a
as well as win data, availability of product profitability infor-
realistic tool for financial services institutions to use the
mation, and constrained optimization, such as balancing tar-
power of the latest analytical tools to increase profitability.
gets for revenue growth, margin, and risk.
Looking across a portfolio of products offered via different
channels to specific customer segments, some products will
be ideal (hot), some not (cold), but many in between. For example, the profitability of many card propositions is based more
on usage than price given the cost of supporting transactions.
The assessment of the ‘heatmap’ can define the potential
benefit of applying PBP, and the priorities for piloting and rollout.
Proof of concept
Assessing PBP requires careful piloting, particularly as it can
involve changes in behavior as well as how prices are calculated. A proof of concept can be used to cover all aspects of a
potential rollout, including data quality and availability, and
raising awareness of the principles of the approach. Typically,
a proof of concept takes two to three months, with three main
objectives. These are to validate expected benefits from
deploying the approach by developing initial segmentation
and pricing models and applying them to past transactions, to
18 - The
Pricing outsourcing
Simon Pilkington
Vice President, State Street Corporation
A lot of ink has been spilled in recent years on the subject of
ate cost savings are to be achieved, this would require the
investment management outsourcing. The concept has
provider to underwrite the costs incurred in the initial years of
gained widespread acceptance as investment managers real-
the agreement.
ize that they can focus better upon their core competencies
— managing money, developing new products, distribution
At this stage in the development of the outsourcing industry,
methods, client service, and so on — by shifting their invest-
it is questionable whether large, well established providers
ment operations, fund accounting, and other administrative
need to pay upfront premiums, as all of the large providers
functions to specialist third-party providers. Managers who
now have existing clients and infrastructures. It is possible
outsource these functions do so with the expectation of con-
that some smaller players looking to enter the market may be
trolling risk levels, improving service quality, gaining access
prepared to pay a premium, but prospective clients need to
to proven and superior technologies, and, ultimately, saving
balance this immediate financial benefit against the risk of
money or at least gaining better control of what can often be
using a provider which has not yet established its skills and
a variable cost.
abilities in the market. The advantage for providers and potential clients in this situation concerns the client’s intellectual
An intelligent, strategic outsourcing solution should yield all
capital, as experienced staff will bring significant benefits to
of these benefits, but as is often the case in many aspects of
the provider in return for cost savings for the client. This is
investment management, the bottom line remains the top
especially true in a lift-out arrangement, in which the provider
concern for many managers thinking about outsourcing. Even
takes over the client’s existing operations, effecting a com-
clients who say that saving money is not their main concern
plete transfer of both technology and staff. But again, estab-
end up focusing upon direct costs or other indirect cost-
lished providers might not necessarily find such arrangements
related business drivers, such as service quality, increased
appealing in the future.
instrument coverage, or improved technology. And this focus
inevitably raises a tricky issue: how does one put a fair price
Obviously, the willingness to compromise on both sides is cru-
on outsourcing services? In what is still a maturing field of
cial in establishing a mutually beneficial outsourcing
the investment business, where costs have not yet coalesced
arrangement. One of the advantages of outsourcing from a
around generally accepted industry standards, there are no
client’s perspective is that it helps them move from a largely
easy answers to this question. But analysis of this question
fixed set of costs to a more variable cost structure, but while
from the standpoint of both outsourcing clients and providers
they want to benefit from economies of scale as their busi-
— considering such factors as length of the deal, up-front con-
ness grows, providers need protection against their business
tract premiums, benchmarking, and rate card structure — is
declining. One could argue that the ideal tariff for a manager
critical in establishing what both sides really want and where
is to pay for services measured by basis points on assets
the middle ground might lie in any given outsourcing con-
under management. This is how managers are typically com-
tract.
pensated, giving them the certainty of costs being a fixed
percentage of revenue as assets under management grow or
Immediate cost savings are usually high on the agenda of
shrink. But most outsourcing clients have indicated a prefer-
potential outsourcing clients, and in some cases they also look
ence to pay a tariff based on volume, and tend to be less
for an upfront premium based on the value they place on their
interested in ad valorum charges. Providers also want a tariff
business. In order to close an outsourcing deal, both sides will
which reflects the economics of providing the business, struc-
need to spend a lot of time, and therefore money, in due dili-
tured to reflect the drivers of volume and complexity. So
gence and implementation planning processes. So if immedi-
while clients typically gain the variable cost advantage they
19
are after, they also need to accept that there is still a fixed
opportunity to benchmark their services and prices. With
cost aspect from the provider’s perspective.
benchmarking exercises, clients hope to protect against the
possibility that the overall market value for services may fall,
One of the questions providers usually ask early in the process
which would put them at a disadvantage relative to firms
of negotiating an outsourcing deal is how much the client’s
which outsource at a later date. In fairness to providers, the
operations currently cost. This question usually puts clients on
benchmarking exercise should also include upside potential
the defensive, probably out of suspicion that the provider is
for them, providing compensation for them if the cost of
going to take their cost and pitch a fee just below it, whereas
service provision becomes more expensive than originally
without the existing costs as a benchmark the provider might
envisaged.
offer a better deal. But in reality, this information is critical to
the potential provider, especially if a lift-out is being contem-
Especially across longer deals, how does one anticipate future
plated, for until the business converts to the provider’s tech-
events such as acquisitions by the client, or of the client by a
nology, the existing costs will be incurred by the provider. By
third party? The contract will probably contain clauses which
being cagey on this subject, a client may put its potential
allow both parties to reassess the relationship in the case of
provider in an impossible situation, leaving it unable to ade-
significant change, but most clients have an acquisitive strat-
quately assess one of its key drivers in any deal. Successful
egy, and are likely to want cost certainty in case they grow by
outsourcing relationships are partnerships based on trust, and
acquisition. This is not always easy to model: it is one thing to
this trust needs to be established early in the negotiation
create a rate card which is tiered for the gradual growth of
process so that both parties can deal with each other in an
existing business, quite another to accommodate the sort of
open, honest way.
explosive growth which may result from an acquisition. And
pricing the transaction is only one element of crystal ball-gaz-
Length of a proposed deal is an important factor, and often a
ing. Will the operations be located in the same city? Will the
complicating one. The longer the arrangement, the more com-
acquired entity have similar or different systems? The price of
pelling a provider can make its proposition, benefits can be
an outsourcing deal already varies if multiple sites have to be
gained over the long haul by using more than one service.
used instead of a single site, or if the existing provider’s site is
Clients, however, will need a potential exit strategy covering
not sufficient and a new site has to be arranged. Connectivity
operational, IT, and cost considerations in case things go
is an important issue when pricing a deal: a single pipe into the
wrong:
client’s data warehouse or data store is more straightforward
and less expensive than a multiple point-to-point system.
■ Operational aspects may be complicated in the case of a
Factoring in the possibility of acquisitions, and their effect on
lift-out, with the possibility that the operation may still be
considerations like these, makes pricing a deal that much
running as a separate and distinct unit at some point in
more difficult.
the future.
■ IT revolves around connectivity and the client’s ability to
retain ownership of their data.
Naturally, the type of deal being pursued will greatly affect the
type of savings a client can hope to gain. Most deals are either
■ Cost considerations will depend on the contract period still
lift-outs or straight conversions, although some are a mix of
to run, and the extent to which the provider has been able
the two. Within our current context, lift-outs can be thought of
to absorb any up-front costs incurred.
as a means to an end: they will involve the transfer of qualified
and experienced staff who know the client to the provider, but
And in longer arrangements, clients are likely to look for the
20 - The
they will inevitably cost more up front, as the business will ini-
tially be run on legacy technology which is not leverageable.
Conversions require the provider to have experienced staff
immediately capable of redeploying to meet the new client’s
needs, and are likely to provide a more immediate financial
advantage. However, this apparent advantage must be
weighed against the costs of redeploying or laying off staff
after the conversion is completed, since most lift-outs will
eventually involve a conversion to leverageable strategic technology. Qualified and experienced staff joining the provider in
a lift-out are likely to be closely involved in defining business
requirements and conversion activity, and as such constitute
an asset in their own right.
In the final analysis, no two outsourcing deals will be hugely
similar. The intricacies of establishing a close relationship
between client and provider mean that the pricing of such
deals can only be determined on a case-by-case basis.
Ultimately, clients usually want a simple rate card, something
which fixes their variable costs at advantageous rates which
can be structured to match the economics of the deal. A tiered
structure may provide protection against growth, but if the
client expects to benefit from unit cost savings over the life of
the deal, the rates need to be discounted accordingly. And of
course, past growth of a client is no guarantee of future
growth. It is difficult to assume anything in this regard, so
financial analysis needs to include sensitivity analysis to
determine the impact of various growth rates for different
drivers on the economics of a deal. Establishing a worthwhile
outsourcing arrangement requires a great deal of trust and
coordination between both client and provider. It is fair to say
that this same level of trust, and the establishment of a comprehensive understanding of each other’s needs, is equally
necessary before any deal is signed.
21
All banks are not alike:
Getting out of the commodity trap
Reed K. Holden
Founder, Holden Advisors
In the eyes of many business clients, all banks look alike.
with those customers who want a consultative relationship
Banking services are viewed by increasingly sophisticated
with their financial services suppliers. Unfortunately, not all
business clients as a series of well-defined commodities that
customers will pay for these points of differentiation. Client
are available from a plethora of banks and financial services
managers must be able to understand and recognize the four
companies. Because banking service vendors have not updat-
primary purchasing behaviors that customers demonstrate:
ed their offering to meet the evolving needs of their business
customers or communicated their unique value to each client,
■ Price buyers focus on purchasing commodities at the low-
business customers have focused primarily on price in their
est price and are unlikely to pay for additional value. They
acquisition process. To avoid this commodity trap, bank man-
do not prioritize value propositions and they will not pay
agers must become adept at diagnosing their customers’ busi-
for differentiation. These customers want to purchase
ness problems, developing targeted solutions, and communicating this value to the client in terms relevant to their busi-
commoditized products and services based on price.
■ Value buyers are willing to pay for more value if it is rele-
ness. Simply stated, the client manager must become a trust-
vant to their business operations. These buyers are open
ed advisor to the customer, partnering with them to deliver
to discussions of targeted value propositions. They will
greater and greater value to their business operations. Absent
participate in the research to identify relevant points of
this relationship, customers will view low-cost as the only
differentiation and will expect a subsequent offering and
value delivered by their banking services provider and will be
happy to let multiple vendors duke it out with low prices for
smaller and smaller pieces of their business.
price.
■ Relationship buyers rely on trusted advisors to meet their
banking needs, and generally have one. To be successful
here, banks need to start with small packages of valuable
Research and years of working with clients tell us that the
services and prove their worth over time, gradually earn-
most productive answer is moving up the customer value
ing greater respect.
chain with solutions based on effective value propositions. In
■ Poker players are value buyers who have learned that
our experience, most customers would like their vendors to
they can get high value at a low price. These buyers will
offer additional services and solution packages, and are quite
say that value propositions are unimportant when they
willing to pay for this added value. To accomplish this, banks
are! By incrementally eliminating valued services while
and suppliers of financial services must recognize that while
lowering prices, vendors can force these customers to
some customers will pay for this added value, others will not,
reveal their hand about what they truly value.
while others will attempt to ‘play poker’ in the hope of negotiating value at a lower price. They also need to understand the
Since each of these types of buyers require a different
needs of their specific customers and then develop services
response, banks need client representatives who have the
and solutions that address these needs, and pass the ‘acid
knowledge to discern each different behavior, the skill to
test’ of value by demonstrating value to customers in eco-
organize the right offering to respond to each type, and the
nomic terms.
poker skills to negotiate with customers who want to play
poker. Differentiation is great, only if you can leverage it with
Who are the poker players?
the right customers at the right price.
The first step in gaining pricing power is for client managers to
22 - The
believe that the higher price they are asking reflects tangible
Building an effective value proposition
incremental value delivered to the customer. This knowledge
The first step in delivering value to the customer is targeting
lays the groundwork for developing a trusted advisor position
important or inefficient aspects of their business operations
where new or enhanced financial service solutions can offer
ing managers may be able to identify points of business value
tangible business improvement. These solutions have to pro-
in the proposed solution.
vide differentiated value; that is, not only do they have to be
more than replications of competitive offerings, they have to
One supplier we worked with had five pages of value state-
be valued by customers. Such differentiation is the first step to
ments. And their competitors delivered the exact same mes-
gaining pricing power.
sages. They were in the middle of negotiations with a purchasing agent who was unlikely to provide any information on
The next step is tangible and measurable value propositions
non-price, value requirements. Fortunately, it was possible to
that demonstrate an understanding of the customer’s real
identify an operational requirement for reliable and timely
business problem. Understanding of the customer’s business
shipment of products. This was collaborated with the client to
challenges drives the customer’s willingness to open a true
craft a sales message around the supplier’s ability to superior
business dialogue, giving the vendor a chance to sell a valu-
performance on this dimension. The customer, who had previ-
able solution. Too many banks and financial institutions miss
ously focused exclusively on price, chose this vendor and
the mark with their value propositions, they are either rhetor-
placed the order at a 15% price premium. The relationship
ical or fail to address the customer’s real business or eco-
proved to be the supplier’s largest and most profitable cus-
nomic problems. Tangible and measurable value propositions
tomer!
serve to justify higher prices for both customers and salespeople. Intangible and generic value propositions do not.
The acid test
In today’s competitive business marketing environment, effec-
Banks that seek to replicate their retail brand campaigns for
tive differentiation must be based on quantification. That is
their B2B customer acquisition and retention strategies are at
the true acid test of whether a financial institution’s value
a significant competitive disadvantage. These retail campaigns
proposition is compelling and believable. Value propositions
rely on image rather than substance. Image is rarely com-
that are ‘me too’ and fail to connect directly with the business
pelling to a large business customer. Even if the financial insti-
customer’s financial performance will be lost in the noise of a
tution is large enough to justify these campaigns, they must
crowded marketplace.
be backed by substantive and important differentiation to be
successful. Selling treasury services to a business requires a
This understanding of the linkages between the features of a
solid understanding of that customer’s business climate and
bank’s offering and the real economic value that a customer
the needs of their customers.
achieves sends a strong message to prospects about the
bank’s ability to partner with its clients to improve their busi-
To be effective, points of differentiation should include value
ness operations. In comparison, brand campaigns are blunt
statements that address real customer business problems and
instruments that have less impact for business accounts.
provide a bottom line result. Validating customer business
issues and priorities requires a systematic program of inter-
The process for building an understanding of customer
viewing the right customers — the ones who want the value
needs and subsequent points of differentiation should be
and appreciate the incremental benefits of value at a higher
systematic. Researchers start with internal interviews with
price — and the right buyers within the customer organization.
the marketing, sales, and service staff within the financial
For example, low to mid-level managers or back-office opera-
institution to identify differentiators that are particularly
tions managers in an organization may focus on price when
effective with customers. Once these areas of differentiation
evaluating a solution, while senior managers or customer-fac-
are identified, the next step is validation with customers and
23
building these differentiators into offerings and supporting
institutions will become true trusted advisors for their cus-
value messages.
tomers. In doing so, they will pull ahead of the competition,
provide service enhancements that deliver compelling offer-
Successful customer interviews require reaching the right
ings, communicate with their customers in terms that are
individuals within the customer’s organization and conducting
meaningful to their business — thus building the basis of sus-
interviews that surface the customer’s needs, and how various
tainable differentiation — and establish the foundations for a
solutions can provide tangible benefits to meet these needs.
good customer relationship, the kind customers really want.
The most accessible person within a customer organization
may not be the most appropriate person. The challenge is
Building the internal capability to understand and continuous-
identifying people with the business insight and customer visi-
ly analyze value that customers receive from their financial
bility to see the potential of a solution and be able to quantify
services is key to sustainable competitive advantage. When
its value. Senior managers, customer-facing managers, and
done properly, systematic monitoring of customer value pro-
operations staff can offer valuable insight and confirmatory
vides the insight to drive sales, improve margins, and enhance
views of the overall problem.
skills when negotiating with the toughest buyer, even the
poker player. This approach is essential to gaining the trusted
The interviewer must be skilled at both in-depth questioning
advisor position with relationship buyers. Whichever customer
and the ability to synthesize qualitative interview results into
type, this process will help banks avoid the commodity trap
a compelling value proposition. One effective approach is
and win in highly competitive environments.
assigning marketing the task of interviewing customers, crafting value propositions, and developing a series of screening
questions for a salesperson to use to qualify a prospect’s business needs.
A skilled interviewer must be able to connect the dots
between the firm’s business problems, the key features needed in an offering, and the subsequent value to the customer.
For example, a customer, an automobile dealership, may say
that the processing time for loan applications is causing lost
sales. The next question should determine how many loans are
closed with the current capabilities, followed by how fast the
applications need to be processed. The last question would
obtain a forecast as to what their close rate would be if the
loans were able to be processed in ten minutes. From those
questions, the interviewer is able to build a required feature
set for the solution as well as the economic benefit a customer
will experience from the improved offering.
By connecting with the real needs of their customers and making tangible improvements in their customers’ operations — via
reduced costs, improved sales, or improved profits — financial
24 - The
Powerful pricing processes: How
banks can escape the profit crisis
Georg Wuebker
Partner, Financial Services, Simon-Kucher & Partners
Many banks are in the midst of a profit crisis, brought about to
100,000 customers), U.S.$5 million (based on 500,000 cus-
a large extent through lack of pricing strategies and poor judg-
tomers), or U.S.$10 million (based on 1,000,000 customers).
ment about the reactions of competitors and customers. Even
those who fare quite well could do much better. The following
These examples demonstrate the power of pricing, also known
article reveals that price is the primary profit driver. Top man-
as ‘power pricing’ [Dolan and Simon (1996)].
agers and decision makers must focus more on the profit
potential hidden on the price side. This does not mean simply
A bank sells its golden credit card for U.S.$100. Sales volume is
increasing prices. Rather, success depends on two factors,
one million units. The variable costs per unit are U.S.$60, which
innovative pricing strategies orientated towards the cus-
results in a contribution margin of U.S.$40 per unit. The bank’s
tomers’ needs and the subsequent complete reorganization of
fixed costs are U.S.$30 million. In this situation, the bank earns
pricing processes.
a profit of U.S.$10 million [(100-60) dollars/unit x 1 million units
— U.S.$30 million]. How does each of the four profit drivers —
Price is the primary profit driver
price, variable costs, volume, and fixed costs — change profit
Many banks are suffering from a crisis into which they have
when improved by 10 percent? A 10 percent increase in price
put themselves. A common solution is to cut costs drastical-
($100 to U.S.$110) leads (ceteris paribus) to a profit increase of
ly. Personnel cutbacks are almost daily occurrences.
100 percent, from U.S.$10 million to U.S.$20 million [(110-60)
American banks, for example, cut more than 100,000 jobs
dollars/unit x 1 million units — U.S.$30 million]. The effect of the
between 2000 and 2004. These measures to reduce costs
other profit drivers is much lower. A 10 percent improvement of
are inevitable. However, after heavy cost cutting in the recent
variable costs, volume, and fixed costs leads (ceteris paribus) to
years, companies have nearly exhausted the potential to
a profit increase of 60, 40 and 30 percent respectively. Bearing
reduce costs any further. Is there a way to escape the crisis?
this in mind, management should concentrate more on intelli-
What else can be done to increase profits? Management must
gent price increases than on other measures, such as cost cut-
concentrate more on revenue and price. In these two areas,
ting. As a result, managers and decision makers must see the
the potential to increase profits today are significantly high-
price as the ‘primary profit driver’. This is especially true in sit-
er than through cutting costs. Furthermore, many price
uations with low unit margins.
measures immediately transform into a profit increase, the
so-called quick wins. Our experience shows that for many
Before a bank decides whether to increase or decrease prices
banks these quick wins can provide a profit potential of mil-
it should analyze the impact of price changes given different
lions of dollars. The following calculations illustrate the prof-
cost-income ratios. The bank needs to ascertain how much vol-
it potential of pricing:
ume has to be gained (price reduction)/can be lost (price
increase) in order to keep the cost-income ratio constant.
Example 1: An average lending rate increase of 10 basis points
Managers should only change a price if the expected effect on
based on the credit volume of a bank could lead to additional
volume is higher/lower than the given percentages. For exam-
profits of U.S.$1 million (based on a volume of credit of U.S.$1
ple, at a cost-income ratio of 0.75, a price reduction of 10%
billion), U.S.$10 million (based on a volume of credit of U.S.$10
only increases profit, if a volume increase of 67% or more is
billion), or U.S.$100 million (based on a volume of credit of
expected. A 10% increase in price only increases profit, if the
U.S.$100 billion).
volume decrease is lower than 29%.
Example 2: A U.S.$10 average increase in per customer profit
Increased margins stimulated by professional pricing immedi-
could lead to additional profits of U.S.$1 million (based on
ately increase profit and do not require expensive upfront
25
investments or severance pays. Relative to cost cutting, price
When companies offer such a large number of products as
management offers three opportunities, it gains time, avoids
many banks do, with retail price lists of banks very often cov-
additional upfront expenses, and increases profit more
ering more than 200 price components, or prices are negotiat-
strongly. Surprisingly, most managers either do not focus on
ed for each transaction, pricing processes are crucial. Due to
the price or they make the wrong decisions. The following
the high number of necessary price decisions, the effort
case reveals the power of pricing. An American bank has
involved in each decision has to be limited. Precisely defined
earned revenues of U.S.$1 billion. The profit is around U.S.$50
processes are required to determine and implement prices and
million. A sophisticated analysis shows that price increases of
thereby foster acceptable yields. The issue of pricing processes
on average around 5% are possible without losses in volume.
is rather new for several reasons. Traditionally, price decisions
Consequently, the profit would increase by 100% — from
have been mostly made based on the feelings and subjective
U.S.$50 million to U.S.$100 million. The key question is: How
judgment of the person in charge. At present, the concept of
can such a measure be successfully implemented?
pricing processes has been implemented consistently only by a
few companies, mostly in the life science and automotive
Pricing processes: The key to success
industries. The second reason why the issue is so new is that
Simple price increases, such as an increase of all prices by 5%,
pricing processes have been a difficult topic for academic
would be very risky and do not work. Just increasing existing
researchers. On the one hand, these processes are very indus-
prices or ordering sales persons to negotiate higher prices will
try-specific and quite often also company-specific, requiring
fail. Banks must apply innovative price strategies that focus on
time and labor-intensive research to understand. On the other
the customers’ need, value pricing, and are supported by a
hand, pricing processes are kept top secret. An automotive sup-
completely restructured pricing process. In our experience,
plier, for instance, is not interested in initiating a public discus-
many banks and insurance companies today do not follow a
sion about its pricing processes. According to our findings,
systematic pricing process. Such a process is comprised of a
effective pricing processes usually increase the return on sales
system of organizational rules, structures, and measures
by about 2 percentage points. In light of the dismal situation
intended to determine and implement prices. Pricing process-
which most companies are currently facing, this is revolution-
es are complex and cover the following aspects:
ary. Figure 1 examines the increase in profit using cases from
various sectors of the financial services industry.
1. The five phases of the pricing process:
■ Strategic guidelines (objectives, positioning, competition) —
What do we want? Where do we want to get to?
■ Status-quo check (current situation and processes) — How
do we do it today?
■ Price decision (structure, level, customization, bundling) —
What is the optimal price/price structure?
■ Implementation (organization, responsibility, IT, incentives)
Figure 1 should be read as follows: In the case of a retail bank,
the margin improved by 1.6 percentage points. The cases presented in the figure prove that the starting points for process
improvements are very specific. An increase in the return on
sales cannot be achieved based on simple price increases.
Instead, more intelligent measures have to be applied, a cru-
— How can the price be enforced into the market?
cial insight for success. Moreover, top management must
■ Controlling/monitoring — How did the prices develop?
commit to the new pricing process. After all, the reorientation
2. Information, methods, models, rules, qualifications, compe-
of the company’s competencies regarding pricing and the
tencies, and deadlines.
3. Subjective (e.g. estimations, experience) and objective (e.g.
market, competition data) components.
26 - The
The increase in the return on sales in the right column of
resulting profit increase are at stake. The following cases from
the banking industry demonstrate the impact of a new pricing
process.
■ In the retail unit of a large bank, profits could be increased
through an improved differentiation of customer seg-
Industry
Revenue
category
Main starting point for
improved process
Private
banking
U.S.$500
million
Pricing process
Pricing audit
5
Retail
banking
U.S.$1-5
billion
Extensive extraction of brand value
Increased pricing competence of
relationship managers
1.6
Funds
U.S.$600
million
Price implementation on indirect channels
Intelligent price segmentation
5
Insurance
U.S.$100500 million
Restructuring and optimization of branches
Optimization of sales strategy
7
ments. One group of regular customers reacted strongly
to the price increases, other groups and new customers
did not show any reaction to the same measures.
Improved coordination between pricing, segmentation,
product customization, and communications significantly
increased marketing efficiency. The bundling of certain
products and prices to packages was crucial, especially for
cross-selling [Wuebker (2003)].
■ Another bank was able to increase its revenue by 10 per-
cent after a sophisticated analysis of the competitors’
Increase in
return on
sales (%)
Figure 1: Efficient pricing processes lead to major profit increase
prices, price elasticities, segmentation, and customized
products. A detailed analysis of several product categories
successful pricing process is about dramatically increasing
demonstrated that no systematic pricing process existed
pricing intelligence.
in the company. Every business unit used a different
approach to determine prices. Pricing guidelines, a frame-
Optimization of pricing processes: A case study
work for the price policy, were missing. The price elastici-
Strategic guidelines (Phase 1)
ties of analyzed products were unknown. Prices were
During the first phase of the pricing process, the price strate-
determined based only on costs or competitors’ prices.
gy and desired price positioning must be defined. In general,
The project served as a pilot for the future pricing organi-
banks do not have guidelines for pricing their products and
zation.
services. These guidelines have to be consistent with the
■ A pragmatic analysis of price sensitivities was identified as
future strategy and the positioning of the bank. One bank
a profit driver for the private banking division of a bank.
established the following guideline in a workshop: ‘We are a
Based on this analysis and some updated price structures,
premium bank. For the high value we deliver we set the appro-
quick wins were generated. The additional revenue was
priate prices. Our price position is in the upper quartile.’
several tens of millions dollars.
■ The sales force of another bank was identified as being
In the next step, the strategic pricing objectives have to be
overly generous with discounts. They made price the cen-
defined and prioritized. In our experience, complex and unin-
tral issue in negotiations with their customers. This prob-
telligible target systems are relatively widespread. The follow-
lem was solved using argumentation guidelines and a new
ing example illustrates this. The conflict between profit and
incentive system.
volume targets is well known. Most bank managers strive for
higher prices without losing volume or market share. In many
These cases support the assertion, that generating profits
banks, only explicit volume targets have been defined (number
through pricing is not an issue of simply increasing or decreas-
of credit cards, number of new contracts, transactions, assets
ing prices. The parameters for improvement are more com-
under management, etc.). Consequently, profit is not the only
plex: information, knowledge, competence, responsibilities,
target that must be considered. A combination of profit and
incentives, price structures such as multidimensional or non-
volume targets is common in business practice. Managers
linear prices, price bundling, multi-person pricing, and cus-
have to find a balance between volume and profit. This trade-
tomization are some of the most important ones. Ultimately, a
off must be resolved and made explicit.
27
Status-quo check and price optimization (Phases 2 and 3)
have proven successful in enforcing higher prices and value on
The profitability of individual customer relationships is
the market, an incentive system for the sales people, indica-
unknown to many banks. In light of this, a structured and sub-
tors for better evaluation and segmentation of customers
stantiated data analysis is required. In general, banks store a
(regarding their price elasticities), and sales guidelines.
great amount of customer information and data. However, this
information is frequently not properly structured. An in-depth
‘Incentive systems’ are crucial for the implementation of a
data analysis clarifies which customer relationships are prof-
centrally planned price process. They are the only means of
itable for the bank under consideration. The case study
achieving the intended price positioning. The purpose of an
reveals that the contribution margin of many customer rela-
incentive system is to link the bank’s objectives to those of the
tionships is below zero and that there is no clear relation
sales person. Defining a sales person’s objectives through a
between assets under management and contribution per cus-
combination of volume (i.e. a number of successfully signed
tomer. This analysis is a crucial prerequisite for future price
contracts or volume of invested capital) and profit targets has
decisions.
proven to make sense. In the long run, only profits, not volume
alone, secure the market presence of a bank.
The analysis of the existing pricing process of the bank
showed that price decisions in general were focused on costs
Another way to enforce higher prices on the market is by
or competitors. The impact of price variations on the sales vol-
using an ‘indicator system’ to estimate the customer’s price
ume was unknown to product managers. The lack of knowl-
sensitivity. Relationship managers could be asked to classify a
edge about the relationship between price and volume and
representative sample of their customers in terms of these
price elasticities repeatedly caused poor decisions regarding
indicators. By aggregating these judgments, an overall estima-
the optimal price. In the future, product managers will gather
tion of the customers’ price sensitivity can be obtained. The
sufficient information for price decisions. This information
advantage of this method is its simple, fast, and pragmatic
involves crucial elements, such as value drivers and benefits
operation. A quantification of the relationship between prices
of the targeted customer segment, the willingness to pay, and
and volumes is not possible off-hand.
segment-specific price elasticities. Methods like expert judgment or conjoint measurement have demonstrated their capa-
When negotiating, relationship managers should never argue
bility in the gathering of such information [(Wuebker and
relying only on price. The customers’ willingness to pay always
Mahajan (1999)]. The result of these methods is a price-
reflects the perceived value of the products and services.
response function, which serves as a base for the calculation
Consequently, value, not price, should be the focus of the
of optimal prices.
negotiation. In business practice, we often notice the opposite
as the following case shows. A wealthy customer intends to
28 - The
Implementation and monitoring (Phases 4 and 5)
invest a huge amount of capital, more than U.S.$1 million, at a
A profit improvement potential of 2 percent (measured in
bank of his choice. He is welcomed with the following words:
terms of return on sales) through the professional optimiza-
‘You are such a wonderful customer. Therefore we will grant
tion of prices and products is realistic for many banks. To turn
you our special price, which is 30% below our regular price.’ In
this potential into reality, the sales force must understand,
saying so, the customer relationship manager started an
accept, and communicate to the customer the new prices and
unnecessary price discussion. As a result, the customer, sur-
their structures. In customer negotiations, the price, and not
prised by the generosity, demanded further discounts, ending
value-to-customer, is frequently the focus, which results in
with a final price 50% below list. To avoid such a disaster, rela-
overly generous discounts. To avoid this, three instruments
tionship managers should emphasize the value and services
generated by the bank. This requires a profound understand-
profit), improved price customization (U.S.$2.8 million addi-
ing of the value drivers. This is the basis for developing ‘sales
tional profit), and implementation of centralized controlling
and argumentation guidelines’. Supported by a value-based
(U.S.$1.0 million additional profit).
argumentation, relationship managers are able to convince
the customer that the demanded price is right. Enforcing price
A systematic pricing process is comprised of five phases: strat-
and value can be significantly bolstered this way.
egy, a status-quo check, the price decision, implementation,
and controlling/monitoring. Most companies do not follow a
Implications: Reaping the harvest
systematic and standardized price decision process. The start-
Many banks are suffering from a profit crisis. Simple price
ing point of professional pricing is substantial information.
reductions in general reduce contribution margins dramatical-
Price elasticities, the willingness to pay for different products,
ly, resulting in a profit collapse. Consequently, the cause of
etc. have to be known to optimize prices and products.
many crises is price erosion, which is frequently started
Reliable and valid methods, such as conjoint measurement, to
because the reactions of competitors and customers are not
collect such information are necessary.
correctly estimated. Many bank managers do not sufficiently
understand the effects of price on volume. Yet price is the pri-
The art of pricing lies in using intelligent and innovative means
mary profit driver.
of price customization to exploit the customers’ willingness to
pay [Schmidt-Gallas (2004)]. Some of these means are non-
The bank’s executive managers must focus more strongly on
linear pricing, multi-person pricing [Dolan and Simon (1996)]
profits and prices. Companies need innovative pricing strate-
and price bundling [Simon and Wuebker (1999)]. Companies
gies, which are in line with customers’ needs and value per-
like Dell or Microsoft have successfully adopted these meth-
ceptions and accompanied by an overall reorientation of pric-
ods. They are a benchmark for value pricing.
ing processes. At successful banks like UBS, pricing is closely
linked to their organization. Other banks are just starting this
References
process.
• Baumgarten, J. and G. Wuebker, 2004, “Strategies against price wars in the financial
service industry,” February 10, offshoretoday.com.
• Dolan, R. J. and H. Simon. Power pricing — How managing price transforms the bottom line. The Free Press, New York (1996).
• Hardock, P. and G. Wuebker, 2003, “Bundling in the banking sector — a promising
strategy to create value,” March 12, offshoretoday.com.
• Lauszus, D., Added value private equity: Professional price management to increase
profitability. SKP White Paper (2004).
• Schmidt-Gallas, D., Profitable growth for insurance companies: Manage your pricing
or lose money, SKP White Paper (2004).
• Simon, H., and G. Wuebker. Bundling — A powerful method to better exploit profit
potential, in: Herrmann, A., R. Fürderer and G. Wuebker. Optimal Bundling. Springer,
New York (1999).
• Wuebker, G., 2002, “Bundles’ effectiveness is often undermined,” March 18,
Marketing News, p. 12.
• Wuebker, G. and V. Mahajan. A conjoint analysis based procedure to measure reservation price and to optimally price product bundles. Herrmann, A., R. Fürderer, R.
and G. Wuebker. Optimal Bundling. Springer, New York (1999).
The value-to-customer of products and services is not completely understood by many banks. Consequently, they do not
charge the appropriate price for the value delivered.
Increasing profits through more effective pricing processes is
a challenge for top management. Gains in the area of several
tens of millions of dollars can be achieved by implementing
professional pricing processes. The additional profit comes
from numerous measures.
At one company the following price and product measures
were implemented: Optimization of prices for core products
(U.S.$5.1 million additional profit), guidelines for systematic
discount strategy (U.S.$4.4 million additional profit), structuring of special discounts (U.S.$3.2 million additional profit),
optimization of key account pricing (U.S.$3.1 million additional
29
Market impact: Transaction cost
analysis and the financial markets
Anders Amundson
Managing Director, Elkins/McSherry
In 1986, a simple regulatory concept focusing on investment
trustees and pension executives were able to identify man-
transactions (U.S. Department of Labor Technical Bulletin, 86-
agers and brokers whose costs diminished overall investment
1) forced the financial markets to place an increased emphasis
performance.
on transaction costs. Almost 20 years later, transaction cost
analysis has not only become ubiquitous amongst institution-
This movement increased the pressure on investment man-
al investors, but created a niche industry focused on providing
agers to justify their brokerage relationships. Many managers
low cost stock transactions. This paper aims to describe the
began performing transaction cost analysis internally.
motivations behind measuring transaction costs, explain how
Eventually, a regulatory concept called best execution1 all but
transaction costs are measured in the financial markets, and
explicitly demanded investment managers to regularly per-
outline how an intensified scrutiny of transactions will impact
form some type of transaction cost analysis.
the future of the institutional investment community.
Initially, investment managers performed the same type of
Why measure transaction costs?
basic, macro-level analysis common among pension funds.
Ideally, transaction costs are measured in an effort to improve
However, with the proliferation of order management technol-
the investment process, however, the intensity of detail and
ogy, transaction cost analysis evolved from a basic evaluation
motivation behind a transaction cost study can vary depend-
tool to a much more precise methodology that investment
ing on the audience. Originally, the idea of transaction cost
managers could actually utilize at the trade level. The wide-
analysis gathered widespread appeal with pension fund man-
spread adoption and integration of order management sys-
agers, however these days, transaction cost analysis has
tems allowed asset management firms to assign a quantitative
become universal amongst asset management firms and is
value to both their internal investment processes and external
very quickly becoming common within institutional brokerage
trading relationships. In fact, from a business perspective,
houses. While the basic philosophy of transaction cost meas-
many investment managers might agree that enhancing per-
urement can be applied to trades involving any type of finan-
formance though a diligent improvement of the transaction
cial instrument, the actual practice of transaction cost analy-
process can dramatically improve the firm’s competitive posi-
sis is most pervasive in the equity markets.
tion within the industry — simply because so many managers
have a difficult time delivering excess performance.
Institutional investment hierarchy
Pension funds (government, corporate, and union pension
Standard and Poor’s recently calculated2 that there have been
funds, as well as foundations and endowments) first started
roughly 1096 distinct investment groups managing large capi-
monitoring transaction costs as part of a government man-
talization investment funds in the U.S. consistently for the
date that required pension trustees to monitor the brokerage
past three years. Of these funds, only 31.1% beat the S&P 500
relationships of their investment managers. The philosophy
large cap stock index. The percentage of index beaters drops
behind the mandate was that brokerage commissions were a
even further for mid-cap and small-cap investment managers.
pension asset and pension executives had a fiduciary respon-
Only 20.9% of mid-cap stock funds beat the S&P MidCap 400
sibility to understand how the brokerage relationships of their
index over the past three years and only 23.2% of small-cap
external investment managers affected the overall perform-
stock managers beat the S&P SmallCap 600 index during the
ance of the pension fund. Before these rules, transaction costs
same time period.
were not even known, let alone understood, by the vast majority of pension trustees. As transaction costs began to be eval-
To put the impact of transaction costs on portfolio perform-
uated by the decision makers within a pension organization,
ance in perspective, consider that during the fourth quarter of
1
30 - The
Gohlke, G., 2000, “What constitutes best execution?” Securities and Exchange
Commission, November 30
2 Pane, R., and S. Dash, 2005, “SPIVA active funds scorecard — 4th Quarter 2004,”
Standard and Poor’s, January 18
2004,3 every NYSE transaction cost the average investment
advertisements proclaiming expertise in delivering high quali-
manager roughly 0.26% per trade and every NASDAQ trans-
ty executions.
action cost the average investment manager about 0.35% per
trade. This total transaction cost encompasses commissions,
Transaction costs in the financial markets
fees, and market impact. While these costs might seem
Academically, a transaction cost is described as the cost of
insignificant, over time, depending on the frequency of trading
making an economic exchange. In the financial markets, the
activity, transaction costs can add up, seriously hampering
measurable costs of an economic exchange can be character-
overall investment performance.
ized by a combination of explicit and implicit costs. Explicit
transaction costs are generally considered easy to estimate.
Estimates have placed the average annual portfolio turnover
These transaction costs consist of commissions paid to bro-
for U.S. equity funds at around 90%. If this is true, the aver-
kers for trading services and fees or taxes paid to exchanges
age active equity manager can expect transaction costs to
and regulatory agencies. Investors usually understand the
reduce overall portfolio performance by roughly 0.50% annu-
financial impact of explicit transaction costs before the actual
ally or 1.50% over a three year period. During the same three
transaction takes place.
4
year time period cited above, the S&P 500 beat large-cap
equity managers by 0.95%. This suggests that an effort to
Implicit transaction costs, on the other hand, can be much
become better than average in terms of transaction costs
trickier to estimate. Implicit transaction costs, commonly
could help an investment manager discover a large portion of
described by the investment community as ‘market impact’,
the extra performance needed to beat both the market and
are the additional costs of actually implementing an invest-
their peers. A recent article published in the Wall Street
ment idea, essentially the simple act of buying or selling a
Journal5 helps to confirm this point. The article notes that
security. Market impact costs are different from explicit costs
fund behemoth Fidelity Investments adds as much as 0.30%
to the extent that market impact is not a cost actually levied
to annual performance due to transaction cost analysis.
by a broker or governing body, but by the supply and demand
forces of the market itself. Market impact is usually not known
Rounding out the bottom of the institutional investment hier-
before the transaction occurs and can be difficult to predict.
archy are brokerage firms. Brokerage firms have experienced
the greatest impact to their business models as a result of the
Measuring market impact
best execution mandate. The increased emphasis placed on
The measurement of any process begins with a benchmark. If
transaction costs coupled with decreased spreads due to dec-
you are jogging from point A to point B, the benchmark can be
imalization6 by both the NYSE and NASDAQ, has markedly
the amount of time it takes to run that distance. If you are
squeezed margins for brokers.
manufacturing cars, the benchmark might be a minimum number of defects per 1,000 cars produced. In the financial mar-
Over the past five years, brokers have witnessed a 40% reduc-
kets, market impact is most commonly measured by compar-
tion in average commissions7 for trades done on the NYSE. As
ing trades against benchmarks composed of price, time, and
a result, many brokerage firms have adapted their operations
trading volume. Of the various benchmarks, the most common
to cater to a more transaction focused marketplace. In fact, it
measurement metric is called the VWAP (Volume weighted
is not uncommon to find brokers who actively tout their abili-
average price).
ty to help investment managers achieve best execution. A cursory glance at industry publications, such as Traders Magazine
The VWAP is simply an average of all market activity through-
or Institutional Investor, will uncover dozens of brokerage
out a specific time period, usually a day, in which larger trades
3 Source: Elkins/McSherry Universe.
4 Bogle, J., 2000, “Mutual funds at the millennium,” Bogle Financial Markets
Research Center, May 15
5 Kelly, K., and J. Hechinger, 2004, “How fidelity’s trading chief pinches pennies,”
Wall Street Journal, October 12
6 The NYSE switched to decimal pricing in January of 2001 and the NASDAQ
switched to decimal pricing in April 2001.
7 Source: Elkins/McSherry Universe.
31
have a greater overall impact on the average price. Common
variants of the VWAP include ‘available VWAP’, which calculates the VWAP from the time the trader starts the order to
the close of trading that day, and ‘interval VWAP’, which calculates the VWAP from the time the trader starts the order to
the last trade execution for the order. Once a VWAP is creat-
Segment
Full day
Portfolio manager to last execution
Portfolio manager to trader
Trader to broker
Broker to last execution
Broker to close
Benchmark
VWAP
Implementation shortfall
Interval VWAP
Available VWAP
Average cost
0.07%
0.52%
0.07%
0.11%
0.03%
0.05%
ed, trade executions are compared to that benchmark to
measure market impact. Market impact is simply the positive
Figure 1: Elkins/McSherry trade cycle, NYSE, 2nd Quarter, 2004
or negative difference between the trade execution and the
benchmark.
helps to determine how much or how little each order participant contributed to the overall cost of the transaction. At that
While the basics of transaction cost measurement certainly
level of analysis, groups can begin to streamline the trade
begins with the comparison benchmark, understanding the
process in an attempt to gain transaction cost efficiency.
personality of the order is critical to the determination of the
correct benchmark. Some types of trades are considered very
When looking at each segment of a transaction, it is important
common and easy to perform, whereas others are considered
to understand the key variables that also contribute to the
quite difficult. Appreciating how all of the key variables con-
execution strategy. Many of these variables are also measured
tribute to the complexity of an order is of chief importance
within a transaction cost analysis. These variables include the
when estimating market impact. More so, many groups will
price volatility of the stock being traded, the size of the order
compare themselves to multiple benchmarks because some
relative to the daily volume of the market, the time horizon for
of the most popular benchmarks, such as VWAP, contain
completing the order, the opportunity cost of an uncompleted
inherent flaws that a savvy trader can game to their own
order, the type of broker used, and a cost described as ‘infor-
advantage.
mation leakage’.8
Some of the other common trading benchmarks include
Information leakage arises when an institutional broker proves
‘implementation shortfall’, which measures the absolute cost
to be less than discreet while handling an order. If word leaks
of a trade, and ‘strike price’, which compares the trade to a
that money manager XYZ is buying or selling a major position,
predetermined target price, such as the closing price of the
traders can and will jump in front of that order in an effort to
stock the day before the trade occurred. With implementation
capture a portion of the inevitable price movement, adversely
shortfall, the metric generated is the price-to-price difference
affecting the overall market impact for manager XYZ and ulti-
between the start of the trade and the final execution of the
mately reducing the overall performance of the portfolio.
order.
Often, because of the potential for information leakage,
investment managers will concede a certain degree of price to
Implementation shortfall, available VWAP, and interval VWAP
preserve anonymity for their trade executions.9
are similar inasmuch that all three benchmarks attempt to
32 - The
quantify costs within a very specific window of time. Using time
The future of transactions
segmented benchmarks is a recent innovation that has allowed
Proof that transaction cost analysis has had a systemic influ-
asset managers to perform separate evaluations of each spe-
ence on the brokerage business is evidenced by one of the
cific participant in the trade process (portfolio manager/
hottest trends in the brokerage industry, algorithmic trading.10
trader/broker). Breaking apart the trade process in this manner
Algorithmic trading is essentially the use of a computer gen-
8 Sofianos, G., and J. Bacidore, 2002, “Trading and market structure,” Goldman
Sachs, October 24
9 Birger, J., 2004, “American Century’s secret weapon,” Money Magazine,
September
10 Risk Waters, 2004, “Algorithmic trading explosion,” Risk Waters Group,
December 13
erated trading strategy to help buy-side traders achieve a specific benchmark. Of the various algorithmic strategies
designed by brokerage houses, the core strategy offered by all
of the major algorithmic desks is a trading engine designed to
mimic the VWAP or its variants.
Other brokerage groups have designed alternative trading
systems that cater to the specific transaction needs of investment managers. Some of these systems aim to discover pools
of liquidity or cross large blocks of stock anonymously. Pretrade analysis software that helps traders analyze orders
before the executions begin is also starting to find a place on
the trading desks of many investment management firms. One
brokerage house even has plans to introduce a derivative
product designed to hedge the VWAP.11
Many of these products are still in the nascent stages of
growth. Over the next several years, a wide range of execution
based tools and services will be available to the investment
community. Also, it is highly likely that the idea of best execution will become increasingly common beyond the equity markets. Demand for fixed income transaction cost analysis has
been gaining steam over the past 12 months and a few investment managers already analyze currency and futures transactions. All things considered, the capital markets are becoming a more transaction focused marketplace.
11 Chapman, P., 2004, “J.P. Morgan’s analytical difference,” Traders Magazine,
December
33
Services
Measuring trade
execution costs
from public data1
Hendrik Bessembinder
A. Blaine Huntsman
Presidential Chair in Finance,
David Eccles School of Business,
University of Utah
Abstract
This study assesses the sensitivity of trading cost estimates
derived from publicly-available trade and quote data to two
methodological issues: the time adjustment made before comparing trades to quotes, and the procedure used to designate
trades as buyer or seller-initiated. The results indicate that
making no allowance for trade reporting lags is optimal when
assessing whether trades are buyer or seller-initiated, for both
Nasdaq and NYSE stocks. However, trade prices are best compared to earlier quotations when assessing trade execution
costs, in order to capture the effect of systematic quotation
revisions in the seconds before trades are reported. Despite
the sensitivity of trading cost measures to these methodological issues, inference as to whether the Nasdaq dealer market
or the NYSE auction market provides lower trade execution
costs is not sensitive.
1
This paper is extracted from Bessembinder, H., 2003, “Issues in assessing trade
execution costs,” Journal of Financial Markets, 6:3, 233-258, with permission from
Elsevier.
35
How much do investors pay to have their trades executed in
The central methodological issue considered here concerns
financial markets? Obtaining accurate measures of trade exe-
the relative timing of trades and quotes contained in public
cution costs and assessing the reasons for their systematic
databases when inferring trade initiation and measuring trad-
variation is important to individual investors, portfolio man-
ing costs. Lee and Ready (1991) recommend comparing trade
agers, those evaluating brokerage firm or financial market
prices to quotes in effect five seconds before the trade report
performance, and corporate managers considering where to
time to allow for delays in trade reporting. However, compar-
list their shares. There seems to be increased interest in
ing trade prices to an earlier reference quote might be justi-
obtaining accurate measures of trading costs in recent years.
fied even if trades were reported without delay. Traders are
This interest may be attributable in part to a realization that
generally concerned with the possibility of adverse price
careful control of trade execution costs may be as, or more,
changes between the time of their trade decision and execu-
important in determining portfolio performance than the abil-
tion. The possibility of adverse pre-trade price movements
ity to identify mis-valued securities in the highly competitive
underlies the recommendation of Perold (1988) to compare
financial markets.
trade prices to a benchmark at the time of the trading decision, as well as the common use in the practitioner literature
The United States Securities and Exchange Commission (SEC)
of prior day quotes or trade prices as the benchmark.
now requires (Regulation 11Ac1-5) individual market centers
Comparing trade prices to earlier benchmark quotes poten-
to use their internal order data to construct and disseminate
tially captures the effect of systematic price movements
monthly reports of average market quality. But, as Bacidore
ahead of trades.
et al. (2003) emphasize, measures of trade execution quality
36 - The
are quite sensitive to detailed methodological choices. It is
Suppose, for example, that trade report times lag actual trade
unclear the extent to which execution quality reports pre-
execution times by five seconds, and that quotes tend to be
pared by individual market centers will be comparable with
systematically revised in the fifteen seconds before trades are
each other. Those who wish to compare market quality meas-
completed. Then, comparing trade prices to quotes five sec-
ures for broad sets of traders and markets, while using com-
onds before the trade report time would be optimal for infer-
pletely uniform definitions and methods, are likely to have to
ring trade direction. However, comparing trades to quotes in
construct their own measures and to rely on the publicly
effect twenty seconds before the trade report time would pro-
available trade and quote data. The same will be true for
vide a more accurate measure of trade execution cost, includ-
those who wish to evaluate market quality measures for time
ing the effect of pre-trade price impact. This study assesses
intervals finer than one month or those who wish to study
the effect on measured trading costs of comparing trade
measures, such as net order imbalances, other than those
prices to quotes in effect from zero to thirty seconds prior to
required by rule 11Ac1-5.
the trade report time.
One shortcoming of the public trade and quote data is that
Roll (1984) introduces a technique for inferring trade execu-
whether a trade was initiated by a buyer or a seller must be
tion costs from the serial covariance of price changes. His
imperfectly inferred from the data. A second issue is that,
method does not require that trades be signed or matched to
although trade prices can be readily compared to quotes in
quotation data. Schultz (2000) reports that the Roll technique
effect at the trade report time, the appropriate comparison
provides good estimates of trade execution costs for his sam-
might be to quotes in effect at an earlier time, such as the time
ple of Nasdaq stocks. This study assesses whether difficulties
of the trading decision or at the time the order arrived at the
arising from the need to sign trades and to match trades with
market, and these times are generally not known.
prevailing quotes can be avoided by simply using the Roll
method in broader samples that include data from the New
cannot be avoided by simply using the Roll procedure instead.
York Stock Exchange (NYSE) as well as Nasdaq.
Finally, despite the sensitivity of trading cost measures to the
methodological issues considered here, inference as to
These measurement issues are considered in the context of a
whether the dealer market or the auction market provided
broad comparison of trade execution costs across the Nasdaq
lower trade execution costs during the sample period is not
dealer market and the NYSE’s specialist-based auction mar-
sensitive.
ket. The study examines 300 stocks traded on the Nasdaq
stock market and 300 matched NYSE stocks during the July
This paper is organized as follows. The next section describes
to December 1998 period.
the sample firms and the trade and quote data that are used.
That is followed by a description of the measures of trading
The results of the study can be summarized as follows. Firstly,
costs and procedures for inferring trade direction. Sub-
measures of rates at which trades are executed at prices bet-
sequently, I will report on the main empirical results, and final-
ter (trades receive ‘price improvement’) or worse (trades
ly conclude.
receive ‘price disimprovement’) than the quotations are quite
sensitive to whether trade prices are compared to contempo-
The sample
raneous or previous quotes. Comparing trade prices to earlier
This study focuses on trades in 300 Nasdaq and 300 NYSE-
quotes decreases the percentage of trades that appear to
listed common stocks during the period July 1 to December 31,
receive price improvement while sharply increasing the per-
1998. The Nasdaq and NYSE samples rely on the Trade and
centage of trades that appear to be disimproved. Comparison
Quote (TAQ) database, and are matched based on beginning-
of these results to those obtained in recent studies [Bacidore
of-sample market capitalization, and include subsets of large,
et al. (2003), Peterson and Sirri (2003), and Ellis et al. (2000)]
medium, and small capitalization stocks. Sample selection pro-
that use proprietary order data suggests that contemporane-
cedures and error filters are described in Bessembinder
ous comparisons are optimal when assigning trades as buyer
(2003). The final sample includes 43.5 million trades and 25.4
or seller-initiated.
million quotes.
Secondly, measures of effective trading costs increase with
Sample Nasdaq stocks are traded more frequently, averaging
longer time adjustments because quotations systematically
946 trades per stock/day in the full sample, compared to 215
rise (fall) in the seconds before customer buy (sell) trades are
trades for sample NYSE stocks. Quotes are also updated more
reported. If the quotation movement prior to the trade report
frequently on Nasdaq, 1094 times per stock/day, compared to
time occurs after the trading decision but before trade execu-
496 on the NYSE. Returns on sample Nasdaq stocks are more
tion, then the increase in measured trading costs with a longer
volatile: the cross-sectional average standard deviation of
time adjustment is real, not illusory. Thirdly, the trading cost
daily returns computed from 4 p.m. quotation midpoints is
estimator due to Roll (1984) provides estimates of effective
4.1% for sample Nasdaq stocks, compared to 3.2% for sample
trading costs on the Nasdaq market that are very similar to
NYSE stocks.
those obtained when comparing trade prices to quotations, a
result that is consistent with the findings of Schultz (2000).
Research methods employed
However, the Roll estimates do not correspond as closely to
the quote-based estimates for NYSE stocks or for large trades
Measures of trading costs
on either market, implying that the difficulties arising from the
This study considers four measures of trade execution costs.2
need to match trades with quotes and to assign trade direction
The first is the quoted bid-ask half-spread, defined as half the
2 Brokerage commission charges are not studied, for two reasons. Firstly, comprehensive data on commission payments is not available. Secondly, individual traders
are aware of the commissions they pay, since these are reported directly to them.
Trade execution costs are not reported to traders, but must be inferred from trade
prices.
37
difference between the inside ask quote and the inside bid
that trades be assigned as being buyer or seller-initiated, and
quote. The average quoted half-spread for each sample stock
that trades be matched with prevailing quotes. A measure of
is computed on a time-weighted basis. Reported are cross-
average trade execution costs that does not impose these
sectional averages of the firm means. The quoted half-spread
requirements is the Roll (1984) spread, which exploits the
does not accurately measure trading costs when trades are
movement of trade prices between the market’s effective bid
executed at prices away from the quotes. A measure of trad-
and ask prices, and infers the effective width of the bid-ask
ing costs that incorporates actual execution prices is the
spread from the magnitude of the negative serial correlation
effective bid-ask spread, measured for trade t in stock i as:
induced in transaction price changes.
Effective Half-spreadit = Dit(Pit – Mit), where Dit is an indicator
variable that equals one for customer buy orders and nega-
I use the modification of the Roll estimator suggested by
tive one for customer sell orders, Pit is the price at which the
Schultz (2000). Letting Pit denote trade t in stock i and COV
trade is executed, and Mit is the midpoint of the reference bid
denote covariance, the estimator is:
and ask quotes, viewed as a proxy for the underlying value of
Si = [-COV (Pit – Pit-1, Pit+1 – Pit)]/[1 – 7/(8(n-1))],
the stock.
where n is the number of trades in the sample. Due to limitations on the number of trades that can be handled by available
If traders possess private information about security values on
computing systems, I implement the Roll measure for each
average, market prices will tend to rise after customer buys
firm on a weekly basis, using all trades completed during the
and fall after sells. These price movements reflect what
week. The final estimate for each stock is obtained as the
Glosten (1987) refers to as adverse selection costs. Some
trade-weighted average of the weekly estimates. Reported are
observers have argued that trading costs should be measured
cross-sectional averages of the firm-by-firm estimates.
based on trades’ temporary or non-informational price impact.
Methods used to assess statistical significance are described
The realized bid-ask half-spread is such a measure. It is
in Bessembinder (2003).
defined as: Realized Half-spreadit = Dit(Pit – Mit+n), where Mit+n
is midpoint of the quotations in effect n periods after the
Algorithms for assigning trade direction
trade, used as a proxy for the post-trade value of the stock.
The most widely used technique for categorizing trades as
buyer or seller-initiated is that recommended by Lee and
The post-trade movement in the quote midpoint reflects, on
Ready (1991), henceforth LR. Their algorithm assigns trades
average, the market’s assessment of the private information
completed at prices above (below) the prevailing quote mid-
that the trade conveys, referred to as the trade’s price impact:
point as customer buys (sells). Trades executed at the quote
Price Impactit = Dit(Mit+n – Mit) = Effective Half-spreadit –
midpoint are assigned by the ‘tick test’, by which trades at a
Realized Half-spreadit.
higher (lower) price as compared to the most recent trade at
a different price are classified as buys (sells).
I use the midpoint of the quotes in effect 30 minutes after the
time of the reference quote, or the 4 p.m. quotations during
Several studies, including Finucane (2000), Odders-White
the last half hour of trading, as Mit+n. Effective and realized
(2000), and Ellis et al. (2000) have recently emerged that
half-spreads are measured for each trade and averaged
use specialized datasets containing order information to
across trades for each stock. Reported are simple cross-sec-
assess the accuracy of the LR algorithm. These papers indi-
tional averages of the firm-by-firm means.
cate that, while the LR algorithm works fairly well overall,
classifying about 85% of trades correctly, alternative algo-
Obtaining estimates of effective or realized spreads requires
38 - The
rithms may perform better. Ellis et al. (henceforth EMO) pro-
pose assigning trades executed at the ask (bid) quote as cus-
Comparing with earlier quotations decreases the percentage
tomer buys (sells), while using the tick test for all other
of trades that appear to be executed within the quotes. For the
trades, and show that their proposed method outperforms
NYSE sample the percentage of trades apparently receiving
the LR method in their Nasdaq sample. Bessembinder (2003)
price improvement decreases from 36.4% for contemporane-
notes that the results in Finucane (2000) imply that the EMO
ous quotes to 34.0% when five seconds are deducted from
method would have outperformed the tick test in NYSE-based
trade report times to 32.5% when trade times are adjusted by
data as well.
thirty seconds. For the Nasdaq sample the effect is more dramatic, as the rate of price improvement declines from 28.1%
with no lag, to 17.2% at a five-second lag, and to 14.5% at a
Empirical results
thirty-second lag.
Quoted bid-ask half-spreads
Though the main focus of this paper is on methodological
In contrast, comparing trade prices to earlier quotes monoto-
issues that arise when computing effective or realized
nically increases the percentage of trades apparently receiv-
spreads, it is useful to initially examine quoted half-spreads as
ing price disimprovement. For the NYSE sample, the percent-
a basis for comparison. When we compared the average quot-
age of trades at prices greater than the ask or lower than the
ed bid-ask half-spreads for a capitalization-matched sample of
bid is 0.6% when comparing trade prices to quotes at the
300 NYSE and 300 Nasdaq Stocks, during the July to
trade report time. The apparent rate of price disimprovement
December 1998 period, we found that the full-sample mean
rises to 1.9% if trade times are reduced by five seconds, and to
quoted half-spread on Nasdaq is 15.7 cents (0.74% of share
5.7% at a thirty-second lag. A similar effect is observed for
price), compared to 8.7 cents (0.49% of share price) on the
Nasdaq firms, as the percentage of trades apparently com-
NYSE. There is, however, variation across firm size groups. For
pleted outside the quotes rises from 5.0% with no trade
large-capitalization stocks differences in average quoted half-
reporting lag to 6.0% at a five-second lag and to 14.7% with a
spreads across markets are minimal. The mean quoted half-
thirty-second lag.
3
spread for large stocks is 7.0 cents (0.21% of share price) on
the NYSE versus 9.7 cents (0.24%) of share price on Nasdaq.
Some indication of the optimal amount by which to adjust
The mean quoted half-spread for medium-size (small-size)
trade times for purposes of assessing trade direction can be
stocks is 8.4 cents (10.8 cents) on the NYSE, compared to 17.7
obtained by assessing the adjustment that leads to the most
cents (19.6 cents) on Nasdaq.
accurate measures of the proportion of trades executed inside
and outside the quotations. This cannot be ascertained using
Price improvement and allowances for trade reporting lags
the TAQ data, since the true trade times are not known.
Recognizing that trade reports can be delayed, researchers
However, the percentages reported can be compared to data
have generally compared trade prices to quotes reported
reported for specialized samples where actual trade times are
slightly earlier than the trade report time. The adjustment is
available.
typically accomplished by reducing trade report times by a
fixed number of seconds before comparing trades to contem-
EMO report that 25.2% of the trades in their proprietary
poraneous quotes. This section assesses the effect of alterna-
Nasdaq sample are completed at prices within the quotes,
tive allowances for trade lags. I first report the percentage of
while 4.3% of trades are executed outside the quotes. Their
trades that are completed at prices inside and outside the
results, based on actual trade times, correspond most closely
matching quotes, when the matching quote is defined as that in
to the Nasdaq results obtained here when trades are com-
effect from zero to thirty seconds before the trade report time.
pared to quotes in effect at trade report times, without any
3 Finding that quoted spreads for large stocks are quite similar across Nasdaq and
the NYSE is consistent with the results reported by Weston (2000), who examines
only large-capitalization stocks.
39
adjustment. Bacidore et al. (2003) use proprietary NYSE data
average realized spreads are not sensitive to the adjustment
to report that 0.7% of NYSE trades resulting from system
for trade-reporting lags.
market orders are executed at prices outside the quotes in
effect at the trade time, while 41.5% of trades are executed at
When measuring the trades’ average price impact when the
prices within the quotes. Again, the closest correspondence
time of the benchmark quote is varied, I find that the average
between results obtained here using publicly available data
price impact for the full sample of NYSE trades is 4.7 cents
and results obtained when using the proprietary database
when quotes 30 minutes after the trade report time are com-
arises when no allowance for trade reporting lags is made. The
pared to quotes at the trade report time. Measured price
results obtained here suggest that trades are best compared
impact for NYSE trades increases to 5.1 cents when quotes 30
to contemporaneous quotations when measuring price
minutes later are compared to quotes in effect 30 seconds
improvement rates, and when assigning trades as buyer or
before the trade report time. For the Nasdaq sample, meas-
seller initiated.
ured price impact increases more dramatically as earlier
quotes are used as the reference point. The signed movement
Measures of trading costs with varying trade
time adjustments
in the quote midpoint from the trade report time until 30 min-
Most studies of trading costs have compared trade prices to
from 30 seconds before the trade report time to 30 minutes
earlier quotes both when signing trades and when computing
later is 6.1 cents.
utes later is 4.6 cents, while the change in the quote midpoint
effective and realized bid-ask spreads. It is of interest to know
whether measured trading costs are sensitive to the time
These results indicate that quote midpoints move systemati-
adjustment used. To assess this issue I next report average
cally away from trades (rising on buy orders and dropping on
effective and realized bid-ask spreads for the present sample,
sell orders) in the seconds before trades are reported. On the
when the time of the reference quote precedes the trade
NYSE the average movement in quote midpoints is 0.44 cents
report time between 0 and 30 seconds. The results reported
during the 30 seconds prior to the trade report. On Nasdaq,
rely on the EMO algorithm to sign trades, without any adjust-
quote midpoints move away from the trade by an average 1.51
ment to the trade time stamps.
cents in the 30 seconds before the trade report. Greater
adjustments to trade report times result in this pre-trade price
I find that the measured effective spreads increase monoton-
impact being included in measures of effective trading costs.
ically with the adjustment to trade times. For the sample of
NYSE stocks, the measured average effective half-spread
Pre-trade price impacts could potentially reflect trade report-
increases from 4.9 cents per share with no lag to 5.4 cents
ing lags, i.e., that the quote is updated during the lag between
per share when trade report times are adjusted by thirty sec-
the actual trade time and the trade report time. However, EMO
onds. For the sample of Nasdaq stocks the measured effec-
report that quotes are rarely updated during this interval in
tive half-spread increases from 9.4 cents with no lag to 10.8
their Nasdaq sample, and Peterson and Sirri (2003) report
cents with a thirty-second lag. T-tests indicate that the
that TAQ trade report times lag actual trade execution times
increase in measured trading costs is statistically significant
by only two seconds, on average.
for time adjustments of 20 seconds or greater for NYSE
stocks and for adjustments of 25 seconds or greater for
The other, and more likely, explanation is that quotes are sys-
Nasdaq stocks.
tematically and adversely updated in the seconds before
trades are executed. Peterson and Sirri (2003) and Werner
In contrast to the effect on effective spreads, measures of
40 - The
(2003) both analyze proprietary NYSE system order data and
provide evidence consistent with this interpretation. Each
The close correspondence between Roll spreads and effective
reports that prices move significantly in the direction of the
spreads on the Nasdaq market might be viewed as suggesting
trades before execution. These adverse average movements in
that trades need not be signed or matched with quotes at all,
quotes ahead of trades could occur because information
as the Roll estimate could simply be used as a general proce-
about pending orders leaks to the market ahead of trades. It
dure. However, estimated Roll spreads for NYSE stocks do not
could also reflect larger orders being broken up by brokerage
match effective spread estimates as closely, particularly for
firms into smaller orders sent to market in succession, or it
small stocks. For small-capitalization NYSE issues the average
may reflect several traders reacting similarly to common infor-
estimated Roll half-spread is 3.7 cents, compared to an aver-
mation events, with quotes being revised after the earliest
age effective half-spread of 6.1 cents. For the full sample of
orders are executed.
NYSE stocks the estimated Roll half-spread is 3.4 cents, which
is closer to, but still below, the effective half-spread estimate
Comparisons of effective and realized spreads to
of 4.9 cents.
Roll-implied spreads
The Roll (1984) technique provides estimates of trade execu-
Estimated Roll half-spreads are reasonably uniform across
tion costs that do not require that trades be signed or that
firm size groups, but not across trade sizes. On the NYSE, Roll
trades be matched to quotes, so errors from these sources
half-spreads are 9.2 cents for large trades, 4.1 cents for medi-
are avoided.4 Here, I assess the extent to which trading cost
um trades, and 3.4 cents for small trades, indicating greater
estimates obtained using the Roll procedure conform with
price reversals after large trades. A similar pattern is evident
those obtained from the effective and realized bid-ask spread
for Nasdaq stocks, where average Roll half-spreads are 18.1
methods.
cents for large trades, 11.8 cents for medium trades, and 9.7
cents for small trades.
Because the results are of some interest, I report the average
Roll half-spread for trades of varying sizes, using the proce-
The Schultz (2000) result that Roll implied spreads provide
dure developed by Schultz (2000). Small trades are defined
good alternative estimates of effective spreads for Nasdaq
here as those of 1000 shares or less, medium trades are those
stocks does not generalize well to trades of varying sizes or to
from 1001 to 9999 shares, and large trades are those of 10,000
NYSE stocks. One possible explanation for the NYSE result is
or more shares. The results indicate that average Roll-implied
the presence of price continuity rules that increase the serial
half-spreads are uniformly and significantly greater for the
dependence of price changes, thereby reducing Roll spread
Nasdaq stocks than for NYSE stocks. The full sample mean for
estimates. Regardless of the explanation, the implication is
NYSE stocks is 3.38 cents, compared to 9.88 cents for Nasdaq
that difficulties in assessing trade execution costs resulting
stocks. Similar differentials are seen for each market-capital-
from the need to sign trades and to match trades with prevail-
ization sub-sample.
ing quotes cannot be readily sidestepped in studies involving
NYSE stocks by simply using the Roll procedure instead.
Comparing spread measures I find that average Roll-implied
half-spreads in the present sample are quite similar to average
Conclusions
effective half-spreads for Nasdaq stocks, consistent with the
This study conducts sensitivity analyses to assess the practi-
findings of Schultz (2000). For the full Nasdaq sample the
cal importance of some methodological issues that arise when
average effective half-spread is 9.4 cents, while the average
attempting to measure trade execution costs using the pub-
Roll-implied half-spread is 9.9 cents. Results for Nasdaq mar-
licly-available quotation and trade price databases. The pub-
ket capitalization sub-samples are similar.
licly available databases contain trade report times, but not
4 However, the Roll method relies on a set of restrictive assumptions. Among these
are the assumptions that the spread width is constant over time, and that trades
do not convey private information about value, i.e. that trades’ average price
impact is zero.
41
order submission or trade execution times, and do not indicate
References
whether trades are buyer or seller-initiated.
• Bacidore, J., K. Ross, and G. Sofianos, 2003 “Quantifying market order execution
quality at the New York Stock Exchange,” Journal of Financial Markets, 6, 281-307
• Bessembinder, H. 2003, “Issues in assessing trade execution costs,” Journal of
Financial Markets, 6, 233-258
• Ellis, K., R. Michaely, and M. O’Hara, 2000, “The accuracy of trade classification
rules: Evidence from Nasdaq”, Journal of Financial and Quantitative Analysis, 35,
529-552
• Finucane, T., 2000, “A direct test of methods for inferring trade direction from intraday data,” Journal of Financial and Quantitative Analysis, 35, 553-576
• Glosten, L. 1987, “Components of the bid-ask spread and the statistical properties of
transactions prices,” Journal of Finance, 42, 1293-1307
• Lee, C., and M. Ready, 1991, “Inferring trade direction from intraday data,” Journal of
Finance, 46, 733-746
• Odders-White, E., 2000, “On the occurrence and consequences of inaccurate trade
classification,” Journal of Financial Markets, 3, 259-286
• Perold, A. 1988, “The implementation shortfall,” Journal of Portfolio Management,
14, 4-9
• Peterson, M. and E. Sirri, 2003, “Evaluation of the biases in execution cost estimates
using trade and quote data,” Journal of Financial Markets, 6, 259-280
• Roll, R., 1984, “A simple measure of the effective bid-ask spread in an efficient market,” Journal of Finance 39, 1127-1139
• Schultz, P., 2000, “Regulatory and legal pressures and the costs of Nasdaq trading,”
Review of Financial Studies, 13, 917-958
• Werner, I., 2003, “NYSE order flow, spreads, and information — Execution costs,”
Journal of Financial Markets, 6, 309-335
Adjusting trade report times as an allowance for possible
reporting lags decreases the percentage of trades that appear
to be executed within the quotes while increasing the percentage of trades that appear to be executed outside the
quotes. Comparing results here with those obtained using proprietary databases that include accurate trade times and
order data, it appears that trade direction and rates of price
improvement are best assessed when making no adjustment
for trade report lags.
Estimated trading costs increase if trade prices are compared
to earlier rather than contemporaneous quotes, reflecting
adverse quote movements prior to trade report times. If these
adverse quote movements occur after order submission but
before trade execution then they comprise a real cost to
traders that will not be captured when trade prices are compared to quotes in effect at trade report times.
On balance, the results obtained here support recommendations to use the EMO technique in preference to the LR
method to sign trades, implement the EMO technique on the
basis of contemporaneous rather than earlier quotations, and
use quotation midpoints in effect somewhat prior to the trade
report time as the benchmark quote when measuring effective bid-ask spreads. This last recommendation is similar in
spirit to the use of the quote midpoint at the time of the trading decision as the reference point [Perold (1988)], in order to
include costs stemming from pre trade price impact.
42 - The
Services
Best execution
regulation: From
orders to markets
Jonathan Macey
Sam Harris Professor of Corporate Law,
Corporate Finance, and Securities Law,
Yale Law School
Maureen O’Hara
Robert W. Purcell Professor of Management,
Professor of Finance, Johnson Graduate School
of Management, Cornell University
Abstract
This article traces the evolution of the legal obligation of best
the modern goal of securities regulators to ensure competi-
execution, from its origin as an application of the common law
tive capital markets. This paper reveals an as yet unrecognized
of agency, to its current incarnation as a rule implemented by
policy trade-off between the goal of giving individual traders
stock exchanges and regulators as a means to regulate mar-
best execution on every trade, particularly where best execu-
ket structure. We show that, over time, the legal duty of best
tion is defined as best price, and the goal of promoting vigor-
execution has shifted from a duty owed by brokers to their
ous competition among trading venues. The article then turns
counterparties to a duty owed by brokers to the markets in
to the question of which institution is most likely to provide
general. From an economic perspective, this shift reveals a
optimal rules of best execution. We show that the best place to
fundamental inconsistency between the historical legal obli-
locate the decision-making authority over trading venue is the
gation of brokers to give their customers best execution and
issuing firm.
43
Among the clearest rules in U.S. securities law is the duty that
order flow and other arrangements that permit trading ven-
brokers have to ‘seek the best execution that is reasonably
ues to contract ex-ante for the right to take and supply liq-
available for its customers’ orders’ whenever a broker exe-
uidity are legally impermissible. Applying the legal duty of
cutes an order for a customer.1 The legal duty of best execution
best execution on an ex-ante market basis necessarily
is derived from the common law fiduciary duty of loyalty,
involves transfers of wealth from certain cohorts of traders to
which requires brokers to maintain undivided allegiance to the
others. For example, a broker-dealer firm may decide that
interests of their clients and bars brokers, who act as agents
allocating all trades to a particular venue constitutes best
on behalf of their customers, from using their position in any
execution because it lowers the average cost of trading for all
manner that allows him/her to garner a personal profit or a
customers, but such a decision is likely to raise costs for some
personal advantage.
clients, even as it lowers costs for others. In particular, exante preferencing arrangements that direct trades to a par-
Building on our earlier work [Macey and O’Hara (1997)], this
ticular venue may benefit larger, block traders at the expense
article examines the legal duty of best execution from an eco-
of smaller retail traders who would receive price improve-
nomics perspective. In the first section of the article, we exam-
ment if their trades were shopped at an exchange rather than
ine the legal origins of the duty of best execution. We observe
executed automatically.
that, over time, there has been a shift from a case-by-case
approach to the duty to a generalized regulatory approach
We will subsequently reconcile these conflicting conceptions
that looks at the overall standards applied by brokerage firms
of the legal duty of best execution. In our view, the problem
when executing trades to determine whether the duty of best
with the current orientation of the policy discussion is that it
execution has been violated. Put another way, gradually the
has focused on the narrow, yet unanswerable, question of
legal duty of best execution has shifted from a duty owed by
which venue provides traders with best execution. This is
brokers to their counterparties to a duty owed by brokers to
because, as we have pointed out in previous work, ‘the term
the markets in general.
best execution does not connote a single execution attribute,
such as price, but rather attaches to a vector of execution
In the following section we examine the most recent SEC ini-
components. These certainly include trade price, but they
tiatives to define the concept of best execution. We show that
also involve the timing of trades the trading mechanism used,
there is a fundamental inconsistency between the original
the commission charged, and even the trading strategy
goals of the historical legal obligation of brokers to give their
employed. Such multi-faceted concerns have long been a fea-
customers’ best execution and the modern goals of securities
ture of institutional trade execution, but their emergence now
regulators, which is to ensure competitive capital markets.
even in retail trading reflects the reality that markets are a
The basic problem involves the policy choice that must be
great deal more competitive and complex than in times past’
made between applying the duty of best execution on a case-
[Macey and O’Hara (1997)]. Clearly, for example, it makes no
by-case regulation or on a broader basis. Both approaches
sense to employ the same, or even a similar, legal definition
have problems (costs). Applying the legal duty of best execu-
of the duty of best execution for large institutional traders as
tion on a case-by-case basis, which necessarily requires that
for small retail traders. Institutional traders’ concerns with
brokers determine which venue is best for each order indi-
respect to the issue of best execution are focused around the
vidually after it is received, can reduce competition among
impact of their trading on the average price on which their
trading venues as market practices such as payment for
trades will execute. By contrast, retail traders are concerned
1
44 - The
http://www.sec.gov/answers/bestex.htm (January 4, 2005)
with the transaction costs of their trading, since, unlike insti-
buy or sell in such market so that the resultant price to the
tutional traders, retail trades will not influence the underlying
customer is as favorable as possible under prevailing market
price of the securities being traded.
conditions.’3
In the next section we examine the alternative institutions
Thus, it is clear that best execution does not necessarily imply
most likely to generate optimal rules regarding best execu-
best price.
tion. The most likely choices include, the trading venues
themselves (in their capacities as self-regulatory organiza-
‘(B)rokers have not been held...to an absolute requirement of
tions), the government (in its administrative capacity as the
achieving the most favorable price on each order... (W)hat has
Securities Exchange Commission), individual shareholders
been required is that the broker endeavor, using due diligence,
and institutions (in their capacities as principals to securities
to obtain the best execution possible given all the facts and
transactions), and issuing firms (in their capacity as issuers of
circumstances.’4
securities who contract with investors via their articles of
incorporation).
We have observed previously that the legal requirement
appears to require only that the broker tried to obtain the best
We develop the argument that, for a variety of institutional
price, not that he actually obtained the best price in fact
and incentive-based reasons, while no institution is ideal, by
[Macey and O’Hara (1997)]. For the purposes of the analysis
far the best place to locate the decision-making authority over
here, what is important is the fact that the legal inquiry is par-
trading venue is the issuing firm. A conclusion follows.
ticularized, that is, the legal inquiry is carried out on a case-by
case basis. This is what is meant by the phrase ‘given all the
The development of the legal obligation of best
execution
facts and circumstances.’ Each trade, under the common law
approach is to be evaluated on a case-by-case basis.
The duty of best execution is firmly grounded in common law
principle of agency, from which the common law fiduciary
Such a narrow focus is relevant because the fiduciary princi-
duties of care and loyalty are derived. A broker-dealer’s duty to
ples of care and loyalty, which provide the historical under-
seek to obtain the best execution of customer orders ‘derives
pinnings for the legal duty of best execution, are particular-
from the common law (duty of) agent(t) loyalty, which obligates
ized duties, based on the common law of agency. These rules,
an agent to act exclusively in the principal’s best interest...(the
in turn, are contractual in nature; they flow from brokers to
agent also) is under a duty to exercise reasonable care to
their clients on an individual basis. Consequently, it is no
obtain the most advantageous terms for the customer.’2
defense against a customer’s claim that he or she was not
given best execution for a broker to respond that some other
Consistent with these common law duties, NYSE and the NASD
customer, such as the customer on the other side of the
both have rules requiring member firms to execute all cus-
transaction, received best execution. It also is no defense to
tomers’ orders at the best available prices. These rules require
respond that the marketplace in general was made better or
only that the price the customer receives be the best possible
more competitive as a result of a particular instance of best
under the circumstances, ‘[i]n any transaction for or with a
execution being denied in a particular circumstance. The duty
customer, a member...shall use reasonable diligence to ascer-
of best execution is static not dynamic, what matters is this
tain the best inter-dealer market for the subject security and
trade, not trades in the future.
2 In re Merrill Lynch, 911 F. Supp 754, 760 -769 (1995) (cited in In re E.F. Hutton & Co.,
Securities Exchange Act Release No. 25887, (1988 Transfer Binder) Fed. Sec. L.
Rep. (CCH) ¶ 84303, 89326 at 89326 (July 6, 1988); Restatement (Second) of
Agency ¶ 1 (1957)).Market 2000: An Examination of Current Equity Market
Developments, Division of Market Regulation of the SEC, Study V, 1994 SEC LEXIS
135, at *5-6 (1994)(hereinafter Market 2000); 15 U.S.C. § 78k-1(a)(1)(c)(iv) (1994).
Restatement of Agency § § 387, 424 (1958).).
3 New York Stock Exchange Rule 123A.41, 2 NYSE Guide (CCH) P 2123A; NASD Rules
of Fair Practice, NASD Manual (CCH), Art. III, Sec. 1, ¶ 2151.03.
4 Merrill Lynch at 770 (citing Second Report on Bank Securities Activities:
Comparative Regulatory Framework Regarding Brokerage-Type Services 97-98, n.
233 (Feb. 3, 1977), reprinted in H.R. Rep. No. 145, 95th Cong., 1st Sess. 2333.).
45
To illustrate why this dynamic issue is important, suppose
orders. During the relevant time period, Knight, upon receipt
that a trade allocated to a particular ECN has a very low prob-
of an institutional customer order, would acquire a substantial
ability of being executed at a price better than the best
position (in the same security) in its own proprietary account.
exchange posted quote or the ‘national best bid — best offer’
Rather than fill the order promptly on terms most favorable to
(NBBO) price,5 while a trade allocated to the New York Stock
the customer, Knight would wait to see if its proprietary posi-
Exchange has a reasonable (and much higher) probability of
tion increased in value during the trading day. When the pre-
executing at a price better than the NBBO. It would not be a
vailing market price for the stock moved significantly away
valid defense against the claim that the legal duty of best
from Knight’s acquisition cost, Knight then filled the cus-
execution has been violated for a broker to say that to
tomer’s order and pocketed the difference as its profit on the
require that each trades be deployed to the NYSE (or any
transaction.
other particular trading venue) would make that venue a
monopoly, and thus would result in other (future) traders
For example, on April 4, 2000, Knight received a customer
receiving inferior prices due to the monopoly pricing power
market not-held order to purchase 250,000 shares of Applied
of the venue going forward.
Micro Circuits Corporation (AMCC). Over the next 18 minutes,
Knight acquired 147,000 shares of AMCC at an average cost
The duty of loyalty encompasses more than just price. This
of U.S.$91 per share. Rather than promptly selling the stock
legal duty also addresses issues of conflicts of interest, and
to the institutional customer at Knight’s cost (plus a reason-
confidentiality. It is improper, for example, for a broker to use
able profit), Knight sold the AMCC stock to the customer over
its position to advance a personal interest, say by front-run-
a period of time at an average profit of approximately U.S.$2
ning a customer’s order, by using the information embedded in
per share. On the entire AMCC order, Knight realized a profit
the order for the advantage of other customers or traders
of over U.S.$1.1 million (or an average of U.S.$3.94 per share).
associated with the firm. For example, on December 16, 2004,
When the market moved unfavorably in relation to the posi-
Knight Securities, L.P. settled a lawsuit brought against it by
tion Knight had established to fill the institutional customer’s
the Securities and Exchange Commission and agreed to pay
order, Knight executed its remaining position in the order to
U.S.$79 million in disgorgement and penalties for defrauding
the customer at prices that still generated a profit for Knight.
its institutional customers by extracting excessive profits out
By engaging in these trading practices, Knight extracted
of such customers’ orders and failing to meet the firm’s duty
enormous profits — as high as U.S.$9 per share — by execut-
to provide ‘best execution’ to the institutions that placed those
ing transactions that involved effectively no risk to Knight.
orders.6
Consequently, Knight improperly realized tens of millions of
dollars in excessive per share profits from its institutional
The SEC found that between January 1999 and November
customers.
2000, Knight — which was, at the time, one of the largest mar-
46
ket-makers on the NASDAQ — earned over U.S.$41 million in
During the same period, Knight failed reasonably to supervise
illegal profits by failing to provide best execution to its institu-
Knight’s former leading sales trader who was primarily
tional customers. Specifically, Knight defrauded its institution-
responsible for Knight’s fraudulent trading. Knight’s senior
al customers by extracting excessive profits out of its cus-
management not only allowed the leading sales trader to be
tomers’ … orders while failing to meet the firm’s duty to pro-
directly supervised by his brother, but also permitted the two
vide best execution to the institutions that placed those
to evenly split the profits generated by the leading sales trad-
5 SEC rules require that any Nasdaq dealer that wishes to hold itself out as a market
maker in a particular security must continually report the prices at which it is willing to buy and sell the security. Such market makers must be willing to honor their
reported bid and offered prices up to the ‘quotation size,’ i.e. the number of shares
that the market maker reports as being willing to buy at the bid side or sell at the
offered side. 17 C.F.R. Section 240.11Ac1-1(c)(1)(2), and (10). Nasdaq is required by
the SEC to collect, process and make available... the highest bid and lowest offer
communicated... by each member... acting in the capacity of an OTC market maker
for each reported security. 17 C.F.R. Section 240.11Ac1-1(b)(1)(ii). This latter quotation has come to be known as the NBBO (National Best Bid and Offer).
6 http://www.sec.gov/news/press/2004-173.htm
er’s trading with institutional customers. The two brothers’
its institutional sales traders. Knight also agreed to hire an
relationship, their positions, and responsibilities within the
independent compliance consultant to conduct a comprehen-
firm, and their profit-sharing arrangement created an inherent
sive review of its policies and procedures with respect to best
conflict of interest that contributed to a substantial break-
execution obligations, and other regulatory obligations as well
down in the supervision over the Leading Sales Trader.
as the firm’s supervisory and compliance structure.
Between 2000 and 2001, Knight failed reasonably to supervise
In announcing the settlement, Stephen M. Cutler, the SEC’s
Knight’s institutional sales traders while they were systemati-
Director of Enforcement observed that ‘customers have a
cally misusing Automated Confirmation Transaction Service
right to expect they are getting fair treatment when they
(ACT) trade modifiers. Knight had no written procedures, no
entrust their broker with orders to buy and sell securities.
adequate systems in place, and no supervisory personnel to
That expectation is betrayed when the broker handling the
prevent Knight’s sales traders from consistently misusing the
orders puts its own financial interests ahead of its customers’
modifiers over a two-year period.
interests.’ The Knight settlement illustrates the severe conflicts of interest that exist whenever a broker or his firm has
The misuse of ACT modifiers led to the sales traders’ record-
a financial interest in a transaction to which the organization
ing inaccurate execution times on the firm’s trading blotters, in
may be a party, such as when a customer’s order is executed
violation of the books and records provisions of the federal
in-house or when the brokerage firm also acts in a dealer
securities laws. By misusing the ACT trade modifiers, Knight
capacity.
sales traders were able to improperly input trades into
Knight’s trading system at prices that were different from the
In response to these scandals, the SEC enacted new rules
inside market at the time the trades were reported. The
requiring disclosure of order execution policies and order
repeated misuse of the ACT modifiers also limited the ability
routing protocols. Now, dealer firms are required to disclose
of Knight’s institutional customers to detect the fact that
each month precisely how they execute trades. Brokers who
Knight was extracting excessive profits at their expense. By
route customer orders must disclose quarterly the identity of
misusing ACT trade modifiers, Knight’s sales traders avoided
each market center that receives a meaningful percentage of
limit order protection protocols and filled more profitable
their orders. While there is no requirement that customers be
institutional ‘not held.’
told where their individual orders were executed, brokers must
divulge this information if asked.7 Similarly, confidentiality
Without admitting or denying the SEC’s findings, Knight, (now
obligations require brokers to protect from disclosure the
known as Knight Equity Markets, L.P.), agreed to pay more
trading plans and strategies of their clients. Thus, there are
than U.S.$41 million in disgorgement of illegal profits, over
conflicts between brokers’ obligations to the firms they work
U.S.$13 million in prejudgment interest and U.S.$12.5 million in
for when those firms are engaged in underwriting or trading
civil penalties. The settlement also required Knight to pay an
activities for their own accounts.
additional U.S.$12.5 million in fines to settle a parallel NASD
proceeding. In the settlement Knight agreed to cease and
The Knight scandal, along with other front-running scandals,
desist from committing or causing any future violations of the
such as those that periodically plague the New York and
broker-dealer anti-fraud and books and records provisions of
American stock exchanges, should be regarded as ‘old fash-
the Exchange Act, and was censured for its failure to supervise
ioned’ best execution scandals. The wrong-doing arises
7 Goodman, B., 2002, “Are things Kosher at your broker?” The Street.Com, June 7,
http://www.thestreet.com/funds/beverlygoodman/10026056.html.
47
because it is extremely difficult for any investor, even sophis-
point is particularly strong under the traditional view of best
ticated institutional investors, to monitor the agents charged
execution, which would require that customers placing orders
with executing their orders. Market discipline works poorly in
with brokers receive the best price available, not just a price
this setting because it is impossible for the client to know if the
that is generally good or better than available in other mar-
price received is due to agency problems or to stochastic mar-
kets [Macey and O’Hara (1997)]. But even where trading ven-
ket fluctuations beyond the broker’s control.
ues are highly efficient, and offer customers rebates on their
trades (payment for order flow), such markets do not, from a
Just as the customer finds it difficult to monitor and control
technical legal perspective, necessarily offer best execution
this behavior ex-ante, the SEC has problems formulating rules
merely because the execution is good, or even excellent. The
to deal with the problem ex-post. Another critical point that
legal requirement is that the execution be the best of all avail-
has been ignored in the current discussions of the legal duty
able alternatives.
of best execution is the effect of the legal rules regarding best
execution on market structure.
Adding yet another layer of complication is the conflict
between the interests of retail customers and institutional
From a market structure perspective, use of the traditional,
investors. Even at the system-wide level this conflict stymies
case-by-case approach to best execution poses a collective
the search for the illusive grail of best execution. This contro-
action problem. Individual traders acting rationally and in
versy manifests itself in the current debate over the rights and
pursuit of their own self-interests may direct order flow in
responsibilities of customers and markets regarding whether
such a way as to damage the quality of secondary markets
customers and/or markets can have their orders ‘trade-
generally by generating trading patterns that give a particu-
through’ the prior, better orders of other customers. A trade-
lar trading venue a monopoly over the provision of secondary
through is the execution of an order in a market at a price that
market liquidity. This puts regulators in a very difficult posi-
is inferior to a price displayed in another market.8 Trade-
tion. To maintain high quality markets, securities markets
through rules bar traders from trading at worse prices in
regulators must insure that there is robust competition
faster electronic markets when there is a better quote in the
among rival trading venues, or else spreads will widen and
slower, exchange market.9
service will deteriorate. In the long-run, this will lead to less
liquidity and to higher capital costs for investors. The com-
From the traditional legal perspective of best execution,
mon law approach to best execution, however, does not allow
the very concept that an order can execute at a price inferior
for this consideration.
to the price displayed in another market poses a problem,
particularly where the transaction is consummated without
Another problem with the traditional, common law approach
the customer’s knowledge or consent. But the problem also
is that it ignores the fact that, once the decision to buy or sell
exists where the trade-through rule prevents a customer
has been made, the gains from improvements on the market
from executing an order at an inferior price on a faster elec-
bid-asked spread are zero sum. Gains to the seller from receiv-
tronic market in order to obtain better overall execution for a
ing more than the best extant bid translate directly into losses
large block trade. For example, if the best bid anywhere for a
for the buyer, who ends up paying more. What then is best
stock is U.S.$100, a large block seller, under the current incar-
execution for firms executing in-house agency crosses or for
nation of the trade-through rule, must execute the trade at
trading venues that make continuous two-sided markets? This
that price, even if the bid were for only 1000 shares, and the
8 Junius W. Peake , “Regulation NMS: Pools or an Ocean of Liquidity” The Handbook
of World Stock, Derivative and Commodity Exchanges. http://www.exchange-handbook.co.uk/articles_story.cfm?id=47680 (accessed January 7, 2005)
9 New York Stock Exchange, The Exchange, V11, No. 6/7, p 1-2 (July 2004).
48 - The
seller would prefer to sell the entire 100,000 share block into
block trader filling its entire order, raising execution costs.
an inferior bid at 99.75. Of course, if the block trader were
Moreover, the longer the delay, the more difficult it will be for
permitted to elect to trade-through the superior U.S.$100 bid,
the block trader to keep its identity and trading plans anony-
as the SEC currently is proposing,10 and consummate the
mous. Once the institutional identity and trading plans
transaction at U.S.$99.75, the retail trader who entered the
become known, rational traders will enter the market in
U.S.$100 bid might not obtain best execution, should the mar-
advance of some of the block trader’s orders, and this will
ket move higher before the trade can be executed.
deprive the block trader of best execution.
11
The SEC has recently proposed, but not enacted, rules that
The current conflict: Trading through best
execution?
will allow traders to choose ‘speed of execution’ over ‘best
The trade-through rule that is now in place was promulgated
price’.15 The proposed rule would limit the scope of the trade-
pursuant to the Intermarket Trading System (‘ITS’) Plan, and
through rule in two important respects. Firstly, it would
it dictates that no market participating in this plan13 can trade
enable those placing orders to opt-out of the trade-through
at a price inferior to a price displayed in another market. The
rule if the trader is able to ‘make an informed decision’ to
trade-through rule dictates that a trading venue receiving an
elect speed of execution over best price.16 Secondly, in auto-
order must match a better price available elsewhere or route
mated markets, such as ECNs, where an order can be instant-
the order to the other market for execution.
ly filled by a computer system, the trade-through rule would
12
not apply within a certain de minimis range of price discrepAt the market level, trade-through protection originally was
ancy between the order price and the best bid or offered
intended to help enforce the general obligation of best exe-
price in the system. This range would be from one to five
cution discussed in the preceding section. A best execution
cents per share, based on the total share price to be trade-
problem arises on the buy-side when a specialist makes a
through-able.
risk-free profit by buying at a lower-pre-existing price to fill
the bid or selling at a higher pre-existing offer price to fill an
The NYSE has vigorously opposed relaxing the trade-through
order. The trade-through rule was designed to promote best
rule, arguing that trades should have to go the market post-
execution of customer orders by preventing specialists and
ing the best price, which traditionally has been the NYSE.
other market makers from executing orders at inferior prices
However, there is one aspect of the rule that the NYSE does
when superior prices are available elsewhere.
support. The SEC is also proposing a uniform trade-through
rule for all NMS market centers that, subject to the excep-
Under the trade-through rule, trades must be executed at the
tions just described, would require a market center to estab-
best price, which is defined as the current best price offer
lish, maintain, and enforce policies and procedures reason-
regardless of the size order.14 Controversy has arisen because
ably designed to prevent trading venues from executing
many block traders would prefer to execute their trades auto-
orders at a price that is inferior to a price displayed in anoth-
matically at inferior prices immediately if they can execute a
er market. This would extend the trade-through rule beyond
trade that covers their entire block. This is because the delay
the NYSE and certain other exchanges to the NASD, ECNs,
itself poses the risk that the market will move prior to the
and other market centers.
10 See Part I of SEC Release 34-47013, “Final Rule: Repeal of the Trade-Through
Disclosure Rules for Options,” (2004), at http://www.sec.gov/rules/final/3447013.htm. The proposed new rules are part of “Reg NMS”, a proposal to change
the current operation of the national market system. For details of Regulation
NMS see http://www.sec.gov/news/press/2004-22.htm. For an analysis of these
proposed changes see O’Hara [2004].
11 Of course the large block trader might elect not to execute the block sale at all if
it must fill the U.S.$100 order before hitting the larger bid at U.S.$99.75. This is
one of the complexities in implementing a strict rule of best execution.
12 Section 11A(a)(2) was adopted by the Securities Acts Amendments of 1975 (‘1975
Amendments’). Pub. L. No. 94-29 (June 4, 1975).
13 Current signatories to the ITS Plan include the American Stock Exchange LLC,
Boston Stock Exchange, Inc., Chicago Board Options Exchange, Inc., Chicago Stock
Exchange, Cincinnati Stock Exchange, NASD, New York Stock Exchange, Inc.,
Pacific Exchange, Inc., and Philadelphia Stock Exchange, Inc.
14 Information on the trade-through rule can be found in Part I of SEC Release 3447013, “Final Rule: Repeal of the Trade-Through Disclosure Rules for Options,”
(2004), at http://www.sec.gov/rules/final/34-47013.htm.
15 These new rules are part of Reg NMS, a proposal to change the current operation
of the national market system. For details of Regulation NMS see
http://www.sec.gov/news/press/2004-22.htm. For an analysis of these proposed
changes see O’Hara [2004]
16 SEC Final Rule, supra note 45.
49
As Junius Peake has observed, the trade-through rule, and its
filled from the broker’s firm’s own inventory.
proposed opt-out exception, is ‘by far the most controversial
piece of proposed Regulation NMS’ because it will ‘have a
The SEC is also, of course, aware that regional exchanges and
defining effect on the structure of U.S. equity markets.’
third market makers make payments to attract order flow,
both for NYSE stocks and for Nasdaq and other over-the-
The New York Stock Exchange, which has been the principal
counter stocks.
beneficiary of the trade-through rule, is fighting tooth and
nail to maintain the status-quo. Its competitors, and would-be
The SEC does not have the power to overturn or even to mod-
competitors, such as ECNs, believe the present iteration of
ify the state common law rules of fiduciary duty from which
the trade-through rule to be old fashioned because it fre-
the general law of agency and the duties of best execution in
quently requires manual intervention before an order can be
particular are derived. However, the SEC has re-interpreted
executed, and gives an unfair advantage to NYSE specialists,
the duty of best execution as a general duty to the markets,
who have time to make up their minds whether or not to par-
rather than as a particularlized contractual obligation
ticipate in a trade.17
between market participants.
In our view, however, the trade-through rule must be evaluat-
The SEC observes, for example, that many firms use automat-
ed in the context of all of the other rules governing best exe-
ed systems to handle the orders they receive from their cus-
cution, and here our point is purely positive. The SEC has engi-
tomers. In deciding how to execute orders, your broker has a
neered a seismic shift in the legal conception of the duty of
duty to seek the best execution that is reasonably available for
best execution from its traditional common law grounding in
its customers’ orders. That means your broker must evaluate
fiduciary duties and highly individualized contractual arrange-
the orders it receives from all customers in the aggregate and
ments between customers and brokers into a generalized duty
periodically assess which competing markets, market makers,
to promote competitive markets, regardless of the effects on
or ECNs offer the most favorable terms of execution. The
individual traders. This change can be seen most clearly in the
opportunity for ‘price improvement’ — which is the opportuni-
SEC’s own articulation of the general rules regarding the exe-
ty, but not the guarantee, for an order to be executed at a bet-
cution of trades by brokers on behalf of customers.18
ter price than what is currently quoted publicly — is an important factor a broker should consider in executing its cus-
Under the SEC’s conception of the rules regarding order exe-
tomers’ orders. Other factors include the speed and the likeli-
cution, there is, stunningly, no duty of best execution. Instead,
hood of execution. Of course, the additional time it takes some
brokers have ‘a choice of markets’ in which to execute trades.
markets to execute orders may result in your getting a worse
Thus, for stocks listed on an exchange, such as the New York
price than the current quote — especially in a fast-moving mar-
Stock Exchange, it appears that brokers are free to direct the
ket. So, your broker is required to consider whether there is a
order to that exchange, to another exchange (such as a
trade-off between providing its customers’ orders with the
regional exchange), to a third market maker willing to buy or
possibility — but not the guarantee — of better prices and the
sell a stock listed on an exchange at publicly quoted prices, to
extra time it may take to do so.
an ECN that automatically matches buy and sell orders at
specified prices, or even to another division of the brokerage
Here, the SEC reveals its position that a brokers is, in its view,
firm receiving the customer’s order, such that the order is
permitted to evaluate the orders it receives from its customers
17 Peake, Regulation NMS: Pools or an Ocean of Liquidity (2004).
18 http://www.sec.gov/investor/pubs/tradexec.htm
50 - The
‘in the aggregate’ in order to determine where trading should
It is tempting to view customers’ ability to direct order flow as
be directed.19 The SEC’s statement on best execution also
a complete solution to the best execution problem. In theory
reflects the view that even that aggregate determination need
at least, the problem could be solved simply by requiring bro-
be made only periodically. By contrast, under the traditional
kers to ask customers where they want their orders sent and
common law approach to best execution discussed in the pre-
how they want them traded. Yet, this approach ignores a fun-
vious section, each order must be evaluated individually, not in
damental problem that the customer hires the broker to solve,
the aggregate, and the determination of what constitutes best
and that is how best to trade his stock? As we have argued
execution must be made at the time each and every trade is
above, it is agency problems that give rise to the need for best
made, not periodically.
execution duties.
From an economic perspective, there are two implications to
this analysis. Firstly, while wealth transfers among various
Our proposal: An inquiry into institutional
competence
investors were clearly impermissible under the traditional
As the recent spate of scandals illustrate, as with other princi-
common law duty of best execution, wealth transfers are per-
pal-agency relationships, there are significant conflicts of
missible under the SEC’s current approach. Secondly, while
interest associated with the broker-client relationship.
the traditional common law approach to best execution
Whether order flow is internalized, or not, brokers can benefit
ignored the implications of the duty of best execution on mar-
personally at the expense of customers when they receive
ket structure, the SEC’s approach is focused primarily on
orders. The private contracting model does not offer a good
issues of market structure. This is not surprising, given the
solution to this problem for two major reasons. Firstly, it is
fact that the SEC’s mandate is to maintain the integrity of the
extremely costly for most traders, particularly retail traders, to
markets and to promote fair competition among market par-
develop the information and expertise necessary to permit
ticipants in the context of the 1975 National Market System
them to make an informed choice about trading venue.
legislation.
Secondly, and perhaps more importantly, individual traders
20
face a collective action problem when deciding where to alloIt clearly is the case that there are a few remaining vestiges of
cate their trades. This is because the decision made individu-
the traditional common law approach to best execution. For
ally by each market participant about which trading venue is
example, customers may, if they specifically request to do so,
best may be the same at a particular point in time, giving that
direct their trades to a particular exchange, market maker, ECN,
venue a monopoly.
or other venue, although, brokers are free to charge for that
service or to decline to execute the trade unless they are given
If individual traders and regulators are unable to make the
discretion about where to execute the transaction. Some bro-
socially efficient, optimal decisions about best execution,
kers offer certain customers the ability to direct orders in
where should the decision-making authority over trading be
Nasdaq stocks to the market maker or ECN of their choice
allocated? The remaining options are the trading venues
when they place their orders. Customers are also permitted to
themselves and the issuing firms.
obtain information about where their trades have been routed
by their brokers during the previous six months, and to obtain
The trading venues
information about their broker’s policies on payment for order
Clearly the trading venues are conflicted with respect to this
flow, internalization, and other trade routing practices.
issue. After all, it is the venues themselves that stand most to
19 The same language is used in the SEC’s Order Execution Obligations, Exchange
Act Release No 34-37619A, 60 Fed. Reg. 48290, at 48323, where the SEC uses the
same phrasing when opining that: ‘[b]roker-dealers routing orders for automatic
execution must periodically assess the quality of competing markets to assure
that order flow is directed to markets providing the most beneficial terms for their
customers’ orders…. Broker-dealers deciding where to route or execute small cus-
tomer orders must carefully examine the extent to which the order flow would be
afforded better terms if executed in a market or with a market maker offering
price-improvement opportunities. In making this evaluation the broker-dealer must
“regularly and rigorously” examine execution quality likely to be obtained from
different markets or market makers trading a security.’
20 Section 11A(a)(1), National Market System legislation, 1975.
51
gain from a decision that trading on their venue is consistent
Thus, issuing firms, at the time of an initial public offering
with the legal obligations of best execution. We pause only to
have strong incentives to establish the rules of best execution
observe that, for years off-board trading restrictions and pro-
that maximize value for all shareholders. Unlike the case-by-
hibitions on delisting gave effective control over the decision
case decisions that individuals make when they make specific
about where to trade to the organized exchanges, first by pro-
trades, firms must make decisions about best execution ex-
hibiting exchange members from trading in listed securities
ante, or essentially before the shares begin trading. And these
off the floor of an exchange, and then by making delisting vir-
decisions must be made on an aggregate basis. But intrigu-
tually impossible. With the relaxation of these rules in recent
ingly, any inefficiency in the trading restrictions imposed by
years, the decisional authority lies uneasily among brokers,
the issuer will be reflected in the share price that investors
bureaucrats, and the traders themselves. We also observe
must pay. This means that issuing firms, and their owners and
that, at least for the New York Stock Exchange, the trade-
venture capital providers, not subsequent investors, bear the
through rules are perhaps the last vestige of venue-based
costs associated with any inefficiency in the best execution
trading restrictions, as the NYSE’s trade-through rule, which
regime established by the firm.
prevents trade-throughs in New York listed stocks, forces the
execution of the vast majority of trades in NYSE listed firms
If issuing firms, rather than bureaucrats, individual traders, or
onto the floor of the big board.
competing trading venues are better suited to establishing
what the rules of best execution should be, then we need to
The listing firms
consider the twin questions of how this legal regime should be
So, by process of elimination, we are left with the listing firms
effectuated, and what limits, if any, should be placed on firms’
themselves. We recognize that principal-agent problems also
powers to constrain shareholders’ secondary market trading
plague the relationship between shareholders and the firms
practices.
in which they exist. But the severity of the agency costs
between firms and investors is not constant over time. For
Implementation
example, when firms are ‘in play’, that is, subject to hostile
We propose that issuing firms decide for themselves, and draft
acquisition, managers have strong incentives to maximize
or amend their corporate charters (articles of incorporation)
firm value, so that their firms’ share prices will be prohibi-
to establish the regime of best execution that best serves the
tively high. Most importantly, from our perspective, when a
interests of their shareholding population. This, in our view,
firm’s shares are initially sold to the public the firm has
can be done through the mechanism of drafting share trans-
extremely strong incentives to maximize the liquidity charac-
fer restrictions that define what, if any, restrictions should be
teristics of the shares it is selling. After all, the whole point of
placed on where firms’ shares are traded.
going public for the prior owners and investors, particularly
52 - The
the firm’s founding entrepreneur, private equity owners, mer-
As the name implies, a share transfer restriction is a provision
chant bankers, and venture capitalists is to gain liquidity. The
in the articles of incorporation of a company that restricts, in
quest for liquidity is what induces firms to incur the substan-
some way or another, the ability of shareholders to transfer
tial costs and potential liability of registering their securities
their shares to other investors. For example, share transfer
with the SEC and going public (as opposed to raising capital
restriction can require that the firm’s general counsel, or its
through private placement or via a private sale of control or
board, (or, if the firm is small enough, the shareholder) gives
other strategy).
permission for shareholders to sell. Alternatively, firms might
impose no share transfer restrictions, or require that trading
Limits
be restricted to a particular exchange or constellation of
As Amihud and Mendelson (1996) have correctly observed, the
exchanges and ECNs. Changes to the best execution rules con-
SEC has taken a dim view of issuers’ efforts to restrict the
tained in a firm’s corporate charter could be amended from
trading venue of their securities, once those securities have
time-to-time as technology changes the nature of the trading
been issued and are already being traded. In particular, the
environment. In general, stock certificates, and other more
SEC routinely grants so-called ‘unlisted trading privileges’ to
modern indicia of share ownership, are regarded as personal
securities exchanges. Unlisted trading privileges, as the name
property, and are subject to the traditional, common law rule
implies, are simply rights that give a particular trading venue
that there be no unreasonable restraint on alienation.21 Share
the privilege of trading a security in situations in which the
transfer restrictions, however, are widely used by corporations
issuer of the securities has not asked permission for its secu-
and serve a number of valid purposes, including ensuring that
rities to be traded in that venue.
a corporation will continue to satisfy certain regulatory
requirements, such as Subchapter S of the Internal Revenue
Under the Unlisted Trading Privileges Act of 1994,25 regional
Code, which grants preferred (pass-through) tax treatment to
stock exchanges were actually encouraged to extend unlisted
corporations but requires them to have no more than 35
trading privileges to stocks listed on other trading venues.
shareholders, or ensuring that the company retains exemp-
That statute simply codified a long-standing SEC policy of
tions from the registration requirements of the Securities Act
acquiescing in requests by regional exchanges for unlisted
of 1933 that prohibit the public offering of unregistered secu-
trading privileges.26
rities. In addition, share transfer restrictions are commonly
used to maintain a family’s control over a particular corpora-
Occasionally, issuers have tried to control trading in their
tion, or to maintain the status-quo ownership structure among
securities after their securities have already been issued, but
shareholders, or to permit shareholders in closely-held corpo-
these efforts have been uniformly unsuccessful.27 Two points
rations to regulate the identity of new investors.22
about these efforts by issuers to control trading venue are
worth making. Firstly, it appears that the SEC’s reluctance to
While the general rule is that shares of stock are freely trans-
block the grant of unlisted trading privileges, at least in some
ferable, share transfer restrictions are valid in the vast major-
cases, has furthered shareholder interests by blocking man-
ity of states, so long as the restrictions they impose are rea-
ager’s efforts to entrench themselves in office. For example, in
sonable under the circumstance.23 The modern rule of share
re Providence Gas Company, managers of a public utility want-
transfer restrictions, in other words, ‘balances two conflicting
ed to limit ownership in the stock of the company to customers
corporate tenets: Free alienability of corporate ownership
of the company. The managers sought to effectuate this poli-
interests and private corporate structuring to meet the partic-
cy by limiting trading in the firm’s securities to the local over-
ipants’ needs.’24
the-counter market. This policy was upset when the New York
21 Rafe v. Hinden, 29 A.D.2d 481, 288 N.Y.S.2d 662, aff’d mem. 23 N.Y.2d 759, 244
N.E.2d 469, 296 N.Y.S.2d 955 (1968); Allen v. Biltmore Tissue Corp., 2 N.Y.2d 534,
540, 161 N.Y.S.2d 418, 421, 141 N.E.2d 812, 814; Penthouse Properties v. 1158 Fifth
Ave., 256 App. Div. 685, 690-691, 11 N.Y.S.2d 417.
22 This latter restriction is valuable in circumstances where, for example, state law
limits share ownership in a professional medical corporation to doctors, or ownership in a professional legal corporation to licensed attorneys. These restrictions
similarly allow shareholders to choose their business associates, to restrict ownership to family members, and to ensure congenial and knowledgeable associates.
Share transfer restrictions also can prevent business competitors from purchasing
shares. There are also important tax planning reasons for the restrictions.
23 RMBCA §6.27; Cal. Corp. §418; Del GCL §202.
24 Lewis D. Solomon & Alan R. Palmiter, Corporations: Examples and Explanations,
(2d edition 1994).
25 Pub. L. No. 103-389, 108 Stat. 408 (1994) (codified as amended at 15 U.S.C. Section
78l(f) (1994) provides that unlisted trading privileges for securities originally listed
on another national exchange may be granted to ‘any security that is listed and
registered on a national securities exchange.’
26 140 Cong. Rec. H6508 (daily ed. August 1, 1994) (statement of Rep. Markey)
27 In re Edison Electric Illuminating Co., Securities Exchange Act Release No. 986
(December 17, 1937) (rejecting effort by company to block the granting of unlisted
trading privileges in its bonds by the New York Curb Exchange); In re Providence
Gas Co., Exchange Act Release No. 1992 (January 19, 1939) (rejecting issuer’s
attempt to terminate the granting of unlisted trading privileges in the company’s
common stock by the New York Curb Exchange); In re Chicago Rivet & Machine
Co., Exchange Act Release No. 3395, Fed. Sec. L. Rep. (CCH) ¶ 75,369 (March 17,
1943) (same); Ludlow Corp. v. SEC, 604 F.2d 704 (D.C. Circuit 1979) (permitting,
over the issuer’s objection, the Boston Stock Exchange to grant unlisted trading
privileges to stock already trading on the New York Stock Exchange).
53
Curb Exchange (now the American Stock Exchange) granted
trade price they are giving to investors reflects a fee for pay-
unlisted trading privileges to the company’s stock. The com-
ment to order flow; and (4) whether allowing one investor to
pany unsuccessfully tried to block the New York Curb
trade-through a price sacrifices best execution for the other
Exchange’s move to extend unlisted trading privileges to the
trader. The issues surrounding attaining best execution are
company’s stock. Here it seems clear that the interests of
indeed complex.
management in restricting trading were unlikely to have been
shared by the company’s shareholders, whose interests were
As we have argued here, however, even the concept of best
in expanding the investor base to improve liquidity in the com-
execution is becoming untenable. Increasingly, trading takes
pany’s shares. Management was, on the other hand, more
place in multiple trading venues, and large orders are split and
interested in limiting outsiders’ access to the company’s
completed in stages. Where there are multiple trade execu-
shares in order to reduce the possibility of a hostile takeover
tions taking place over a number of days, not only does the
attempt.
concept of best execution become extremely imprecise, but
the common law idea of using fiduciary principles, and viewing
Thus, in this context at least, it appears that the liberal use of
each trade on a case-by-case basis in isolation, is difficult to
unlisted trading privileges serves shareholder interests and
defend. Moreover, whatever regime of best execution is select-
reduces agency costs. But merely because unlisted trading
ed, that legal regime should be organized to reflect the fact
privileges are liberally granted does not mean that issuers are
that the rules governing best execution will profoundly affect
helpless to effectuate restrictions on the venues on which
not only the costs associated with individual trades, but also
their securities trade. Share transfer restrictions, imposed as
the ultimate market structure as a whole.
part of the initial stock issuance, can require stock to be traded in certain settings, effectively allowing issuers to influence
Thus, deriving a single, operational legal definition of best
the best execution of their securities.
execution is simply not possible in today’s complex markets,
where traders’ preferences are heterogeneous and where
Conclusion
trading venues offer a wide variety of benefits for traders. For
In this Article we have considered, from a law-and-economics
all of these reasons, we are of the view that the critical ques-
perspective, how best to achieve the elusive goal of best exe-
tion to answer in formulating a best execution regime is where
cution of trades in today’s increasingly fractured and complex
to allocate the decision over trading, rather than what partic-
trading markets. In earlier work we have observed that
ular rules should be applied to particular trades. As among the
‘[d]espite the seeming simplicity of this concept, few issues in
various potential places to locate the decision about what
today’s securities markets are more contentious than the
regime of best execution to discuss, all have flaws. However,
debate surrounding best execution.’ The quest for a workable
among individual traders themselves, the government (SEC),
legal rule is confounded by issues such as: (1) whether clearing
the trading venues themselves, and the issuers, clearly the
a trade in one market at the best available current quote con-
issuers are the institution with the strongest incentives to for-
stitute best execution if trades frequently clear between the
mulate efficient rules of best execution.28 Perhaps the answer
quotes in another market; (2) whether trade size should be
to how best to regulate best execution lies not at the order- or
considered when determining what constitutes best execu-
the market-level, but at the issuer level.
tion; (3) whether brokers and investment advisers are in compliance with their legal right of best execution obligation if the
54 - The
28 Of course we say this with the proviso that issuing firms have the strongest incentives to establish execution rules at the time of the initial IPO, and at other times
the protections and discipline required for charter amendments (including the
requirement of a shareholder vote) should be required before issuers can change
the rules relating to securities trading ex post, that is, after shares are issued.
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55
56 - The
Services
Credit card pricing
developments and
their disclosure
Mark Furletti
Payment Cards Center,
The Federal Reserve Bank of Philadelphia1
Abstract
Public data, proprietary issuer data, and data collected by
myself from a review of over 150 lender-borrower contracts
from 15 of the largest issuers in the U.S. suggest that, over the
past 10 years, credit card issuers have drastically changed the
way that they price their products. This paper outlines the history and dynamics of credit card pricing over the past 10 years
and examines how new pricing methods are addressed by current regulatory disclosure requirements.
1
The views expressed here are not necessarily those of the Federal Reserve Bank of
Philadelphia or of the Federal Reserve System.
57
Intense competition for new customers and the adoption of
that most consumers do not have to work very hard to find a
new technologies in the credit card industry has decreased the
new card. Product innovations, such as transferring balances
price of credit for most consumers, as measured by one well-
and eliminating annual fees, have also made it easier for cus-
understood metric, the nominal annual percentage rate (APR).
tomers to switch cards. Customer loyalty, once ensured by an
For card issuers, this has meant surrendering some of the net
annual fee and a revolving balance built through years or
interest margin they enjoyed as a result of high APRs in the
months of purchases, can now be easily captured by competi-
late 1980s and early 1990s and instituting pricing strategies
tors with a no-fee, low-rate offer to transfer balances. As a
that consider an individual borrower’s risk and behavior pro-
result of these developments, issuers have struggled to main-
file. As nominal APRs have decreased, issuers have come to
tain customer loyalty through rewards programs, affinity/co-
rely on new pricing techniques to maintain or increase portfo-
brand relationships, and enhanced customer service. Despite
lio profitability. These techniques include new APR strategies,
these efforts, a card’s nominal APR remains one of its most
fee structures, and methodologies to compute finance
distinguishing characteristics. The envelopes, letters, and
charges.
applications that issuers use to solicit new business focus
potential customers’ attention on either very low introductory
This paper outlines the history and dynamics of credit card
APRs, such as 0 percent, or low permanent APRs, such as 7.9
pricing over the past 10 years and examines how pricing meth-
percent. Low rates, however, are relatively new phenomena in
ods are disclosed to consumers. The analysis concludes by dis-
the card industry. Researchers studying the card industry in
cussing the challenges that newer, more complex pricing
the 1980s and early 1990s found that credit cards had sub-
strategies pose to the current disclosure framework estab-
stantially higher rates and returns than most other bank cred-
lished by the Truth in Lending Act.
it products.4 Further research showed that credit card rates
remained high when other interest rates fell, leading Calem
Industry pricing dynamics
and Mester to conclude that card rates in that environment
Over the past 10 years, a series of innovations and market
were sticky.5
developments have significantly changed the credit card
industry. Advances in credit scoring, response modeling, and
From 1992 to 2001, however, the average interest rate that
solicitation technologies (i.e. e-mail, direct mail, telemarket-
issuers charged revolving customers fell 320 basis points,
ing) have allowed experienced issuers to more efficiently mar-
from 17.4 percent to 14.2 percent. Issuer markup, a metric that
ket their products and enabled new issuers to enter the card
normalizes for funding costs by subtracting the six-month
market and grow quickly.2 At the same time, it has become
Treasury bill rate from the average APR, decreased 330 basis
easier for consumers to find better credit card alternatives
points during the same period. Margins also narrowed com-
and move their card balances from one issuer to another.
pared with those of other consumer loan products. The difference between the average interest rate charged on a 24-
58
From 1991 to 2001, the number of mailed credit card solicita-
month personal installment loan and a revolving credit card
tions increased fivefold to 5.01 billion. According to BAI Global,
loan fell from 3.8 percent in 1992 to 1.6 percent in 2001. Taken
these solicitations in 2001 reached 79 percent of U.S. house-
together, it is clear that for low-risk consumers who have
holds, which, on average, received five offers each month.3
revolving balances, credit card costs, as measured by APR,
Issuers’ aggressive mail marketing efforts have been aug-
have significantly declined over the past 10 years. At the same
mented by telephone, event, and Internet campaigns, such
time, more consumers gained access to credit cards, including
2 In the eight months since launching its Visa program at the end of 2001, Target
Corporation issued 6 million credit cards and captured over U.S.$2 billion in outstandings. Similarly, other new entrants like Sears and Juniper Bank have been
able to grow very rapidly and compete against much larger issuers.
3 Compared with 73 percent of U.S. households receiving four offers in 2000. BAI
Global, “All time record high credit card mail volume set in 2001,” press release,
April 2002
4 Ausubel, L. M, 1991, “The failure of competition in the credit card market,”
American Economic Review, March, pp. 50-81
5 Calem, P. S., and Loretta J. Mester, 1995, “Consumer behavior and the stickiness of
credit-card interest rates,” American Economic Review, December, 1327-36. This
paper is primarily focused on pricing changes that occurred in the mid- to late1990s. For detailed information about credit card pricing in the 1970s and 1980s,
please refer to Lewis Mandell’s The Credit Card Industry: A History (G. K. Hall &
Co., 1990).
those with lower incomes. Between 1989 and 1998, the largest
or limits for any charges. Instead, it requires that issuers
increases in bankcard ownership were observed among con-
inform potential customers about specific pricing terms at
sumers with the lowest levels of income. With generally lower
specific times. Regulation Z specifies that select terms be dis-
liquidity buffers and weaker credit histories, lower income con-
closed at specific points, such as upon solicitation or applica-
sumers are typically assessed higher annual percentage rates.
tion, before first use of the card, and upon receiving a state-
An overall decrease in the average APR, coupled with an
ment.8 The level of detail for disclosure at each point varies.
6
increase in the number of lower income credit users, suggests
that the average rate decrease for many cardholders was even
When first promulgated, TILA rules required that issuers of
more pronounced than the average APR indicates.
credit cards disclose information about the computation of
APRs and finance charges to customers ‘before the first trans-
Consumer awareness of annual percentage rate as a key cost
action [was] made’ on the account. To meet this requirement,
measure, combined with the ability to easily find new card
issuers mailed consumers a ‘single written statement’ that
offers and switch issuers, inevitably affected price competition
explained the costs of the card after his or her account was
and rate stickiness. According to surveys conducted in 2000
opened. Since 1968 both Congress and the Board of Governors
by the Survey Research Center of the University of Michigan,
(‘the Board’) have mandated changes to TILA disclosure
91 percent of consumers who have a credit card are aware of
requirements. One of the most well-known features, being a
the APR they are charged on their outstanding balances,
pricing disclosure box, resulted from the amendment of TILA
based on a broad definition of awareness.7 Federal Reserve
by the Fair Credit and Charge Card Disclosure Act of 1988.
Board economist Thomas Durkin concludes that ‘it is clear
Informally referred to as the ‘Schumer box’ — after the con-
that awareness of rates charged on outstanding balances…
gressman from New York who was instrumental in the legisla-
has risen sharply since implementation of the Truth in Lending
tion’s passage — the box displays APR and fee information on
Act’ in 1968.
card applications and solicitations in a table designed to be
easy for consumers to read and use for comparison purposes.
The Truth in Lending Act and price disclosure
By requiring that issuers display this box on applications and
The Truth in Lending Act (TILA) was enacted as Title I of the
solicitations, the act enabled consumers to compare offers
Consumer Credit Protection Act in 1968. The act stated that
and rates before opening an account. Similarly, in response to
‘economic stabilization would be enhanced and that competi-
the potentially confusing number of different APRs that can
tion would be strengthened by the informed use of credit
now be associated with a single credit card account — such as
resulting from an awareness of credit costs on the part of con-
balance transfer, cash advance, and purchase APRs — the
sumers.’ TILA charged the Federal Reserve with creating and
Board further modified Regulation Z in 2000. As a result of
enforcing the specific rules needed to implement the legisla-
this modification, issuers are required to disclose the APR for
tion. These rules are embodied in the Board of Governors’
purchases in at least 18-point type on applications and solici-
Regulation Z (Truth in Lending).
tations. The modification also requires them to disclose balance-transfer fees that apply to an account.
TILA, as it applies to credit card accounts, is primarily disclosure focused. The act is silent about the number, amount, vari-
The Board, through modifications to Regulation Z, and
ety, or frequency of fees and credit-related charges that
Congress, through legislation, have updated Truth in Lending
issuers can impose. It does not suggest ceilings, price controls,
to take into account product evolution. Recent changes in how
6 Durkin, T. A, 2000, “Credit cards: Use and consumer attitudes, 1970-2000,” Federal
Reserve Bulletin, September 623-34. The following are the changes in the percentage of respondents to the survey cited by Durkin by income quintile who indicated
that they owned a bank-type credit card: lowest +65 percent; second lowest +61
percent; middle +16 percent; second highest +13 percent; highest +7 percent.
7 Awareness was measured using a narrow and a broad definition. Under the broad
definition, only those reporting that they did not know the rate were considered
unaware. Under the narrow definition, those reporting a rate less than 7.9 percent
were also considered unaware. Using the narrow definition, awareness in 2000
was measured at 85 percent. Previous measures of awareness from the Survey of
Consumer Finance did not distinguish between narrow and broad. These measures
showed 27 percent in 1969, 63 percent in 1970, and 71 percent in 1977. [Durkin
(2000)].
8 Regulation Z also requires that specific information be disclosed in advertisements for credit (i.e. adverts on television or in magazines) and when certain credit terms are changed. This paper does not examine these regulatory disclosure
requirements.
59
issuers price credit cards, however, have resulted in new levels
released to the media in the early 1990s.10 At the time, issuers
of pricing complexity and created a structure of credit costs
generally had one rate that they extended to all customers.
that can impact some customers very differently than others.
When they lowered this rate, they did so for almost all of their
That is, the cost that a consumer faces greatly depends on the
accounts. A 1993 issue of CardTrack, a publication of
way he or she uses the credit card.
CardWeb.com, reported that Citibank was offering a 15.4 percent rate to all new applicants.11 This was the same rate it was
This paper will explore the evolution of credit card pricing and
offering to virtually all of its current customers. CardTrack also
examine the disclosure requirements of Truth in Lending
reported that 90 percent of Citibank cardholders had been
(Regulation Z) that relate to these pricing changes. Analysis
paying an APR of 19.7 percent a few years earlier. Other large
will rely on public data, proprietary issuer data, and data col-
issuers, such as Chase, Chemical, AT&T, and Bank One, made
lected by the author from a review of over 150 lender-borrow-
rate-cut announcements that were similarly applied to all cur-
er contracts from 15 of the largest issuers in the U.S. over a
rent and new customers.12 Competitive pressures and increas-
five-year period. Pricing and fee changes are organized into
ing price awareness among consumers, however, eventually
three categories — nominal APR, fee structure, and computa-
made these undifferentiated pricing strategies obsolete.
9
tional technique changes — and presented in order of most to
least consistent with the current format of regulatory disclo-
Risk-based solicitation APRs
sure requirements. Examples of each type of change are pro-
Issuers have generally used risk-based pricing techniques in
vided, along with an analysis of each change’s impact on
two ways. The first is in setting the interest rate initially
issuers’ revenues.
offered to a consumer. Using credit bureau attributes, issuers
assess the default risk of a consumer and essentially charge
Nominal APR changes
him or her a premium for that risk. This premium is typically
Until the early 1990s, credit card pricing, as it related to nom-
reflected in the APR stated in the card application or solicita-
inal APRs, might best be characterized in two ways, high and
tion. Prior to the early 1990s, by charging every customer the
simple. Card issuers generally had one or two card products,
same rate, issuers made much higher profits from customers
such as a classic card and/or a gold card, that each had a sin-
with very low default risk.13 These excess profits could be used
gle annual percentage rate of around 18 percent. If an appli-
to cover defaults generated by customers whose risk, over
cant for credit could pass the risk threshold set by the issuer,
time, had increased. As issuers began competing on APR, how-
he or she would receive a card. If the applicant’s credit behav-
ever, they were forced to eliminate this cross-subsidization
ior was determined to be too risky, his or her application was
and assess APRs based on an analysis of individual borrower
denied. This resulted in a portfolio of customers who were
risk.
priced as if they had very similar probabilities of default.
Ultimately, a card’s nominal APR became a competitive focal
60
Evidence of these risk-indifferent APR strategies can be
point and drove widespread adoption of risk-based pricing.
observed in public ‘rate decrease announcements’ that issuers
Issuers who failed to adjust pricing appropriately by risk seg-
9 Lender-borrower contracts are the documents issuers send their customers that
often include fee disclosures, account usage terms and conditions, borrower and
lender responsibilities, etc. Issuers typically refer to them as Cardmember
Agreements or Required Disclosures, and modify them with Change in Term
Notices. These documents are usually made available to cardholders before the
first transaction is made on the account.
10 Stango (2002) observes that comments about high card rates from President
George H. Bush in 1991 and the Senate’s passage of a bill in that same year capping APRs influenced many large issuers to lower rates. (The Senate’s bill was
never signed into law.)
11 Cardweb.com, CardTrack. “National Credit Education Week,”
<http://www.cardweb.com/cardtrack/> April 1993.
12 Stango, V., 2002, “Strategic responses to regulatory threat in the credit card market,” Federal Reserve Bank of Chicago Working Paper 2002-02, February
13 The risk-based pricing techniques referred to in this section impact customers
only to the extent to which they carry a balance on their credit card. For customers who always pay their balance in full, such pricing techniques are effectively inconsequential.
ments would expose themselves to serious adverse selection
fail to make a payment to us when due, you exceed your cred-
problems. Issuers today may have hundreds of different APR
it line, or you make a payment to us that is not honored by
price points. With few exceptions, these points are highly cor-
your bank.’ I also found that issuers had taken these policies a
related to some risk measure.14 When we look at the difference
step further in recent years. Agreements were changed to
between the effective finance charge yield for the highest risk
allow issuers to incorporate into the penalty pricing decision
revolving customers (FICO scores less than 600) and cus-
information they obtained from credit bureaus about other
tomers in other risk cohorts, we find that the discount that
loan behavior. Newer policies read as follows: ‘We may
lower risk customers receive on their APR has increased sig-
increase the annual percentage rate on all balances to a
nificantly since the early days of risk-indifferent pricing. The
default rate of up to 24.99 percent… if you fail to make a pay-
lowest risk customers, who once paid the same price as high-
ment to us or any other creditor when due, you exceed your
risk customers, now enjoy rate discounts that can reach more
credit line, or you make a payment to us that is not honored
than 800 basis points.15 At the other end of the risk spectrum,
by your bank’ [emphasis added].20
these strategies have enabled issuers to grant more people
(i.e. immigrants, lower income consumers, those without any
credit experience) access to credit, albeit at higher prices.
Nominal APR changes and regulatory disclosure
requirements
Former Federal Reserve Governor Lawrence Lindsey has
The risk-based pricing strategies described above are exclu-
referred to this phenomenon as ‘the democratization of cred-
sively focused on the nominal APR component of credit card
it.’16 Examining data from the Survey of Consumer Finance,
pricing. Disclosures required by Regulation Z inform cus-
Stavins also noted the same risk-based pricing trend. She
tomers about such APRs upon solicitation in two sections of
observes that ‘consumers with higher ratios of unpaid credit
the ‘Schumer box’, APR for Purchases and Other APRs, and on
card debt to income, and thus [who were] worse credit risks for
periodic statements. In addition, Regulation Z requires that
the issuers, were charged higher interest rates.’17
the non-introductory purchase APR be displayed in 18-point
type in the ‘Schumer box’ on new card offers. Overall, Truth in
Risk-based penalty APRs
Lending disclosure requirements ensure prominent display of
Risk-based pricing strategies can also be used to modify a cus-
each APR associated with an account. The nominal APR-focus
tomer’s APR after he or she has started using the account.
of Truth in Lending statements and of issuers’ marketing
Issuers have recently implemented ‘penalty APR’ strategies
materials has no doubt contributed to consumer awareness of
that allow them to adjust upward the nominal APR of cus-
APRs as key determinants of credit cost.
tomers whose risk, perhaps because of recent late payments
or increasing levels of debt, is no longer in line with their orig-
Fee structure changes
inal APR. In my own study of lender-borrower contracts I
Another way that credit card pricing has developed is in the
found that penalty pricing strategies were first introduced in
unbundling of costs in the form of fees. As previously men-
the late 1990s.19 An example of language that explained these
tioned, card pricing in the 1980s and early 1990s was relative-
policies in 1997 read as follows: ‘Your APRs may increase if you
ly simple. Issuers typically charged a relatively high interest
14 One notable exception to the risk-based pricing strategy is the co-branded airline
portfolio. Co-branded air cards that reward users with frequent-flyer miles typically attract low-risk business travelers despite having a high rate (e.g., 18.9 percent)
and an annual fee.
15 One could argue that the customers at any given FICO score might be riskier
today than in 1998 (i.e., a 650 FICO score in 2002 carries a higher risk of default
than a 650 did in 1998) because of changes in issuers’ underwriting standards or
a less favorable economic environment. There are three reasons to doubt the
material impact of such factors. Firstly, in an attempt to control for the impact of
economic cycles, the data are presented relative to the yield of highest risk customers (FICO scores < 600). Secondly, credit modeling experts believe that Fair
Isaac frequently recalibrates its FICO model in order to ensure that its score-odds
ratio is relatively stable. This mitigates the effects that different economic environments might have on the score. Finally, the underwriting standards of the
prime/super-prime issuers in the Argus study are thought to have been stable
throughout the period with little or no sub-prime origination.
16 Black, S. E., and D. P. Morgan, 1998, “Risk and the democratization of credit cards,”
Federal Reserve Bank of New York, Research Paper 9815
17 Stavins, J., 2000, “Credit card borrowing, delinquency, and personal bankruptcy,”
New England Economic Review, July/August, 15-30
18 Penalty pricing tactics employed by Direct Merchants (Metris) led CardTrack to
observe that ‘credit card interest rates have passed the 30% barrier!’ As reported
in May 2000, a 31.99 percent APR was imposed on Metris customers who were
late three times during the year or who fell 60 days delinquent.
19 I would like to thank MarketIQ, a direct marketing competitive intelligence firm in
Fair Haven, New Jersey, for contributing to the study.
20 Some issuers’ policies explained that a consumer could get his or her pre-penalty
rate back after making 12 consecutive on-time payments.
18
61
rate and an annual fee of around U.S.$25 that covered most of
based fee levels and created new fees. For example, in 1997,
the expenses associated with card usage. Few issuers charged
the risk-based fee that most issuers charged customers who
over-limit fees or late fees, and when they did, these fees were
had exceeded their credit line was less than U.S.$20. By 2002,
relatively small.21 The increased competition for new accounts
most top issuers had adopted an over-limit fee structure that
that developed in the mid-1990s, however, changed all of this.
was tiered by balance size and nearly doubled the fee for over-
Rates came down, as described in the previous section, and
limit customers. These issuers now assess a U.S.$35 fee to
issuers eliminated the once universal annual fee. Today, these
those customers who exceed their credit line and have a bal-
fees are almost nonexistent in prime portfolios not associated
ance of over U.S.$1000. Similar increases were observed for
with a rewards program. The data that Argus Information &
late fees and returned-check (NSF) fees.24
Advisory Services collected from top issuers show that just 14
percent of customers who are not enrolled in a rewards pro-
Issuers were also observed introducing new risk-based fees
gram, such as frequent-flyer-miles program, paid an annual
during this period. For example, in the late 1990s, issuers
fee in 1998 and just 2 percent did in 2002.22
began assessing a returned-check fee for credit card convenience checks. Such checks allow customers to access their
With average interest rates on the decline and annual fees
credit card’s line of credit using a paper check. If a customer
becoming unpopular among their customers, issuers devel-
writes a convenience check for an amount that exceeds his or
oped more targeted fee structures to replace lost revenues. In
her available credit line and the issuer chooses not to honor
lieu of charging all of their customers an annual fee that sub-
the check, most issuers now assess that customer a fee that
sidized the costs associated with the behaviors of a few, they
ranges from U.S.$29 to U.S.$35.
began to assess fees directly on those customers whose card
usage behaviors drove costs higher. As issuers started
The impact of higher risk-based fees on issuers’ revenues has
unbundling costs and creating behavior-based fees, fees
been substantial. In May 2002, Cardweb.com estimated that
rebounded and have again become an important component
half of all consumers in the U.S. who had a credit card had
of issuer revenues. Ultimately, two distinct families of fees
been late at least once in the previous 12 months. Issuers’
have emerged, risk-related fees and convenience/service fees.
annual late fee revenues more than quadrupled from 1996 to
2001 (U.S.$1.7 to U.S.$7.3 billion) while average late fees only
62
Risk-related fees
doubled (U.S.$13 to U.S.$27). This indicates that, in addition to
In addition to using different APRs to better price for risk,
an increase in the amount of the average late fee, there has
issuers have significantly increased the use of risk-related
been a substantial increase in late fee incidence. Cardweb.com
fees. These include late fees, over-limit fees, and bounced-
also noted that late-fee revenues currently represent the third
check fees. The industry’s modeling and analysis efforts have
largest revenue stream for issuers after interest and inter-
shown that customers who are late or over their credit limit or
change revenue.25 Argus Information & Advisory Services data
who write bad checks are more likely to default. Risk-related
compiled from top prime issuers during the first quarter of
fees help compensate issuers for this increased risk.23 For
2002 showed that 5 percent of issuers’ active cardholders
lower risk customers, risk-related fees can deter sloppy pay-
were assessed an over-credit-limit fee during the three-month
ment behavior and poor credit-line management. Examination
period. Information on the size and growth of other risk-based
of lender-borrower contracts from 1997 through 2002
fee types is not available. The examples above, however,
revealed that issuers significantly increased traditional risk-
strongly suggest that risk-based fees have become an impor-
21 Typical late fees ranged from U.S.$5 to U.S.$10. The average late fee charged in
1990, according to CardWeb, was U.S.$9.
22 The data from Argus also show that the average annual fee charged on a nonrewards card has fallen from U.S.$3.31 in 1998 to U.S.$0.50 in 2002.
23 Issuers may also be aware that customers who are consistently paying these fees
are likely to have fewer and less attractive credit alternatives.
24 NSF is a return check reason code that stands for not sufficient funds.
25 Interchange revenue is derived from a fee set by the card associations that issuers
assess merchants each time a credit card purchase is made. Depending on the
card association, the fee can range from 1.5 to 4.0 percent of the value of the
transaction.
tant source of revenue for card issuers and have replaced a
Finally, most issuers have adopted balance transfer fees.
significant portion of the revenues lost from the elimination of
These fees, typically around 3 percent of the amount trans-
annual fees and lowered APRs.
ferred with various minimums and maximums, are often
assessed on balances transferred from a competitor’s card.
Convenience and service fees
These balances often qualify for a discounted promotional
Issuers have also unbundled servicing costs, introducing fees
APR. The balance transfer fee helps offset costs associated
for services and conveniences that were once paid for by all
with customer service representatives who initiate the bal-
customers out of annual fee and interest revenues. Some of
ance transfers and may help reduce ‘rate surfing’ (i.e., the act
these new fees, like those levied on the credit card purchase
of continually moving balances among cards to take advan-
of casino chips or on cash advances, compensate issuers for
tage of short-term promotional rates).27
the fraud risk thought to be inherent in cash or cash-equivalent transactions. Other fees, like those imposed for stop
Information on the revenue impact of convenience and serv-
payment requests, statement copies, or replacement cards,
ice fees is limited. Argus Information and Advisory Services
more directly compensate issuers for out-of-pocket expenses,
data indicate that the top prime issuers are earning about
such as customer service representative time or telecommu-
U.S.$8 per active account per year in cash advance fees and
nications expense. In addition to defraying operational costs,
U.S.$6 per active account per year in other fees (excluding
these new fees are generally priced to provide attractive prof-
risk-related fees). The actual impact that fees have on rev-
it margins.
enue per account can be observed only among the few
issuers who separately list non-securitization fee income in
Starting in the late 1990s, a number of issuers began assess-
their annual reports. One such annual report revealed a dou-
ing a foreign currency conversion fee of 2 percent on pur-
bling of fee revenue per account from U.S.$4 in 1998 to
chases that cardholders make outside the U.S. This fee was
U.S.$8 in 2001.
added on top of a 1 percent fee already assessed by
MasterCard and Visa. The 1 percent fee charged by the associations covers the transaction costs associated with the actual
Fee changes and regulatory disclosure
requirements
exchange. Some industry sources suggest that the 2 percent
Regulation Z requires that issuers, upon application or solici-
fee levied by issuers is related to the long-distance telecom-
tation, inform customers about the annual fee, minimum
munications charges associated with customer service calls
finance charge, cash advance fee, balance transfer fee, late
that originate in foreign countries from traveling customers.
fee, and over-limit fee associated with an account. Before the
first transaction is made on the account, issuers must disclose
More recently, several issuers have added a phone payment
other charges, that is ‘any charge other than a finance charge
convenience fee. This fee, which ranges between U.S.$10 and
that may be imposed as part of the plan, or an explanation of
U.S.$25, is assessed when customers choose to pay over the
how the charge is determined.’ The official staff commentary
phone instead of through the mail.26 While this fee may seem
on Regulation Z, which represents the Board staff’s interpre-
like an expensive alternative when compared to the cost of
tations of the regulation, further provides that only ‘signifi-
postage, customers who typically rely on phone payments are
cant charges’ must be disclosed as other charges. The com-
often close to missing their payment due date and being
mentary offers late fees, annual fees, over-limit fees, and
assessed a U.S.$35 late fee.
account closure fees as examples of significant charges.
26 When an issuer accepts a payment over the phone, it receives authorization from
its customer to debit the customer’s checking account for the payment amount.
27 If these fees become universally adopted, they will make it more expensive for
consumers to switch cards.
63
Regulation Z does not explicitly address disclosure of the for-
card at an APR of 2.9 percent. Since the customer’s payments
eign currency conversion fee. Unlike most fees that can be
are allocated to the 2.9 percent balance first, the issuer effec-
observed upon a detailed review of a card statement, foreign
tively protects or locks in the U.S.$2500 balance at 18.9 per-
currency conversion fees are often rolled into the transaction
cent until the lower rate balance is repaid.
amount or the conversion factor.28 Other fees that are not
specifically mentioned in the regulation include phone pay-
Compounded interest
ment fees, wire transfer fees, and stop payment fees on cred-
By 1997, most issuers had switched from monthly to daily
it card convenience checks.29 Issuers generally disclose these
compounding of interest by changing the computational
fees to consumers by including a menu or a description of
method for calculating average daily balances. Before the
these other fees in welcome kit mailings to new customers or
adoption of daily compounding, disclosures typically
in Cardmember Agreements. The organization, detail, and
explained that ‘on each day of the billing period we subtract
prominence of these menus or descriptions vary by issuer.
payments, add new purchases and fees, and make adjustments’ to calculate the average daily balance. By the end of
Computational technique changes
the 1990s, however, the language had changed as follows: ‘To
In addition to adopting risk-based pricing and expanding fees,
get the daily balance we take the beginning balance for every
issuers are employing new computational practices that
day, add any new transactions, fees, and any finance charge
increase effective yields without affecting the disclosed nomi-
on the previous day’s balance, subtract any credits or pay-
nal APRs. My own lender-borrower contract research uncov-
ments, and make other adjustments [emphasis added].’ By
ered many such examples among the major issuers. Three of
adding finance charges to the balance each day, issuers
the more common practices are detailed below.
increased finance charge revenue without increasing stated
annual percentage rates.30 This has the effect of increasing
Payment allocation
the effective finance charge yield of a portfolio by as much as
Many issuers have added sections to their contracts to
10 to 20 basis points. For instance, the annual effective port-
explain how they allocate payments to revolving balances. As
folio yield on a loan with an APR of 18.99 percent compound-
mentioned previously, the number of APRs that can be
ed 12 times a year is 20.73 percent. If the same loan is com-
applied to the balances on an account has increased dramat-
pounded 365 times per year, its effective yield increases 18
ically over the past 10 years, such as purchase, promotional,
basis points to 20.91 percent.
cash, and balance transfer APRs. Issuers have created vari-
64
ous average daily balance categories to which these different
Double-cycle interest
rates are applied. One issuer’s disclosure statement explained
Another pricing innovation involves a change in the treatment
the way in which payments would be applied to different bal-
of the grace period during which interest does not accrue. One
ance categories as follows: ‘We will allocate your payment
of the unique advantages of credit card borrowing has been
and any credits to pay off balances at low periodic rates
the interest-free period consumers who pay their bill in full
before paying off balances at higher periodic rates.’ This com-
receive from the time they make a purchase until the date
putational methodology effectively protects revolving bal-
their payment is due. This period can vary from 40 to 60 days.
ances at higher rates. For example, issuers can offer a cus-
The lender-borrower contract study revealed that a number of
tomer with a U.S.$2500 revolving balance at 18.9 percent an
issuers have effectively eliminated the grace period for con-
opportunity to transfer another U.S.$2500 balance onto the
sumers who, after making a full payment or not having had a
28 Stellin, S., 2002, “Credit card swipe: Concealed charges,” New York Times, July 12,
reports that just three major issuers separate out their foreign currency exchange
charges on customers’ statements.
29 On November 26, 2002, the Board proposed credit card-specific revisions to
Regulation Z’s official staff commentary. One of these revisions would add phone
payment fees to the list of ‘other charges’ that must be disclosed before the first
transaction occurs on an account.
30 The annual percentage rate (APR) disclosed on a customer’s statement is calculated by dividing finance charges for the period by the average daily balance for the
period. While increasing the frequency of compounding increases the finance
charge, the numerator, adding finance charges to the average daily balance, the
denominator, each day offsets the effect of compounding on the disclosed APR.
balance in the previous month, do not make a full payment in
chases), two-cycle average daily balance (excluding new pur-
the next month.
chases), adjusted balance, or previous balance. Additional
explanations or definitions are not required by the regulation
For example, consider a customer without a previous balance
upon solicitation or application. Issuers are not required to
who has a 10 percent APR on purchases and who makes a
provide detailed explanations of balance-computation tech-
purchase of U.S.$1000 on May 1 (the first day of the cus-
niques until after the account is opened. This means that con-
tomer’s May cycle). The customer then receives a bill for
sumers wanting to find out what the term ‘two-cycle average
U.S.$1000 on June 1. Instead of paying the entire balance, the
daily balance’ signifies before filling out an application for a
customer sends the issuer a minimum payment of U.S.$20,
card would have to conduct their own research. As a practical
which arrives on June 30. When the customer’s account
matter, this may be easier for consumers with access to the
cycles on the night of June 30, the issuer will assess finance
Internet than for others.31
charges for the month of June and reach back and add
finance charges for the entire month of May. In this example,
Detailed descriptions of the practices referred to above are
instead of billing approximately U.S.$8 in finance charges
usually not featured in application or solicitation materials.32
(based on the APR of 10 percent), the issuer will bill approxi-
Issuers disclose the details of these computational tech-
mately U.S.$16. It should be noted that double-cycle interest
niques in various ways in their lender-borrower contracts and
is assessed only in the month in which a customer moves
factor their effects into TILA-required periodic statement dis-
from a non-revolving to a revolving state. The interest com-
closures. For example, consumers who revolve a balance
putation returns to a single-cycle method for the remaining
might become aware of the impact of daily compounded
months in the revolving period.
interest if, upon receiving their statement, they carefully
review the issuer’s calculation of the total finance charges
Data on the revenue impact of the changes described above
disclosed on their statement. Similarly, customers who pay
are limited. Given that approximately three-fifths of all card-
finance charges on their late fees, on their balance between
holders pay interest on their balance and that half of those
the statement date and payment date, or from their transac-
who pay interest make only the minimum payment [CardWeb
tion date to their posting date might notice, upon an excep-
(March 7, 2002)], it seems likely that these changes have had
tionally careful review, increased finance charge amounts on
at least a material effect on issuers’ revenues and have con-
their statement.
tributed to the shift in industry revenue profiles.
Conclusion
Computational technique changes and disclosure
requirements
Substantial changes in the dynamics of credit card pricing
Double-cycle billing is explicitly addressed by Regulation Z in a
forward pricing model of a single APR, an annual fee, and mod-
section of the ‘Schumer box’ entitled ‘Method of computing
est penalty fees has been replaced by a model with a complex
the balance for purchases.’ Here issuers are required to indi-
set of APRs, new and increased fee structures, and sophisti-
cate the balance-computation technique they use with one of
cated finance charge computation techniques. This ‘unbun-
the following descriptors: average daily balance (including
dled’ pricing structure has created a card product for which
new purchases), average daily balance (excluding new pur-
consumers pay substantially different prices based on individ-
chases), two-cycle average daily balance (including new pur-
ual behavior. During this time, however, the overall disclosure
31 A search on ‘two-cycle average daily balance’ on Google.com returns 10 non-governmental, consumer-oriented web sites, such as practicalmoneyskills.com, creditcards.com, and bankrate.com, that explain how two-cycle interest can influence the
cost of credit.
32 The balance computation technique is disclosed with a brief descriptor in the
‘Schumer box,’ but it does not give consumers the details necessary to understand
how the interest is actually computed.
have occurred over the past decade. The relatively straight-
65
framework mandated by the Truth in Lending Act has changed
it is clear that others pose significant disclosure challenges. Is
very little.33
there a simple way to communicate two-cycle billing such that
consumers understand that their credit costs will be higher if
The adoption of new pricing structures has increased credit
they occasionally revolve balances? Can payment allocation
costs for some consumers and decreased it for others. Low-
methods be explained in a way that customers with low-rate
risk borrowers, who behave in such a way as to avoid new and
promotional balances understand the cost implications of
increased fees, generally experience lower credit costs than
making higher-rate purchases? Is there a simple way to
they might have several years ago. Higher risk borrowers, who
explain that when consumers miss a payment with one issuer,
may not have previously qualified for unsecured credit, can
it can affect the price they pay for credit to another?
now obtain credit cards by paying a risk premium. Other borrowers, because of their consumption of fee-based services or
Recent survey results indicate that consumers have mixed
perceived level of risk, now face higher credit costs. To a large
feelings about Truth in Lending statements. Durkin (2002)
extent the new pricing structure results in more credit card
points out that, in consumer surveys conducted for the Board
users ‘paying their own way.’
of Governors in 1994, 1997, and 2001, over three-quarters of
respondents agreed that Truth in Lending statements are
A pricing structure that better allocates issuer’s risk and serv-
complicated.35 Forty percent of those surveyed did not find the
icing expenses has likely come at a cost, in the form of a com-
statements helpful as they relate to bank-type credit cards,
plex and customized product whose pricing is difficult to sum-
and 77 percent said that the statements did not affect their
marize. In today’s environment of highly individualized pricing,
decision to use credit cards in any way. Although consumers
it is difficult to imagine a generic disclosure requirement that
may find these disclosures complex and not always helpful,
could meet the burden of clearly explaining the total costs of
Durkin concludes that consumers ‘appear to like knowing that
credit that any given consumer would face. In 1996, in a report
the behavior of creditors is being monitored.’
to Congress on TILA, the Board of Governors foresaw this possibility when it reported the following: ‘The ability to ensure
Based on this survey data, it is not clear that requiring more
accurate disclosure of the ‘true’ costs gets more difficult as
details in regulatory disclosures would be useful for con-
creditors increase the number of credit products, pricing alter-
sumers. An alternative is to promote understanding of credit
natives, and optional services. The permutations of possible
costs through education. Educated consumers can change the
costs to be disclosed — and the potential for error — also
terms on which issuers compete and force transparency in
increase.’34
price structures. In either case, understanding new developments in credit card pricing is important for ensuring that
66
While some of the pricing innovations described in this paper
information is available for consumers to make an informed
might easily fit into the existing regulatory disclosure format,
decision about credit.
33 As previously mentioned, the last major modification occurred with the passage of
the Fair Credit and Charge Card Disclosure Act (FCCDA) 14 years ago. The FCCDA
amended TILA and introduced the conspicuously placed ‘Schumer box.’ Since that
time, the Board of Governors has modified TILA’s underlying regulation and regulation staff commentary to respond to some of these pricing changes, such as
requiring larger point type, penalty rate disclosures, and cash advance and balance
transfer APR disclosures.
34 Board of Governors’ Report to Congress, 1996, “Finance charges for consumer
credit under the Truth in Lending Act,” April
35 Durkin, T. A., 2002, “Consumers and credit disclosures: Credit cards and credit
insurance,” Federal Reserve Bulletin, April, 201-13. This includes Truth in Lending
statements required for credit cards, home equity loans, and installment loans.
Real options
The interaction between real options and financial hedging
in non-financial firms
Mergers and acquisitions as a response to economic change
Valuing real options: Frequently made errors
A real options approach to bankruptcy costs:
Evidence from failed commercial banks during the 1990s
Strategic investment under uncertainty:
A survey of game theoretic real options models
The interaction between real
options and financial hedging in
non-financial firms1
Tom Aabo, Associate Professor, Aarhus School of Business
Betty J. Simkins, Associate Professor, Department of Finance,
Oklahoma State University
Financial hedging is often utilized to hedge transaction expo-
Exploit growth options by entering a new foreign market or
sure (a nominal exposure tied to contractual obligations) and
offering new products in an existing foreign market —
other short-term exposures caused by fluctuations in
Investment in a foreign subsidiary network generates the real
exchange rates. This article examines the hedging of operat-
option to introduce new products in foreign countries. Firms
ing exposure (sometimes called economic exposure, compet-
with a presence in a country find it easier to introduce a new
itive exposure, or strategic exposure) through the use of real
product than a firm without such presence. By establishing
option strategies.2 Operating exposure is a real exposure and
operations in a new country a firm also acquires the option to
is concerned with the impact of unexpected changes in
expand its product line at a later point in time.
exchange rates on the operations of the firm and consequently on the operating profits, the cash flows, and the value
Abandon a foreign market — Another real option strategy is
of the firm.
the ability to abandon a foreign market when profitability is
low due to such factors as low prices on outputs, high costs of
While financial hedges are well-suited to hedge short-term
inputs, or lack of competitiveness in the market relative to
and certain exposures, hedging quickly becomes more com-
other producers. Effectively, this is the option to terminate all
plicated when managing operating exposure. In the long-run
production and operations and sell the asset for its current
business conditions may change so that the underlying trans-
market value. The abandonment decision is permanent unless
action may not materialize, and what was supposed to be a
the firm expects to return in the future. In the latter case the
financial hedge turns into a financial speculation without
firm will face re-entry costs.
underlying business rationale. Furthermore, when taking a
long-term perspective, firms have other options than finan-
Shift input sources across borders or between substitute
cial hedging. For example, a European firm that produces in
inputs — This is a switching option and is common in industries
Europe and exports its goods to the U.S. may react to a
where production inputs are flexible. If adjustment costs (i.e.,
depreciating U.S. dollar by establishing production in the U.S.
the cost to switch between suppliers) and lags (i.e., time lag in
This real option strategy makes it possible for the European
switching suppliers) are low, firms can expand purchases of
firm to regain its competitiveness. Accordingly, managers are
inputs from suppliers in countries with beneficial exchange
not restricted to financial hedging when they are maneuver-
rates and reduce purchases from other suppliers.
ing in the minefield of operating exposure. An alternative is to
change the set-up of the firm by exercising real options. The
Shift production locations or factors of production — A firm
focus of this article is on the interaction between financial
can react to exchange rate changes by varying the capacity
hedging and real options in managerial decision-making in
utilization of different plants. Investing in production flexibility
non-financial companies.
measures that facilitate production reallocation between
countries can be profitable when cost fluctuations between
Real option strategies
countries are not identical. This real option is more valuable
At least four real option strategies are relevant to non-finan-
when the correlation between marginal costs (including
cial firms that export and/or have foreign subsidiaries. These
exchange rates) in the two countries is low, the standardiza-
strategies are:
tion of products is high, switching costs are low, and exchange
rate volatility is high.
1
68
An extended version of this article is forthcoming in the Review of Financial
Economics (2005).
2 Real options are options on real, or non-financial, assets. For example, a company
that has real options has the right, but not the obligation, to make value-adding
managerial decisions through the strategic use of the firm’s operations. The real
option approach applies financial option theory to real investments, such as manufacturing plants, product or business extensions, R&D investments, and global
operations.
Firms in sample
and had subsidiaries in 10 foreign countries (median 6 foreign
This study is based on survey results from a representative
countries).
sample of Danish, non-financial firms listed on the Copenhagen Stock Exchange as of the end of 2001. Denmark is a
Real options exercised
small (5.4 million inhabitants), open (exports as a percent of
One of the main reasons for not hedging operating exposures
GDP = 45 percent) economy with a GDP per capita in 2001 of
by financial means is the inadequacy of such hedging to
U.S.$30,000. The 2001 GDP per capita of the U.S. was 35,000
address the real problem of operating exposures. As an alter-
U.S. dollars. Denmark has been a member of the E.U. since
native, a firm may react to changes in exchange rates by exer-
1973, but has not adopted the euro, although the Danish
cising real options using the strategies previously discussed.
Krone (DKK) is tightly linked to it.
Our survey of the decision-making process in Danish nonfinancial firms confirm that such considerations are made in a
A total of 117 Danish, non-financial firms listed on the Copen-
number of firms. More than one-half of the firms in our sam-
hagen Stock Exchange were mailed surveys in October 2001.
ple state that they sometimes or frequently do not hedge an
The survey consisted of a questionnaire containing 17 closed-
operating exposure by financial means because the operating
ended questions and was mailed to a target employee at each
exposure is managed by real means.3
of the 117 firms. The target employees were primarily finance
managers, but CFOs and treasurers were also surveyed. By
Various real options can be exercised when managing operat-
the end of December 2001, 52 firms had sent in filled-out
ing exposures caused by fluctuation in exchange rates. Figure
questionnaires, resulting in a total survey response rate of 44
1 shows the real option strategies likely to be exercised by our
percent.
sample firms within a time frame of two to three years and
partly or fully due to the development in exchange rates.
Using the Global Industry Classification Standard (GICS), 5
[Note: For brevity, hereafter, we use the words ‘due to
firms are from Materials, 19 firms from Industrials, 7 firms
exchange rate changes’ in place of the actual words used in
from Consumer Discretionary, 5 firms from Consumer
the survey ‘partly or fully due to the development of exchange
Staples, 9 firms from Health Care, 6 firms from Information
rates.’]
Technology, and 1 firm from Utilities. Except for Heath Care
firms that are more likely to respond than the average firm,
More than half of the firms (54 percent) indicated that it is
no non-response bias is detected. In other words, the sample
should be representative for the population of Danish nonfinancial firms listed on the Copenhagen Stock Exchange.
The average firm in our sample had a consolidated total
assets of DKK 7,421 million (median DKK 1,756 million) in 2001.
In U.S. dollar terms, this translates into average consolidated
total assets of less than one billion dollars (8.41 DKK per U.S.
Change sourcing between suppliers in different countries
Buy a foreign firm (sales and/or production)
Establish production in a country where your firm did not
have production before
Shift production between production outlets in different countries
Sell a firm/close down a production subsidiary in a foreign country
Enter a foreign market where your firm did not have sales before
Abandon a foreign market (stop selling to that market)
No
Yes
46%
67%
54%
33%
69%
69%
75%
77%
81%
31%
31%
25%
23%
19%
dollar as of the end of 2001). Our average firm had foreign
sales-to-total sales ratio of 61 percent (median 75 percent)
3 The question asked was: ‘What are the likely reasons for your company to not
hedge an operating exposure?’ The respondents were asked to prioritize different
reasons. The most important reason was that the particular operating exposure
was not significant. The second most important reason was: ‘Operating exposure is
managed by real means’. Fifty-two percent of the firms stated that this reason was
the first, second or third most important reason for not financially hedging an
operating exposure.
Figure 1: Real options likely to be exercised4
4 The question asked was: ‘A firm may react to changes in exchange rates by taking
real actions (exercising real options) such as to reallocate production facilities, to
abandon a market, to buy a foreign firm, etc. Is it likely that your firm within a
time frame of two to three years and partly or fully due to the development of
exchange rates would take the following actions?’ Respondents were asked to
respond ‘yes’ or ‘no’ to the options listed.
69
35
A large company should have the necessary resources to exer-
Mean value = 2.2 real option strategies used
cise real options. Furthermore, a company that has a large
30
exposure to exchange rates (such as a high foreign sales-toPercentage of firms
25
total sales ratio) should be more motivated to exercise real
options. And finally, a company with subsidiaries in many
20
countries should have a better ability to react to changing
exchange rates by exercising real options. As a result, all three
15
variables that we study (size, foreign sales ratio, and geo-
10
graphical coverage) are hypothesized to be positively correlated with real options usage.
5
0
1
2
3
4
5
6
7
8
Number or real option strategies used
Figure 2: Number of real option strategies likely to be exercised
For our empirical tests, it is important to point out that several of the variables are highly correlated. The highest correlation coefficient (0.66) is between size (log of total assets) and
geographical coverage (square root of the number of foreign
likely that they will change sourcing between suppliers in dif-
countries in which the firm has subsidiaries). Large firms tend
ferent countries. The equivalent likelihood of sample firms
to have subsidiaries in more countries than small companies.
using other and more radical changes, such as buying or sell-
Another high correlation coefficient (0.58) is between the for-
ing a foreign firm, is much smaller. The real option that is most
eign sales ratio (foreign sales/total sales) and geographical
unlikely to be exercised is to abandon a market (19 percent).
coverage. Firms that earn a lot of their revenues abroad also
tend to have subsidiaries in several foreign countries. Finally,
Figure 2 illustrates the percentage of firms likely to use differ-
there is only a modest correlation (0.29) between the size of
ent real option strategies. As shown, the average number of
the company and its relative sales abroad.
real option strategies likely to be utilized within a time frame
of two to three years due to exchange rate changes is 2.2. At
In order to minimize the problem of multicollinearity because
one extreme, one third of the firms in this study (35 percent)
of high correlations between the three variables (size, foreign
do not think that it is likely that they will exercise any real
sales ratio, and geographical coverage) and to test an alterna-
options. At the other extreme, three firms (6 percent) think
tive economic reasoning, we also construct a new integrated
that all real options are likely to be exercised. All firms (except
variable called multinationality.5 This new variable is a combi-
one) that indicated that only one option was likely to be exer-
nation of the three variables. The economic reasoning is that
cised responded that this real option strategy was to ‘change
when viewed separately, it is not size, nor foreign sales, nor
sourcing between suppliers in different countries’.
foreign subsidiaries that determines the willingness and ability of a firm to react to changes in exchange rates by exercis-
Factors behind real options usage
ing real options. Rather, it is a combination of the three vari-
The likelihood that real options are exercised within a time
ables. A firm has to be large (ability) to have many foreign sub-
horizon of two to three years and in response to changes in
sidiaries (ability) and to be exposed (willingness) in order to
exchange rates varies markedly among the firms in this study.
react to changes in exchange rates by exercising real options.
At least three factors are candidates for explaining this varia-
70 - The
tion: Size, foreign sales ratio, and geographical coverage of
We conduct regression analysis using an ordered probit
subsidiaries. We discuss this next.
regression to examine the significance of the four variables
5 ‘Multinationality’ is the square root of (log total assets times foreign sales/total
sales times the square root of the number of foreign countries in which the firm
has subsidiaries).
(i.e., size, foreign sales ratio, geographical coverage, and the
In pursuit of flexibility
combination variable, multinationality) in explaining the
The ability to react to changes in exchange rates by exercising
extent of real options usage. The dependent variable is the
real options depends on the set-up of the firm. A firm that
extent of options usage and ranges from 0 to 7 according to
keeps contact and business relations with various suppliers in
the number of real options likely to be exercised as shown in
different countries should experience, at most, only minor
Figure 2. We also include economic sector variables in the
obstacles when changing suppliers. Likewise, a company that
regression analysis. Overall, while we do not find statistically
has production facilities in several countries and excess capac-
significant coefficients for the three variables when analyzed
ity in these facilities should also experience, at most, only
separately, the combination variable multinationality, which
minor obstacles when moving production from one country to
captures the interaction between size, foreign sales and geo-
another. More generally, a firm with international experience
graphical coverage, is statistically significant in explaining the
and presence will be more flexible in exploiting the risk reduc-
extent of options usage. The analysis suggests that the use of
ing and opportunity enhancing possibilities that the fluctua-
real options in relation to changes in exchange rates depends
tions in exchange rates create.
6
on the combined existence of a certain size, a certain exposure, and a certain range of foreign subsidiaries. In other
words, just being a large firm, a firm heavily exposed to
changes in exchange rates, or a firm with an extensive net of
foreign subsidiaries is not sufficient.
Number of firms
Percentage of firms
Average number of real options
likely to be exercised
None
Partly
Almost fully
20
39%
28
55%
3
6%
0.5
3.3
2.0
We also find that firms in Materials and in Consumer
Discretionary tend to be statistically significantly more
Figure 3: Extent to which flexibility is sought8
inclined to exercise real options in response to changes in
exchange rates than firms in other sectors. However, due to
The level of flexibility is not just a by-product or something
the limited number of sample firms in each economic sector,
granted from above. It is also a result of discretionary actions
we do not want to overemphasize this finding. Nevertheless,
taken by each firm. Figure 3 shows the extent to which sample
the finding that firms in Materials are more inclined to exer-
firms pursue a strategy of being flexible. As we can see, 55
cise real options in reaction to fluctuating exchange rates is
percent of the firms partly pursue a strategy of being flexible,
supported by empirical evidence on U.S. firms.7 Furthermore,
6 percent of the firms pursue a full (or almost full) strategy of
economic intuition is supportive. The CIGS Materials econom-
being flexible, and 39 percent of the firms do not seek flexibil-
ic sector includes commodity-related manufacturing indus-
ity. There is a close relationship between the extent to which
tries, such as Chemicals, Construction Materials, Containers &
flexibility is sought and the likelihood that the firm will react to
Packaging, Metals and Mining, and Paper & Forest Products. In
changes in exchange rates by exercising real options. While
these industries firms face a high degree of uncertainty, espe-
the firms that partly pursue a strategy of being flexible on
cially in the form of volatile commodity prices. To survive in
average consider more than three real options likely to be
such an environment, firms must be able to react to risk fac-
exercised due to exchange rate changes, the corresponding
tors by all means including the exercise of real options.
figure for the group of firms that do not seek flexibility is as
low as 0.5. The small group of firms that pursue a strategy of
6 For more information on the ordered probit regression method, see Greene,
William H. (2000), Econometric Analysis (4th Edition), Prentice Hall: New Jersey,
pp 875-879 or Pindyck, Robert S. and Daniel L. Rubinfeld (1997), Econometric
Models and Economic Forecasts (4th Edition), McGraw-Hill Inc: New York.
7 Carter, D., C. Pantzalis, and B. J. Simkins, 2003, “Asymmetric exposure to foreignexchange risk: financial and real option hedges implemented by U.S. multinational
corporations,” Proceedings from the 7th Annual International Conference on Real
Options: Theory Meets Practice, Washington D.C. The authors suggest that companies operating in industries with greater commodity-type inputs and outputs have
a greater ability to employ real option strategies.
8 The question asked is: ‘Exchange rates and business conditions change. In such
circumstances, it may be profitable to improve flexibility partly at the expense of
economies of scale (i.e. by having two minor production outlets in two different
countries instead of one production outlet in one country; keeping contact with
several suppliers in different countries instead of few suppliers in few countries;
and by keeping options open by continuing to sell in markets that are not profitable at the present exchange rates). To what extent does your firm pursue a
strategy of being flexible (at the expense of economies of scale)?’ The respondents were asked to choose between ‘none’, ‘partly’, or ‘almost fully’. One sample
firm chose not to answer this question.
71
almost full flexibility illustrates that the picture of a clear linear relationship is not without deviations. The strong relationship between the extent to which flexibility is sought and the
likelihood that the firm will react to changes in exchange rates
by exercising real options is confirmed by regression analysis.
Conclusion
This study of the exchange rate exposure management of
Danish non-financial firms shows that decisions on whether or
not to financially hedge such an exposure is dependant on the
ability of the firms to react to changes in exchange rates by
exercising real options. Furthermore, the study shows that the
combined interaction of a firm’s size, foreign sales, and foreign
subsidiaries, as well as the firm’s managerial emphasis on flexibility, are important to real options usage. The results are
important in understanding the degree to which a firm may
react to changes in exchange rates by exercising real options.
Although the conclusions are based on Danish firms, we
believe that the generality of the findings can be extended to
a wide range of firms in countries with open economies.
72 - The
Mergers and acquisitions as
a response to economic change
Bart M. Lambrecht
Professor of Finance, Lancaster University Management School
What causes mergers and acquisitions (M&A)? This is an issue
of scale with respect to transportation costs and the develop-
that still remains to some extent a puzzle. While we can, of
ment of a national economy.
course, come up with a story or motive for each individual
merger or takeover case, finance theory has not quite man-
As in the first merger movement, the second wave of mergers
aged yet to formulate a coherent theory that is generally
also began with an upturn in business activity in 1922 and
applicable.
ended with the economic slowdown in 1929. As for the motivational factors Markham (1955) emphasized major develop-
Mergers as a response to economic change
ments in transportation (more consumer mobility through
One good starting point for the development of a reasonable
motor vehicles and automobiles), communication (more prod-
theory is to consider first historical and empirical evidence.
uct differentiation through national-brand advertising with
When one considers M&A activity over the past century then
the rise of home radios) and merchandising (mass distribution
a first striking observation is that it is not constant over time.
with low profit margins). These developments caused an
Instead M&A activity seems to occur in waves. There are peri-
increase in the scale of operations and hence encouraged
ods of high and low takeover activity. This leads us to the ques-
mergers. The second wave consisted mainly of vertical merg-
tion why there are regime shifts in takeover activity. The most
ers. The advantages were related to technological economies,
plausible answer is that a change in takeover activity is caused
such as shortening processes or reliability of input supply.
by a change in the economic environment within which firms
are operating.1 This brings us to the key proposition of this
Merger activity reached its then historically highest level
article, namely the idea that M&A activity occurs in response
during the three year period of 1967 to 1969. The period was
to economic change. This inevitably prompts the next ques-
also one of a booming economy. The number of mergers
tion: What kind of economic change causes M&A activity?
declined sharply as the economic activity slowed down from
Historical and empirical evidence may again shed some light
1970 onwards leading ultimately to the recession linked to
on the matter.
the 1973 oil crisis. Most mergers in the sixties were conglomerate mergers.2
Merger waves
There were five main merger waves in the 20th century. These
A fourth peak of merger activity was reached during the years
waves typically coincided with economic expansion, booming
1988 and 1989. This was the era of raiders and leveraged buy-
stock markets, and fundamental changes to the economic
outs. The fifth merger wave started in 1993 and slowed down
environment, often under the form of technological innovation
after the collapse of the Internet bubble in 2000. The mergers
leading to higher economies of scale and larger geographical
boom in the eighties and especially the nineties coincided with
markets.
strong economic growth, rising stock markets, and advances
in telecommunication and computer technology. These tech-
The merger movement in the U.S. at the turn of the century
nological advances resulted in an economy where firms were
(1895-1904) consisted mainly of horizontal mergers and coin-
operating on a global level. The advent of the Internet brought
cided with a period of rapid economic growth which ended
with it the so called ‘new economy’ and gave the concept of
with the onset of an economic recession in 1903. Weston et al.
returns to scale a new dimension. Globalization has surpris-
(1990) comment that this wave was driven by major changes
ingly not led to a substantial number of cross-border acquisi-
in economic infrastructure and production technologies, such
tions. Improvements in technology and communications stim-
as the advent of electricity and the completion of the
ulated takeover activity particularly in banking, insurance,
transcontinental railroad system. The latter led to economies
media, and telecommunications.
1
2 Ravenscraft and Scherer (1987) note that many mergers and acquisitions during
the 1960s were disappointing and were subsequently broken up in the 1980s.
An alternative explanation, which we do not pursue in this paper, might be that
merger waves are driven by some kind of herding behavior. The origin of this
herding behavior could be informational or behavioral in nature.
73
While most of the above discussed economic shocks seem to
The pro-cyclicality of merger activity
be affecting the economy as a whole, this is not necessarily
The above argument by Brealey and Myers points to another
always the case. Regulatory changes, for example, may affect
empirical feature of M&A activity. Apart from the fact that
one particular industry and trigger a series of mergers in that
mergers seem to occur in waves, a second notable feature is
industry alone. For example, in 1999 the Financial Services
that merger activity is pro-cyclical, in that we observe more
Modernization Act in the U.S. repealed the 1933 Glass-Steagall
mergers during economic booms than during economic
Act that forced investment banks, commercial banks, and
recession.
insurance companies to be separate entities. This regulatory
change may have contributed to the recent wave of mergers
A recent paper by Maksimovic and Philips (2001) provides fur-
in the banking industry.
ther evidence on the procyclicality of merger waves. Analyzing
the market for corporate assets, they find that over the peri-
Empirical evidence confirms that merger activity is related to
od 1974-1992, on average, 3.89% of plants change ownership
shocks to the economic environment in which firms are oper-
each year. In expansion years, close to 7% of plants annually
ating. Mitchell and Mulherin (1996) studied industry-level pat-
change ownership. They found mergers and acquisitions to be
terns in takeover and restructuring activity during the 1982-
strongly procyclical, rising in periods of economic expansion
1989 period. Across 51 industries, they find significant differ-
and falling during recessions. There is still very little theoreti-
ences in both the rate and time-series clustering of these
cal evidence as to why merger activity should be procyclical.
activities. They find that the inter-industry patterns in the rate
One exception is Lambrecht (2004) who analyzes the case of
of takeovers and restructurings are directly related to eco-
mergers motivated by economies of scale. In his model, the
nomic shocks borne by the sample industries.
surplus (synergies) that firms receive from merging is generated by economies of scale: by combining their production
Theoretical models attempting to explain takeover waves are
facilities firms can produce more than the combined produc-
very rare. One notable exception is Gort’s (1969) ‘economic
tion when they each operate individually. The extra units of
disturbance theory’. Gort (1969) argues that at certain times
output that are created by merging can be sold at a stochas-
shareholders have differing opinions as to the true value of a
tic product price. The surplus from merging is therefore not
share because of imperfections in the information available
only stochastic, but it is also procyclical: it rises (falls) in peri-
and how it is assessed. These differences in valuation lead to
ods of high (low) product market demand.
takeover transactions. According to Gort, valuation differences are greater at times of dramatic change, such as rapid
Upon merging, each firm incurs a fixed merger cost. Since this
movements in stock prices, changes in technology, and in the
is a sunk cost it introduces an element of irreversibility into
relative price of energy.
the merger, and the decision to merge is therefore similar to
3
the exercise of a call option. When merging, both companies
74 - The
Brealey and Myers (2002) acknowledge that takeovers may
therefore have to trade off the stochastic benefit of merging
result from mistakes in valuations on the part of the stock
against the cost of merging. Since both firms have the right,
market, but argue that mistakes are made in bear markets as
but not the obligation to merge, each firm’s payoff resembles
well as bull markets, and wonder therefore why we do not see
an option and the decision to merge resembles the exercise of
just as many firms hunting for bargain acquisitions when the
an option. The higher profits that firms forgo by not merging
stock market is low. They conclude that ‘it is possible that
act as an incentive to exercise this option, while the (at least
suckers are born every minute, but it is difficult to believe that
partially) irreversible nature of the merger acts as an incentive
they can be harvested only in bull markets’ (p. 967).
to delay. The optimal merger timing strikes a balance between
3 A more recent paper by Shleifer and Vishny (2001) also assumes that the stock
market may misvalue potential acquirers, potential targets and their combinations.
Managers of the firms understand stock market inefficiencies, and take advantage
of them, in part through merger decisions. The takeover surplus and merger
waves are driven by the relative valuations of the merging firms.
the two. Since the gains from mergers motivated by
Counter-cyclical takeover activity
economies of scale are positively correlated to product market
While the above discussion emphasized the fact that merger
demand, mergers happen in rising product markets. This cre-
waves are pro-cyclical, this does not mean that no takeover
ates merger activity at high output prices and merger inactiv-
activity takes place in economic downturns [as was previously
ity at low output prices. Cyclical product markets will therefore
illustrated by the empirical evidence of Maksimovic and Philips
generate a pattern of merger waves with mergers being pro-
(2000)]. However, the type of takeovers in booms versus
cyclical.
recessions may be quite different. While in booms takeovers
may be expansive in nature, during recessions takeovers are
Lambrecht (2004) also examines whether mergers take place
more likely to be consolidating or contractive in nature. For
at the efficient time when both firm act in a non-cooperative
example Lambrecht and Myers (2004) study a category of
way. Each party holds a call option on a fraction of the
takeovers that happen during downturns, namely takeovers
enlarged firm (i.e. the ownership share each party has in the
motivated by agency problems and disinvestment. They argue
new, combined firm) with the strike price being the sum of its
that when the market declines firms may have certain assets
fixed merger cost and the standalone value of its existing firm.
that become unproductive and that ought to be sold off with
The merger can only take place if both parties agree on the
the proceeds going to shareholders. Management may, how-
timing of the merger (i.e. at what product price level the merg-
ever, be reluctant to do this and may prefer to keep the assets
er should happen) and the terms of the merger (i.e. the post-
within the firm (even if these assets do not provide sharehold-
merger ownership share of each party in the new firm).
ers with a sufficient return). Those inefficiencies create a role
for takeovers. A raider or hostile acquirer could take over the
It follows that, unlike financial options, the exercise of ‘merger
firm and create value by selling off some of the firm’s assets,
options’ is also influenced by strategic considerations since
returning the proceeds to shareholders, and by putting the
the payoff to each firm ultimately depends on the post-merg-
firm on a ‘diet deal’.
er ownership share it obtains in the new firm. The restructuring mechanism (i.e. how the merger gains are divided up) can
While the takeovers studied by Lambrecht and Myers (2004)
therefore also influence the timing of the restructuring. The
are primarily driven by agency problems, one can, of course,
paper considers two different mechanisms, namely friendly
also observe takeovers in downward markets that are driven
mergers and hostile takeovers, and shows that ceteris paribus
by other considerations such as cost cutting, taxes, misvalua-
they should occur at different stages in a merger wave.
tion, or where takeovers are an alternative to (costly) bankruptcy. Much research still needs to be done in those areas.
Since mergers are modelled as an investment decision, the
model also allows us to analyze the determinants of this deci-
Conclusion
sion. For example, the model predicts that a lower interest
Empirical evidence suggests that merger activity happens in
rate, higher synergy benefits, higher economic growth, and
response to economic shocks. Furthermore, mergers tend to
reduced economic uncertainty (volatility) speed up and stim-
happen in waves and are pro-cyclical: merger activity is high-
ulate merger activity. This is consistent with empirical evi-
er during economic booms than during recessions. To date
dence. Melicher et al. (1983) examining the period 1947-1977
there is still no theory that fully explains merger activity.
find support for viewing changes in aggregate merger activity as a capital market phenomenon. In particular, increased
merger activity is associated with higher stock prices and
lower interest rates.
75
References
• Brealey, R. A., and S. C. Myers, 2002, Principles of Corporate Finance. McGraw-Hill,
Boston, MA, seventh edition.
• Gort, M., 1969, “An economic disturbance theory of mergers,” Quarterly Journal of
Economics, 83:4, 624-642.
• Lambrecht, B. M., 2004, “The timing and terms of mergers motivated by economies
of scale,” Journal of Financial Economics, 72:1, 41-62.
• Lambrecht, B. M., and S. C. Myers, 2004, “A theory of takeovers and disinvestment,”
University of Lancaster, Lancaster.
• Maksimovic, V., and G. Philips, 2001, “The market for corporate assets: Who engages
in mergers and asset sales and are there efficiency gains?” Journal of Finance,
56:6, 2019-2065.
• Markham, J. W., 1955, “Survey of evidence and findings on mergers,” in Business
Concentration and Price Policy. Princeton University Press, Princeton, New Jersey
• Melicher, R. W., J. Ledolter, and L. J. D’Antonio, 1983, “A time series analysis of
aggregate merger activity,” Review of Economics and Statistics, 65:3, 423-430.
• Mitchell, M. L., and H. Mulherin, 1996, “The impact of industry shocks on takeover
and restructuring activity,” Journal of Financial Economics, 41, 193-229.
• Ravenscraft, D. J., and F. Scherer, 1987, “Mergers, sell-offs, and economic efficiency,”
The Brookings Institutions, Washington, D.C.
• Shleifer, A., and R. W. Vishny, 2003, “Stock market driven acquisitions,” Journal of
Financial Economics, 70:3, 295-311.
• Weston, J. F., K. S. Chung, and S. E. Hoag, 1990. Mergers, restructuring, and corporate control. Prentice Hall International, Englewood Cliffs, New Jersey.
76 - The
Valuing real options:
Frequently made errors
Pablo Fernández, PricewaterhouseCoopers Professor of Corporate
Finance, IESE Business School – University of Navarra
There are many approaches used to valuing real options, many
has the option of expanding its production facilities or cancel-
of which have serious inherent problems. The objective of this
ing distribution, depending on the market’s future growth.
paper is to highlight some of these errors. Perhaps the best
Investments in research and development can also be analyzed
way of doing so is through an example. I will, therefore, ana-
using options theory [Grenadier, S. and A. Weiss (1997)].
lyze Damodaran’s proposal to value the option to expand the
business of Home Depot and discuss some of the errors and
Corporate policy strategists and professors have repeatedly
problems of this and other approaches.
reproached finance — and financial analysts — for their lack of
tools for valuing investment projects’ strategic implications.
The formulas used to value financial options are based on risk-
Before using options theory, most new investments were
less arbitrage (the possibility of forming a portfolio that pro-
made solely on the basis of qualitative corporate policy crite-
vides exactly the same return as the financial option) and are
ria. The numbers, if any, were crunched afterwards so that
very accurate. However, we will see that very rarely does it
they could give the results that the strategist needed to back
make sense to use these formulas directly to value real
his decision. Options theory seems to enable projects’ strate-
options because real options are hardly ever replicable.
gic opportunities to be valued. By combining quantitative
However, we can modify the formulas to take non-replicability
analysis of the options with qualitative and strategic analysis
into account.
of the corporate policy, it is possible to make more correct and
more rational decisions about the firm’s future. Not consider-
Some problems we encounter when valuing real options are
ing the options contained in a project may lead us to under-
the difficulties faced in communicating the valuation due to its
value it and, in general, turn down projects that we should
higher technical complexity than the present value, in defining
undertake.1
the necessary parameters for valuing real options, in defining
and quantifying the volatility of the sources of uncertainty, in
One classification of real options is provided in Figure 1.
calibrating the option’s exclusiveness, and in valuing the
options adequately. In any case, their valuation is much less
accurate than the valuation of financial options.
Real options
Contractual options
Growth or learning options
Oil concessions
Expand
Defer the investment
Mining concessions
Research and development
Downsize the project
Franchises
Acquisitions
Alternative uses
New businesses
Renegotiations
of contracts
It is not possible to correctly value a firm or a project that pro-
Flexibility options
vides some type of future flexibility — real options — using the
New customers
Outsourcing
traditional techniques for discounting future flows (NPV or
Internet venture
Abandon
Greater efficiency in
increasing entry barriers
Modification of
products
IRR). There are many types of real options: options to exploit
mining or oil concessions, options to defer investments,
options to expand businesses, options to abandon businesses,
Figure 1: Real options
options to change the use of certain assets, etc.
People also talk about compound options, which are those
A real option exists in an investment project when there are
that provide new options when they are exercised. Rainbow
future possibilities for action and when the solution to a cur-
options is the term used to describe those that have more
rent uncertainty is known. Oil concessions are a typical exam-
than one source of uncertainty, for example, an oil concession
ple. The oil well will be operated or not depending on the future
in which the uncertainty arises from the price of oil, an uncer-
price of oil. Designing a new product is also a real option. A firm
tain quantity of barrels, and uncertain extraction costs.2
1
2 For a compilation of the different types of real options, see the books published by
Trigeorgis (1996), and Amram & Kulatilaka (1999), both with the same title: Real
Options.
Similarly, if the projects we are considering contain options that may be exercised
by third parties (the future flexibility plays against us), non-consideration of the
options contained by the projects will lead us to invest in projects that we should
turn down.
77
Frequently made errors when valuing real options
— the example
Home Depot is considering the possibility of opening a store in
obvious that the option to open a second store is not
replicable.3
■ The estimation of the option’s volatility is arbitrary and
France. The store’s cost will be €24 million and the present
has a decisive effect on the option’s value — Damodaran’s
value of the expected cash flows is €20 million. Consequently,
hypotheses regarding volatility (28.3%), present value of
the project’s value will be –€4 million and it would not be a
the expected cash flows (30 million), the option’s life
good idea. However, Home Depot believes that by opening this
(5 years) and the option’s replicability (μ = ln(r) – σ2/2 =
store, it will have the option to open another larger store in the
1.82%) are synthesized in the distribution of the expected
next 5 years. The cost of the hypothetical second store would
cash flows in 5 years’ time shown in Figure 2.4
be €40 million and the present value of the expected cash
flows is €30 million, although there is a lot of uncertainty
It is obvious that a volatility of 28.3% per year means assum-
regarding this parameter. Home Depot estimates the volatility
ing an enormous scatter of cash flows, which is tantamount to
(s) of the present value of the expected cash flows of the sec-
having no idea what those cash flows may be. One thing is that
ond store at 28.3%. Damodaran (2000) proposes valuing the
a greater uncertainty increases real options’ value and anoth-
option to open the second store using Black and Scholes’ for-
er altogether that real options may have a high value (i.e. must
mula. According to him, the option of opening the second
undertake projects) because we have not the slightest idea of
store is a call with the following parameters:
what may happen in the future. Figure 2 also shows the shape
of two distributions with annual volatilities of 15%.
Option of opening the second store = Call (S=30; K=40; r =
1.06; t = 5 years; σ = 28.3%) = €7.5 million
■ As there is no riskless arbitrage, the value of the option
to expand basically depends on Home Depot’s expectaConsequently, according to Damodaran, Home Depot should
tions about future cash flows — Damodaran assumes that
open the store in France because the project’s present value
this parameter does not influence the option’s value
plus the value of the option to expand is –€4 + €7.5 = €3.5 million. Some of the errors and problems of this approach are:
because he assumes that the option is replicable.
■ It is not appropriate to discount the expected value of
the cash flows at the risk-free rate (as is done implicitly
■ Assuming that the option is replicable — This is why Black
when Black and Scholes’ formula is used) — Although a
real option will be exercised when a future uncertainty is
and Scholes’ formula is used in the valuation. It is fairly
settled (in this case, if the first store is a success), this
does not mean that it is a risk-free project. The present
0,04
value of the cash flows (€30 million in the above example)
μ = 1,82%, σ = 15%
0,03
is calculated using a rate that reflects the estimated risk
μ = 1,82%, σ = 28,3%
today. Once the outcome of the first store is known, if it is
0,02
a failure, the second store will not be opened; if it is a
μ = 8%, σ = 15%
success, the second store will be opened, but the project
0,01
of opening the second store will still have risks: the uncer-
0,00
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
Value of expected flows in year 5 (million euros)
Figure 2: Distribution of the expected cash flows in 5 years’ time according to
Damodaran
78
3 To get around the non-replicability issue, Amram and Kulatilaka define real options
as ‘the subset of strategic options in which the decision to exercise the option is
basically determined by financial instruments or assets traded on markets’. The
problem is that, according to this definition, only a few oil and mining concessions
would be real options. See page 10 of Amram and Kulatilaka (2000).
tainty of costs and sales in five years’ time may be greater
or less than that estimated today. Therefore, the cash
flows must be discounted at a rate greater than the riskfree rate.
4 Another way of expressing the scatter is that Damodaran assumes that the value
of the expected cash flows in 5 years’ time will lie between 22 and 79 with a probability of 66%; and between 12 and 149 with a probability of 95%.
■ Damodaran’s valuation assumes that we know exactly
■ If they are not replicable, by any of the above methods but
the cost of opening the second store and that it will be
taking into account the non-replicability. For example, it is
€40 million — Obviously, there is uncertainty as to how
not possible to apply Black and Scholes’ formula but
much it will cost to open a store in five years’ time. The
rather a modified formula that takes into consideration
formula used assumes that the risk of the opening cost is
the expected value of the uncertainties and uses a
equal to the risk of the cash flows generated by opening
discount rate higher than the risk-free rate [Fernandez
the store, which is not entirely correct. Normally, the cash
(2002, chapter 22)].
flows generated by opening the store will have a greater
risk than the opening cost and should be discounted at a
The factors that determine the value of a financial option are
higher rate.
different from those that affect a real option. These differ-
■ Another error is to assume that the options’ value
ences in the parameters are shown in Figure 3.
increases when interest rates increase — For example,
Leslie and Michaels (1997) say that ‘an increase in interest
If the real options cannot be replicated, using financial
rates increases the option’s value, in spite of its negative
option formulas is completely inappropriate for valuing real
effect on the net present value, because it reduces the
options, as all the formulas are based on the existence of a
present value of the exercise price’. This is wrong because
replicate portfolio. The logic of options theory is based on
the negative effect of increased interest rates on the pres-
arbitrage: as it is possible to form a replicate portfolio that will
ent value of the expected cash flows (as on the value of
have exactly the same return as the option we are trying to
shares) is always greater than the positive effect of the
value, (in order to avoid arbitrage) the option must have the
reduction of the present value of the exercise price.
same value as the replicate portfolio. If it is not possible to
form the replicate portfolio, this reasoning loses its entire
Applying options theory in a firm
basis.
Real options can be valued using the following methods:
In the following paragraphs, we have included a number of
■ If they are replicable, use Black and Scholes’ formula, the
formulas developed for valuing exotic options, by simula-
considerations on the practical application of options theory
to the analysis of investment projects.
tion, the binomial formula, or by solving the differential
equations characterizing the options.5
■ High interest rates mean high discount rates, which
reduces the present value of future flows. Obviously, this
Financial call option
Real call option
Share price
Exercise price
Risk-free interest rate
Share’s volatility
Time to exercise
Dividends
Expected value of cash flows
Cost of investment
Discount rate with risk
Volatility of expected cash flows
Time to exercise
Cost of holding the option
Its value does not depend on the
expected appreciation of the
underlying asset
Its value does depend on the expected
appreciation of the underlying asset
Figure 3: Parameters that influence the value of a financial option and of a real
option
5 It is important to realize that Black and Scholes’ formula interpreted as net present value considers μ = 0.379% = ln(r) – σ2/2 and discounts the option’s expected
value E[Max(S-K,0)] with the risk-free rate r.
should decrease the value of the option to undertake a
project. However, high discount rates also reduce the present value of the option’s exercise price. This compensatory
effect helps sustain the option’s value when interest rates
increase, which may give certain types of projects — particularly growth options — an enormous value that should
be taken into account when analyzing investments.
■ Kester (1984) suggests one feature of options that should
be considered, the extent to which the holder of an option
has an exclusive right to exercise it. Unlike share options,
there are two types of growth option, exclusive and
79
shared. The former are the more valuable because they
immediate decision on the entire project from those in
These options derive from patents, unique knowledge of
which there is decision flexibility in the future. Finally, the
the market held by the firm, or technology that its com-
firm must ask itself if it can realize all the option’s bene-
petitors cannot imitate. Shared growth options are less
fits or whether they will also be available for other com-
valuable. They represent ‘collective’ opportunities held by
petitors.
the industry, such as, for example, the possibility of enter-
■ When examining investment opportunities from the
ing a market that is not protected by high entry barriers
option valuation viewpoint, managers will find it easier to
or of building a new factory to supply a particular geo-
recognize that: (a) the conventional NPV may undervalue
graphical segment of the market. Cost reduction projects
certain projects by eliminating the value of the options
are normally shared options, because, as a general rule,
already existing in the project; (b) projects with a nega-
they can also be undertaken by competitors.
tive NPV can be accepted if the value of the option asso-
■ Kester also suggests that when analyzing investment
ciated with future flexibility exceeds the NPV of the pro-
projects, firms should classify the projects in accordance
ject’s expected cash flows; and (c) the extent of the
with the options they include. The classification using the
undervaluation and the degree to which managers can
traditional criteria of replacement, cost reduction, capaci-
justifiably invest more than what the conventional rules
ty increase, and new product introduction is not very use-
regarding the NPV would indicate can be quantified using
ful. A more appropriate classification would be to distin-
options theory.6
guish between projects whose future benefits are mainly
■ The options framework indicates that the value of the
generated through cash flows (simple options) and those
management’s future flexibility is greater in more uncer-
that include subsequent investment options (compound
tain environments. This value is greatest in periods with
options). Simple growth options, such as routine cost
high interest rates and availability of the investment
reductions and maintenance and replacement projects,
opportunities for extended periods. Consequently, contra-
only create value through the cash flows generated by
dicting generally held opinion, greater uncertainty, high
the underlying assets. Compound growth options — such
interest rates, and more distant investment horizons
as research and development projects, a major expansion
(when part of the investment can be deferred) are not
in an existing market, entry in a new market, and acquisi-
necessarily harmful for an investment opportunity’s
tions (of new businesses or firms) — lead to new invest-
value. Although these variables reduce a project’s static
ment opportunities and affect the value of the existing
NPV, they can also increase the value of the project’s
growth options. Given their complexity, their role in giving
options (value of management flexibility) to a level that
shape to the firm’s strategy, and their impact even on the
organization’s survival, compound options require a deep-
80 - The
■ The firm must separate the projects that require an
give their holder the exclusive right to exercise them.
may counteract the previous negative effect.
■ A real option will only be valuable if it provides a sustain-
er analysis. The firm must view these projects as part of a
able competitive advantage. This competitive advantage
larger group of projects or as a series of investment deci-
basically depends on the nature of the competitors (nor-
sions that follow a time continuum. In light of the firm’s
mally, if competition is fierce and the competitors are
strategy, its executives must ask themselves whether a
strong, the advantage’s sustainability will be less) and on
particular option will provide suitable investment oppor-
the nature of the competitive advantage (if it is a scarce
tunities in the appropriate markets, within a suitable time
resource, for example, scarce buildable land, the advan-
frame, that are matched to their firm’s needs.
tage’s sustainability will be greater).
6 For a good study on the application of real options to mining companies, see Moel
and Tufano (2002).
References
• Amram M., and N. Kulatilaka, 2000, “Strategy and shareholder value creation: The
real options frontier,” Journal of Applied Corporate Finance, 13:2, 8-21
• Amram, M. and N. Kulatilaka, 1999, “Real Options,” Harvard Business School Press
• Damodaran, A., 2000, “The promise of real options”, Journal of Applied Corporate
Finance, 13:2
• Damodaran, A., 1999, “The promise and peril of real options”, Working Paper, Stern
School of Business
• Fernandez, P., 2002, “Valuation and shareholder value creation,” Academic Press.
San Diego, CA
• Grenadier, S. and A. Weiss, 1997, “Investment in technological innovations: An option
pricing approach”, Journal of Financial Economics, 44, 397-416
• Kester, W. C., 1984, “Today’s options for tomorrow’s growth”, Harvard Business
Review, March-April, 153-160
• Leslie, K. J. and M. P. Michaels, 1997, “The real power of real options”, The McKinsey
Quarterly, Number 3, 5-22
• Luehrman, T. A., 1995, “Capital projects as real options: An introduction”, Harvard
Business School, 9-295-074
• McDonald R., and D. Siegal, 1986, “The value of waiting to invest”, Quantitative
Journal of Economics, 101, 707-727
• Tufano, P., and A. Moel, 2002, “When are real options exercised? An empirical study
of mine closings”. Review of Financial Studies 15:1, 35-64
• Margrabe, W., 1978, “The value of an option to exchange one asset for another”,
Journal of Finance, 33:1, pp. 177-198.
• Trigeorgis, L., 1996, Real Options, The MIT Press
81
Real options
Real options and
flexibility
Thomas E. Copeland
Managing Director of Corporate Finance,
Monitor Group, and Senior Lecturer,
Sloan School of Management, MIT
Abstract
Never heard of real options? It is a new technique for making
large investment decisions that will replace Net Present Value
as the dominant tool. In a survey of 4,000 U.S. based CFOs,
fully 27 percent said that they always or almost always used it
for important capital expenditures. Real options captures the
value of flexibility and gives you trigger points that tell you
when to take action — to develop an oil field, to stop a research
and development effort, to get out of a business, to expand a
business, or to turn on and off a peak load power plant. This
article gives several examples of how real options have turned
the tide of sentiment for or against strategic investments.
83
A better decision-making tool is invented only a few times
evolved in the future. After all, that is what it means to man-
each century, and each advance goes farther to capture
age something. All of this flexibility is ignored when one esti-
human intuition and sometimes to improve it. Every year tril-
mates the expected cash flows of a project. Depending on the
lions of dollars are either invested in major capital projects or
winds of fortune the project may do better than expected. If
withheld from investment. Net present value (NPV) is the tool
so, management can change course and spend additional
that is currently used most often for these decisions. It has
funds to expand the project to take advantage of greater
been recommended for 50 years by graduate schools of man-
demand, or to extend its life. These actions are conditional on
agement throughout the world. But now it is being replaced by
favorable states of nature within which they will be exercised,
a new tool called real options analysis (ROA). This article
because the value captured, given the state of nature, is
explains why CFOs are changing from NPV to ROA, gives some
greater than the cost of the additional investment (the exer-
ROA examples based on actual business applications, and dis-
cise price of a real option). In less favorable states of nature
cusses some of the new implications of ROA for the financing
they will not be exercised.
of companies.
What we have just described are two types of real option —
Why real option analysis is replacing NPV
expansion and extension of the life of a project. A real option
In a recent survey of 4,000 chief financial officers of U.S. com-
is the right, but not the obligation, to take an action in the
panies, when asked whether they were familiar with real
future contingent upon information that resolves (completely
options, fully 27% of the respondents answered that for major
or partially) an uncertainty. Most projects have call options like
capital investment decisions they always or almost always used
expansion or extension to capture the value of an opportunity
real options [Graham and Harvey (2001)]. Industries where the
by paying an additional amount of money, called the exercise
use of ROA is common include aerospace, oil and gas, comput-
price. They also have put options to shrink a project or to
ers, pharmaceuticals, high tech, and power generation.
abandon it altogether and receive an amount of cash, also
called the exercise price. Finally, many projects can be
They are switching away from NPV because it fails to capture
deferred and that too is a valuable option.
flexibility of decision-making. All it does is estimate the
expected future cash flows of the project (including its oper-
Every project has at least five real options, five types of flexi-
ating profit after taxes, depreciation tax shield, capital expen-
bility, built in. The NPV methodology ignores all of them.
ditures, and working capital requirements), discounts them
Therefore, after over 30 years as a teacher of corporate
back to the present at the weighted average cost of capital,
finance at UCLA, NYU, MIT, and Harvard, I have reached the
and subtracts the initial capital outlay. If the NPV is negative,
point of view that the NPV method provides an estimate of the
executives who review the project are supposed to reject the
value of a project without flexibility, and consequently it sys-
capital spending request. But in my years as a professor and
tematically undervalues every project, with the only question
consultant, I have seen many negative NPV projects accepted
being by how much. For high positive NPV projects the value
by senior management for so-called ‘strategic reasons’. In
of flexibility may be low simply because the project should
other words, the wisdom of experienced managers out-
move forward as quickly as possible, no optionality is neces-
weighed the quantitative result of the NPV technique.
sary. For highly negative NPV projects, no amount of flexibility can save them. But for projects that are close decisions,
84 - The
One senior executive explained his objection to NPV this way.
their flexibility can swing the answer from negative to positive.
In his role as manager, he had the flexibility to manage the risk
I have seen real options change the answer several hundred
of the project by steering it, or changing its course, as it
percent.
One of the first real option cases that I worked on serves to
Notice that since the spread between the price of coal and the
illustrate another shortcoming of NPV, namely that it forces
cost of extraction is positive now and since it continues to
one to compare false mutually exclusive alternatives. An
grow, all 5 NPV estimates are positive. ROA is a more sophis-
Australian company was about to bid on a government lease
ticated approach because it models not only the expected
that would give the winning bidder the exclusive right to devel-
price but also the variability of that price. As the price goes up
op and extract coal from a proven reserve. Like most leases of
or down, the value does too. When the valuation is done we
this type, development did not have to start immediately but
start at the back of the tree, i.e. in year 5, and determine what
if it did not start within five years, the lease would revert to the
states of nature would have a coal price high enough to devel-
government. At the time of bidding the price per ton of coal
op the lease property. These are the states where we would no
was only U.S.$1 higher than the extraction cost, so no one was
longer defer (D), but would exercise our option to invest (I). In
sure that the lease property should be developed immediate-
all other states we would defer any investment. Next, we would
ly. A one dollar drop in the price could wipe out all profit while
move to year 4 and examine the deferral decision in each state
a one dollar increase would double it. The company analyzed
— deciding whether we are better off deferring or investing. In
five mutually exclusive alternatives using the NPV method,
this way we work back in the tree to its root — where we have
namely develop immediately, after one year, after two, and so
an estimate of the value of the project with the right to defer
on. It estimated that the highest value alternative was worth
as well as decision rules made up of trigger prices that would
about U.S.$59 million. However, rumor had it that this bid
cause us to invest in a given year.
would be too low. Upon rethinking the problem, the management decided to use real option analysis because they were
NPV logic forces us to assume that we develop for sure in a
paying not only for the developed lease but also for a five year
given year then compares the resulting mutually exclusive
deferral option that would give them the right to first see how
alternatives. ROA provides a single value, not 5, and that value
the price of coal would change and then decide whether to
represents the value of the project with the flexibility to defer
develop the lease. Given the volatility of coal prices the proj-
the investment until the time when the price of coal goes high
ect with the right to defer turned out to be a little over
enough to trigger the exercise of our option by spending the
U.S.$100 million.
money to develop the leased property. NPV fails because it
forces false mutually exclusive choices.
Figure 1 contrasts the difference between NPV and real
options for the coal lease example. NPV forecasts the expected price of coal as it grows over time and uses it for the start-
Examples of real options with different types of
flexibility
ing point of each of the five mutually exclusive alternatives.
An example of a real call option nearly 2500 years ago
Mutually exclusive choices
Historians have found examples of real options in writings as
ROA tree
old as the 4th century B.C. by the Greek philosopher Aristotle.
NPV if developed immediately
NPV if developed in year 1
MAX NPV < ROA
D
D
D
D
D
I
D
D
D
I
I
D
D
D
I
I
I
as Ito’s lemma, but he did know a real option when he saw one.
D
His story is about Thales the Milesian who read the tea leaves
D
and interpreted them as predicting a bountiful olive harvest
D
Key D = Defer I = Invest
Figure 1: The ROA value will always be higher than NPV
He did not have the advantage of modern mathematics such
that year. Being a man of action, he took his meager savings
and offered it to the owners of olive presses, which were used
to extract the olive oil from the olives, in return for the right to
85
rent the presses at the normal rate during harvest. When they
are usually several types of uncertainty, such as price, quanti-
agreed, he had just purchased history’s earliest recorded call
ty sold, manufacturing cost per unit, and technology. The proj-
option. It gave him the right, but not the obligation to pur-
ect pays and requires cash flows. There are multiple phases,
chase time on the presses at a fixed price. Later on, when the
such as design, engineering, pre-construction, and final con-
harvest was truly plentiful, the olive farmers rushed to the
struction. It has taken three decades since the original work of
presses. Thales charged them a price that was higher than
Black, Scholes, and Merton to develop lattice methods for
normal due to the unprecedented demand, paid the normal
solving these problems but there is literature to show the way
rental rate to the owners of the presses, and kept a large prof-
[Copeland and Antikarov (2003)].
it. His option had finished in-the-money and he became a
wealthy man.
Examples of compound real options include any phased
investment where each phase is an option and is contingent
We can see, in this simple example, all of the general factors
on other options. Research and development programs have
that affect the value of a real option. First one must identify
multiple phases, so does oil and gas exploration and develop-
the underlying risky asset and its uncertainty. In this case it
ment, any new product development, phased construction,
was the rental price of the olive presses and the annual vari-
and merger and acquisition programs.
ability of the rental rate. Although this uncertainty is driven by
the unavailability of the olive harvest we must be careful to
A very simple example of a compound option is given in a
measure the standard deviation of the rental price of the
Harvard Business Review article that I co-authored with
presses and not the variability in the quantity of olives. The
Professor Peter Tufano entitled ‘Real ways of managing real
value of the option increases when the price of the underlying
options.’ It is a simplification of the Xylene’s Basement case
asset goes up, but it also goes up when the variance of the
that I wrote [Copeland (2002)]. The setting for the case is a
underlying goes up. The exercise price was the normal rental
commodity chemical company that is contemplating the con-
rate. Higher exercise prices decrease the value of a call option
struction of a PTA plant that will cost U.S.$1.26 billion in three
(the right to buy) and increase the value of a put option (the
stages: a design phase costing U.S.$60 million and payable
right to sell). The life of the option was the time between
immediately and requiring one year to complete, an engineer-
Thales’ purchase of the option and the date of the olive har-
ing phase that will cost U.S.$400 million and take 2 years, and
vest, and the value of the option increases with longer life.
final construction that will cost U.S.$800 million. A traditional
Finally, the value of the option increases when the risk-free
NPV analysis values the project at U.S.$260 million but
rate does.
assumes that all three phases will be completed lockstep one
after the other without turning back. However, the company
86 - The
Modern compound real options
recognizes that the project is really a compound option with
Most real options are options on options, called compound
three phases and that it can decide to defer or abandon the
options. They are much more complex than the original Black-
project after each phase. The decision about whether to go
Scholes (1973) and Merton (1973) models that started the
into the design phase depends on the payouts of the engi-
modern science of option pricing. To contrast them, Black-
neering phase, which in turn depends on the payouts of the
Scholes prices a European call that can be exercised only at
construction phase. Therefore the initial decision is an option
maturity, on an underlying risky asset that pays no dividends
on an option on an option, a three level compound option.
or cash flows of any kind, and that is driven by a single source
Management’s decision is driven primarily by two uncertain-
of uncertainty. An example of a compound option is the
ties, the price of the output commodity chemical PTA, and the
phased construction of a large manufacturing facility. There
cost of the input commodity chemical, p-xylene, and the cor-
relation between them. When flexibility to defer or abandon
300 thousand units per year at a variable cost of U.S.$1450
was taken into account, the value of the project increased to
each for a profit of U.S.$550. It too lasts 3 years and the com-
U.S.$71 million and management decided to start into the ini-
pany plans to build one of these smaller plants each year for 3
tial phase.
years. Either type of plant can be sold for its book value, the
tax rate is 40%, the risk-free rate is 5%, and the weighted
We recently helped a high-tech company address the trade-off
average cost of capital is 8% for the small plant and 9% for
between a large, very efficient, but very expensive plant (sev-
the big plant.
eral billion dollars to build) and a less efficient plant but one
that provided more flexibility. The following, stylized example
Using these facts and assuming straight line depreciation, the
illustrates the essence of the idea, but is not exactly the same.
company calculated the NPV of the large plant to be U.S.$112
Suppose a company in a high tech industry anticipates rapidly
million as shown in Figure 2. The NPV of the small plants is
growing demand for its product — 300,000 units in the first
only U.S.$101 million (Figure 3).
year, 600,000 in the second, and 900,000 units in the third
year (then no demand from year 4 on). Demand is very uncer-
We cannot stop here, however, because there are two rather
tain and could be 30 percent higher or 23 percent lower. The
significant mistakes in our analysis. The first is that we have
revenue per unit is expected to be U.S.$2000. Two types of
failed to account for a capacity cap that reduces expected
production facility are being considered. The first is a world
output because in some states of nature we do not have
class, efficient 900 thousand unit plant that can be construct-
enough capacity to supply all of the units that are demanded.
ed in time for the first year demand, lasts 3 years, and has
The event tree shown in Figure 4 shows the demand in vari-
variable cost of U.S.$1200 per unit — an U.S.$800 profit mar-
ous states of nature. At the end of the first year, for example,
gin. The second plant is smaller and less efficient. It produces
if we had built the 900 thousand unit plant, there would be no
0
1
2
3
0
1
2
3
Quantity
-
300
600
900
Quantity
-
300
600
900
Price/unit
-
2.00
2.00
2.00
Price/unit
-
2.00
2.00
2.00
Revenue
-
600
1,200
1,800
Revenue
-
600
1,200
1,800
Variable cost/unit
-
1.20
1.20
1.20
Variable cost/unit
-
1.45
1.45
1.45
Variable cost
-
(360)
(720)
(1,080)
Variable cost
-
(435)
(870)
(1,305)
Depreciation
-
(300)
(300)
(300)
Depreciation
-
(100)
(200)
(300)
EBIT
-
(60)
180
420
EBIT
-
65
130
195
Tax @ 40%
-
(24)
72
168
Tax @ 40%
-
26
52
78
Net income
-
(36)
108
252
Net income
-
39
78
117
(300)
(300)
(300)
-
-
-
-
300
Capital expenditures
(900)
-
-
-
Free cash flows
(900)
264
408
552
Discount factor (9%)
1.0000
0.9174
0.8417
0.7722
PV
(900)
242
343
426
NPV
111.85
Figure 2: Large plant NPV analysis
Note: Quantities in thousands. Per unit costs in U.S.$ thousands. Aggregate cash
flows in U.S.$ millions.
Salvage
Free cash flows
(300)
(161)
(22)
717
1.0000
0.9259
0.8573
0.7938
PV
(300)
(149)
(19)
569
NPV
101.24
Figure 3: NPV analysis of three small plants
flows in U.S.$ millions.
87
problem if demand is high (390 thousand units), but if we
The presence of a capacity cap is equivalent to selling a call
build on the small plant, our capacity is only 300 thousand
option on the quantity produced, and the NPV methodology
units. With the small plant we would stock out by 90 thousand
ignores it completely. We can attempt to adjust the expected
units if demand is high. Calculations to the right of the bino-
output downward as shown in Figure 5, but the NPVs of both
mial tree in Figure 4 indicate that the expected supply that
types of facility fall in unison so that their relative ranking
can be sold is lower due to the capacity cap. Actual expected
does not change. Given the correction, the NPV of the large
output becomes 261 units in year 1, 522 units in year two, and
plant is U.S.$38 million and it is U.S.$21 million for the three
725 units in year 3.
small plants.
Market demand
0
Our second mistake was that we did not consider that we have
1,014
390
1,977
600
231
the (compound) option of whether or not to invest in a second,
1,170
and later on a third, or even a fourth small plant. If we take
692
355
advantage of the modularity of the strategy that gains flexi-
410
bility by investing in a sequence of smaller plants, we can build
Small plant output
Year 1
Year 2
supply that evolves to respond to innovations in demand.
Year 3
Prob.
Output
Prob.
Output
Prob.
Output
Figure 6 shows that, by using a forward-backward algorithm
.43
300
.18
600
.08
900
we find the optimal solution to be that we build one small plant
.57
231
.50
600
.32
900
.32
355
.41
692
.14
Expected:
261
410
522
Flexible value tree
725
Figure 4: Demand tree (thousands of units per year)
0
1
2
Quantity
-
261
522
725
Price/unit
-
2.00
2.00
2.00
Revenue
-
522
1,044
1,450
Variable cost/unit
-
1.45
1.45
1.45
Variable cost
-
(378)
(757)
(1,051)
Depreciation
-
(100)
(200)
(300)
EBIT
-
44
87
99
Tax @ 40%
-
17
35
39
Net income
-
26
52
59
(300)
(300)
(300)
300
Salvage
-
-
-
(300)
(174)
(48)
659
1.0000
0.9259
0.8573
0.7938
PV
(300)
(161)
(41)
523
NPV
21.33
Free cash flows
Figure 5: NPV analysis of three small plants with constrained capacity
flows in U.S.$ millions
88 - The
Value: 679.2
Plants: 2
Demand: 1,014
3
Value: 467.3
Plants: 1
Demand: 390
Value: 638.0
Plants: 2
Demand: 600
ROA
Value: 108.4
Plants: 0
Value: 294.2
Plants: 1
Demand: 600
Value: 386.1
Plants: 1
Demand: 231
Value: 274.4
Plants: 1
Demand: 355
Figure 6: Value tree for flexible investment
Value: 1,056.0
Plants: 4
Demand: 1,977
Value: 1,046.1
Plants: 4
Demand: 1,170
Value: 378.0
Plants: 2
Demand: 1,170
Value: 378.0
Plants: 2
Demand: 692
Value: 478.0
Plants: 4
Demand: 1,170
Value: 478.0
Plants: 2
Demand: 692
Value: 139.0
Plants: 1
Demand: 692
Value: 139.0
Plants: 1
Demand: 410
to start with in the higher outcome states of nature and one
start up. If the price falls to U.S.$39.99 per barrel, the com-
plant in the lower state. From there we build another plant in
pany loses U.S.$0.01 on every barrel it produces, but if it
the up state but no plants otherwise. In the third year we build
shuts down it loses the shutdown cost and the restart cost as
2 plants in the upper state for a total of 4, and no plants in the
well. Furthermore, there is a 50-50 chance that the next day
two middle states for a total of 2, and no plants in the lowest
the price will return to the U.S. U.S.$40 mark. Therefore, the
state, for a total of one. The modularity of the smaller plants
well should operate at a loss until the expected loss equals
provides us with the flexibility to increase capacity in order to
the present value of the shut down and restart costs. Real
meet high demand, or of saving capital by refusing to invest
options analysis provides the answer to how low the price can
when demand does not grow. In the final analysis, the NPV of
fall before it becomes optimal to shut down.
the small plant alternative is U.S.$108 million, compared with
U.S.$38 million for the single large, efficient plant.
Multiple sources of uncertainty
In addition to the many types of real options (expansion, exten-
Financial flexibility and operating flexibility are
substitutes
sion, shrinkage, abandonment, deferral, compound, and switch-
In the aforementioned Graham and Harvey survey, chief finan-
with. The uncertainties may also be complicated, for example
cial officers stated that flexibility was the single most impor-
they may be cyclical, mean-reverting, continuous, or discontin-
tant consideration when deciding how much to borrow. The
uous. The approach that I recommend is to start with each driv-
previous example shows that flexibility on the assets side of
er of uncertainty and estimate the way that it moves over time,
the balance sheet is a substitute for flexibility on the liability
for example, a commodity chemical may be cyclical (i.e. mean-
side. If it turns out that the large plant is more desirable
reverting). Then estimate the way that it covaries with other
because its efficiency outweighs its lack of flexibility it will still
drivers of uncertainty over time, for example high prices are
require less debt and more equity financing as a hedge against
often associated with maximum production so that price and
downside risk. In contrast, the more flexible modular con-
quantity are positively related. Then use these estimates and
struction will allow more debt and less equity because in unfa-
the spreadsheet for the NPV of the project to implement a
vorable states of nature the company need not have commit-
Monte Carlo analysis that provides an estimate of the distribu-
ted itself to excess capital.
tion of returns based on simulations of the changes in value.
ing) there are often multiple sources of uncertainty to deal
The resulting standard deviation of return is the basis for the
Switching options
up and down movements in the binomial lattice.
A switching option is the right to shut down and then restart
an economic activity. For example, an automotive assembly
Doing the mathematics
plant, a mine, a computer assembly plant, or a peak load
The very attempt to capture the subtlety of flexibility, if
power generating plant can be shut down and restarted later
worthwhile, requires an investment in learning how to do the
on. The fixed cost of shutting down and restarting are exer-
calculations well. This article is written for top management
cise prices of the option. Not only does ROA provide the extra
and for my friends in academia as an introduction to the
value due to the flexibility of switching, but it also gives the
importance of the idea. It is not a primer in mathematical
trigger points for taking action. To illustrate what we mean,
methods. However, the interested reader should know that
suppose that a company operates an oil well that costs
many of the more complicated problems have been solved
U.S.$40 per barrel to extract oil, and that the world price per
using lattice approaches that are primarily algebraic and
barrel has been falling from U.S.$50 down to near U.S.$40. It
therefore, it is not necessary to use advanced stochastic cal-
costs U.S.$1 million to shut down and another U.S.$1 million to
culus methods for solutions.
89
At the risk of getting too detailed, one very simple example
To solve this problem we form a portfolio made up of two
can be used to show the mathematics involved and most of
assets whose prices we already know, and do so in such a way
the assumptions behind it. Suppose we are going to bid on an
that this portfolio gives exactly the same payouts as the
oil lease for a magic well that produces a barrel of oil immedi-
deferral option. Called the replicating portfolio, it consists of
ately and then a barrel per year forever. The current profit per
‘m’ percent of the underlying risky project and ‘B’ dollars of
barrel is U.S.$200 but it has a 50% chance of rising to
the risk-free bond. Since its payouts at the end of the period
U.S.$300 per barrel or falling to U.S.$100 per barrel by the end
are identical in every state of nature with the deferral option,
of the first year. We make the simplifying assumptions that
the current price of this replicating portfolio must be the
there are no costs of production, that the discount rate for the
same as the price of the option.
project is 10%, the risk-free rate is 5%, and that the price will
Next, we calculate the value of the replicating portfolio by
remain at its new level forever.
starting with its payout in the up state (equation 1) and in the
First, we estimate the net present value of the project. The
down state (equation 2), then solve for the two unknowns, m
current cash flow is U.S.$200, and the expected cash flow is
and B:
.5($300) + .5($100 ) = $200 each year forever, therefore the
present value of the project is:
PV = $200 + ($200/0.1) = $2200
muV + (1 + rf)B = Max[uV – I,0] = Cu = 1,700
(1)
mdV + (1 + rf)B = Max[dV – I,0] = Cd = 1,700
(2)
m = (Cu – Cd)/V(u – d) = 1700/2200 = 0.773
(3)
B = (Cu – muV)/(1 + rf) = [1700–(0.773(3300))]/1.05 = -810 (4)
And if the investment to develop the lease is U.S.$1600, the
net present value of the project is U.S.$600. This is illustrated
Thus, if we put our money into a 77.3% share of the project
in the left-hand side of Figure 7.
and borrow U.S.$810 we will get exactly the same payouts as
the option. In the up state we get:
Now suppose that we can defer development for one year. We
can make an informed decision at that time that gives us the
muV + (1+r)B= .773(3300) – (1.05)810 = 1,700
maximum of either the NPV of the project or zero, as illustrated in the right-hand side of Figure 7. Note that we would
and in the down state we get:
invest if the price goes up and would not invest if it goes
down. Also, we cannot discount the payouts from the option
mdV + (1+r)B = .773(1100) – (1.05)810 = 0
at 10% because the option has different risk than the project.
The payouts on the replicating portfolio are the same as on
the option, therefore they must have the same present value,
.5
300
uV = 300 +
.1
V = 2200
–I = 1600
NPV = 600
[uV-I,0]=Cu
MAX [3300-1600,0]
MAX
ROA
= 891
.5
dV = 100 +
ROA = mV + B = .773(2200) – 810 = 891
[dV-I,0]=Cd
MAX [1100-1600,0]=0
100
.1
Underlying risky asset
NPV = V – I = $600
namely
(5)
MAX
With a deferral option
ROA = mV – B = $891
Recall that the net present value of the project without any
deferral option was U.S.$600. With the option to defer, the
value has increased by U.S.$291, which is the value of the right
Figure 7: Payouts on an underlying asset and the asset with a deferral option
90 - The
to defer.
Conclusion
Real option analysis (ROA) is a much more intuitive concept
than the traditional net present value (NPV) method for evaluating corporate capital investments and consequently it is
replacing NPV. It takes time, of course, for people to learn
about a new decision-making tool, more time to experiment
with it, and still more time to change their habits. This article
has been written to serve notice that there is a better way —
called real options.
References
• Black, F., and M. Scholes, 1973, “The pricing of options and corporate liabilities,”
Journal of Political Economy, May-June 1973, 637-654
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91
92 - The
Real options
Venture investment
contracts as baskets
of real options1
Didier Cossin
UBS Professor of Finance, IMD
Benoît Leleux
Stephan Schmidheiny Professor of
Entrepreneurship and Finance, IMD
Entela Saliasi
FAME and HEC, University of Lausanne
Abstract
Valuing early-stage high-technology growth-oriented compa-
and contract design are considered. It is shown, for example,
nies is a challenge to current valuation methodologies. This
how ‘contingent pre-contracting’ for follow-up rounds is the-
inability to come up with robust point estimates of value
oretically a better proposition than the simple ‘rights of first
should not and does not lead to a breakdown of market liq-
refusal’ commonly found in many contracts. We also provide
uidity. Instead, efforts are redirected towards the design of
for results — such as timing of investments, length of rounds,
investment contracts which materially skew the distribution
choices of liquidation levels, and conversion levels — that take
of payoffs in favor of the venture investors. In effect, limita-
into account full interaction of the different features consid-
tions in valuation are addressed by designing the investment
ered. We document some complex facts, such as the concav-
contracts as baskets of real options instead of linear payoff
ity of the VC contract value depending on the amount invest-
functions. In this article, we investigate four common fea-
ed at the different stages, the actual share impact of the most
tures (covenants) of venture capital investment contracts
common antidilution feature, some endogenous motivation
from a real option perspective, using both analytical solutions
for early VC exits from otherwise performing companies, and
and numerical analysis to draw inferences for a better under-
stress overall the importance of a full option analysis for effi-
standing of the value of the contract features. The impact of
cient contract negotiation and understanding.
this conceptual approach for pricing, valuation negotiation,
1
This paper is an abridged version of ‘Understanding the economic value of legal
covenants in investment contracts: A real-options approach to venture equity contracts’ by the same authors. We are grateful to Jerome Detemple, Michel Habib,
Frederic Martel, Spiros Martzoukos, James Schallheim, Rene Stulz, Ernst-Ludwig
Von Thaden, and Ton Vorst for their helpful comments and suggestions. We also
would like to thank the seminar participants at Tilburg Institute of Advanced
Studies Business School’s Law and Economics 2000 and University of Southern
California 2002 and conference participants at IAFE 2001, FMA 2001, and EFMA
2001. Financing was partly provided by the Swiss National Science Foundation
(FNRS) and IMD. Financial support by the National Centre of Competence in
Research ‘Financial Valuation and Risk Management’ is gratefully acknowledged.
The National Centre of Competence in Research are managed by the Swiss
National Science Foundation on behalf of the Federal Authorities.
93
Valuing early-stage high-technology growth-oriented compa-
Obtaining a better understanding of the economic value of the
nies is a challenge to current valuation methodologies. This
legal features of investment contracts is a pre-condition to
inability to come up with robust point estimates of value could
understanding their optimality as well. While our model
potentially lead to a breakdown of market liquidity. However,
includes many realistic features of current VC markets, the
this is not what is witnessed. In fact, billions of dollars of early
analysis remains very much a partial equilibrium approach. A
stage venture capital has been poured into promising start-
richer model would incorporate agency issues, adverse selec-
ups in Europe and the United States over the last few years.
tion and/or asymmetry of information that justify the use of
So, how do venture capitalists cope with the valuation uncer-
these contract features in the first place. The model could be
tainties?
extended to combine the continuous time analysis we provide
with a complex game theoretical approach. While this has
The pioneering work of Sahlman (1990) pointed the way to the
been attempted in the credit risk literature [Anderson and
solution, or at least the ‘coping’ mechanism used. He suggests
Sundaresan (1996)], this is beyond the scope of this paper,
that instead of expending useless amounts of time and effort
since the combination of multiple complex optional features in
coming up with a better estimate of an inherently uncertain
itself presents a big enough challenge.
future, efforts should be redirected towards the design of
investment contracts which materially skew the distribution of
The features specifically addressed here are the liquidation
payoffs in favor of the venture investors and active involve-
preference, the convertibility of the securities, the ex-ante
ment in the development process of the invested company. In
staging of the investments, and the antidilution provisions. All
effect, limitations in valuation abilities are addressed by
these features have been shown to be common in venture cap-
designing the investment contracts as baskets of real options
ital contracts (with staging remaining in general informal
instead of linear payoff functions and by directly intervening
rather than contractual: we analyze the strong difference this
in the underlying processes.
leads to) [see Sahlman (1990), Kaplan and Stromberg
(2000/2002)].
The key items outlined by Sahlman (1990) in the relationship
between venture capitalists and entrepreneurial ventures
In the original paper, we present closed-form solutions under
include, the staging of the commitment of capital, the use of
restrictive assumptions, thus allowing for analytical experi-
convertible securities instead of straight equity investments
mentation. We also provide numerical analyses (using finite
and the presence of liquidation preference for the VC, and
difference methods) of more general cases. From these analy-
anti-dilution provisions to secure the investor’s equity position
ses we obtain interesting insights into the value contribution
in the company. While the recent empirical literature has
of the various covenants. It is shown in particular how ‘contin-
explored further the presence of these features in VC con-
gent pre-contracting’ for follow-up rounds [or ‘ex-ante staging’
tracts and analyzed theoretical arguments for their use
as described in Kaplan and Stromberg (2000)] is theoretically
[Kaplan and Stromberg (2000)], no paper to date has system-
a better proposition than the simple ‘rights of first refusal’
atically valued them, both in isolation and as a whole. We
commonly found in many contracts. We also provide results on
exploit the real options literature to obtain a better under-
timing of investments, the impact of the length of rounds con-
standing of the economic value of some classical features of
sidered, the liquidation level to be chosen, the critical conver-
VC contracts.
sion level at which the VC will convert, and these with all features integrated and interacting.
Some authors have mentioned the optionality of VC contract
features without developing systematically their analyses.
94 - The
This abridged version of the paper is organized as follows. We
first locate the paper at the intersection of different strands of
The second class of research includes empirical studies that
literature on venture capital and real options. We then intro-
analyze the specificities of venture backed projects, such as
duce the general framework and discuss the model’s underly-
Cochrane (2001), Gompers (1995), Kaplan and Stromberg
ing assumptions. The following sections discuss the key con-
(2000, 2002), Lerner (1994), Gompers and Lerner (1996),
tractual features, such as liquidation preference and staging.
Seppa and Laamanen (2000), Manigart et al. (2002), etc. The
We show that the liquidation preference itself is a package of
closest papers to our concern study specifically the contractu-
liquidation rights and automatic conversion. It is important to
al features investigated here and their prevalence in VC con-
note that the analytical and numerical solutions do take
tracts.
account of the complete interdependence of the features.
Whereas liquidation preference sets up the framework for the
The third class of research is closest in methodology to what
VC end payoff and the conditions (event) under which it is
we develop here, although its goal is different. The real options
exercised, staging aims to not only maximize the final payoff
literature has contributed to a better understanding of the
by optimally distributing the investment amount over discrete
value of the investments, notably high-technology investments
stages but also to minimize the downside risk, given the early
[Berk et al. (1998), Schwartz and Moon (2000), Schwartz and
exit option. We also tackle the most common antidilution fea-
Gorostiza (2000)]. American options, in terms of valuation and
ture, carefully analyzing the impact of the issuing price on the
optimal exercise, present some of the most challenging prob-
VC ownership stake. It highlights in particular the concave
lems in finance. Consequently, many papers applying option
shape of the VC ownership stake.
models to real assets resort to the Black and Scholes approximation methodology [Benaroch and Kauffman (1999), Hull
Literature review
(1997)], or approximate the option to a European one
This paper lies at the crossroad of the venture capital and the
[Trigeorgis and Panayi (1998)]. Others refer to Magrabe’s for-
real options literatures, breaking new ground by bringing them
mula when modeling the investment opportunity as an
together in a way not attempted before for private equity
exchange option with uncertain cash flows [Kumar (1996,
investment contracts. The current literature on venture capital
1999)]. Perlitz et al. (1999) applied Kemna’s (1993) adjustment
can be subdivided into three main classes, depending on
of the Geske approximation in an R&D project valuation. Jagle
whether it addresses the theoretical optimality of contracts,
(1999) uses a binomial model as its numerical pricing tech-
empirically analyses the existing contracts used in practice, or
nique.2 Schwartz and Cortazar (1998) use the Barraquand and
values the investments underlying the contracts (notably with
Martineau (1995) methodology to price the underdeveloped oil
real-options techniques).
field as a two dimension American Option. Schwartz and Moon
(2000) used the Least Square Monte Carlo approach to price
A rich, mostly game-theoretic literature addresses the agency
the Internet companies with uncertainty in expected return and
and moral hazard problems arising in a multi-stage financial
growth rate. Lastly Schwartz and Gorostiza (2000) implement
contracting environment with information asymmetries [Dessi
the successive over-relaxation and alternating direction implic-
(2001), Casamatta (2001), Aghion et al. (2000), Bergmann and
it methodology in pricing the information technology acquisi-
Hege (1998), Bergmann and Hege (2000), Admati and
tion and development with stochastic stream of cash flows.3
Pfleiderer (1994), Noldeke and Schmidt (1998), Bascha and
Beyond classical investment valuation, the real-options litera-
Walz (2001), and Bascha (2001)]. While this literature would
ture has also provided interesting strategic results in innova-
have much to bring to this paper in terms of optimality (and
tion management, with for example Grenadier and Weiss (1997)
vice versa), we have simplified the issue and taken actual con-
and more recently Bernardo and Chowdry (2002) sharing some
tracts as given.
technical similitude to ours.
2 A more extended summary of these papers is provided in Schwartz and Gorostiza
(2000), p. 2.
3 Recently Fourier transformation of the characteristic function has been used to
calculate the respective probabilities, achieving a closed form solution, for high
dimension state-variable European option.
95
We are not aware of prior literature addressing specifically the
options. Each feature separately is either an option or a bun-
valuation of the contract features themselves, even though
dle of options. Bringing all the features together in one con-
the idea has been mentioned before [Trigeorgis (1997)]. Our
tract creates interactions between these options, interactions
approach relies on an original application of the real options
which affect their values.5 Because all the options considered
literature applied to investment contracts. Where most of the
tend to be of the American type (where early exercise is pos-
literature in that field tries to resolve the uncertainty of the
sible), we also address the issue of timing, a problem well-
project value through complex valuation techniques (and thus
known by practitioners and to which we add an analytical
tries to reach a point estimate of project values), we attach a
understanding.
strong uncertainty to the project value itself (assumed to follow a stochastic process) and try to determine the impact of
General framework
this uncertainty on the VC contract and its different features.
This paper investigates specifically four common features
(covenants) of venture capital investment contracts, liquida-
While equity investment contracts have not been analyzed
tion preference, staging, convertibility, and anti-dilution.
systematically in this way, a rich literature applies similar
techniques to debt contracts, for example in the context of
The preferred stock investment format provides the venture
credit risk. Indeed, understanding the value of legal contracts
capitalist with preferences in liquidation, a feature reinforced
using real options methodologies is now classical (and highly
by the accruing dividends. The latter are not meant to be paid
successful in practice) for credit risk. Since the seminal work
unless the exit mechanism is not rich enough to provide ade-
of Merton (1974), which valued a simple zero-coupon straight
quate returns to the investors. In such circumstances, for
debt contract, research has concentrated on more complex
example liquidation, accruing dividends (often 10-20% per
features, such as convertibility [Ingersoll (1977)], safety
annum) guarantee a disproportionate share of the assets to
covenants [Black and Cox (1976)], and agency issues
the venture capital investors. The net effect of the preferred
[Anderson and Sundaresan (1996)]. The lack of consideration
equity format with accruing dividend is to skew the payoff dis-
granted to private equity contracts is often justified by the
tribution in case of liquidation in favor of the venture capital-
lack of market completeness, which is not a satisfactory expla-
ist. Venture capitalists rarely invest in a single stage, instead,
nation since debt contracts face the same constraints (the
they stagger (stage) the investments over time in synch with
assets of a firm are typically not traded). We show that such
distinct milestones in the development of the investee.
an analysis, when brought to equity contracts, provides for
Enough capital is provided at each stage to reach the next one,
rich and meaningful results and should drive further research
at which point the venture capitalist reserves the right to
on contract optimality and design.
release the next round of capital or to abandon the project
4
funding. Staging of the investment is said to be a mutually
The objective of this paper is to provide the first systematic
beneficial arrangement. It gives the venture capitalist the
analysis of the economic value of some key legal covenants
option to reinvest or abandon the project. It provides the
used in venture capital contracts. It develops an intuitive
investee with gradually cheaper funding, as the sources of
framework to evaluate these main covenants both separately
uncertainty are progressively removed.
and together. The framework is flexible enough to accommo-
96 - The
date any possible interaction between covenants, adding an
To capture the upside potential of the investment, venture
entirely new dimension to the corresponding real-option liter-
capitalists reserve the right to convert the preferred equity or
ature. Mathematically speaking, we show that the pricing of a
bond into common stock at a predefined conversion rate. Most
VC contract is similar to that of a complex package of financial
conversions tend to be automatic conversions. Black and
4 See Cossin and Pirotte (2000) for an extensive review of that literature.
5 These options interactions have been analyzed in a different context by Trigeorgis
(1997) and mentioned as a specific limitation of current optimal contract theory in
Kaplan and Stromberg (2000).
Gilson (1998) and Kaplan and Stromberg (2002) argue that
(through monitoring and active involvement in the business).
the effect of the conversion feature is to create a strong incen-
Consequently, instead of using replication arguments that rely
tive for the entrepreneur to perform, as the venture capitalists
on complete markets (and lead to risk-neutral pricing), we
give up their superior proposition explicitly modeled here in
make use of the more realistic dynamic programming argu-
case of high performance by the firm.
ment developed in Dixit and Pindyck (1996) that uses the discount rate ζ.
The conversion feature of the preferred equity or bond investment is often contingent on the pricing of future rounds of
Empirical results, such as Gompers (1995), and research stud-
funding, providing a level of protection for the venture
ies, such as Berk et al. (1998), have shown that the systemat-
investors. The intensity of these anti-dilution provisions varies
ic risk, as well as the volatility levels, are highest early in a pro-
greatly from ‘top-off’ provisions, which guarantee the mainte-
ject’s life and decrease as the project approaches completion.
nance of the equity percentage of the initial investor in future
The cost of capital should thus decrease through the life of the
rounds, ‘full ratchets’, which reset the conversion price of all
project, due to the higher leverage of the project early in its
pre-existing series of funding to the lowest price of follow-up
life. In order to study the impact of these factors in the con-
rounds, maintaining the value of the investor’s stake if not its
tracting value process, we consider stepwise parameters such
actual equity percentage in the investee company, or ‘weight-
as volatility, drift rates, and cost of capital.
ed average ratchets’, which provide for a readjustment of the
conversion price of prior series to a weighted average of suc-
Firm value as a diffusion process
ceeding rounds of fund raising.
The dynamics of the firm value is modeled as a diffusion
process, with a drift parameter affected by the VC’s effort in
Discount rate
the firm. The role of the VC value-add (his/her supportive non-
As described in Sahlman (1990): ‘In theory, the required rate
financial contribution) affects the probability of success. The
of return on an entrepreneurial investment reflects the risk-
drift of the firm value process is defined as the sum of a drift
free interest rate in the economy, the systematic risk of the
of a similar project plus the VC value-add given its involve-
particular asset and the market risk premium, the liquidity of
ment in the project. The larger the VC contribution the higher
the asset, and compensation for the value added by the sup-
the project’s drift.
plier of capital. This last adjustment is required to compensate
the VC for monitoring and playing an active role in manage-
The VC non financial contribution is a crucial component in
ment’.
valuing the venture project contract, since it captures the VC
dual role as financier as well as project coach (non-financial
A crucial but realistic assumption concerns the stochastic
contribution), which not only affect the drift of the firm value,
changes in the firm value, which cannot be ‘spanned’ or repli-
but also entitles the venture capitalist to an additional reward
cated from the existing assets in the economy. The underlying
(higher ownership stake on the final venture project’s payoff).
state variable in our model is a non traded asset (as often in
Although the VC value-add is beneficial for the firm value (i.e.
the real options literature, and frequently in the credit risk lit-
increases the probability of success of the venture project),
erature as well). Therefore the riskless portfolio cannot be
the VC does incur some additional costs by participating. This
constructed. We are thus making use of the discount rate per
could lead to a premature VC exit from the venture backed
stage ζ which accounts for the decision maker’s subjective val-
project, if no additional reward, in terms of a higher ownership
uation of risk [Dixit and Pyndick (1996)]. Furthermore, the risk
stake, is provided. The existence of the VC value-add has major
free rate cannot cover the VC cost for providing value-add
implications, which make the private equity investment differ-
97
ent from an outside equity financing. Indeed, as these actions
money liquidation preference features have been known to be
are costly for the VC, they deserve additional reward. The VC
implemented in order to skew values even more towards the
thus uses a higher discount rate, as presented by Sahlman
venture capitalist (or a specific member of a syndicate). The
(1990). Because of the efforts put in to increase the chances
net effect of the preferred security format with accruing divi-
of success of the firm, the preference for liquidity effects, as
dend is to skew the payoff distribution in case of liquidation.
well as the opportunity cost of focusing on a particular company rather than another one (the number of firms a venture
The most common security used by venture capitalists are
capitalist can oversee is limited), we assume that the discount
convertible preferred stocks and debentures, as shown by
rate is larger than the drift of the process when the VC partic-
Kaplan and Stromberg (2000) and Sahlman (1990). Schmidt
ipates.
(2001) summarizes the papers dealing with optimal contract
design for an inside investor.
We further propose that the VC ownership stake is a convex
increasing function of the VC additional costs. The later the VC
The conversion feature can be understood as a reallocation of
decides to invest, the lower his/her stake. In other words the
control rights in case of success of the project from the ven-
VC ownership stake is a decreasing convex function of the
ture capitalist to the entrepreneur. It is an incentive to perform
investment time. The VC ownership stake increases at a
for the entrepreneur, above and beyond the direct financial
decreasing rate for increasing investment levels. Lastly, the VC
incentives offered by the venture capitalist. The conversion
claim on project value is lower if the project value at that
feature can thus be understood as a barrier that transforms
moment is higher.
the considered features, such as liquidation preference, in barrier options of the up-and-out type. In other words, if a certain
Liquidation preference and convertibility
milestone is achieved, i.e. a certain level of value for the proj-
Liquidation preferences appear in venture contracts in differ-
ect, the previous options, in this case the liquidation prefer-
ent formats. Most often, the liquidation preference is con-
ence, are canceled, thus reducing the differences in rights
structed as a participating feature in the convertible preferred
between the venture capitalist and the entrepreneur. The con-
securities design, whereby the first tranche of capital obtained
vertibility is thus as much a redistribution of rights towards
in an exit is entirely committed to the investor group and any
the entrepreneur as it is an upside potential for the VC. From
residual is then distributed pro-rata to the equity owners. The
the VC’s perspective, the object is to maximize the value of the
participating feature usually disappears once the exit valua-
shareholding in case the project is successful and recoup the
tions are sufficiently high to guarantee the outside investors a
maximum possible value in case the project is a failure.
solid return on their initial investments.
The value of the VC contract with both convertibility and liqui-
98 - The
The participating preferred debentures or preferred stock
dation preference integrated corresponds to the linear combi-
investment format provides the venture capitalist with prefer-
nation of two option payoffs, one corresponding to the liqui-
ence in liquidation, a feature reinforced by the accruing divi-
dation right and the other to an automatic conversion feature.
dends. The accruing cash flows, dividends or coupons, are not
This expression seems similar to the classical analysis of a
meant to be paid unless the exit mechanism is not rich enough
convertible as a bond + a call but differs. Indeed, the second
to provide adequate returns to the investors. In such circum-
option payoff differs from a pure upside potential. Because the
stances, for example liquidation, accruing dividends, often 10-
VC gives up on the liquidation preference by converting, the
20% per annum, guarantee a disproportionate share of the
liquidation preference level affects the conversion decision.
assets to the venture capital investors. Very high, out of the
The automatic conversion feature is less valuable than a sim-
ple call, which has a pure upside potential. Liquidation levels
similar to a compound call option. The next financing round
affect conversion policies. There is thus a strong interaction
can take place as soon as the project value reaches the opti-
between features.
mal project value endogenously determined from the model.
The venture capitalist has first rights to further investments in
The analyses show indeed that liquidation preferences and
the company. We consider the possibility that these rights are
convertibility interact strongly in venture capital contracts, in
formal (ex-ante staging), i.e. that the VC commits to further
particular the liquidation level affects the level at which con-
financing of a certain amount at a certain valuation if some
version occurs. A contract with a high liquidation value will be
milestone is achieved. We compare this to informal rights
converted later, at a given conversion price, than a contract
(linked notably to competitive issues, in which the VC has a
at low liquidation value. Typically, a larger shareholder, who
first right to participate but where the pricing is set competi-
will hold a higher liquidation value, will thus wait longer to liq-
tively at the time of the financing) and to the situation in
uidate. The two features considered illustrate the strong
which no rights (formal or informal) are acquired by the VC, so
optionality integrated in VC contracts. We derived the option
that the VC’s investment corresponds to a short-term (full
values in both infinite and finite horizons and show that the
commitment) or a one shot (no staging) investment.
value of the automatic conversion is affected by all parameters — value of the project, investment, volatility, drift, and
The analyses show that the option to reinvest brings higher
time horizon — while the liquidation right is mostly sensitive
value to the VC contract. Formal staging dominates the infor-
to changes in liquidation levels, and investment if liquidation
mal staging, even though the latter is frequently seen in cur-
is done at par, as is common.
rent VC contracts. It also dominates the absence of staging or
a full commitment to future investments [Trigeorgis (1997)].
Staged financing
One shot investing is not the optimal decision. Determining
Sequential investment is strongly related to the existence of
the optimal investment level requires the full analysis to be
great uncertainty concerning high technology, R&D, and gen-
drawn as the timing of investments through stages has a con-
erally VC-financed projects, a phenomenon specifically ana-
cave shape that varies strongly depending on the parameters
lyzed in Gompers (1995). Staged capital infusions allow ven-
considered. While the number of stages matter, the marginal
ture capitalists to periodically gather information and monitor
impact seems to be decreasing with the number of stages.
the progress of the project, and notably the evolution of the
Overall, liquidation right values are less affected by timing and
risk of the project, or project volatility, as it matures. Staging
staging issues than the upside potential (and automatic con-
can be organized formally or informally. Kaplan and
version) is. They nonetheless can be affected in opposite direc-
Stromberg (2000) for example analyze ex-ante staging in
tions by the timing of the investment.
which VCs commit at initiation to future investments with contingencies on milestones being met. They also mention that
Antidilution
‘most VC financings are at least implicitly staged, in the sense
The antidilution feature appears in different forms in venture
that even when all the funding in the initial round is released
agreements. Its purpose is to protect the early rounds
immediately, it is understood that future financing rounds will
investors from dilution when additional stock splits, stock div-
be needed to support the firm until the IPO.’
idends, and any new financing at a lower price per share occur,
driving the value of the initial investors down. The antidilution
We consider also both the case of endogenous staging and the
feature analyzed is similar to a long put option, which guaran-
case of deterministic times for sequential investments. In the
tees to the VC an additional value in case the share price drops
case of endogenous staging, the staging is considered to be
below the old conversion rate. The additional value that the VC
99
receives consists of free shares to compensate for the dilution
able to look at the basket of options as a basket, not a collec-
effect of the negative change in project value.
tion of individually priced options. A first attempt at this can
be found in the original paper.
Our analyses show the impact on the contract value of the
antidilution feature and show how it transforms the underly-
This is but a first glimpse at the complex universe of venture
ing distribution. In particular, the classical weighted average
capital investment contracts form a real options standpoint.
antidilution clause leads to a situation where the VC share is
The contribution from the real options approach should not be
not necessarily increasing with the issue price. The protected
underestimated though, and it holds the promise of significant
stake becomes a V-function of the issue price. This contractu-
advances in the understanding of the true value-added of con-
al feature can be balanced economically in a contractual nego-
tractual features which have often been part of ‘boilerplate’
tiation versus other features. The analysis can be pushed fur-
contracts for decades with little understanding of their effect
ther, for example to provide a comparison of the value impact
on the investors’ wealth nor behavior.
of different antidilution formulae, such as the ‘top off’, which
guarantees equity percentage, or the ‘full ratchets’ that main-
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• Black B. S., and R. J. Gilson, 1998, “Venture capital and the structure of capital markets: Banks versus stock markets,” Journal of Financial Economics, 47:3, 243-277
• Casamatta C., 2001, “Financing and advising: Optimal financial contracts with venture capitalist,” mimeo, University of Toulouse
• Cochrane J. H., 2001, “Risk and return of venture capital,” Working Paper, University
of Chicago
• Cossin D., and H. Pirotte, 2000, “Advanced credit risk analysis,” John Wiley & Sons
• Dessi R., 2001, “Start-up finance, monitoring and collusion,” Working Paper, IDEI
University of Toulouse
• Dixit A. K., and R. S. Pindyck, 1996, “Investment under uncertainty,” Princeton
University Press
• Gompers P. A., and J. Lerner, 1996, “The use of covenants: An empirical analysis of
Conclusion
We use advanced real option methodologies and frameworks
to investigate the value of four classic features of venture capital contracts: staging, liquidation preference, convertibility,
and antidilution. We show the effects of these covenants not
only on the value of the contracts but also on the distribution
of the final payoffs. We also show the complex interaction of
the features and how they affect each other.
The results of this work can shed some light on contract negotiations, but also provide valuable help in designing optimal
contracts. The high non-linearities of the features analyzed
should convince the reader that linear analysis of the IRR or
NPV-type do not provide valid approaches to valuation.
Beyond valuation, better design, as demonstrated in the staging feature of contracts, was shown to improve current contracts and contract negotiations.
As outlined by Kaplan and Stromberg (2000), venture capital
contracts are best seen as flexible contracting mechanisms for
the contingent reallocation of control, ownership, and cash
flow rights. But for this complex package of real options to
attain its goal of optimally balancing incentives, risk protections, and the sharing of the upside potential, we need to be
100 - The
venture partnership agreement,” Journal of Law and Economics, 39, 566-599
• Gompers P. A., 1995, “Optimal investment, monitoring, and the staging of venture
capital,” Journal of Finance, 50, 1461-1489
• Grenadier S., and A. M. Weiss, 1997, “Investment in technological innovations: An
option pricing approach,” Journal of Financial Economics, 44, 397-416
• Ingersoll J. E., 1977, “A contingent-claims valuation of convertible securities,”
Journal of Financial Economics, 4:3, 289-231
• Jagle J. J., 1999, “Shareholder value, real options, and innovations in technologyintensive companies,” R&D Management, 29:3, 271-287
• Kaplan, S. N., and P. Strömberg, 2000, “Financial contracting theory meets the real
world, an empirical analysis of venture capital contracts,” NBER Working Paper No.
W7660
• Kaplan S. N., and P. Strömberg, 2002, “Characteristics, contracts, and actions:
Evidence from venture capitalist analyses,” University of Chicago, Working Paper
• Kumar R. L., 1996, “A note on project risk and option values of investments in information technologies,” Journal of Management Information Systems, 13:1, 187-193
• Kumar R. L., 1999, “Understanding DSS value: An options perspective,” The
International Journal of Management Science, 27, 295-304
• Lerner J., 1994, “The syndication of venture capital investment,” Financial
Management, 23, 16-27
• Manigart, S.; H. Sapienza, M. Wright, an K. Robbie, 2002, “Determinants of required
returns in venture capital context,” Journal of Business Venturing, 17:4, 291 – 312
• Margrabe W., 1978, “The value of an option to exchange one asset for another,”
Journal of Finance, 33:1, 176-186
• Merton R. C., 1974, “On the pricing of corporate debt -the risk structure of interest
rates,” Journal of Finance, 29:2, 449-470
• Noldeke G., and K. M. Schmidt, 1998, “Sequential investment and options to own,”
RAND Journal of Economics, 29:4, 633-653
• Sahlman W. A., 1990, “The structure and governance of venture capital organizations,” Journal of Financial Economics, 27, 473-521
• Schmidt, K. M., 2001, “Convertible securities and venture capital finance,” Working
Paper, University of Munich, CESifo and CEPR
• Schwartz E. S., and C. Z. Gorostiza, 2000, “Valuation of information technology
investment as real options,” Working Paper UCLA
• Schwartz, E. S., and G. Cortazar, 1998, “Monte-Carlo evaluation model of an underdeveloped oil field,” Finance Working Paper CMS
• Schwartz, E. S., and M. Moon, 2000, “Rational pricing of internet companies,”
Working Paper UCLA
• Seppa, T., and T. Laamanen, 2000, “Valuation of venture capital investments:
Empirical evidence,” Working Paper, Helsinki University of Technology
• Trigeorgis L., 1996, “Real options: Managerial flexibility and strategy in resource
allocation,” MIT Press.
101
Titel artikel
102 - The
Real options
A real options
approach to
bankruptcy costs:
Evidence from failed
commercial banks
during the 1990s1
Joseph R. Mason
LeBow College of Business, Drexel University,
Wharton Financial Institutions Center,
and Federal Reserve Bank of Philadelphia
Abstract
Literature to date has identified three main aspects of liquida-
Expectations of asset price growth are based on previous
tion costs, firm size, asset specificity, and industry concentra-
asset price growth and asset price volatility, which are related
tion. This paper unifies the theory behind these three aspects
to firm size, asset specificity, and industry concentration.
of bankruptcy costs by treating them as components of a
Testing the hypothesized asset price relationships on FDIC
broader option valuation problem faced by the liquidating
failed bank liquidation data with OLS, three-stage least
trustee. In the options valuation framework, at time t the
squares, and duration specifications yields the appropriate
trustee may choose to liquidate at current asset values and
results. Furthermore, it appears that liquidation time alone
incur a known loss, or hold until the next period t+1 at a posi-
can be used as an effective second order proxy for asset value
tive opportunity cost. The trustee may not sell in the current
growth where market value estimates are unavailable.
period if expected asset price growth is sufficiently large.
1
Forthcoming, Journal of Business
103
Costly bankruptcies hurt creditors and may contribute to
but rather a target variable like optimal time or value growth.
sluggish economic growth. Moreover, the substitutability of
debt and equity in finance theory is predicated upon low
Researchers in the real options literature typically obtain the
bankruptcy costs. Hence, the financial literature has long
solution to a deterministic growth specification (one with no
sought a better understanding of bankruptcy.
uncertainty) and use that to estimate ‘feasible’ models. In the
present context, the deterministic specification suggests that
Though it is generally accepted that direct bankruptcy costs,
if asset values are expected to fall divestment will occur imme-
such as legal and administrative fees, are determined prima-
diately (liquidation time will decrease) and if asset values are
rily by the amount of time spent in liquidation, the determi-
expected to rise divestment will be delayed (liquidation time
nants of time itself are not well understood. Literature to date
will increase). Of course, those implications mask significant
has identified three main aspects of liquidation time (and
complexity. What determines expectations in an uncertain
costs), firm size, asset specificity, and industry concentration
world? The stochastic growth representation parameterizes
[Alderson and Betker (1995, 1996), Warner (1977), and Weiss
expectations as a function of asset value growth (above the
(1990)]. This paper unifies the theory behind these three
discount rate) and volatility. The paper shows mathematically
aspects of bankruptcy costs by treating them as components
that the solution to the stochastic growth representation is
of a broader option valuation problem faced by the liquidat-
denominated in target asset value growth across the
ing trustee.
(unknown) liquidation period rather than simple liquidation
time. Furthermore, that optimal ‘divestment value (V*)’ rises
Intuitively, the paper models the trustee’s option valuation
in response to greater volatility and declines in response to
problem in the following manner. Assume the trustee bears a
higher discount rate-price growth spreads.
fiduciary duty to maximize creditor recoveries. Having taken
possession of the firm’s assets at a loss to creditors, the
While the solution concept is intuitively appealing (in that
trustee’s task becomes one of loss minimization. At any time
investors target growth and holding period together rather
t the trustee may choose to either liquidate at current asset
than holding period alone) it is inherently unmeasurable in
values and incur a known loss, or hold until the next period t+1
most applications, because market values for all but a small
at a positive opportunity cost. The trustee will not sell in the
minority of financial contracts are typically unknown until the
current period if expected asset price growth is sufficiently
assets are actually sold. This paper contributes, therefore, not
large. Expectations of asset price growth are partially based
only a theoretical representation of the real options process,
on asset price volatility, which is itself related to firm size,
but also empirical tests of the stochastic growth model that
asset specificity, and industry concentration. Since the option
have been hitherto unavailable. Those results are measurable
to liquidate is not typically in the money, the trustee will
because in some instances, investors have occasionally
rationally liquidate when marginal gains from waiting
recorded market value estimates at the time of taking posses-
approach zero, that is, when the value of the option stabilizes.
sion of the assets in order to guide their divestment decisions.
Hence, following Dixit and Pindyck (1994), the trustee’s
104 - The
divestment opportunity is equivalent to a perpetual put
The paper obtains and tests both deterministic and stochastic
option. Therefore the decision to divest is equivalent to decid-
growth specifications and finds empirical results estimated
ing when to exercise that option.2 The trustee therefore
using time and recovery value, for the most part, agree. The
chooses the optimal time to exercise, such that the expected
stochastic representation, however, yields logical extensions
option value is maximized. Note, however, that in a real
of the liquidation process that do not arise in the determinis-
options context the value may not be analogous to a price,
tic concept: ways that will require extensions of real options
2 An American option can be though of as a variant of the perpetual option that is
forced to exercise at a limit date. The perpetual option, however, has no such limit
date so the exercise needs to be derived from a fundamental limit on the option
value. It may be useful to bear in mind the results for a Black-Scholes model of the
value of an option on an equity index that pays dividends through the following
discussion.
theory in order to fully account for their effects. Specifically,
Figure 1 represents liquidation outcomes (recoveries) for
the results that follow show evidence that divestment option
banks that failed between 1980 and the present. The recover-
values depend crucially upon the direction of the growth trend
ies represented in the figure are measured at the end of 2000.
and may therefore contain a jump component depending on
While it is important to keep in mind that the figure includes
the expected direction of asset markets.
results from liquidations that are not yet finished, almost all
liquidations that began before 1996 are substantially complete.
Data
This paper measures liquidation outcomes using Federal
Deposit Insurance Corporation (FDIC) Failed Bank Cost
On the basis of Figure 1 it is immediately apparent that recov-
Analysis (FBCA) data on liquidations of 1,581 banks that failed
eries associated with failures during periods of banking
between 1986 and 1996. The FDIC was the majority stakehold-
industry difficulty, such as the early and late 1980s, were
er in each case. Therefore in principle the FDIC attempted to
lower than those that occurred in other periods. Recoveries
extract at least enough value to cover the shortfall incurred
of banks that failed in 1981-1982 averaged 36.5%, those that
from paying depositors (creditors) in full at the time of failure.
failed in 1989-1990 averaged 44.1%, whereas recoveries for
For both individual and aggregate records, the report provides
banks failing in other years over the period 1980-1995 aver-
data on the (book value) amount of total assets and liabilities
aged 69.8%, with a maximum aggregate recovery rate from
at time of failure, deposit insurance payouts, and the amount
1995 bank failures of 86.6%. Such diminished recoveries dur-
recovered up to the date of the report.
ing periods of economic or industry distress have been noted
Annual percent of total recovery in each of years after failure
Failure Number of
Disbursements
year
new failures (U.S.$ thousands)
0
1
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
11
10
42
48
80
120
145
203
221
207
169
127
122
41
13
6
5
1
3
7
1581
152,355
888,999
2,275,150
3,807,082
7,696,215
2,920,687
4,790,969
5,037,871
12,163,006
11,445,829
10,816,602
21,412,647
14,084,663
1,797,297
1,224,797
609,045
169,397
25,546
285,763
1,234,278
31.64
25.03
14.14
23.68
50.86
26.24
26.04
22.81
32.11
33.37
19.15
29.21
26.74
71.35
22.16
55.03
0.00
0.00
12.29
100.00
27.95
59.19
18.11
25.68
8.41
27.22
34.42
40.61
31.22
35.52
56.58
22.49
34.88
8.19
34.18
16.95
88.31
97.26
87.71
2
3
4
5
6
7
8
9
19.22
4.30
11.08
9.44
10.02
18.74
15.55
12.28
2.25
18.00
7.53
36.97
28.54
12.10
19.07
24.42
4.04
2.74
4.87
4.23
11.70
9.55
7.06
12.76
8.31
7.58
5.12
0.64
9.44
6.48
1.09
2.28
22.02
3.59
7.65
4.93
3.32
6.52
10.79
9.38
3.84
4.46
6.29
5.12
0.64
1.37
1.39
2.71
2.28
1.60
0.00
5.53
0.54
9.74
7.30
3.93
1.57
0.77
4.83
5.12
0.64
0.53
0.61
2.71
3.12
0.96
2.98
2.21
2.64
3.42
6.10
0.02
7.66
2.58
0.45
1.04
3.19
-1.74
2.29
0.68
1.77
0.69
28.18
1.30
1.48
3.41
1.94
0.94
0.40
6.43
1.23
3.18
1.05
0.53
0.02
0.24
2.14
2.55
4.73
0.75
0.87
0.90
2.72
0.72
1.41
0.60
0.47
-2.15
5.92
0.15
0.22
0.00
0.65
16.86
0.46
0.25
10
0.00
0.00
-0.20
0.78
0.05
1.26
0.10
0.56
0.43
0.55
Total recovery,
2000 (%)
75.32
36.75
36.36
59.47
71.55
58.26
63.24
59.79
43.07
45.84
74.19
70.68
73.64
63.73
84.28
86.58
75.41
77.00
15.46
0.90
U.S.$102,838,198
Figure 1: Annual number, size, and progress of bank liquidations, 1980-2000
Sources: FDIC Annual Reports and author’s calculations. Note: In most cases prior to 1996, total recovery reflects the percent of total claims that were recovered during the entire
period of liquidation. Total recoveries after 1996 are more substantially incomplete. Negative recoveries may arise when banks return some assets previously purchased from the
FDIC under put-back options. Dark shading indicates period over which liquidation proceeds at ten percent per year. Lighter shading indicates progress of five percent per year.
105
by other authors writing on bankruptcy costs and are some-
asset appreciation across the liquidation period, yielding a V*
times thought to be associated with asset fire sales and/or
estimate that can be used to empirically test the stochastic
rapid liquidation [Pulvino (1998) and Shleifer and Vishny (1992)].
real options specification.
Figure 1, however, suggests that the fire sale/rapid liquidation
The FBCA database does not, however, contain details on bank
hypothesis may not adequately explain these liquidation out-
asset and liability compositions. Furthermore, once a bank
comes. Figure 1 presents aggregate FBCA data on both recov-
fails its charter is retired and each bank is assigned a unique
eries and liquidation speed. The main body of the figure shows
liquidation case number. I therefore hand-matched each
the percent of the total recovered amount that is collected in
bank’s liquidation case number to its pre-failure charter num-
each year of the liquidation. Shaded areas in the figure indi-
ber in order to link financial details of each at the last
cate the length of time that liquidation progresses at over five
observed call prior to failure to the liquidation reports in the
(light) and ten (dark) percent per year. If liquidation slows
FBCA. The resulting cross-sectional data set relates ex-ante
below that rate and then re-accelerates, the intervening peri-
bank asset and liability compositions to liquidation experi-
ods are also shaded. Although bank failures after 1997 are also
ences, measured by both liquidation speeds and asset value
included, their liquidations may not have progressed enough
growth
to be meaningful.
The crisis of the 1980s that caused the majority of bank failIn contrast to the fire sale/rapid liquidation hypothesis, the
ures in the sample is known to be the result of price volatility
rates and shading in Figure 1 suggest that the periods of bank
among several specific asset classes. The FDIC’s own accounts
failures associated with years of industry distress (and low
of the crises suggest that the favorable tax treatment for real
recovery rates) are associated with slower liquidation speed
estate development projects in the Economic Recovery Tax
(shading extending further to the right) than those occurring
Act of 1981 provided substantial incentive for construction
in other years. This coexistence of reduced recoveries and
lending [Federal Deposit Insurance Corporation (1997, 1998)].
slower liquidations may be the result of a rational application
The Tax Reform Act of 1986, however, removed this incentive,
of the options valuation framework described above. Firstly,
reducing the potential profit margins of a substantial number
lower asset values during periods of distress add value to the
of projects. Additionally, geographic areas that were particu-
timing option, so the trustee may rationally delay liquidation.
larly overbuilt (especially New England and the West) faced
Secondly, if periods of distress are accompanied by high asset
additional pressures when the national recession of 1990-91
price volatility and therefore high expected price growth in
reduced real estate demand, producing significant declines in
recovery, the option may be quite valuable and the trustee
rents, prices, and values of all types of real estate properties.
may rationally wait to liquidate.
Given the FDIC’s anecdotal evidence, I assume that banks’ real
For individual banks, the FBCA database provides the date of
estate and C&I loan compositions were the primary source of
failure and the date of resolution (if complete). Beginning in
their exposures to volatility and growth expectations that
1991, the FBCA report also contains estimated market values
affect the real options problem we want to measure. I use the
of expected final recoveries. These market values were esti-
Freddie Mac Conventional Mortgage Home Price Index to
mated each year by taking a sample portfolio of that year’s liq-
derive real estate growth spreads and volatilities and com-
uidations and reconciling those values with a statistical model
mercial & industrial loan interest and fee income as a percent
of historical market value estimates maintained at the FDIC.
of total loans (derived from Call Report data) to derive C&I
3
I use changes in these estimated market values to measure
106 - The
loan growth spreads and volatilities.
3 I thank Richard Brown of the FDIC for providing details on the market value estimation procedure.
Analysis and results
Figure 2 presents results of an OLS asset value growth model
for the 276 completed bank liquidations that began after 1990.
The asset volatility and discount rate — price growth spread
Model type: independent OLS
n
R2
Adjusted R2
(1)
(2)
276
0.105
0.092
272
0.146
0.103
Coefficient
(std. err.)
-0.290
(0.146)
125.703b
(73.767)
-0.011c
(0.007)
79.723c
(51.134)
8.12E-06
(0.004)
Coefficient
(std. err.)
-0.685a
(0.292)
76.972
(80.658)
-0.007
(0.007)
85.694c
(52.802)
-7.04E-05
(0.004)
0.015b
(0.008)
0.040
(0.097)
-0.087
(0.137)
0.180
(0.154)
0.031
(0.057)
0.055
(0.049)
-0.005
(0.026)
-0.053c
(0.038)
-0.027
(0.030)
variables alone (Column 1) explain 9.2 percent of the variation
in asset value growth in the present sample. In Column 1, the
Independent variable: asset appreciation
C&I Loan Price Volatility, the Discount Rate-C&I Loan Price
Constant
Growth Spread, and the Real Estate Price Volatility variables
all obtain the correct signs and are statistically significant. The
C&I loan price volatility
coefficient on the Discount Rate-Real Estate Price Growth
Discount rate – C&I loan price growth spread
Spread is statistically insignificant.
Real estate price volatility
The specification in Column 2 adds the control variables. The
addition raises the adjusted r-squared of the specification (to
10.3 percent), and the signs on all of the real options valuation
Discount rate – real estate price growth spread
Log of total assets
Past due and non-accrual loans/total loans
variables obtain the correct signs. However, only the coefficient on Real Estate Price Volatility remains statistically significant at conventional levels. Bank size is positively associated with asset value growth, V*, and banks located in the
Southeast realize lower asset value growth than those in the
Southwest (the omitted group).
Other real estate owned/total loans
Total deposits/total liabilities
Central
Midwest
Northeast
Figure 3 again relies on the restricted sample of 272 completed
bank liquidations beginning after 1990. However, here I esti-
Southeast
mate a process where both asset appreciation and liquidation
West
time are believed to be determined jointly by asset volatilities
and discount rate — price growth spreads, the control variables,
and each other in a three-stage least squares (3SLS) specification. I use different liquidation strategies employed by the FDIC
(a) Statistical significance at 1% (b) Statistical significance at 5%
(c) Statistical significance at 10%
Figure 2: OLS estimates of asset appreciation, 1991-1996 failed banks with complete resolutions
as exogenous variables. The three-stage least squares system
in Figure 3 explains more than 48 percent of the combined variation in asset value growth and liquidation time and the two
processes have a correlation coefficient of 0.26.
The results of the liquidation time specification in Figure 3,
Column 2, seem even stronger than those for asset value
The OLS results for asset value growth reported in Figure 2
growth, which may be affected by errors in the FDIC market
are robust enough to jointly estimate liquidation time in via
value estimation process. Both the Discount Rate — Real Estate
3SLS in Figure 3. All asset volatility and discount rate — price
Price Growth and Discount Rate — C&I Loan Price Growth
growth spread variables obtain the correct signs. Again, bank
Spread variable coefficients are negative and statistically sig-
size and location in the Southeast are statistically significant
nificant. Coefficients on the C&I Loan and Real Estate Price
control variables.
Volatility variables are positive and statistically significant.
107
Model type: 3SLS
n
R2 (System-wide for 3SLS)
Correlation between dependent variables:
Independent variable:
Constant
Discount rate – real estate price growth spread
Log of total assets
Past due and non-accrual loans/total loans
Length of liquidation (endogenous)
272
0.487
0.259
(1)
Asset
appreciation
Coefficient
(std. err.)
-0.869
(0.813)
71.615
(83.564)
-0.006
(0.007)
82.317c
(54.567)
-4.00E-05
(0.004)
0.015b
(0.008)
0.040
(0.097)
-0.084
(0.137)
0.178
(0.154)
0.027
(0.110)
Asset appreciation (endogenous)
Central
Midwest
Northeast
Southeast
0.032
(0.058)
0.057
(0.050)
-0.006
(0.026)
-0.054c
(0.039)
West
-0.027
(0.030)
Loglinear survival model: Logistic
Dependent variable (all models):
(2)
(log)
Liquidation
time
Coefficient
(std. err.)
4.135a
(0.333)
474.145a
(93.727)
-0.027a
(0.008)
693.164a
(61.216)
-0.008c
(0.005)
0.018b
(0.009)
0.318a
(0.110)
0.512a
(0.156)
0.022
(0.175)
0.407
(0.456)
0.057
(0.065)
0.003
(0.056)
0.073a
(0.030)
-0.022
(0.044)
0.047c
(0.034)
Figure 3: 3SLS estimates of resolution time and asset appreciation, 1991-1996
failed banks with complete resolutions
Log likelihood
Log likelihood (coef=0)
LR test of Sig. (χ2k)
Significance level
Number of total obs.
Number of obs. still active
272
0
1200
64
1200
64
Constant
Coefficient
(std. err.)
4.266a
Coefficient
(std. err.)
5.736a
Coefficient
(std. err.)
2.341a
(0.367)
502.935a
(90.533)
-0.029a
(0.274)
0.013a
(0.001)
-0.012a
(0.008)
719.644a
(55.149)
-0.007c
(0.001)
-335.088a
(32.298)
0.042a
(0.426)
297.175c
(186.658)
-0.012
(0.017)
693.440a
(123.463)
-0.008
(0.010)
-297.174c
(186.658)
0.011
(0.017)
-770.667a
(135.029)
0.013
(0.012)
0.118a
(0.009)
0.034
(0.086)
0.134
(0.119)
0.430a
Discount rate –
C&I loan price growth spread
Discount rate –
real estate price growth spread
(0.005)
* pre-trough indicator
Discount rate – Real estate price growth spread
Log of total assets
0.005
(0.008)
Past due and non-accrual loans/
0.229a
total loans
(0.091)
0.370a
(0.144)
0.058
(0.225)
(0.004)
0.108a
(0.009)
0.036
(0.089)
0.086
(0.122)
0.310b
(0.177)
Pre-trough indicator
Central
0.075
-0.087
(0.052)
(0.055)
Midwest
0.095
-0.356
(0.061)
(0.029)
Northeast
0.080
-0.105
(0.028)
(0.044)
Southeast
0.043
-0.078
(0.037)
(0.051)
West
0.047
-0.133
(0.027)
(0.028)
Figure 4: Duration estimates of liquidation time
108 - The
(log) Liquidation time
(2)
-437.0
-654.8
435.5
0.00
(1)
82.2
-20.2
204.8
0.00
(3)
-335.9
-654.8
637.6
0.00
(0.146)
2.987a
(0.358)
-0.065
(0.050)
-0.363
(0.027)
-0.066
(0.043)
-0.051
(0.048)
-0.064
(0.029)
The endogenous liquidation time and asset appreciation vari-
This result suggests that the options valuation problem may
ables are insignificant in Columns 1 and 2, respectively, sug-
also depend upon the direction of the economy. Only the
gesting that the real options and control variables adequately
volatility coefficients are significant in this specification, and
capture the endogenous effects. Given the positive correlation
the signs on volatility are negative in falling markets (suggest-
coefficient between the two processes and the performance of
ing quick disposal of volatile assets) and positive in expanding
the liquidation model, liquidation time may indeed serve as a
markets (suggesting delayed disposal of volatile assets).
useful second order proxy for asset value growth.
Hence it appears that volatility is a double-edged sword, benefiting the trustee in expansionary periods but posing a risk of
The first column of Figure 4 contains duration estimates of liq-
prolonged exposure to depressed asset values in contrac-
uidation time based on the previously analyzed sample of 272
tionary periods.
completed liquidations that began after 1990. Although the
sample size in Column 1 remains small all the volatility and dis-
Conclusion
count rate — price growth spread variables obtain the correct
Overall, I find evidence of a rational application of the trustee’s
signs and are statistically significant.
real options problem. Banks exposed to volatile assets or
assets with low discount rate — price growth spreads general-
Column 2, reports results of a duration model using all 1,200
ly take longer to liquidate and yield a greater value apprecia-
observations in the data set from 1986 to 1996.4 Here, the C&I
tion (higher V*) than others. Moreover, OLS estimates of the
Loan Price Volatility and Discount Rate — C&I Loan Price
stochastic model are correlated with the results of the three-
Growth Spread variables again obtain the correct signs and
stage least squares and duration models, suggesting that liq-
are statistically significant. However, the Real Estate Price
uidation time may provide a useful proxy for applying the
Volatility and Discount Rate — Real Estate Price Growth
options valuation approach in the real world, where market
Spread variables obtain the wrong sign and are statistically
value asset appreciation may be difficult to measure. Work is
significant. Column 3, adds the Pre-Trough Indicator (a peak-
already proceeding to test the robustness of the real options
to-trough indicator variable), which allows the coefficients on
specification to corporate bond defaults and recoveries
the volatility and discount rate — price growth spread vari-
[Cangemi et al. (2005)] and in the historical context of nine-
ables to vary across the business cycle. The coefficients on
teenth century and Depression-era bank liquidations [Mason
the original Real Estate Price and C&I Loan Price Volatility
and Redenius (2005a) and Calomiris and Mason (2005),
and Discount Rate — Real Estate Price Growth and Discount
respectively].
Rate — C&I Loan Price Growth Spread variables in Column 3
again obtain their appropriate signs in the presence of the
From an economic policy perspective, liquidation differences
Pre-Trough Indicator and interaction variables. This result
across the business cycle can be a source of a substantial pro-
occurs because the original variables now reflect real option
cyclicality, where fast liquidations when the economy is con-
valuation only during the business cycle growth period. The
tracting may help push prices downward and delay sales,
signs on the Real Estate Price and C&I Loan Price Volatility
heightening price volatility, economic uncertainty, and busi-
and Discount Rate — Real Estate Price Growth and Discount
ness cycle depth and persistence. Related work by Calomiris
Rate — C&I Loan Price Growth Spread interaction variables
and Mason (2003a), Anari, Kolari, and Mason (2005), and
(reflecting the contractionary period) are exactly opposite
Mason and Redenius (2005b) is already exploring these impli-
those of their expansionary counterparts.
cations in detail, although much work remains to be done.
4 The vastly different sample sizes result because the previous models rely crucially
upon estimated recovery data, which the FDIC only archived after 1990, to accurately measure asset appreciation. The earlier OLS was also estimated using 1991
estimated recovery data for banks failing before that year. The reported results
were qualitatively robust to the data adjustment. FBCA data is not available before
1986.
109
References
• Alderson, M. J., and B. L. Betker, 1995, “Liquidation costs and capital structure,”
Journal of Financial Economics, 39, 45-69
• Alderson, M. J., and B. L. Betker, 1996, “Liquidation costs and accounting data,”
Financial Management, 25, 25-36
• Anari, A., J. Kolari, and J. R. Mason, 2005, “Bank asset liquidation and the propagation of the U.S. Great Depression,” Journal of Money, Credit, and Banking (forthcoming). This is a revised version of Wharton Financial Institutions Center (Philadelphia,
PA) Working Paper No. 02-35, August 2002
• Calomiris, C. W. and J. R. Mason, 2005, “Rational divestiture in real options-based
liquidation cycles: Evidence from failed bank assets in the Great Depression,” Drexel
University Working Paper
• Calomiris, C. W., and J. R. Mason, 2003a, “The consequences of bank distress during
the Great Depression,” American Economic Review, 93, 937-47
• Calomiris, C. W., and J. R. Mason, 2003b, “Fundamentals, panics and bank distress
during the Depression,” American Economic Review, 93, 1615-1647
• Cangemi, R., J. R. Mason, and M. Pagano, 2005, “A real options approach to bankruptcy costs: Evidence from corporate bond defaults and recoveries,” Mimeo
• Dixit, A. K., and R. S. Pindyck, 1994, “Investment Under Uncertainty,” Princeton, NJ:
Princeton University Press
• Federal Deposit Insurance Corporation, 1997, “History of the Eighties — Lessons for
the future,” Washington, D.C. Federal Deposit Insurance Corporation, 1998,
“Managing the crisis: The FDIC and RTC experience 1980-1994,” Washington, D.C.
• Federal Deposit Insurance Corporation, “Annual report,” Various years,
Washington, D.C.
• Federal Deposit Insurance Corporation, “Failed bank cost analysis,” Various years,
Washington, D.C.
• Federal Deposit Insurance Corporation, “Reports of condition and income,” Various
years, Washington, D.C.
• Mason, J. R. and S. Redenius, 2005a, “A real options approach to bankruptcy costs:
Evidence from National Bank-era liquidations,” Mimeo
• Mason, J. R. and S. Redenius, 2005b, “Bank asset liquidation and the propagation of
nineteenth century business cycles,” Mimeo
• Pulvino, T. C., 1998, “Do asset fire sales exist: An empirical investigation of commercial aircraft transactions,” Journal of Finance, 53, 939-978
• Warner, J. B., 1977, “Bankruptcy costs: Some evidence,” Journal of Finance, 32, 337347
• Weiss, L. A., 1990, “Bankruptcy resolution: Direct costs and violation of priority of
claims,” Journal of Financial Economics, 27, 285-314
110 - The
Real options
Kuno J. M. Huisman
Consultant, Centre for Quantitative Methods
CQM B.V, and Researcher, Department of
Econometrics & Operations Research and CentER,
Tilburg University
Peter M. Kort
Professor, Department of Econometrics &
Operations Research and CentER,
Tilburg University, and Professor, Department of
Economics, University of Antwerp
Grzegorz Pawlina
Strategic investment
under uncertainty:
A survey of game
theoretic real options
models
Lecturer, Department of Accounting and Finance,
Management School, Lancaster University
Jacco J.J. Thijssen
Lecturer, Department of Economics,
Trinity College Dublin
Abstract
The non-exclusivity of real options for individual firms and the
growing importance of strategic interactions have given rise
to a research field that is situated on the intersection of real
options theory and game theory. This paper provides an
overview of the state of the art of game theoretic real options
models.
111
The main difference between financial options and real
only if the other firm refrains from undertaking the project.
options is that in most cases real options are not exclusive.
While discussing the standard model we show that imposing
Exercising a given option by one party results in the termina-
mixed strategies can deal with this coordination problem in
tion of corresponding options held by other parties. For
an economically meaningful way. This approach, being
example, an option to open an outlet in an attractive location
inspired by the deterministic analysis in Fudenberg and Tirole
is alive only until a competitive firm opens its own store
(1985), was developed in Huisman (2001) (see also Huisman
there.
and Kort (2003)) and formalized in Thijssen et al. (2002). A
similar attempt can be found in Boyer et al. (2001). We show
Currently, however, real options theory mainly considers sin-
that joint investment can occur even if it is optimal for only
gle decision-maker problems of firms operating in monopo-
one firm to invest. Furthermore, we discuss why it may be
listic or perfectly competitive markets. But capital budgeting
impossible to rule out such a joint investment even when pre-
decisions can be strongly influenced by existing as well as
play communication is allowed. In other words, we argue that
potential competitors. The growth of Asian economies like
the outcome with both firms coordinating and investing
China and India, as well as the extension of the European
sequentially with probability one, as in Smets (1991) and Dixit
Union are prime examples of developments leading to
and Pindyck (1994), may be unlikely to achieve.
increased interdependencies among firms around the globe.
As a result, former domestic market leaders now have to deal
One of the main results of the strategic real options literature
with competition. The conclusion is that there is a strong
is the rent equalization principle. According to this principle,
need to consider situations where several firms share the
the payoffs of the first mover (leader) and of the second
option to invest in the same project. This new topic requires
mover (follower) are equal. This results from the fact that the
a merger between game theory and real options.
leader has to invest no later than when the stochastic
demand reaches the preemption point, i.e. the level at which
Until a few years ago only a small number of contributions
the leader and the follower value functions intersect. Waiting
dealt with the effects of strategic interactions on the option
longer would ultimately result in a preemptive investment by
value of waiting associated with investments under uncer-
the competitor, attracted by the opportunity of realizing the
tainty. One of the main reasons is that the application of
leader’s payoff. A direct economic interpretation of the rent
game theory to continuous-time models is not well developed
equalization principle is that competition erodes the value of
and often quite tricky. However, due to the importance of
the option to wait.
studying the topic of investment under uncertainty in an oligopolistic setting, more publications have appeared recently
Subsequently, we show that if the initial level of demand is
[Grenadier (2000), Boyer et al. (2004), and Huisman et al.
higher than the demand level at the preemption point, but
(2004)].
lower than the demand level at which the second firm invests,
the only symmetric Nash equilibrium is the one in which the
This paper provides an overview of the state of the art, where
firms play mixed strategies. As a consequence, the firms may
we mainly concentrate on identical firms in a duopoly con-
end up investing simultaneously when it is not optimal to do
text. We begin by discussing a standard model. The model is
so, which could even lead to performing projects with nega-
a new market model and based on Dixit and Pindyck (1994).
tive net present values (NPVs). This is a result of the coordi-
Since the firms are identical it seems natural to consider sym-
nation problem associated with the selection of the leader
metric strategies. However, it can be expected that coordina-
and the follower roles.
tion problems arise in situations where investment is optimal
112 - The
Standard model
Given the stochastic process (Y(t))t≥0, we can define the pay-
The first paper dealing with a multiple decision-maker model
off functions for the firms. If there is a firm that invests first
in a real option context is Smets (1991). It considers an inter-
while the other firm does not, this firm is called the leader.
national duopoly where both firms can increase their revenue
When it invests at time t its discounted profit stream is given
stream by investing. Like in Fudenberg and Tirole (1985) two
by L(Y(t)). The other firm is called the follower. When the
equilibria arise: a preemption equilibrium, where one of the
leader invests at time t the optimal investment strategy of the
firms invests early, and a simultaneous one, where both firms
follower leads to a discounted profit stream F(Y(t)). If both
delay their investment considerably. A simplified version was
firms invest simultaneously at time t, the discounted profit
discussed in Dixit and Pindyck (1994) in the sense that the
stream for both firms is given by M(Y(t)). In the remainder of
firms are not active before the investment is undertaken. The
the paper, the time dependency of Y will be omitted. In most
resulting new market model only admits the preemption
cases, finding the optimal investment rule of a firm entails
equilibrium. In this section our symmetric mixed strategy
finding the value-maximizing threshold level of Y at which the
approach is applied to the new market model [Dixit and
firm should exercise its real option. In a strategic case, it often
Pindyck (1994), for a more thorough analysis see Thijssen et
happens (as in the game considered in this section) that no
al. (2002)].
pure strategy symmetric equilibria exist. In such a case the
equilibrium strategy entails exercising the option at a given
This model considers an investment project with sunk costs
threshold with a probability strictly smaller than 1.
I > 0. After the investment is made the firm can produce one
unit of output at any point in time. Since the number of firms
Let us first consider the optimal investment threshold of the
is two, market supply is Q ε {0, 1, 2}. It is assumed that the
follower, which we denote by YF. If the leader invests at Y < YF,
firms are risk neutral, value maximizing, discount with con-
the follower’s value is maximized when the follower invests at
stant rate r, and variable costs of production are absent. The
YF. The follower’s profit flow will be YD(2). Following familiar
market demand curve is subject to shocks that follow a geo-
steps [cf. Dixit and Pindyck (1994)], we can find YF. It satisfies
metric Brownian motion. In particular, it is assumed that the
unit output price is given by
P(t) = Y(t)D(Q),
YF = [β/(β-1)] x [(r – μ)I/D(2)
(1)
where β is given by
β = 1/2 – μσ2 + [(1/2 – μ/σ2)2 + 2r/σ2]1/2 > 1
in which
dY(t) = μY(t) dt + σY(t) dω(t),
(2)
Y(0) = y,
(3)
(4)
(5)
By rewriting (4) as
YFD(2)/r – μ = ξ I,
(6)
where y > 0, 0 < μ < r, σ > 0, and the dω (t)’s are independently and identically distributed according to a normal distribu-
where ξ ≡ β/(β–1), we can observe that the optimal investment
tion with mean zero and variance dt. Furthermore, D(Q) is a
rule is a modified NPV formula with a mark-up ξ, which is larg-
decreasing function, comprising the strategic part of the
er than 1. The mark-up ξ reflects the impact of irreversibility
inverse demand curve. Equations (1) and (2) imply that the
and uncertainty (both not taken into account in the tradition-
output price P(t) fluctuates randomly with drift μ and standard
al NPV rule) and is increasing in uncertainty (it holds that
deviation σ and that it always takes positive values.
∂β/∂σ < 0).
113
Since firms are identical, there seems to be no reason why one
Since we restrict ourselves to symmetric strategies, the only
of them should be given the leader role beforehand. The fact
possibility left is to apply mixed strategies. Denote the proba-
that firms are rational and identical also implies that it is hard
bility that Firm i invests at Y by αi. Consequently, αi can be
to establish coordination on a non-symmetric equilibrium.
interpreted as the probability that Firm i chooses row 1 in the
Therefore, we concentrate on equilibria that are supported by
matrix game depicted in Figure 1.
symmetric strategies. We use the subgame perfect equilibrium
concept for timing games as formalized in Thijssen et al.
Invest
Not invest
(2002). This approach extends the perfect equilibrium con-
Invest
( M(Y), M(Y) )
( M(Y), M(Y) )
cept of Fudenberg and Tirole (1985) to stochastic games. We
Not invest
( M(Y), M(Y) )
repeat game
present a less formal discussion of the firms’ strategies.
To describe the equilibrium, first define the preemption point
YP = minY {Y\L(Y) = F(Y)},
(7)
Figure 1: Payoffs and actions in the bimatrix game. Firm 1 is the row player and
firm 2 the column player
The game is played at Y if no firm has invested so far. For Y >
YP this can happen either by mistake or that Y is the initial
This point is called preemption point because to the right of
value. In all the other cases, at least one of the firms would
this point the leader value, L(Y), exceeds the follower value,
have invested before the process presented in (2) has reached
F(Y), and this results in strategic behavior of the firms trying
Y. Playing the game costs no time and if Firm i chooses row 2
to preempt each other by investing, as will become apparent
and Firm j column 2 the game is repeated. If necessary the
from the description below. The equilibrium under considera-
game will be repeated infinitely many times. Since αi and αi
tion is therefore called a preemption equilibrium.
are the probabilities that Firm i and Firm j invest at a given
level of Y, they are the control variables that need to be opti-
There are three potential scenarios that we can consider. The
mally determined. To do so, define Vi as the value of Firm i,
first can be defined by Y ≥ YF. This outcome exhibits immedi-
which is given by:
ate joint investment. Here the unit output price is large
enough for both firms to enter the market. The second scenario is where YP ≤ Y < YF. Immediate joint investment gives a
payoff M(Y). This is not a Nash equilibrium since if one of the
Vi = Max [αi (1 – αj)]L(Y) + (1 – αi)αjF(Y) + αiαjM(Y) +
αi
(1 – αi)( 1 – αj)Vi
(8)
firms deviates by waiting with investment until the process Y
hits the trigger YF, it obtains the follower value F(Y). This fol-
Since Firm i invests with probability αi and Firm j with proba-
lower value exceeds M(Y) as long as YP ≤ Y < YF. M(Y) can be
bility αj, the probability that Firm i obtains the leader role, and
negative for Y values belonging to the interval (YP, YF), which
thus receives L(Y), is αi [1–αj]. Similarly, with probability [1 – αi]
is equivalent to a negative NPV.
αj Firm i is the follower, αiαj is the joint investment probability,
and with probability [1–αi] [1–αj] nothing happens and the
In case both firms refrain from investment and wait until Y
game is repeated. After determining down the first order con-
hits YF, they get the follower payoff F(Y). Again this is not a
ditions for Firm i and Firm j, and imposing symmetric strate-
Nash equilibrium, because if one of the firms deviates by
gies, i.e. αi = αj = α, it is obtained that
investing, this firm receives a payoff L(Y) that exceeds F(Y)
on this interval.
114 - The
α = [L(Y) – F(Y)]/[L(Y) – M(Y)]
(9)
We know that M(Y) < F(Y) ≤ L(Y) on the relevant Y-interval
which leaves less room for the equal probabilities of being the
[YP, YF), so that we are sure that the probability α lies
first or second investor.
between zero and one. From (9) it is obtained that, given the
difference L(Y) – M(Y), the firm is more eager to invest when
In the third scenario it holds that Y < YP, in which the follower
the difference between the payoffs associated with investing
value exceeds the leader value. Hence, investing first is not
first and second is large.
optimal so that both firms refrain from investing and wait until
After substitution of α = αi = αj into (8), the value of Firm i can
ing that L(YP) = F(YP), it can be obtained from (9) that α = 0.
be expressed as
From (12) we get that the probability for a firm to become
Y = YP. Then the second scenario is entered, and upon observ-
leader is one half, and with the same probability this firm will
Vi = [α(1 – α)L(Y) + (1 – α)αF(Y) +
α2M(Y)]/(2α
–
α2)
(10)
be the second investor. Furthermore, from (11) it can be concluded that the probability of simultaneous investment at YP
Of course, both firms do not want to invest at the same time,
is zero. All this implies that one of the firms will invest at YP
because it leaves them with the lowest possible payoff M(Y).
and the other one, being the follower, will wait until Y equals
From (10) it can be obtained that the probability of occurrence
YF. Since the values of leader and follower are equal at YP, the
of such a mistake is
firms have equal preferences of becoming the first or the second investor in this case, so that we have rent equalization.
α/(2 – α)
(11)
The first mover advantage results in equilibrium strategies in
which increases with α. We also see that, whenever α is
which both firms take a positive probability of making a mis-
greater than zero, which is the case for Y ε (YP , YF), the prob-
take in order to get the leader payoff. Substitution of equation
ability that the firms invest simultaneously is strictly positive.
(9) in (10) eventually shows that a firm sets its intensity α such
This is not in accordance with many contributions in the liter-
that its expected value equals the follower value. Due to the
ature. For instance, Smets (1991) and Dixit and Pindyck (1994)
risk-neutrality the firm is indifferent between obtaining the fol-
state that ‘if both players move simultaneously, each of them
lower payoff for sure (α equal to zero) and obtaining the fol-
becomes leader with probability one half and follower with
lower payoff as expected value (α as defined in (9)).
probability one half’.
Our analysis is based on the assumption that the firms do not
Similarly, it can be obtained that the probability of a firm being
communicate in an attempt to coordinate their actions. This
the first investor equals
results in a positive probability of making a mistake, i.e. investing jointly while the level of demand is not sufficiently high.
(1 – α)/(2 – α)
(12)
Such an outcome is ruled out by some authors, e.g. Smets
(1991) and Dixit and Pindyck (1994), who assume that coordi-
Due to symmetry this is also the probability of the firm ending
nation is possible via ‘tossing a coin’. Consequently, the game
up as the follower. Since the probability of simultaneous
analyzed in these papers require introducing a third player,
investment increases with α, it follows that the probability of
nature, who assigns the roles to the firms in the situation,
being the first investor decreases with α, which is at first sight
where both of them want to invest immediately.
a strange result. But it is not that unexpected, because if one
firm increases its probability to invest, the other firm does the
We argue that such a coordination as in Smets (1991) and Dixit
same. This results in a higher probability of investing jointly,
and Pindyck (1994) seem unfeasible without introducing a
115
third player (nature), even when firms are allowed to commu-
nates rent equalization present in the basic strategic real
nicate. Any collusive agreement among firms in region (YP, YF)
option model. Among other things, a surprising result is found
would be hard to sustain because of the following arguments.
that the value of the high cost firm can increase in its own
Firstly, none of the firms would accept the follower role, which
investment cost. In Huisman and Kort (2004) firms take into
is associated with a lower payoff than that of the opponent.
account the occurrence of future technologies when deciding
Consequently, the only remaining possibility is an agreement
about investment. A scenario is identified where the possibili-
on the firms’ roles with a monetary transfer from the leader to
ty of the arrival of a new technology results in a game with a
the follower. However, even if we ignore the fact that such an
second mover advantage. In such a case, it is optimal for a firm
act is illegal, the leader cannot credibly commit to meet his
to be the follower and to wait for the new technology rather
obligations once his investment is made. The follower, who
than to be the first mover locked into the inferior older tech-
anticipates the leader’s default on its promised payment,
nology. Finally, Thijssen (2004, Part I) extends the existing real
enters the preemption game, which results in the mixed strat-
option literature by studying a framework where over time
egy equilibrium described above.
information arrives in the form of signals. This information
reduces uncertainty. In analyzing a new market model it is
The outcome of Smets (1991) and Dixit and Pindyck (1994) is
found that the mode of the game depends on the first mover
unlikely to occur even if successful coordination is allowed for
advantage relative to the value of information free riding of
(e.g. if some mechanism exists that enables credible commit-
the second mover, who observes the true state of the market
ment of the leader). Allowing for the possibility of pre-play
after the leader’s entry. Consequently, a firm has to trade off
agreement on the roles of the leader and of the follower will
the benefit of entering the market earlier with the risk of
neutralize the incentive to preempt (since preemption is not
incurring the investment cost in the bad state of the market.
associated with the maximization of the firms’ joint value). So,
any binding agreement will not result in an equilibrium à la
Besides our own extensions, the framework being presented in
Smets (1991) and Dixit and Pindyck (1994).
the previous section is used for many other applications.
Grenadier (1996) applies it to the real estate market, Weeds
Instead, the leader will invest at some Y, say YL, which is
(2002) and Miltersen and Schwartz (2003) study R&D invest-
greater than YP but smaller than YF, such that YL maximizes
ments, Pennings (2004) and Pawlina and Kort (2002) analyze
the leader value.
the product quality choice, Mason and Weeds (2003) and
Lambrecht (2004) study merger policy and entry, Boyer et al.
116 - The
Extensions
(2001) look at incremental indivisible capacity investments,
As an illustration of the applicability of the strategic real
Lambrecht (2001) takes into account debt financing, Nielsen
option framework, we proceed by reviewing some of our own
(2002) and Mason and Weeds (2001) analyze the effects of
work. Huisman (2001) shows that if firms already compete in
positive externalities, Grenadier (1999), Lambrecht and
the product market, they may avoid entering the preemption
Perraudin (2003), and Décamps and Mariotti (2004) consider
game and invest jointly when demand is sufficiently high. This
incomplete information, Pawlina and Kort (2003) explicitly
results from the fact that foregoing a part of the future cash
model demand uncertainty, Cottrell and Sick (2001, 2002)
flow due to postponing the investment beyond the leader’s
study the interaction of first mover advantages and real
optimal threshold can be more than compensated by a reduc-
options, Sparla (2004) and Murto (2004) consider the deci-
tion in the present value of the investment cost (which will be
sion to close down, while Williams (1993), Baldursson (1998),
incurred later). In Pawlina and Kort (2001) it is shown that
Grenadier (2002), Aguerrevere (2003), and Murto et al.
introducing asymmetry in the investment cost function elimi-
(2004) study oligopolies with more than two firms.
Application of our method to the standard model showed that
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• Grenadier, S. R., 1999, “Information revelation through option exercise,” The Review
of Financial Studies, 12, 95–129
• Grenadier, S. R., 2000, “Game Choices: The Intersection of Real Options and Game
Theory,” Risk Books, London, United Kingdom
• Grenadier, S. R., 2002, “Option exercise games: An application to the equilibrium
investment strategies of firms,” The Review of Financial Studies, 15, 691–721
• Huisman, K. J. M., 2001, “Technology Investment: A Game Theoretic Real Options
Approach,” Kluwer Academic Publishers, Dordrecht, The Netherlands
• Huisman, K. J. M. and P. M. Kort, 2003, “Strategic investment in technological innovations,” European Journal of Operational Research, 144, 209–223
• Huisman, K. J. M. and P. M. Kort, 2004, “Strategic technology adoption taking into
account future technological improvements: A real options approach,” European
Journal of Operational Research, 159, 705–728
• Huisman, K. J. M., P. M. Kort, G. Pawlina, and J. J. J. Thijssen, 2004, “Strategic
investment under uncertainty: Merging real options with game theory,” Zeitschrift
für Betriebswirtschaft, 67, 97–123
• Lambrecht, B. M., 2001, “The impact of debt financing on entry and exit in a
duopoly,” The Review of Financial Studies, 14, 765–804
• Lambrecht, B. M., 2004, “The timing and terms of mergers motivated by economies
of scale,” Journal of Financial Economics, 72, 41–62
• Lambrecht, B. M. and W. Perraudin, 2003, “Real options and preemption under
incomplete information,” Journal of Economic Dynamics & Control, 27, 619–643
• Mason, R. and H. Weeds, 2001, “Irreversible investment with strategic interactions,”
CEPR Discussion Paper No. 3013, London, United Kingdom
• Mason, R. and H. Weeds, 2003, “The failing firm defence: Merger policy and entry,”
University of Southampton, Southampton, United Kingdom
• Miltersen, K. R. and E. S. Schwartz, 2003, “R&D investments with competitive interactions,” EFA 2003 Annual Conference Paper No. 430
• Murto, P., 2004, “Exit in duopoly under uncertainty,” The Rand Journal of
Economics, 35, 111–127
• Murto, P., E. Näsäkkälä, and J. Keppo, 2004, “Timing of investments in oligopoly
under uncertainty: A framework for numerical analysis,” European Journal of
Operational Research, 157, 486–500
fashion. Nevertheless, in the literature the prevailing method
is to rule out simultaneous exercise beforehand [besides our
own work, an exception is Boyer et al. (2001)]. This is either
done by (i) assumption or by (ii) avoiding cases where suboptimal simultaneous investment can occur. Examples of (i) are,
for instance, Grenadier (1996) who assumes that ‘if each tries
to build first, one will randomly (i.e. through the toss of a coin)
win the race’, or Dutta et al. (1995) where it is assumed that ‘If
both i and j attempt to enter at any period t, then only one of
them succeeds in doing so’ [for a similar argument, see
Nielsen (2002)]. Examples of (ii) are Weeds (2002) who in a
new market model assumes that the initial value lies below the
preemption point, so that sequential investment is the only
equilibrium outcome, or Pennings (2004), Mason and Weeds
(2003) and Pawlina and Kort (2002), where the leader and follower roles are exogenously assigned.
Overall, with this contribution we attempted to show that the
strategic real option framework is a suitable tool to extend the
industrial organization literature in a dynamic stochastic
direction. By reviewing some existing research in this field, this
paper proves that the interplay of game theory and real option
valuation is a fascinating area that can generate economic
results being significantly different from what is known from
the existing industrial organization literature.
117
• Nielsen, M. J., 2002, “Competition and irreversible investments,” International
Journal of Industrial Organization, 20, 731–743
• Pawlina, G. and P. M. Kort, 2001, “Real options in an asymmetric duopoly: Who benefits from your competitive disadvantage?” CentER Discussion Paper 2001-95,
Tilburg University, CentER, Tilburg, The Netherlands
• Pawlina, G. and P. M. Kort, 2002, “The strategic value of flexible quality choice: A
real options analysis,” Working paper, Tilburg University, Tilburg, The Netherlands.
• Pawlina, G. and P. M. Kort, 2003, “Strategic capital budgeting: Asset replacement
under market uncertainty,” OR Spektrum, 25, 443–480
• Pennings, E., 2004, “Optimal pricing and quality choice when investment in quality
is irreversible,” The Journal of Industrial Economics, 52, 569–589
• Smets, F., 1991, “Exporting versus FDI: The effect of uncertainty, irreversibilities and
strategic interactions,” Working Paper, Yale University, New Haven, Connecticut,
United States of America
• Sparla, T., 2004, “Closure Options in a Duopoly with Strong Strategic Externalities,”
Zeitschrift für Betriebswirtschaft, 67, 125-155
• Thijssen, J. J. J., 2004, “Investment under Uncertainty, Coalition Spillovers and
Market Evolution in a Game Theoretic Perspective,” Kluwer Academic Publishers,
Dordrecht, The Netherlands
• Thijssen, J. J. J., K. J. M. Huisman, and P. M. Kort, 2002, “Symmetric equilibrium
strategies in game theoretic real option models,” CentER Discussion Paper 2002-81,
Tilburg University, CentER, Tilburg, The Netherlands
• Weeds, H., 2002, “Strategic delay in a real options model of R-D competition,” The
Review of Economic Studies, 69, 729–747
• Williams, J. T., 1993, “Equilibrium and options on real assets,” The Review of
Financial Studies, 6, 825–850
118 - The
Assets
Pricing with time-technology and timescapes
Inflation-induced valuation errors in the stock market
Is the investor sentiment approach the
solution to the IPO underpricing phenomenon?
The credit spread puzzle
Impact of seasonality on inflation derivatives pricing
Efficient pricing of default risk:
Different approaches for a single goal
Pricing with time-technology and
timescapes
Bala R. Subramanian
Associate Professor, DeVry University
Wisdom, knowledge, and information are required to survive in
Review, the 1974 Nobel Laureate in Economics, Frederick
the 21st century. Is there a way to provide these without having
Hayek (1945) admired the ‘efficiency with which the market
to spend years in schools, colleges, and universities? It would
processes the pricing information and sparingly allocates the
seem humanity is on the verge of making such a transforma-
scarce resource in a multiplicity of its use throughout the
tion. This article discusses some of the issues and their poten-
economy.‘ So, pricing has become central to our economic
tial in a very novel way.
processes and hence perhaps even for the wellbeing of human
kind.
The economics of pricing1 is a complex subject and includes
many fields of human knowledge and endeavors. The princi-
In an Internet culture, a functioning knowledge society has
ple of scarcity has been the basis of economic models.
come to rely on the pricing mechanism to provide the appro-
Scarcity is a function of time. Hence, speed [Mansfeld
priate signals necessary to adjust allocations of not only all
(2004)] is valued, advocated, and sought to bring about
resources, but also to impart value to actions in many con-
financial transformations of economic systems. Time and its
texts. Through differential pricing [Clemons et al. (2002)] it is
measurement have thus become central to modern
believed, disintermediation could be avoided in the presence
economies and their studies. Economists have computed
of customer heterogeneity. This paper examines the implica-
their time series3 of economic data based on the geographi-
tions of this conventional wisdom and proposes an alternative
cal time (solar clocks and solar calendar); both micro and
to the complete dependence on the geographical time scale in
macro studies of economic variables are computed using this
order to solve societal conflicts. This proposed framework
geographical time parameter. In international trade world
might foster true egalitarianism and pragmatism [James
wide pricing has acquired a unique complexity due to its influ-
(2000)] which might provide true and complete freedom from
ence on the profits, taxes, and regulations pertaining to its
any and all societal strife which has been the declared goal of
implications on domestic market structures [Wild et al.
modern governments [Davies (1996)].
2
(2003)]. In the pricing of the financial products such as
options, futures, and bonds time durations help measure the
The flow of time in addition to being geographical (i.e., based
risks [McDonald (2004)]. The durations included in these
on the location of our planet in the solar system and the lon-
computations also are traditionally a function of the solar
gitude and latitude on the globe, or what is denoted as ‘spa-
clock times as well. Price differentials, both in the products
tial’) is a function of societal relationships. When it comes to
and factors markets, cause economic agents to either specu-
pricing or establishing a value of exchange the latter measure
late or conduct time and/or market arbitrages. Here again,
of time and its duration has a greater significance than
the solar clock time plays the central role. An outcome of
understood by the economists and scientists of the industrial
either a profitable or unprofitable speculation is essentially a
era who were preoccupied with our physical universe and the
solar clock dependent phenomenon. Determinants of eco-
human relationship with that universe. When we eliminate an
nomic profits are functions of costs and costs are measured
important step or an intermediary layer of societal-time4 that
using the geographic time units. When it comes to the cost-
has a vital role on the outcome, we risk losing valuable infor-
ing of information we include the value of time spent to
mation necessary for its measurement and inclusion in our
acquire it, since ‘time is money.’ But, here again we are con-
valuations. Before we include the spatial time in our compu-
sistent in the use of solar clocks and solar calendar time to
tations we need to account for the time and the durations
help value this scarce economic resource.
inherent in societal relationships and processes. If we do not
account for these variations and the resulting costs associat-
120
According to Paul Gregory, writing in American Economic
ed with that phenomenon of time then the outcomes of our
1
3 A time series is a measurement of one or more variables over a designated period
of time, such as months, years, or quarters.
4 Societal-time is a new phrase coined by this author to denote the unique combination of the relationships of individuals to one another and to their societal institutions, processes, and methods that govern the outcome of such relationships.
A money price is a price expressed in monetary units, a relative price is a price
expressed in terms of other commodities, while a price system is the entire set of
relative prices.
2 Scarcity exists when the amount of the good or resource offered is less than what
users would want if it were given away free.
decision-making processes become unpredictable. In the
value creation cycles of individuals and communities that cre-
parable of the householder (King James Version of Bible,
ate and sustain the wealth of nations?
Matthew ch. 20) the Kingdom of Heaven prices the services
of a laborer equally at the first hour and the eleventh hour
Many authors [Hayami (1997)] and economists have correctly
and attributes this inequity to the goodness of that house-
identified the interdisciplinary nature of this wealth building
holder. In the 21st century how can we account for our busi-
task but have failed to recognize that one of the main reasons
ness cycles and pricing inequities beyond statistical and data
for this complexity is the misunderstanding and perhaps even
input errors? The most effective way to include and measure
misuse of our geographical time as a substitute for the socie-
the goodness of the heavenly householder and its present
tal time. In my view the measurement and streamlining of the
day equivalent societal values is to measure the phenomena
societal processes using individual and appropriate clocks
of societal-time, using timescapes [Subramanian (2003b)]
could lead to the successful integration of global economies
and by the development of time-technologies akin to our
much more easily. Even if we could successfully integrate
present day space-technologies that could further our knowl-
regional economies using common markets and could modify
edge about our valuations and perhaps improve the dismal
our human behaviors to a single and uniform set of standards,
status of our economic sciences.
which may take many years and many a political battles, liberating the human capital and obtaining the liquidity [Shojai et
The flow of the geographical-time is a summary of many a
al. (2001)] would be impossible using our geographic-clocks
societal-times akin to the white light from the suns rays we see
and that measure of durations alone because of the variations
which is a summary of many other colors of differing frequen-
inherent in the creativity, health, individuality, and thought
cies in the visible spectrum of lights. If our economic data
processes of humans.
series fail to differentiate the many shades and color values of
time and the durations associated with those units of meas-
Data mining experts in finance [Kovalerchuk and Vityaev
ures, then the interpretation of those series become question-
(2004)] have concluded that matching tasks with methods is
able at best and meaningless and incorrect for useful eco-
a very complex endeavor leaving one to conclude, it is more an
nomic analysis and its application at its very least.
art than a science. The noise described with those time series
could perhaps be due to the failure to associate data with a
Time-technology is the science of decoding the mystery of
societal-time framework prior to their conversion to the geo-
geographical time and its relationship to human existence. The
graphical-time used in these computations.
geographical time produces seasons and weather conditions
that affect the lives of many kingdoms (plant, animal, and
With the introduction of the Internet and the benefits of e-
many other organisms). The bio-clocks in these kingdoms gov-
commerce [Litan and Rivlin (2001)] the geographical time unit
ern the flow of events necessary for their survival and their
has entered a new phase of obscurity for economic data.
interdependence. In like manner the economic-clock that gov-
According to Prof. Samuelson (2004), ‘there is no valid reason
erns the value creation processes of the universe balance our
to think that if we were only a little more knowledgeable and
ecosystems. Our present day monetary, pricing, trading, and
a little more energetic, we could converge on highly accurate
exchanging mechanisms seems to have been created without
macro forecasts. Mass behaviors answer to no simple discov-
regard to this truism. Could this anomaly be the reason that
erable set of rules.’ The best way to discover rules of behavior
produces our social and family strife? If so, what could be done
is by mapping events and their durations on a virtual
to improve this? How can we create and use the many eco-
timescape independent of any geographical limitations. The
nomic-clocks that could provide the correct rhythms for the
U.S. asset management industry as well as the global investors
121
whose equity market capitalization amounted to U.S.$36 tril-
productivity by being in multiple locations concurrently to
lion in 1999 [Shojai and Preece (2001)], lack a uniform meas-
safeguard their interests in all relevant virtual meeting places.
ure of time to value their interests. The future no longer is
Collaborative networks, be they financial trading (CTN) [Shojai
merely represented by the calendar year millennia but resides
(2001)] or of any other kind, should be capable of detecting
in the thought processes of the future generations [Feiger and
nuances to data not only according to the Enterprise
Shojai (2003)]. Any data collection and its use for meaningful
Integration (EAI) principles of Extract, Transform and Load
analysis should begin by associating that data with the indi-
(ETL) [Dilkes (2004)] or Extract, Load and Transform (ELT) but
vidual entities that cause an event to occur in their respective
also relate the many contexts affected by its societal relation-
time horizons and yet be amenable to integration. The cre-
ships contained in timescapes [Subramanian (2004)].
ation of trust and a sustainable point of differentiation for
financial relationships have to begin with the use of
The complexity of wealth management in the 21st century
timescapes that show changes over many generations and
[Feiger and Shojai (2001)] may not be addressed fully without
many societal cultures. Brands conceived in the transactions
a sophisticated link to the social contexts of the individual
era may have to be evaluated in the relationship era [Boone
economies and the global citizenry. Trust [Zak (2003)] and
and Kurtz (2003)] using cultural and social contexts of greater
risk [Bryan (2002)] are all related to social contexts and soci-
depth to show product performance. The predicted disinter-
etal processes that may not be summarized in solar
mediation [Shojai and Wang (2003)] of financial intermedi-
timescape measurements alone. If the laboratory experi-
aries might not happen even after ‘the dust settles over the
ments belie the predicted outcome of Nash equilibrium we
internet landscape’ as those authors argue due to the fact that
could attribute this deviation to the lack of data mapping of
‘improving the efficiency of the world we live in’ is likely to
societal processes and their significance for understanding
remain invisible in solar timescape. I tend to agree with Myron
human behavior. Fear of the unknown is the natural outcome
Scholes (2004) that complex securities are hard to value espe-
of giving greater importance to the landscapes and the real
cially when using solar time alone. Using societal timescapes
estates than to the timescapes and the human societal val-
that measure the efficiency of markets in meaningful ways to
ues. The perceived law of motion [Kedar-Levy (2003)] (PLM)
an individual investor or a group of investors of uniform
and the actual law of motion (ALM) could be based on socie-
demography might bring about the much needed transparen-
tal time and long periodic events caused by human sociology
cy in that industry for its survival.
rather than market portfolio valuations or simple dynamic
asset pricing models. Economists [Walter (2001)] will have to
If we look at the evolution of currency [Turk (2004)] and try
look beyond a ‘New Economy’ to study the causes and effects
to provide all of the properties of money to money substi-
of events. Integration for banks [Derrer (2002)] can not be
tutes using new technologies as suggested by that author
complete by bringing ‘together a wide range of different
then, to guarantee the purchasing power to money substi-
processes, based on different technologies, and synthesize
tutes we need to develop timescapes and time-technologies
them into a coherent whole’ unless that includes the human
[Subramanian (2003)].
values and the human societal processes on which financial
assets are created and used.
If we want to extract the business value of IT by increasing its
122 - The
usage [Marchand (2004)], we should be able to link every user
The virtual matching utilities (VMU) that ‘allow for the seam-
to that technology in meaningful ways using each user’s soci-
less real time matching of trade data throughout the trade life-
etal time and societal roles by providing the timescapes to
cycle’ [Walsh (2001)] need not limit its concept of real-time to
software agents that can help that individual enhance his/her
the present day geographical time. By not doing so, the cul-
tural aspects of a societal relationship that caused that transaction are not utilized and are lost in the analytical studies.
If we extend this understanding to hedge fund investing
[Lhabitant (2003)] we might question the effectiveness of a
diversification strategy that is limited to styles and market
inefficiencies alone. Diversification by demographic characteristics and the societal timescapes of the investing and the
marketing members of the global citizenry is likely to produce
the hedge funds of the right radar type.
Conclusion
Societal time and timescape is a dynamic and comprehensive
medium to value exchanges. Societal-time pricing mechanism
could be trusted to incorporate all relevant variables in realtime and the economic analysis of that data-time series would
be able to better signify the effects of macro and micro policy.
Information technology has a role to play in bringing about the
integration of an individual with all of the communities and all
of the roles taken-up in those communities and their impact
on the rest of those community members and their roles.
Since all these relationships are changing, evolving, and occurring simultaneously data, information, knowledge, and wisdom
have to be extracted continually to fit a societal need and its
scope. The technology, architecture, and the logic to transform the meaning of these relationships are likely to preoccupy the minds of many next generation solution providers for
several decades to come. I hope they could be trusted to look
into these societal-time phenomena as well to impart a degree
of utility to their integration mechanisms [Thillairajah (2004)].
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123
Inflation-induced valuation errors
in the stock market1
Kevin J. Lansing, Senior Economist, Research Department,
Federal Reserve Bank of San Francisco
The long-run rate of return on stocks is ultimately determined
This valuation technique is often referred to as the ‘Fed
by the stream of corporate earnings distributions (cash flows)
model,’ but it is important to note that the Federal Reserve
that accrue to shareholders. In assigning prices to stocks, effi-
neither uses nor endorses it. Many authors, including Ritter
cient valuation theory says that rational investors should dis-
and Warr (2002) and Asness (2003), have pointed out that
count real/nominal cash flows using real/nominal interest
the practice of comparing a real number like the E/P ratio to
rates. A recent front-page article in the Wall Street Journal,
a nominal yield does not make sense. It would be more cor-
however, documented an increasing tendency among econo-
rect to compare the E/P ratio to a real bond yield, but that
mists to move away from theories of efficient stock market
comparison still ignores the different risk characteristics of
valuation in favor of ‘behavioral’ models that emphasize the
stocks versus bonds and the reality that, over the past four
role of irrational investors [Hilsenrath (2004)]. Twenty-six
decades, cash distributions to shareholders in the form of
years ago, Modigliani and Cohn (1979) put forth the hypothe-
dividends have averaged only about 50% of earnings.
sis that investors may irrationally discount real cash flows
using nominal interest rates — a behavioral trait that would
Long-run yield comparison
lead to inflation-induced valuation errors. This article exam-
Wall Street practitioners often argue that comparing the E/P
ines some recent research that finds support for the
ratio to a nominal bond yield is justified by the observed co-
Modigliani-Cohn hypothesis. In particular, studies show that
movement of the two series in the data. I tested this hypothe-
the Standard & Poor’s (S&P) 500 stock index tends to be
sis by looking at the relationship between the E/P ratio of the
undervalued during periods of high expected inflation (such as
S&P 500 index (based on 12-month trailing reported earnings)
the late 1970s and early 1980s) and overvalued during periods
and both the nominal and real yields on a long-term U.S.
of low expected inflation (such as the late 1990s and early
Treasury bond (with a maturity near 20 years) over the period
2000s). This result implies that the long bull market that
December 1945 to June 2004. The real yield is obtained by
began in 1982 can be partially attributed to the stock market’s
subtracting expected inflation from the nominal yield.
shift from a state of undervaluation to one of overvaluation.
Expected inflation is constructed as an exponentially weighted
Going forward, the return on stocks could be influenced by a
moving average of past (12-month) CPI inflation, where the
shift in the opposite direction.
weighting scheme is set to approximate the time-series behavior of the one-year-ahead inflation forecast from the Survey of
Stock as a ‘disguised bond’
Professional Forecasters.
Famed investor Warren Buffett has described a stock as a
type of ‘disguised bond’. A stock represents a claim to a
I found that the E/P ratio is more strongly correlated with
stream of earnings distributions whereas a bond represents a
movements in the nominal yield than with the real yield, par-
claim to a stream of coupon payments. Given that stocks and
ticularly since the mid-1960s. This result is a puzzle from the
bonds can be viewed as competing assets in a portfolio,
perspective of efficient valuation theory. Observed move-
investors may wish to compare the valuations of these two
ments in the nominal yield can be largely attributed to
asset classes in some quantitative way. Wall Street practi-
changes in expected inflation which, in turn, have been driven
tioners typically compare the earnings yield on stocks (denot-
by changes in actual inflation. If investors were rationally dis-
ed here by the E/P ratio, the inverse of the price-earnings
counting future nominal cash flows using nominal interest
ratio) with the nominal yield on a long-term U.S. Treasury
rates, they would understand that inflation-induced changes in
bond. Stocks are supposedly undervalued relative to bonds
the nominal bond yield are accompanied by inflation-induced
when the E/P ratio exceeds the nominal bond yield and over-
changes in the magnitude of future nominal cash flows.
valued when the E/P ratio is below the nominal bond yield.
Indeed, Asness (2003) shows that low-frequency movements
1
124 - The
This article is adapted from the Economic Letter series published by the Federal
Reserve Bank of San Francisco. The views stated here are those of the author and
not necessarily those of the Federal Reserve Bank of San Francisco or of the Board
of Governors of the Federal Reserve System.
in the U.S. inflation rate are almost entirely passed through to
out that this simple behavioral model can account for 70% of
changes in the growth rate of nominal earnings for the
the variance in the observed E/P ratio from December 1945
S&P 500 index. Thus, to a first approximation, a real valuation
to June 2004. In contrast, an otherwise identical model that
number like the E/P ratio (or its inverse, the P/E ratio) should
employs real explanatory variables can account for only 26%
not move at all in response to changes in the nominal bond
of the variance in the observed E/P ratio. When the fitted E/P
yield. Similar logic applies to the residential housing market;
ratios from both the nominal and real models are inverted for
the ratio of house prices to rents (a real valuation number)
comparison with the observed P/E ratio of the S&P 500 index
should not be affected by inflation-induced changes in mort-
we find that the nominal model does a much better job of
gage interest rates. Nevertheless, the data show that the ratio
matching the level and volatility of the observed P/E ratio.
of house prices to rents in the U.S. economy has been trend-
The real model, in contrast, predicts a relatively stable P/E
ing up since the mid-1980s as inflation and mortgage interest
ratio — one that remains close to its long-run average over
rates have been trending down.
much of the sample period, particularly during the so-called
‘new economy’ years of the late-1990s and beyond. At the
The observation that real valuation ratios are correlated with
end of the sample period in June 2004, the observed P/E
movements in nominal interest rates lends credence to the
ratio is 20.2. The predicted P/E ratio from the nominal model
Modigliani-Cohn hypothesis. Investors and home buyers
is 24.1, while that from the real model is 14.8.
appear to be adjusting their discount rates to match the prevailing nominal interest rate. However, for some unexplained
Inflation-induced valuation errors
reason, they do not simultaneously adjust their forecasts of
The predicted P/E ratio from real model can be interpreted as
future nominal cash flows, i.e., earnings distributions or imput-
an estimate of the rational (or fundamentals-based) P/E ratio
ed rents. The failure to take into account the influence of infla-
because the model assumes that investors discount real cash
tion on future nominal cash flows is an expectational error
flows using real interest rates. In this case, the difference
that is equivalent to discounting real cash flows using a nomi-
between the observed P/E ratio and the real-model prediction
nal interest rate.
can be viewed as a measure of overvaluation. When I plot valuation errors against expected inflation, I find that overvalua-
Changing risk perceptions
tion (measured as a percent of fundamental value) is nega-
Asness (2000) shows that movements in the E/P ratio also
tively correlated with the level of expected inflation; overvalu-
appear to be driven by changes in investors’ risk perceptions.
ation tends to be high when expected inflation is low, and vice
According to Ibbotson Associates, monthly stock return
versa. According to the analysis, overvaluation was highest
volatility has declined relative to monthly bond return volatil-
during the late 1990s and early 2000s — a period when expect-
ity, regardless of whether returns are measured in nominal or
ed and actual inflation were quite low. The late 1990s wit-
real terms. If investors’ risk perceptions are based on their
nessed the emergence of the biggest bubble in history. The
own generation’s volatility experience, then stocks will
bubble burst in March 2000, setting off a chain of events that
appear to have become less risky relative to bonds over time.
eventually dragged the U.S. economy into a recession in 2001
Following Asness, a statistical model of investor behavior can
[Lansing (2003)]. The recession-induced collapse in corporate
be constructed by regressing the E/P ratio on a constant
earnings caused the market P/E ratio to spike above 45, there-
term against three nominal explanatory variables, the yield
by exceeding the previous high that had prevailed near the
on a long-term government bond, the volatility of monthly
bubble peak. In contrast, the high inflation era of the late
stock returns over the preceding 20 years, and the volatility
1970s and early 1980s was characterized by substantial under-
of monthly bond returns over the preceding 20 years. It turns
valuation, as the market P/E ratio languished below its long-
125
run average for more than a decade. These findings reinforce
References
those of Ritter and Warr (2002) and Campbell and
• Asness, C. S., 2003. “Fight the fed model,” Journal of Portfolio Management, Fall,
30:1, 11-24
• Asness, C. S., 2000. “Stocks versus bonds: Explaining the equity risk premium,”
Financial Analysts Journal, 56:2, 96-113
• Campbell, J. Y., and T. Vuolteenaho, 2004, “Inflation illusion and stock prices,”
American Economic Review, Papers and Proceedings, 94, 19-23
• Hilsenrath, J. E., 2004, “Stock characters: As two economists debate markets, the
tide shifts,” Wall Street Journal, October 18, p. A1
• Lansing, K. J., 2003. “Growth in the post-bubble economy,” FRBSF Economic Letter,
2003-17 (June 24), http://www.frbsf.org/publications/economics/letter/2003/el200317.html
• Lansing, K. J., 2004, “Lock-in of extrapolative expectations in an asset pricing
model.” FRBSF, Working Paper 2004-06, http://www.frbsf.org/publications/economics/papers/2004/wp04-06bk.pdf
• Modigliani, F., and R. A. Cohn, 1979, “Inflation, rational valuation and the market,”
Financial Analysts Journal, 35, 24-44
• Ritter, J. R. and R. S. Warr, 2002, “The decline of inflation and the bull market of
1982-1999,” Journal of Financial and Quantitative Analysis, 37:1, 29-61
• Ibbotson Associates, Stocks, bonds, bills, and inflation 2004 Yearbook. Chicago
Vuolteenaho (2004) who find strong support for the
Modigliani-Cohn hypothesis using more sophisticated empirical methods.
Conclusion
In recent years, contributors to the rapidly growing field of
behavioral finance have been refining a new class of asset
pricing models. These models are motivated by a variety of
empirical and laboratory evidence which shows that people’s
decisions and forecasts are often less than fully rational.
Simple behavioral models can account for many observed features of real-world stock market data including: excess volatility of stock prices, time-varying volatility of returns, long-horizon predictability of returns, bubbles driven by optimism
about the future, and market crashes that restore attention to
fundamentals [Lansing (2004)].
Twenty-six years ago, Modigliani and Cohn (1979) put forth a
behavioral finance model that predicted mispricing of stocks
in the presence of changing inflation. The co-movement of
the stock market E/P ratio with the nominal bond yield
observed since the mid-1960s (when U.S. inflation started
rising) is consistent with the Modigliani-Cohn hypothesis. A
regression model that includes a constant term and three
nominal variables can account for 70% of the variance in the
observed E/P ratio over the past four decades. However, as
noted by Asness (2003), the success of this model in describing investor behavior should not be confused with the
model’s ability to forecast what investors should really care
about, namely, long-run real returns. Investors of the early
1980s probably did not anticipate the 20-year declining trend
of inflation and nominal interest rates that helped produce
above-average real returns as stocks moved from a state of
undervaluation to one of overvaluation in the manner
described by Modigliani and Cohn (1979). Today’s investors
may suffer the opposite fate if a secular trend of rising inflation and nominal interest rates causes the stock market to
move back towards a state of undervaluation.
126 - The
Is the investor sentiment
approach the solution to the IPO
underpricing phenomenon?1
Andreas Oehler, Professor of Finance, Bamberg University
Marco Rummer, Ph.D. Student, Teaching and Research Assistant,
Department of Economics and Management, Bamberg University
Peter N. Smith, Professor of Economics and Finance, University of York
During the process of going public the company owners offer
time. This argument is normally based on the assumption that
shares to outsiders for the first time and naturally try to raise
not all groups involved in the IPO pricing process possess the
as much money as possible in order to be able to finance
same level of information, given the missing track record of
future endeavors and growth. To achieve this, an appropriate
the firm. Rock (1986) suggests, in his pioneering work, that
offer price has to be found which should not be set too low,
underwriters have to underprice IPOs in order to compensate
as this will be like a generous present to the new investors,
uninformed investors for receiving most of the least profitable
or too high, as this dispels interested outsiders. With the pur-
issues, as the informed investors only place orders on the
pose of finding the perfect price and preparing the company
advantageous IPOs due to their informational advantage.
to go public, issuers spend on average a tremendously high
Welch (1989) believes that high-quality issuers can afford to
7% of the gross proceeds in underwriter fees [Chen and
sell their shares at a discount to investors in order to signal the
Ritter (2000)]. Therefore, it is rather surprising that most of
company’s high quality. Given the degree of initial returns with
the firms show a significant increase in share price between
a maximum of 444% and a mean of 52% in our sample exam-
the offering and the first trading day. These astonishing and
ined below, these theories are hardly reconcilable with empir-
time varying initial returns have been labeled the under-
ical findings. This is especially the case during the dot-com
pricing phenomenon and have been confirmed for all major
boom where most investors appeared to not really care about
stock markets around the world [Loughran, Ritter and
risk and uncertainty. Coming to a similar conclusion, Ritter and
Rydqvist (1994)].
Welch (2002) argue that these theories are unlikely to explain
the persistent pattern of high initial returns during the first
A vast number of theoretical models and even more empirical
trading day and discuss additionally that over-enthusiasm
examinations have been proposed since the pioneering work
among retail investors may explain the pattern of high initial
of Logue (1973) and Ibbotson (1975). From our point of view
returns.
there are two major possible scenarios which could cause the
empirically observed increase in stock prices between the
The second strand of research therefore focuses on behavioral
offering date and the first trading day. Firstly, it could be that
finance in order explain the pattern of time variance and per-
the offer price is set too low due to ex-ante uncertainty about
sistence of initial returns. From our point of view the notion of
the true market value of the newly issued stock. Secondly, the
investor sentiment seems to be most promising. This
offer price might be at a ‘fair value’ but demand for the IPO
approach argues that high and fluctuating initial returns are
and therefore the sentiment of investors is so overwhelmingly
caused by demand from different groups of investors and are
high that this generates the observed initial returns.
not induced by a required discount due to asymmetrically distributed information and ex-ante uncertainty. Cornelli et al.
The first strand of explanation focuses mainly on the assump-
(2004) corroborate our argument, that high pre-IPO prices,
tion that underpricing is a deliberate act by either the under-
which indicate overly optimistic investors, are a good predic-
writer or the issuer due to ex-ante uncertainty about the true
tor of high initial returns during the first trading day.
market value of the firm planning to go public for the first
Ljungqvist et al. (2004) show for the first time in a rational
1
The paper benefited from discussions with Wolfgang Bühler, James Gill, Leslie
Godfrey, John Hutton, Aydin Ozkan, Klaus Röder, Ray da Silva Rosa, Dirk Schiefer,
Oliver Schwindler and Ben Werner. We also thank seminar participants at the
Bambeg University and Freiburg University and participants at the workshop
‘Economics Meets Psychology 2004’ held by the Deutsche Bundesbank, the
Portuguese Finance Network Conference 2004, SAM/IFSAM-Conference 2004,
Money Macro and Finance Conference 2004 and European Investment Review
Conference 2004. The usual disclaimer applies.
127
model that investors are willing to pay a price in excess of their
demand for the stocks to be issued will then lead to a reduc-
rational belief if sentiment is high towards newly issued stocks.
tion in initial returns. On the other side, a decrease in the
bookbuilding range due to more potential demand will lead to
Empirical analysis
an increase in initial returns.3
Given the argument above one could conclude that investor
sentiment indeed seems to have a strong influence on initial
Our other measures capturing the impact of investor senti-
returns. In order to provide an additional empirical explana-
ment are related to the behavior of prices prior to the offering.
tion we combine the analysis of Oehler et al. (2004), Löffler et
The variable gm measures the impact of grey market4 prices,
al. (2004) and Cornelli et al. (2004).
which are simply calculated as the midpoint of the bid-ask
2
spread during the last pre-IPO trading day. We expect a posi-
Hypothesis
tive sign on gm in explaining initial returns as a high demand
To help assess which strand of research provides the least
should cause high pre-IPO trading prices, which additionally
explanation of the behavior of initial returns we use the vari-
leads to high underpricing.
able ‘bbwidth’ which describes the width of the bookbuilding
range, measured as the difference between the upper and
Finally, a widely used measure of investor sentiment is the
lower bounds of the initial price range. With this variable we
performance of a suitable stock market index prior to the
are able to measure the effect of ex-ante uncertainty, due to
offering. As we are analyzing IPOs going public on the German
asymmetrically distributed information, and the consequence
‘Neuer Markt’ we use the Nemax-All-Share-Index as this
of investor sentiment, due to demand of potential investors,
benchmark.5 This index covers all stocks listed on this stock
within one variable. The result simply depends on the sign of
market segment. We expect a positive sign for the variable
the impact of the bookbuilding range on initial returns meas-
nemax, as an increase in the stock market should indicate a
ured from multivariate cross-section econometric analysis.
positive attitude in the market and therefore should lead to
high initial returns.
If deliberate underpricing due to ex-ante uncertainty about the
firm value is critical we expect a positive sign for the impact of
Database
the width of the bookbuilding range. For example, the issuer or
We analyze 288 IPOs on the German ‘Neuer Markt’ during the
underwriter is unsure about the potential demand for the
period 1998-2000. This stock market segment had been the
stocks to be issued and the achievable market price.
centre of attention during the dot-com bubble and had
Therefore, they increase the width of the bookbuilding range.
become, besides NASDAQ, the market of choice for young
This is then expected to have a positive impact on initial
firms undergoing IPOs during the dot-com boom. IPOs are
returns, as traditional theories assume that increase in ex-
identified by using the web-pages and the fact books of the
ante uncertainty about the firm value will lead to higher
Frankfurt Stock Exchange. All firms were double-checked
underpricing due to a necessary discount for potential
using the web-pages of the ‘Börsenzeitung’ and OnVista AG,
investors.
as well as information from IPO prospectuses, companies’
homepages, and investor relations departments. Firms that
128
Contrary, if investor sentiment is critical we expect the impact
had traded nationally or internationally prior to the offering at
of the width of the bookbuilding range to be negative. An
the Frankfurt Stock Exchange have been excluded from the
increase in the bookbuilding range due to little expected
study, as a market price already existed for these firms. The
2 For a more detailed empirical analysis on the importance of investor sentiment
see for example Cornelli et al. (2004) or Oehler et al. (2004).
3 These arguments show that initial returns and underpricing, which have commonly
been used interchangeably in prior research, describe in our opinion different
effects, even if measured identically as the difference between the offer and first
day trading price of an IPO. Therefore, the notion underpricing signifies that the
described increase in share prices between primary and secondary market are due
to a discount on the offer price. Contrary, the notion initial return refers to an
increase due to the impact of investors demand on the first day trading price.
4 For a detailed description of the pre-IPO trading in Germany see Löffler, Panther
and Theissen (2004)
5 Admittedly, this might induce some bias into our analyses as many firms listed in
this index have gone public during the examined time period. Nevertheless, using
a different benchmark like the DAX-Index, which covers the 30 biggest German
blue chips, would not proxy the attitude towards IPOs well enough. Therefore, the
bias is acceptable, as our goal is to study the impact of sentiment towards newly
issued stocks.
information about the bookbuilding range is taken from the
IPO prospectus, the web pages of the Frankfurt Stock
Exchange, the ‘Börsenzeitung’ and OnVista AG. The pre-IPO
prices are obtained from Schnigge AG. The secondary market
prices of the examined stocks are taken from the KKMDB database at the University of Karlsruhe6 and the daily closing
prices of the Nemax-All-Share-Index are from Datastream.
Dependent variable
constant
bbwidth
gm
nemax
IR
-0.652b
-0.129a
0.010a
1.18b
R2 (adjusted)
F-statistic
0.448
78.721a
T-stats in brackets
Empirical analysis
(a) Significant at the 1% level
(-2.358)
(-5.210)
(7.700)
(4.409)
(b) Significant at the 5% level
Figure 1
Initial returns have an average of 52.35%, a minimum of
-30.00% for Pixelpark AG and an astonishing 444.44% for
Germany. The variable bbwidth, whose sign is supposed to dif-
Biodata Information Technology AG. It is very interesting to
fer depending on the importance of investor sentiment and ex-
note that the Nemax-All-Share-Index performed very well
ante uncertainty, shows a negative relationship between the
before Biodata’s IPO but very poorly prior to Pixelpark AG
width of the bookbuilding range and the initial return during
going public. The age of the examined firms, measured as the
the IPO. From this we have to conclude that the investor sen-
difference between the foundation and the initial offering,
timent effect is more important.7 This finding is supported by
varies quite substantially and ranges from 62 years to one
the positive signs on the highly significant variables gm and
year. The latter group of IPOs (i.e. one year) therefore only
nemax. These estimates support the notion that investor sen-
marginally fulfill the minimum listing requirement imposed by
timent is fundamental for explaining the IPO underpricing
the law during this time period.
phenomenon.
Our brief empirical analysis is based on the following regres-
The magnitude of the impact of the variable nemax is quite
sion, which is estimated using OLS (standard errors are adjust-
substantial. According to our results, an increase of one per-
ed for heteroskedasticity of the error term using White’s
centage point in the Nemax-All-Share-Index prior to an IPO will
(1980) methodology):
lead to an increase in the initial return of 1.181 percentage
points. This is explained, given our argument, by the positive
IRi = αi + β1,ibbwidth + β2,igm + β3,inemax + εi
sentiment in the stock market, which naturally has an effect
on the demand for upcoming stock issues too. In our analysis,
where the dependent variable IR is measured as the percent-
all variables are at least significant at the 5% level, meaning
age difference between the first day trading price and the
that the population value of our variables is in deed different
offering price. The explanatory variables bbwidth, gm, and
from zero with a likelihood of 95%.
nemax are described in detail above. The results can be found
below in Figure 1.
Conclusion
The extensively documented existence of positive initial
It can be seen that our model nearly explains 45% of the vari-
returns during the first trading day of an IPO has been
ations in initial returns, which is quite a substantial amount for
labeled the underpricing phenomenon. Most researchers
a cross-sectional analysis of stock returns. The adjusted R2 is
assume that the issuer or underwriter fail to choose a higher
well above the 31.2% reported by Ljungqvist (1997) for
offer price due to asymmetrically distributed information. In
6 We thank Hermann Göppl for providing the data.
7 For a more detailed analysis of the relative importance of investor sentiment in
the IPO-Pricing process see Oehler, Rummer and Smith (2004).
129
a short literature review we have shown that the unusually
high degree of first day returns can in fact hardly be due to
deliberate actions by the underwriter or issuer. This argument is backed up by our brief empirical analysis during
which we provide strong evidence that initial returns are
determined by investor sentiment and not by ex-ante uncertainty.
References
• Baron, D. P., 1982, “A model of the demand for investment bank advising and distribution services for new issues,” Journal of Finance, 37, 955-976
• Chen, H. C., and J. R. Ritter, 2000, “The seven percent solution,” Journal of Finance,
55:3, 1105-1131
• Cornelli, F., D. Goldreich, and A. Ljungqvist, 2004, “Investor sentiment and pre-IPO
markets,” Working Paper, London Business School.
• Ibbotson, R. G., 1975, “Price performance of common stock new issues,” Journal of
Financial Economics 2, 235-272
• Ljungqvist, A. P., 1997, “Pricing initial public offerings: Further evidence from
Germany,” European Economic Review, 41, 1309-1320
• Ljungqvist, A. P., V. Nanda, and R. Singh, 2003, “Hot markets, investor sentiment,
and IPO pricing,” forthcoming Journal of Business
• Löffler, G., P. F. Panther, and E. Theissen, 2004, “Who Knows What When? The
Information Content of Pre-IPO Market Prices,” forthcoming Journal of Financial
Intermediation.
• Logue, D. E., 1973, “On the pricing of unseasoned equity issues: 1965-1969,” Journal
of Financial and Quantitative Analysis, 8, 91-103.
• Loughran, T., J. R. Ritter, and K. Rydqvist, 1994, “Initial public offerings: International
insights,” Pacific-Basin Finance Journal, 2, 165-199.
• Oehler, A., M. Rummer, and P. N. Smith, 2004, “IPO pricing and the relative importance of investor sentiment,” Working Paper, University of Bamberg.
• Ritter, J. R., I. Welch, 2002, “A review of IPO activity, pricing, and allocations,”
Journal of Finance, 57, 1795-1828
• Rock, K., 1986, “Why new issues are underpriced,” Journal of Financial Economics
15, 187-212
• Ruud, J. S., 1993, “Underwriter price support and the IPO underpricing puzzle,”
Journal of Financial Economics 34, 135–151
• Welch, I., 1989, “Seasoned offerings, initiation costs, and the underpricing of initial
public offerings,” Journal of Finance, 44, 421-450
• White, H., 1980, “A heteroskedasticity-consistent covariance matrix estimator and a
direct test of heteroskedasticity,” Econometrics, 48, 817-838
130 - The
The credit spread puzzle1
John Hull, Professor of Finance, Director, Bonham Centre for Finance
and Maple Financial Group Chair in Derivatives and Risk Management,
Rotman School of Management, University of Toronto
Mirela Predescu, PhD. Candidate in Finance,
Alan White, Peter L. Mitchelson/SIT Investment Associates Foundation
Chair in Investment Strategy and Professor of Finance,
Estimation of default probabilities is becoming increasingly
are sometimes referred to as ‘real-world default probabilities’
important in risk management. A new regulatory framework
or ‘physical default probabilities’.
for banks, Basel II, is expected to be implemented in 2007. This
gives banks much more freedom than its predecessor, Basel I,
To estimate the default probability implied by bond prices we
to use internal models to estimate default probabilities. The
first calculated the average spread over the risk-free rate for
estimation of default probabilities is also important in the val-
a seven year corporate bond. We used the Merrill Lynch bond
uation of credit derivatives, the market for which is growing
indices between December 1996 and July 2004. Consider, for
fast. Most credit derivatives provide payoffs contingent on
example, A-rated bonds. The average yield on bonds with a
whether particular companies default on their obligations. The
life of approximately seven years was 6.274% per annum. The
estimation of default probabilities is therefore central to the
average risk-free rate was 5.505% per annum. The average
evaluation of credit derivatives.
credit spread was therefore 0.769% per annum. The credit
spread is an indicator of the probability of default. We receive
One approach to estimating default probabilities involves
an extra 0.769% per year in additional bond yield because we
looking at historical data and assuming that the future will in
expect to lose about 0.769% of the principal per year due to
some sense be similar to the past. Another involves implying
defaults.
default probabilities from corporate bond yields. It turns out
that the two approaches give quite different estimates. Our
The probability of default is greater than the credit spread
objective in this article is to quantify just how different the
because some recovery is made in the event of a default. We
estimates are and then to provide possible reasons for the
suppose a recovery rate of 40% (which is fairly close to the
difference.
average of the recovery rates observed in practice). This
means that for A-rated bonds the probability of default
Default probability estimates
implied by bond prices is 0.769% / (1 - 0.4) or about 1.28% per
Figure 1 shows estimates of the average probability of default
annum. To look at this another way, when the average proba-
per year during a seven-year period calculated from historical data and bond prices. The historical data are cumulative
default rates published by Moody’s for the period between
Rating
Default
probabilities
from historical
data
(% per year)
Default
probabilities
implied from
bond prices
(% per year)
Ratio
Difference
Aaa
Aa
A
Baa
Ba
B
Caa and lower
0.04
0.06
0.13
0.47
2.40
7.49
16.90
0.67
0.78
1.28
2.38
5.07
9.02
21.30
16.8
13.0
9.8
5.1
2.1
1.2
1.3
0.63
0.72
1.15
1.91
2.67
1.53
4.40
1970 and 2003. This data give the probability of a company
default during a seven-year period given that it has a particular credit rating at the beginning of the period. For example,
a company that starts with an Aaa credit rating has an average default probability per year of 0.04% (or about 0.28%
over the whole seven year period). A company that starts
with a credit rating of Aa has an average default probability
of 0.06% per year (or about 0.42% over the whole sevenyear period). Default probabilities implied from historical data
1
The ideas in this paper will be published in a paper by the authors entitled “Credit
Spreads, Default Probabilities, and Risk Premiums” in Journal of Credit Risk. We
are grateful to Moody’s Investors Service for supporting this research.
Figure 1: Average default probabilities per year over a seven-year period
131
bility of default is 1.28% per year the loss of principal per year
This leads many market participants to regard swap rates as
is 1.28% x (1 – 0.4) or 0.769%, which is the credit spread
better proxies for risk-free rates than Treasury rates.2
earned. Default probabilities backed out from bond prices in
this way are known as ‘risk-neutral default probabilities’.
The credit default swap (CDS) market provides a way of estimating the benchmark risk-free rate used by participants in
Figure 1 shows that the ratio of the default probability esti-
credit markets. If a five-year par yield corporate bond pro-
mates derived from bond prices to those derived from histori-
vides a yield of 6% and five-year protection can be bought
cal data decreases as the credit quality declines. However, the
against the issuer for 150 basis points a year, an investor can
difference between the default probabilities increases as cred-
obtain a (approximate) risk-free return of 4.5% by buying the
it quality declines. The size of the difference between the two
bond and buying credit protection. This suggests that the
default probability estimates is sometimes referred to as the
risk-free rate being used by market participants is 4.5%.
‘credit spread puzzle’.
Using this type of analysis across many corporations we estimate that the benchmark risk-free rate being used by market
The benchmark risk-free rate
participants is the swap rate less 10 basis points.3 This is sim-
The default probabilities implied from a bond price depend on
ilar to estimates that have been made by Moody’s KMV.4 We
the bond’s yield spread over the risk-free rate. The estimates
therefore set the risk-free rate equal to the seven-year swap
in Figure 1 therefore depend critically on the assumption made
rate minus 10 basis points in producing the results in Figure 1.
about the risk-free rate. A natural choice for the risk-free rate
It is worth noting that if we instead chose the risk-free rate to
is the Treasury rate. Treasury rates are yields on bonds that
be to be the seven-year Treasury rate the default probabili-
have no default risk. Furthermore the bond yield spreads that
ties implied from bond prices would be even higher, making
are quoted in the market are usually spreads relative to a
the differences in Figure 1 even more marked. For example the
Treasury bond that has a similar maturity. However, Treasury
ratio of the risk-neutral to real world default probability for
rates tend to be lower than other rates that have a very low
A-rated companies in Figure 1 would rise from 9.8 to over 15.
credit risk for a number of reasons:
Risk premiums
■ Treasury bills and Treasury bonds must be purchased by
From the results in Figure 1 we can calculate the risk premi-
financial institutions to fulfill a variety of regulatory
ums earned by holders of corporate bonds. The expected
requirements. This increases demand for these Treasury
excess return of corporate bonds over Treasuries has a num-
instruments driving the price up and the yield down.
ber of components. One component is the difference between
the Treasury yield and our estimate of the benchmark risk-
■ The amount of capital a bank is required to hold to sup-
free yield used by market participants. During the 92 months
port an investment in Treasury bills and bonds is substan-
covered by our Merrill Lynch data this averaged 43 basis
tially smaller than that required to support a similar
points. Another component is a spread to compensate for
investment in other very low-risk instruments.
defaults. Given that we are assuming a recovery rate of 40%,
this is the historic default probability in Figure 1 multiplied by
■ In the United States, Treasury instruments are given a
132
0.6. The final component is the extra risk premium earned by
favorable tax treatment compared with most other fixed-
the holders of corporate bonds. Note that if the risk premium
income investments because they are not taxed at the
were zero, there would be no difference between historic
state level.
default probabilities and those derived from bond prices.
2 A similar point is made forcefully by Duffee, G. R., 1996 “Idiosyncratic variation of
treasury bill yields,” Journal of Finance, 51, 527-551. He argues that ‘Since the
early 1980’s [Treasury] bill yields have become increasingly irrelevant as a benchmark. This is not news to market participants…but nonetheless [is] likely a surprise
to many academic economists.’
3 See J. Hull, M. Predescu, and A. White, 2004 “The relationship between credit
default swap spreads, bond yields, and credit rating announcements,” Journal of
Banking and Finance, Nov
4 For example, Stephen Kealhofer’s estimate of the risk-free rate in his presentation
at the Moody’s/New York University conference on Recent Advances in Credit Risk
Research in May 2004 was very close to our estimate.
bonds earn the risk premiums over the risk-free rate shown in
Rating
Aaa
Aa
A
Baa
Ba
B
Caa and lower
Bond yield
spread over
treasuries
Spread of
risk-free rate
used by market
over treasuries
Spread to
compensate
for historic
default rate
Extra risk
premium
(% per annum)
(% per annum)
(% per annum)
(% per annum)
0.83
0.90
1.20
1.86
3.47
5.85
13.21
0.43
0.43
0.43
0.43
0.43
0.43
0.43
0.02
0.04
0.08
0.28
1.44
4.49
10.14
0.38
0.43
0.69
1.15
1.60
0.93
2.64
Figure 2: Excess expected returns earned by bond traders
Figure 2? There appear to be four main reasons:
■ Corporate bonds are relatively illiquid. It is less easy to sell
corporate bonds than many other types of securities. As a
result investors in corporate bonds demand what is
termed a liquidity risk premium. This is part of the risk
premium shown in the final column of Figure 2. Most
researchers estimate the liquidity risk premium to be
between 10 and 25 basis points.
■ Figures 1 and 2 assume that traders use historical data to
determine the probability of default in the future. In practice traders may be assigning positive subjective probabiliFigure 2 shows the allocation of the yield spread into its vari-
ties to depression scenarios that are much worse than any
ous components. For example, A-rated bonds earned 120 basis
seen since 1970. If we use average default statistics for the
points more than Treasuries on average. Forty-three basis
whole 1920 to 2003 period we find that the historic
points of this is the difference between Treasuries and the
default probabilities in Figure 1 do increase somewhat. For
market’s risk-free benchmark. A further 8 basis points is nec-
Aaa the historic default probability increases from 0.04%
essary to cover defaults. The remaining 69 basis points is a
to 0.06%; for Aa it increases from 0.06% to 0.22%; for A
risk premium earned by bondholders. We can see from Figure
it increases from 0.13% to 0.29%; for Baa it increases
2 that as the quality of the bond declines from Aaa to Ba the
risk premium increases. It then declines as we move from Ba
from 0.46% to 0.73%; and so on.
■ Bonds do not default independently of each other. There
to B and increases sharply as we move from Ba to Caa. The
are periods of time when default rates are very low and
extra risk premium reported in the last column of Figure 2 can
other periods when they are very high. (Evidence for this
be characterized as the expected return on a portfolio that is
can be obtained by looking at the default rates in different
long a corporate bond and short a default-free bond.
years. Between 1970 and 2003 the default rate per year
ranged from a low 0.09% in 1979 to a high of 3.81% in
Our results are consistent with those produced by Edward
2001.) This phenomenon is sometimes referred to as ‘cred-
Altman some time ago. He showed that, even after taking
it contagion’. It is a form of systematic risk (i.e., it is a form
account of the impact of defaults, an investor could expect
of risk that cannot be diversified away) and bond traders
significantly higher returns from investing in corporate bonds
should require a return in excess of the risk-free rate for
than from investing in Treasury bonds. As the credit rating of
bearing this risk.
the corporate bonds declined, the extent of the higher returns
■ Bond returns are highly negatively skewed with limited
increased. (Altman found that B bonds ran counter to the
upside. As a result it is much more difficult to diversify
overall pattern, just as we do in Figure 2.)
risks in a bond portfolio than in an equity portfolio.6 A very
large number of different bonds must be held. In practice,
Reasons for the difference
many bond portfolios are far from fully diversified. As a
Why are the probabilities backed out of bond prices in Figure 1
result bond traders may require an extra return for bear-
so much higher than those estimated from historical data?
ing unsystematic risk as well as for bearing the systematic
An equivalent question is: Why do investors in corporate
risk mentioned above.
5 Altman, E. I., 1989 “Measuring Corporate Bond Mortality and Performance,”
Journal of Finance, 44, 902-22.
6 See J. D. Amato and E. M. Remolona, “The pricing of unexpected credit losses,”
Working paper, Bank for International Settlements, Basel Switzerland.
133
Conclusions
In comparing Figures 1 and 2 we see that there are huge differences between default probability estimates estimated
from corporate bond prices and those estimated from historical data. These differences translate into relatively modest
(but non-negligible) premiums demanded by bond traders for
the risks they are bearing. We have identified four types of
risk. The first is liquidity risk; the second is the risk that default
losses may be much worse than anything seen in recent history; the third is the systematic (non-diversifiable) risk;s and the
fourth is the risk which is diversifiable but in practice quite difficult to handle.
134 - The
Impact of seasonality on inflation
derivatives pricing1
Nabyl Belgrade, Interest Rates Derivatives Research, CDC IXIS CM
Eric Benhamou, Head of Quantitative Interest Rates Derivatives
Research, CDC IXIS CM
Motivations and static seasonality modeling
sonality dynamically we use a static pattern to reshape the
Unlike interest rates, inflation forwards are not really smooth
forward curve of CPIs. Hence, it is only the forward curve that
and exhibit repeatable seasonal patterns. These patterns take
is modified while the inflation dynamics stays unchanged. In
their roots in various recurrent economic phases, like con-
addition, we take yearly seasonality on a monthly basis.
sumer spending increase during Christmas, winter, and or
Yearly pattern is not very restrictive as most of the seasonal-
summer sales, cyclic variations in energy and food consump-
ity is on a yearly basis. We, therefore, use a vector of yearly
tion, and many other periodic effects. Consequently, the
seasonal up and down bumps {B(i)}i=1..12 indexed by their
assumption of a linear growth for month-on-month inflation
corresponding months i with the convention that January
changes is clearly misleading. This month-on-month change
equals 1.
may be far away from its monthly average for a month with
strong seasonality effect. This advocates energetically for the
The incorporation of seasonality in our model is then
incorporation of seasonality in any inflation pricing model.
straightforward. When computing the spot value of the CPI
forward value CPI(0,T), maturing at time T with correspon-
In fact, macro-economists have known for quite some time
ding month m, we first look at the two adjacent liquid market
now that inflation markets should and do exhibit strong sea-
points with corresponding times Td and Tu that bound lower
sonality behavior [Bryan and Cecchetti (1995)]. But when
and upper time T. We then compute the interpolated forward
inflation derivatives were still in their infancy with only a few
CPI value CPI(0,T) using the CPI market value CPI(0,Tdown)
traded products, seasonality was not really an issue. This is
and CPI(0,Tup). This interpolation may be assuming linear,
not the case any more. The market has experienced tremen-
stepwise constant or cubic spline interpolation on either
dous growth both in terms of hedging instruments (inflation
inflation spot zero coupon rates, forward CPI, or forward zero
linkers issued by states, sovereigns, or corporations) and OTC
coupon. Insights of the paper are not on this interpolation
derivatives (inflation swap and other vanilla inflation deriva-
method but rather on what follows. To the interpolated for-
tives). In Europe, an estimated €3 billion to €7 billions were
ward CPI value CPIint(0,T), we apply a seasonal bump, com-
being traded monthly during 2004. This compares with only
puted as the difference between the seasonal bump of month
€500 million a year before. And more is to come. In France,
M and its interpolated seasonal bump using the same inter-
for instance, the total amount of regulated saving account
polation assumption as the one for the forward CPI. For the
Livret A, tied up to inflation rates, should reach €400 billions
sake of simplicity, we will assume linear interpolation on for-
by the end of year. Seasonality modeling is now not a choice
ward CPIs. In this case, the seasonal bump for the time T and
but a necessity.
denoted by SB(T) is given by:
Incorporating seasonality within a stochastic model may at
SB(T) = B(m) – (m – md)
first sight look complex. One may think to include seasonality
in the diffusion equation itself, via its drift, or the volatility
(
B(mu) – B(md)
mu – md
)
+ B(md)
(1.1)
where md and mu are the months corresponding to the times
term or both. The model could be taken as the limit of sea-
Td and Tu. We can notice that that the (linear) interpolation
sonal discrete time model like SARIMA and periodic GARCH.
reshapes our vector of yearly up and down bumps to guaran-
This would come at the price of both confusing the model and
tee market points to have zero seasonality adjustment. This
making it harder to calibrate. In this paper, we suggest a sim-
is because market points already incorporate seasonality in
pler approach, similar in spirit to the one used for end of year
their price. In addition the seasonality interpolation is done
effect in interest rate derivatives. Instead of modeling sea-
consistently with the one of CPI to create similar interpola-
1
We would like to thank G. Couzineau and A. Bayle for useful remarks and comments. All ideas and opinion expressed herein are the ones of the authors and do
not necessarily reflect those of CDC Ixis CM.
135
tion effect. Equation (1.1) assumes additive bumps, meaning
data into a variety of components, more or less observable
that the corrected CPI is obtained as the interpolated CPI plus
and easy to discriminate. We assume that our time series of
the seasonality bumps:
CPI data is summarized by a general trend, that may be stochastic or not and that represents the long-term evolution of
CPI(0,T) = CPIint(0,T) + SB(T)
(1.2)
the CPI, a seasonal effect corresponding to yearly fluctuations and a noise represented by a random variable. Note also
If we were to assume a multiplicative correction, we would
that a multiplicative correction is as an additive one on the
correct the raw interpolated forward CPI as follows:
logarithm of the CPI data. We will, therefore, look at additive
correction as the processing for multiplicative is then
CPI(0,T) =
CPIint(0,T)
* SB(T)
(1.3)
straightforward.
with the seasonal bump computed as the monthly bump
At this stage, we could decide to either assume a parametric
renormalized by the interpolated bump as given in equation
form for the data and do an OLS to estimate the seasonal
(1.4). This equation is the simple translation of the interpola-
component, or determine sequentially the trend of the time
tion equation (1.1) of the seasonal bump but for multiplicative
series and on the de-trended data, the seasonal component.
bump:
(
SB(T) = B(m) / (m – md)
B(mu) – B(md)
mu – md
)
+ B(md)
The first method is a parametric estimation of the seasonal
(1.4)
component that spreads the noise error on both the trend
and the seasonal component. But this advantage is counterweighted by the parametric assumption used to do every-
Once the spot value for forward CPI has been estimated, it is
thing in one go. The second method is a non-parametric
easy to adapt the stochastic model described in Belgrade et
method, straight application of the X11 method to our CPI
al. (2004a, b). The forward CPI inflation index CPI(t,T)
data. Key advantage is to make no assumption on the trend
observed at time t that fixes at time T keeps its diffusion
and seasonal component. We let the filter recover the trend
equation given by
iteratively. However, because of this two-stage estimation,
dCPI(t,T)
CPI(t,T)
noise affects only the seasonal component and not the
= μ(t,T)dt + σInf(t,T)dW(t)
(1.5)
trend.
Parametric estimation of seasonality
but the boundary condition is modified to include the sea-
The method first used by Buys-Ballot to see seasonality in
sonality adjustment. This is given by equation (1.2) in an addi-
astronomy assumes that our time series (Xt)t=1,..T, (here the
tive correction and by equation (1.3) in a multiplicative one. In
logarithm of CPI), has an additive decomposition schema
this framework, it is then easy to price any inflation linked
‘trend + seasonality + noise’. The two first components have
derivatives.
also parametric forms. For an annual seasonality, the model
is written as follows:
We understand that the seasonality estimation comes to the
finding of a vector of 12 up and down (additive or multiplicative) bumps from historical CPI data. Following standard
econometric theory, we decompose our time series of CPI
136 - The
Xt = Tt + St + εt, t = 1,..T, with
(2.1)
p
■ Tt = α0 +
p
j=1
12
Σ
i=1
ity is done according to the following steps:
j=0
the trend modeled by a polynomial of degree p,
■ St =
Tiao (1976)]. The non-parametric estimation of CPI seasonal-
Σ αjTtj = Σ α jtj :
(2.2)
12
B(mi)Sti =
Σ B(mi)1{t mod i=0} :
i=1
the annual seasonality seen as 12 average bumps, (2.3)
■ (εt)t=1,..T is a white noise sequence.
■ Determine the trend Tt by taking the moving average
over a period of thirteen data:
Tt = M(Xt)
(3.1)
with the filtering moving average given by:
6
M=
Σ
θi Li
(3.2)
i= –6
The parameters (aj)j=1,..p and (B(mi))i=1,..12 and are estimated by
the OLS’s Best Linear Unbiased Estimators. The seasonal
where θi = 1/6 for i = -5,..5 and the first and the last terms
average bumps (B(mi))i=1,..12 constitute successively a regular
are equal to 1/12.
cycle and they compensate themselves
Σ
12
i=1
B(mi) = 0.
This approach presents four advantages. Firstly, being para-
■ Estimate the seasonal component on the residuals with
St = (1 – M)M’(Xt – Tt)
metric, it easily provides estimation’s error for forecast.
Secondly, it can detect not only yearly seasonality but also
monthly pattern. Thirdly, it spreads the error estimation not
(3.3)
with
2
M’ =
Σ
i= –2
θi Li
(3.4)
only on the seasonality but also on the trend estimation.
with θi = 1/9 for i ∈ {– 2,2}, θi = 2/9 for i ∈ {– 1,1} and
Finally, it uses the whole set of data computing in one go on
θi = 1/3 else.
both the trend and the seasonality pattern.
■ Look that applying the moving average M =
These advantages are offset by the strong assumption on the
wastes the m1 data and the m2 last ones.
Σ
m2
i=–m1
θi Li
parametric form.
Please note that we could have used a different filtering periWhen we undertake an estimation of the seasonality and look
od and come up with the X8 or X12 or any Xn method which
at the trend component of the European and U.S. CPI, we find
is also traditionally used in econometrics. But with regards to
that there is less irregularity in the U.S. seasonality pattern
the noise of the estimation, Xn methods should conduct to
than in the European one. This is consistent with empirical
similar quantitative results.
studies that confirm stronger seasonality of U.S. CPI data
compared to European ones. This estimation is done with a
When we compare the seasonality component extracted from
polynomial estimation of order 5.
the European and the U.S. CPI data we find that the ‘crude’
U.S. seasonal component is more regular than the European
Non-parametric estimation of seasonality
one, with the amplitude being less variable. The difference in
Let us denote by Xt the CPI data and by L the standard lag
regularity between the European and U.S. inflation is even
operator. Standard econometric literature supports the use of
more striking than in the parametric method. When conduct-
a 12 data period in our filtering process, leading to a straight
ing a comparison between trend components extracted from
application of the X11 method as described in [Cleveland and
the European and U.S. CPI data, we find that the two CPIs’
137
trend components are very close to the parametric results.
Conclusion
Because of the tightening of quotes on inflation linked deriv-
To obtain the twelve monthly bumps (B(mi))i=1,..12 for the sea-
atives, models should incorporate seasonality for more accu-
sonality adjustment, we have to regularize the seasonality
rate pricing. Using simple harmonic analysis tools, we can
component to an annual cycle. For this, we can simply apply
extract seasonality component of the inflation data and
to seasonality component the parametric model (2.1) without
superimpose this effect to the bootstrapped inflation curve.
trend.
Pricing shows that it can have a significant impact on seasonality sensitive trades.
For both the European and U.S. CPI, the seasonality estimation
is here less important in magnitude than in the parametric
References
estimation. This is associated with the fact that the approxi-
• Belgrade, N., 2004a, ”Market inflation Seasonality Management,” CERMSEM
Working paper 2004.51, April
• Belgrade, N., E. Benhamou, and E. Koehler., 2004b, “A Market Model for Inflation,”
CERMSEM Working paper 2004.50 and SSRN Working paper
• Belgrade, N., and E. Benhamou, 2004, “Reconciling year on year and zero coupon
inflation swap: a market model approach,” CDC Ixis Capital Market Research Note
• Bryan, M.F. and S. G. Cecchetti, 1995, “The Seasonality of Consumer Prices,” NBER
Working Paper No. W5173, 1995.
• Buys-Ballot, C. 1847, “Les changements périodiques de températures,” Utrecht
• Shishkin, J., A. Young, and J. Musgrave, 1965, “The X11 Variant of the Census
Method X11 Seasonal Adjustment Program,” technical paper 15, Bureau of Census
• Cleveland and Tiao, 1976, “Decomposition of Seasonal Time Series: a model for the
Census X11 program”
mation replicates at best the yearly effect but smoothes the
pattern.
Pricing impact on various inflation linked
derivatives
To measure the influence of seasonality, we price with and
without various products: Zero coupon and year-to-year
inflation swap. Impact on more exotic structures such as
options on real interest rates (and interest rates structured
coupons floored with inflation-linked strikes) is similar but
harder to analyze because of the increased complexity of
these products. However, the same conclusions hold.
First of all, accounting for seasonality imposes a periodic
cycle on the naïve price (price without seasonality). Impact
varies according to the month of the fixing. For instance, the
impact of seasonality on a 10 year IFRF inflation zero coupon
swap fluctuates between -1.5bps to 2 bps. For a 10 year annual IFRF inflation year-to-year swap this difference goes from
-2bps to 2bps. Secondly, we should not ignore seasonality on
options. Obviously, this changes along the lines of the options
characteristics. For example, on 1% IFRF inflation floor, seasonality adjusts the price by -6 to 9 bps.
1
138 - The
This is a revised version of the article published in International Payments,
March 2004
Assets
Pricing default-free
fixed rate mortgages:
A primer1
Patric H. Hendershott
Professor, Aberdeen University
Robert Van Order
Lecturer, University of Pennsylvania
Abstract
It is by now generally recognized that a wide range of con-
comes from determining equilibrium prices by imposing only
tracts can be viewed as contingent claims, which can be mod-
the conditions of zero arbitrage profits and rational (wealth-
eled like financial options. For instance, mortgages usually
maximizing) exercise of options. Such models give exact,
have prepayment and default options. Prepayment is a call
rather than simply qualitative, predictions about prices, using
option (i.e., an option to buy back or call the mortgage at par);
relatively few parameters. In particular, they derive the central
whereas default can be viewed as a put option (an option to
proposition, that the value of a security is the risk-adjusted
sell or put the house to the lender at a price equal to the value
expected present value of its cash flows, and they show how
of the mortgage). The purpose of this paper is to provide a
expected values and the risk-adjusted discount rate are deter-
primer on the application of option pricing techniques to
mined. Our approach is heuristic; we do not provide proofs.
mortgages, focusing on the prepayment (call) option. The
Rather we try to provide intuition for the major results of this
great insight of the option pricing/contingent claims models
line of research.
1
This is adapted from Hendershott and Van Order (1987).
139
It is by now generally recognized that a wide range of con-
of analyzing mortgage pricing, this is not a bad abstraction,
tracts can be viewed as contingent claims, which can be mod-
first because most (prime) mortgages3 that are traded have
eled like financial options. This approach is also applicable to
credit risk insured or guaranteed by a third party or they are
mortgages [Hendershott and Van Order (1987), and Kau and
structured in such a way that the bulk of what is traded has an
Keenan (1995)]. For instance, mortgages usually have prepay-
AA or AAA rating, and second because default risk is general-
ment and default options. Prepayment is a call option (i.e., an
ly much smaller than prepayment risk. On a typical, nationally
option to buy back or call the mortgage at par); whereas
diversified portfolio of conventional single family mortgages
default can be viewed as a put option (an option to sell or put
default rates (the fraction of loans that go through foreclosure
the house to the lender at a price equal to the value of the
in a year) typically range from 10 to 30 basis points per year.
mortgage). The application of formal stock and bond option-
Prepayment speeds, on the other hand, run between 5% and
pricing methodology [Black and Scholes (1973), Brennan and
40% per year.4
Schwartz (1977), Cox, Ingersoll, and Ross (CI&R) (1985), and
Merton (1973)] has been the centerpiece of much mortgage
Pricing depends on the contract structure of the mortgage
pricing research.
and the way borrowers exercise their options. We assume that
borrowers exercise their option in a way that maximizes their
The great insight of the option pricing/contingent claims mod-
wealth. That means that at any moment in time when borrow-
els comes from determining equilibrium prices by imposing
ers are contemplating whether to prepay or simply make their
only the conditions of zero arbitrage profits and rational
scheduled payment they will ask which of these alternatives
(wealth-maximizing) exercise of options. Such models give
leads to greater wealth. The wealth maximization strategy is
exact, rather than simply qualitative, predictions about prices,
also the strategy that minimizes the value of the mortgage.
using relatively few parameters. In particular, they derive the
Our approach is heuristic; we do not provide proofs.
central proposition, that the value of a security is the riskadjusted expected present value of its cash flows, and they
We begin with a simple ‘warm up’ model that assumes, rather
show how expected values and the risk-adjusted discount
than derives, that price is expected present value. This model
rates are determined. When transaction and other costs are
captures most of the essentials of callable mortgages. We then
incorporated, pricing is more complex but still doable.
turn to a more rigorous continuous time model and then to
some extensions and modifications.
Our focus is on ‘frictionless’ models, that is, models without
transaction costs and where borrowers exercise options
A ward up model
rationally. The basic approach to pricing is the same for mort-
Until rather recently (less than 25 years ago) the dominant
gages as it is to, say, corporate or Treasury bonds. Our inten-
approach to pricing mortgages might be characterized as
tion is to provide some intuition and a unifying framework for
‘certainty equivalence’. Models of this type forecast expected
analyzing long-term fixed-rate, pre-payable mortgages
cash flows from the mortgage, including scheduled monthly
(FRMs), which comprise well over half of all U.S. mortgages.
payments and prepayments, and then treat this forecast as if
it were certain. The value of the mortgage is the present
140
Finance theory has developed a large arsenal for pricing
value of the projected mortgage cash flows, discounted at a
options, and the advent of trading mortgages in secondary
rate that adjusts for the risk that the scenario will not be
markets has presented opportunities to apply these tools to
right. For example, one might use the Public Securities
an important part of the financial system. In this primer we
Association (PSA) prepayment model, which assumes a pre-
focus on prepayment risk and ignore credit risk.2 For purposes
payment rate that begins at 0.2 percent per year and rises
2 Hendershott and Van Order (1987) survey option approaches to default modeling.
Kau et al. (1995) analyze the complications involved in the jointness of the options
because exercising one of the options means giving up the right to exercise the
other.
3 ‘Prime’ refers to standard high quality mortgages (often defined by credit score of
the borrower). A recent development has been the securitization of ‘subprime’
mortgages; this is still a rather small (probably 10%) part of the market.
4 In terms of value, default costs for conventional FRMs with 20% down payments
of the type bought by Fannie Mae and Freddie Mac are on the order of 5 basis
points per year; whereas the premium for the right to prepay is more like 50 basis
points. For riskier, such as ‘subprime’ or low down payment mortgages the two
risks are comparable in value.
gradually over 30 months to 6 percent or some multiple of it
the current market interest rate. For example, if we are hold-
and remains at that rate.
ing a bond bearing a 10 percent coupon when the market interest rate is 8 percent, we would simply discount the future cash
This is not a very good approach. It leaves the choice of risk
flows at 8 percent, and the bond would be worth more than
adjustment unclear, and for long-term securities relatively
par. At a current interest rate of 10 percent, the bond’s value
small errors in discount rate can lead to large errors in price.
would be exactly par. If we plotted the value of the bond at dif-
More importantly, prepayments change with interest rates, so
ferent interest rates, the result would be a convex5 shaped
that, assuming anything like historic interest rate volatility, no
curve, expressing the usual downward-sloping relationship
benchmark is likely to be accurate for very long. This might
between interest rates and bond prices. This is a property of
not be a major problem if the gains from over-predicting pre-
all noncallable fixed-income securities, and it has an important
payments balanced the losses from under-predicting them,
implication: a drop in interest rates increases bond value by
but because prepayment is an option at the discretion of the
more than the same rise in interest rates lowers bond value,
borrower, the gains and losses do not balance. When rates go
which leads us to the result that the expected value of the
up, fixed rate mortgages fall in value, but when rates go down,
security is greater than it’s current value from the price curve
investors reap smaller gains because borrowers tend to refi-
— a 10% coupon bond is worth more than par when the mar-
nance their mortgages at par. This means that the value of
ket coupon rate is 10%.6 This means that the model must be
investments in mortgages or mortgage-related securities
reworked to account explicitly for uncertainty — even without
depends critically and asymmetrically on the course of inter-
investor risk aversion.
est rates. And no one is very good at forecasting interest rates.
For example, assume that the basic risk-free rate for the time
The option-based approach looks at interest rates and prepay-
period relevant for repricing, such as a day, changes random-
ment in a probabilistic sense and explicitly acknowledges the
ly, and will either go up or down by Δ basis points, and draws
inability to predict interest rates. It specifies the probability
are independent over time. The probability that it will rise is p
distribution of interest rates and evaluates the effects of ran-
and the probability that it will fall is 1-p. Although the p and Δ
dom interest rate changes on mortgage values. This method
can change over time — for example, when monetary policy
has two advantages, it requires predicting only the probability
changes — we can almost certainly estimate these changes
of rates changing, rather than the rates themselves, and it
more accurately than we can predict future interest rates, and
explicitly addresses the borrower’s prepayment option and
indeed there are markets where these changes can be inferred
illustrates how the sheer volatility (and hence the unpre-
from prices of options, such as on Treasury securities.7
dictability) of interest rates affects mortgage pricing. Applying
the method to both callable and non-callable mortgages
Consider the simple case depicted in Figure 1. Initially, the
reveals some important differences in the shapes of their
rate is 10 percent. If Δ equals one percentage point and p
price/interest-rate relationships and in their reactions to
equals 0.5, the rate will either go up or down by 100 basis
volatility.
points, and each possibility is equally likely. Figure 1 shows,
for these values of Δ and p, how rates can change over the
Interest rate variation
next three periods.8
If we expected interest rates to remain close to current levels,
the certainty equivalence approach would be fine; we could
Pricing non-callable bonds
price any default free bond by calculating the present value of
How do we price a non-callable bond with this model?
future cash flows (perhaps adjusting for taxes), discounting at
Consider a bond that pays a U.S.$10 coupon at the end of the
5 The value of an n year pure discount bond is 1/(1+r)n, where r is the n year discount rate, which is convex in r (the second derivative with respect to r is positive).
6 This is nothing more than Jensen’s Inequality.
7 See Barter and Rendleman ((1979) for an early application of binomial rate models
in a more rigorous, arbitrage free contest.
8 This process is not entirely realistic because it implies that interest rates can be
negative.
141
97.35
13
12
sibilities. This is: [.5($97.35) + .5($99.10) + $10]/1.12 = $96.63
The first term in the numerator is the value of the bond if the
96.63
rate rises to 13 percent times the probability of the rise. The
11
97.59
11
99.10
second term is the value if the rate falls to 11 percent times the
probability of rates falling. The third term is the U.S.$10 coupon,
10
10
100.07
9
9
100.01
which is received in either case. The sum is discounted at the
100.92
102.56
8
103.57
End of
period:
1
2
Figure 1: Distribution of
interest rates over time
3
End of
period:
the 10 percent coupon rate, the bond’s value is below par.
We can use this same procedure to evaluate the bond for the
102.80
7
prevailing 12 percent interest rate. Because this rate exceeds
other two rate possibilities (8 and 10 percent) at the end of
year two. Now we have three possible bond prices at the end
1
2
3
Figure 2: Pricing non-callable
bonds
of the second year, shown in the next-to-last column of Figure
2. Working backward, we can use these values to obtain two
prices at the end of the first year (U.S.$$97.59 and
U.S.$102.56), one for each possible rate (11 and 9 percent).
first three years and the coupon plus U.S.$100 in principal (its
Finally, we can solve backward to find the initial price of the
par value) at the end of the fourth year. At the end of the third
bond, which is U.S.$100.07; i.e., it is worth more than the face
year, a one-period bond paying U.S.$110 remains. At this point
value. It can be shown that for the bond to be worth par (100)
there are four possible one-period rates: 7, 9, 11, and 13 percent.
at origination the coupon would have to be 9.98.10
Once the rate in the last period is known there is no further
uncertainty, so the last payment can be priced easily. If rates
This corresponds to the convexity of the bond curve; interest
have risen to 13 percent, the bond will be worth U.S.$110/1.13 or
rate decreases have a bigger effect, in absolute value, on value
U.S.$97.35. If rates have fallen to 7 percent, the bond will be
than do interest rate increases, which increases the value of
worth U.S.$110/1.07 or U.S.$102.80. The last column in Figure 2
the bond. This is perhaps a surprising result, but it is only part
shows all possible bond prices with one year to maturity.
of the story. Recall that we assumed that investors were risk
neutral. In fact, they seem to be averse to the risk of capital
With two years to maturity, the problem is more complicated
losses on bonds. In terms of our model, they may behave as if
because of uncertainty. Suppose the one-year interest rate
they raise p (the probability of rates going up) in their calcula-
has risen to 12 percent (the top branch of the tree in Figure 1)
tions to compensate for the risk associated with higher volatil-
at the end of two years. The rate will either rise to 13 percent
ity. If p is a positive function of volatility, then the net effect of
in the next year, in which case the bond will be worth
volatility on bond price could be negative — the coupon rate
U.S.$97.35, or it will fall to 11 percent, in which case the bond
needed to get the bond to sell at par would exceed 10 percent.11
will be worth U.S.$99.10. There is equal chance that either will
142
happen. In both cases, we get the U.S.$10 coupon payment.
Pricing callable fixed-rate mortgages
Suppose traders in the market are risk neutral, meaning indif-
For callable mortgages, the shapes of the relationships among
ferent between a fair bet on rates and a sure thing.9 In that
prices, interest rates, and volatility look quite different from
case, the value of the bond at the end of the second year, given
those for non-callable mortgages. The reason is that the
a 12 percent rate, is the expected present value of the two pos-
option to prepay (the call option) induces negative convexity
9 More generally, the discount rate would reflect the market’s attitude toward risk.
In the next section, we use an arbitrage free assumption to handle both the risk
adjustment and the expected present value approach to pricing. Here we simply
assume away risk aversion and postulate that value is expected present value.
10 The backward solution techniques are entirely analogous to ‘Bellman equations’ in
intertemporal programming [Sargent (1987)].
11 Indeed, it probably will be negative. For instance, from Figure 4 it can be seen that
the effect of high volatility on price in a risk neutral world is rather small.
Suppose rates have risen from 10 percent at origination to 13
97.35
percent (highest rate in the last column of Figure 1). The borrower can make the final payment, which in present value
96.63
terms costs him U.S.$97.35, or prepay it, which means buying it
97.40
back for U.S.$100. Clearly, being a wealth-maximizer, he will not
99.10
want to pay U.S.$100 for something worth only U.S.$97.35, so
99.59
98.82
he will not prepay. But suppose rates have fallen to 7 percent.
The present value of carrying the loan another period is
100
100
U.S.$102.80, but he can buy back the loan for U.S.$100. Clearly
the borrower increases wealth by paying off the loan and refi-
100
nancing, with a one year loan at the new market rate. Indeed,
he should prepay at any time the value of the remaining pay-
100
End of period:
1
2
3
Implies prepayment
ments is greater than par. At the end of period three, he should
prepay when rates have fallen to either 7 percent or 9 percent.
Figure 3: Pricing callable non-amortizing mortgages
Figure 3, which traces out callable mortgage prices just as
for callable debt. Over some range of interest rates the shape
Figure 2 traced out non-callable bond prices, shows the effect
of the curve is reversed, so that rate increases lower price by
of these prepayments at par by recording U.S.$100 in the
more than rate decreases raise them, and thus volatility low-
lower two boxes in the last column. This means that if interest
ers value.
rates have fallen since origination, the mortgage holder
should expect prepayment immediately, making his invest-
Negative convexity is the central difference between callable
ment worth only U.S.$100 at the end of year 3.
mortgages (and all callable debt) and non-callable bonds. To
illustrate this, we compare the bond analyzed above with a
Using the same procedure as in the bond case, we now go back
non-amortizing mortgage (i.e. a callable bond). The instru-
one year. Suppose the interest rate is 10 percent at the end of
ments are the same in every respect except that the mortgage
year two. If the mortgage is not prepaid it will be worth either
borrower has the option to prepay the loan at par (or unpaid
U.S.$99.10 or U.S.$100 (and called) next year. The expected
balance), always U.S.$100 in this case of no amortization, and
present value of these two possibilities plus the coupon is
take out a new mortgage at the new market rate without
U.S.$99.59. The possibility of call the next period causes the
penalty or other cost.
mortgage to have a lower value than the non-callable bond at
the same interest rate. Solving backward, as in the bond case,
Assume that the borrower is not planning to sell the house
gives a mortgage value at origination of U.S.$98.82, which is
before the mortgage is paid off (three years in the example),
U.S.$1.25 less than the value of the non-callable bond. This
or if the house is sold the new owner can costlessly assume
U.S.$1.25 represents the market’s implied value of the call
the mortgage. Under these conditions the borrower’s prepay-
option. The difference between 100 and 98.82, 1.18, is often
ment decisions are based solely on financial concerns, which
referred to as the ‘points’ charged upfront on the mortgage.
require maximizing borrower wealth by minimizing the value
of the mortgage. When should the borrower prepay the mort-
We could also calculate the coupon rate given by the discount
gage? As with the non-callable bond, we can begin by looking
rate that makes the present value of the promised payments
at the borrower’s choice with just one period left.
equal to U.S.$100. That is, we discount at (1+coup) and search
143
over coupon values until the initial value is U.S.$100. This
■ Volatility lowers callable mortgage value, especially when
coupon is 10.28 percent versus 9.98 percent for the non-
the option is close to par; it increases value for the non-
callable bond. The 30 basis point spread between the two
callable mortgage. For high rates the callable mortgage
yields is the amount by which the call option increases the
looks like a non-callable mortgage.
mortgage rate on a mortgage originated at par.12 Alternately,
10.28 is the rate on a loan with no points.
‘Suboptimal’ prepayment
The model depicted above focuses on purely financial motives
Note that the decision-making by the borrower is not compli-
for prepayment, but borrowers also prepay for other reasons.
cated even if the pricing calculations are. The borrower need
For example, borrowers typically prepay when they move
only know the market value of his loan and does not need to
because most mortgages are ‘due-on-sale’ (cannot be
make complicated present value calculations. In particular, the
assumed by the new owner without the lender’s permission).
borrower need only know if the coupon on a mortgage with
In principle, we can handle this by extending the model to
zero points (and a term equal to the term remaining on his
include the probability of moving. Suppose there is a 10 per-
loan) has fallen below the coupon on his loan, which means
cent chance each period that the borrower will move. We can
that the market value has fallen below the outstanding unpaid
price the mortgage by including this possibility in our expect-
balance.13
ed present value calculations. If mortgages are not assumable,
the possibility of moving always makes them more valuable
Determinants of the value of the callable
mortgage
because it forces some prepayments when rates are high and
We can redo both the non-callable and callable mortgage val-
the mortgage can be assumed without cost, moving and refi-
uations for different coupon rates and volatilities (Δ). Figure 4
nancing will again be entirely separate decisions. If the mort-
recalculates for the non-callable mortgage and Figure 5 for
gage is valuable to the current borrower (has a market value
the same mortgage, but with the call option. Basic results are:
below par) the mortgage will be assumed by the new owner; if
borrowers would like to keep their mortgages. In contrast, if
not, it will be prepaid in any case, so the analysis of the previ■ The callable mortgage is always worth less than the non-
ous section still applies.
callable; that is, the call option is always worth something.
But for high interest rates relative to the 10 percent
coupon, borrowers are unlikely to prepay (the call option is
‘out of the money’) and callable mortgage values are close
to non-callable values.
■ There is a basic asymmetry that callable value does not go
above 100 when rates fall but can drop sharply if rates
rise. This, again, is negative convexity; the shape contrasts
Initial rate
8
9
10
11
12
50
106.7
103.3
100.1
96.9
93.9
Volatility
100
150
106.7
106.8
103.4
103.4
100.1
100.1
97.0
97.0
94.0
94.0
200
106.9
103.5
100.3
97.1
94.2
Figure 4: Prices of non-callable mortgages for various initial rates and volatility
sharply with the noncallable curve, which becomes steeper as rates fall. Negative convexity is also called price compression. Both expressions refer to the same property: as
rates fall there is an upper limit on mortgage price
increases. Negative convexity reflects the market anticipating the possibility of exercising the prepayment option
before it actually occurs.
144
12 This is not quite correct. When the original three-year mortgage is called, we are
effectively replacing it with a mortgage with the remaining term of the original
loan but assuming that the call premium on this mortgage is the same as that of
a three-year mortgage. In fact, it must be less given the shorter life. Alternatively,
we could just assume that the investor invests the called mortgage in a noncallable bond, paying the certain 10 percent.
Initial rate
8
9
10
11
12
50
100
100
99.4
96.9
93.9
100
100
100
98.8
96.6
93.9
Volatility
150
100
100
98.3
96.2
93.7
200
100
99.5
97.7
95.9
93.4
Figure 5: Prices of callable mortgages for various initial rates and volatilities
13 Of course, markets are not all that complete and there may not actually be quotes
on a 23.5 year mortgage. For relatively new mortgages with close to 30 years
remaining, quotes on new 30 year mortgages will be pretty close.
In reality, most mortgages14 are not assumable, and people
The basic equilibrium condition for any fixed income security
might not prepay as ruthlessly as in the simple model because
is that the expected yield on a security should equal the risk-
of transaction costs and/or general inertia. The model can be
free rate plus an appropriate risk premium, which also implies
modified to conform more closely to real behavior by modify-
that price equals the expected present value of cash flows dis-
ing the option approach. For example, we might assume (or
counted at a risk-adjusted interest rate. These two notions
better still have empirical results that imply) that only half the
come from the condition that pricing be arbitrage free.16
borrowers prepay when it is optimal and that 10 percent of the
Contingent claims models derive the conditions [Cox, Ingersol
borrowers prepay when the mortgage value is below par
and Ross (1985)], but because this notion of equilibrium is so
(interest rates have risen) because they are moving and must
straightforward, we could start by making it an initial assump-
give up the low rate loan.
tion, as was done in the warmup model.
This is a modified, option-based approach, and it is a simple
The equilibrium condition for a default-free, fully-assumable
version of the more behavioral approach used by most Wall
FRM turns out to be a second-order partial differential equa-
Street firms that trade mortgages. Models like this incorporate
tion in R and t. This sort of equation will apply to any claim
major extensions to take account of factors like household
that is contingent on those state variables. Hence, many func-
mobility, unemployment, divorce, etc. Such models are more
tions satisfy the equation. To determine the one function that
realistic but are subject to the very real problem that their
applies to the mortgage being priced, we incorporate condi-
parameters cannot be expected to remain constant. For
tions specifying the details of the contract, such as the coupon
instance, as costs of refinancing have decreased over the past
rate, the term of the mortgage, and the value of R at which the
decade the probability of prepayment conditional on ‘being in
mortgage will be called (usually determined via an optimal call
the money’ has increased.
strategy).
Continuous time pricing models
The model determines mortgage price, not yield. Yield is usu-
The warm up model captures all of the important elements of
ally measured as the internal rate of return computed for a
pricing callable debt, but it needs to be extended. While the
given assumption about prepayment (i.e. prepayment in 12
assumption of trading at discrete intervals with a simple bino-
years or the PSA model discussed above). Because prepay-
mial process is sometimes a good approximation (as the num-
ment can vary greatly, depending on the mortgage coupon,
ber of steps increases the binomial distribution approaches a
and the expected volatility and drift of interest rates, conven-
normal distribution), it is not general enough. We shall devel-
tional yield calculations can be very misleading. The models
op models that take place in continuous time with broader
can be used to find the coupon rate that is consistent with
probability distributions. Moreover, because investors appear
some price, say par, but that is not the same as determining
to be risk averse, we need to allow explicitly for risk aversion.
the expected yield.
15
The formal option pricing methodology requires some technical apparatus, but that is not our major concern. Rather, we
Here we discuss a simple frictionless continuous-time model
continue to focus on intuitive interpretations to underscore
of mortgage pricing, which draws heavily on Dunn and
the economic logic underlying the analysis.
McConnell (1981), and Brennan and Schwartz (1985). We begin
by specifying the state variables and the arbitrage condition
In general a pricing model seeks to find and evaluate a func-
and then derive the pricing equation. Finally, we add exten-
tion M(R,t), where R is a vector of interest rates and t is time
sions.
from origination, that explains observed prices of mortgages.
14 FHA insured mortgages are generally assumable.
15 See for instance, Deng et al (2000) for a model with sluggish prepayment
behavior and heterogeneous borrowers.
16 Discrete time models can also be solved from arbitrage free conditions.
145
Equilibrium conditions
t)Mr (2), or um = [r + λ(r, t)δ(r, t)Mr]/M(r, t) (2), where um is the
Because a mortgage can be outstanding for up to 30 years, all
expected instantaneous rate of return on the mortgage, r
interest rates up to 30 years are potential state variables,
the instantaneous risk-free rate, λ the market price of risk,
which is to say M(R,t) could depend on a large number of vari-
δ(r, t) the volatility of short rate changes, and Mr the partial
ables. The problem can only be managed if a small number of
derivative of M with respect to r. Equation (2) says that in
basic interest rates determine the other rates. Like most
equilibrium the expected return equals the current rate plus
authors, Cox, Ingersoll, and Ross (1985) being the first, we
a risk-adjustment term, where the risk-adjustment term
begin by assuming that all interest rates are driven by a single
becomes the product of three terms: the price of the risk
exogenous rate, the instantaneous short rate, r, which deter-
that r changes, λ, the amount of risk, δ, and the interest-rate
mines the entire yield curve. Changes in this rate are taken to
sensitivity (alternatively the duration) of mortgage value,
follow an ‘Ito process’ [Maliaris and Brock (1981), Merton
Mr/M(r, t). If more state variables exist, more risk-adjustment
(1995)], the evolution of which is governed by the following
terms, each with its own risk price, come into being.
stochastic differential equation: dr = u(r, t)dt + δ(r, t)dz (1),
where u(r, t)dt is the expected drift in r over a small interval of
The arbitrage model does not derive the λ’s; their derivation is
time of length dt, δ(r, t)dz is a disturbance made up of dz,
a general equilibrium problem that requires knowledge of
which is normally distributed with zero mean and unit vari-
such market forces as traders’ risk aversion. The model does
ance, and δ(r, t), which is the volatility of dr.
imply that the λ’s are objective prices, which are the same for
all traders and can be inferred from market prices. Thus, the
Equation (1) is a continuous-time version of a standard differ-
λ’s may be viewed as competitive market prices for risk.
ence equation. Cox, Ingersol and Ross (1985) and others have
shown how (1) can be used to determine the entire Treasury
Pricing equations
yield curve.
The next step is the derivation of um, the expected rate of
return on the mortgage. This is a technical step that requires
We assume that markets are complete enough that traders
some knowledge of Stochastic Calculus. Use is made of Ito’s
can construct portfolios of traded assets that over a short
lemma, which is the stochastic analogue of the chain rule of
period of time mimic the cash flows of mortgages. Then mort-
ordinary calculus. The result, which we simply assert, has a
gage prices come from the assumption of no arbitrage profits.
fairly straightforward interpretation. The expected instanta-
In particular, under rather general circumstances a portfolio of
neous return consists of the coupon rate and expected per-
default free bonds, such as Treasuries, can be constructed
centage capital gains. The coupon rate is simply the coupon
such that the combination of the mortgage and a short posi-
payment, C, divided by M. Expected percentage capital gains
tion in the Treasury portfolio (the hedge portfolio) absorbs
come from two sources. The first can be called ‘certainty
zero wealth and has zero short-term (with continuous time
equivalent’ gains, which occur if variables change as expected.
instantaneous) risk. Brennan and Schwartz (1977, 1985),
These are given by Mt/M (amortization and capital gain from
among others, show how this portfolio is derived.
selling at a discount) and u(r, t)Mt/M (expected change in r
times the interest sensitivity (duration) of value with respect
Absence of arbitrage profits implies a zero instantaneous
to interest rates).
return. From this zero return, the basic equilibrium condition
146 - The
is deduced: the instantaneous expected yield on the mort-
The second source flows from the stochastic nature of r and
gage must equal the risk-free short rate plus a risk factor. In
is the vehicle that introduces the negative convexity dis-
the case of one state variable, umM (r, t) = rM(r, t) + λ(r, t)δ(r,
cussed above. Because M is, in general, not linear in r random
increases in r will not have the same effect on M, in absolute
discounted at the appropriate rates read off the yield curve
value, as random decreases. Thus, as above, the certainty
determined by (1). Hence M*(r, t) has the usual downward slop-
equivalent approach of assuming that r changes exactly by
ing concave shape of a fixed-income security [Brennan and
u(r,t) will not fully reflect expected capital gains. Accounting
Schwartz (1977) and Cox, Ingersol and Ross (1985)].
for this extra capital gain requires using Ito’s lemma. Here we
simply assert that expected capital gains from the dispersion
1/ δ2M /M,
2
rr
The curve for the callable mortgage, M(r,t), lies below M*(r, t)
that is, they depend on the
by an amount equal to the value of the call option. Because
volatility of r and the shape of M, disappearing if M is linear
the mortgage can be called when M equals PAR, we know that
or r is nonstochastic.17
points in the region above the PAR line cannot be points on
of r are given by
M; the borrower would maximize wealth by prepaying if that
Adding the returns from coupons and capital gains, we have
happened. Rational borrowers (ignoring transaction costs) will
umM (r, t) = C + Mt + u(r, t)Mr + 1/2δ2(r, t)Mrr (3). Equating (1) and
choose the call strategy that minimizes the value of M, which
(3), C + Mt + [u(r, t) – λ(r, t)δ(r, t)]Mr + 1/2δ2(r, t)Mrr= rM (4)
maximizes wealth. Of all the M functions satisfying (4)–(6), the
rational borrower chooses the function that has the smallest
This second-order partial differential equation is the basic
value subject to touching the PAR line (the option will never be
equilibrium condition for the one state variable model. An infi-
exercised at less than par). The curve that does this (assuming
nite number of functions of r and t satisfy this condition (an
an interior solution) must be tangent to the PAR line, and the
infinite combination of coupon and capital gains streams pro-
level of r at which it touches is the optimal call rate for a given
vide a normal or equilibrium return).
t. Hence, the final boundary condition is Mr(rc, t) = 0 at M =
PAR (7), which gives the minimum M(r,t).19
To obtain an expression for a specific debt instrument, we
must specify the terms of the instrument. Mathematically we
Note that if (7) represents the minimum value of M(r,t) sub-
need three boundary conditions, one for t and two for r (equa-
ject to touching PAR, then M(r,t) must be concave from below
tion 4 is second order in r). The t boundary is the terminal con-
(Mrr < 0) in the neighborhood of the exercise rate, rc, reflect-
dition that comes from the amortization schedule of the mort-
ing the price of the security anticipating the call option even
gage. For a fully amortizing mortgage, M(r, T) = 0 (5), where T
when r is not especially close to rc. This concavity (negative
is the time at which the last payment is made. The other two
convexity) comes from the second order condition for optimal
conditions relate to how M is valued when r takes on extreme
exercise. From (3) negative convexity implies that volatility
values. The first of these conditions incorporates the econom-
produces a lower return on mortgages due to capital losses
ic intuition that M becomes worthless as r approaches infinity.
on average for mortgages close to being called. Hence,
M(∞, t) = 0 (6). The final condition specifies the interest rate
volatility makes callable mortgages less valuable.
18
at which the mortgage is called, rc. The assumption is that
the call option will be exercised in a way that maximizes bor-
As was the case in the binomial example above, the borrower
rower wealth.
does not have to go through the optimization problem
described here and does not need to be acquainted with Ito’s
But before turning to that, we consider, as we did above, the
Lemma for the model to work. A strategy of prepaying when-
pricing of a benchmark security, a non-callable mortgage, M*,
ever the coupon on a new par (no points) mortgage with the
which is equivalent to a portfolio of Treasury securities with
same remaining term is less than the coupon on the loan will
constant payout for T years. This is easy to price because the
also minimize mortgage value. Because this new coupon rate
value of M* is just the present value of the known cash flows
is what is to be determined, outside pricers do have to solve
17 Note that if Mr > 0, then the premium is positive, and vice versa. The Mrr < 0 corresponds to negative convexity, which lowers value. A mortgage can take on both
positive and negative values of Mrr as r varies (the options goes in or out of the
money).
18 In the non-amortizing case in the warm up model the condition is that M(T) = PAR.
19 Not surprisingly this implies that the duration is zero near the exercise point; then
the mortgage will be priced so that it earns the risk-free rate.
147
the partial differential equation, so as to make M(r,t) a function
condition (4), as discussed in the previous section. The expect-
of exogenous variables (like the yield curve), but the borrower
ed return on the mortgage now equals the risk-free rate plus
need only know current market rates.
adjustments for the risks of the short rate or the long rate
changing. This leads to a generalization of (4). If we let c be
The solution has an expected-present-value interpretation, but
the long-term (consol) rate, δ12 and δ22 be the variances of
here it is derived rather than assumed, as was the case in the
changes in r and c, ρ be their correlation coefficient, u1 and u2
warm up model. In particular, M is the expected present value
be their means and λ1 and λ2 be their risk prices, then equilib-
of future cash flows, discounted at r, with the expected value
rium is given by
of dr given by u – λδ rather than just u [Cox, Ingersol and Ross
(1985), Lemma 4].20 Risk aversion is allowed, and it is, in effect,
1/2Mrrδ12 + Mrcρδ1δ2 + 1/2Mccδ22 + Mr (u1 – λ1δ1) + Mc (u2 – λ2δ2)
a market price that is shared by all fixed income securities.
+ Mt + C = rM (8), which is similar in spirit to (7) except now
Finally, optimal exercise of the option is derived, coming from
there is a more complicated convexity term and two risk prices
wealth maximization at every decision point, and it leads to an
instead of one.
intuitively appealing tangency condition.
What is especially interesting in this case is that the values of
In general there is not a closed form solution for M(r.t).
λ2 and u2 can be inferred. Because (8) applies to the value of a
Solutions come from techniques that involve carving the r–t
consol, by substituting the value, 1/c, of a consol paying U.S.$1
space into a grid, converting (partial) differential equations
into (8) and evaluating the derivatives [Mc = -1/c2, Mcc = 2/c3, Mr
into difference equations. It is necessary, as in the warm up
= 0] we can solve for λ2δ2, and, by substituting the result back
model, to solve the model backwards from the last period back
into (8) produce an expression that contains neither λ2 nor U2
to the first, because at any decision point except at the end of
[Brennan and Schwartz (1985)]. This insight comes directly
the term it is necessary to know future options in order to
from the arbitrage approach and is directly analogous to the
make decisions [Kau and Keenan (1995)].
result in Black and Scholes (1973) that we do not need to know
the mean-reverting value of a stock or its risk price to price an
Extensions
option on the stock. In the one-state model, we could not
A logical extension of the model is to increase the number of
eliminate u or λ because the instantaneous security is not a
interest rate variables. Taken literally, the one-rate model
traded asset (it matures too quickly). As a result it does not
above implies a constant rate toward which the short rate
have a price that we can plug back into (8).21
reverts for all time. Given the obvious importance of changing
inflation on interest rates, this seems like a difficult model to
Another extension is to allow sub-optimal prepayments
take seriously (although this may not be of much empirical sig-
because households do not always exercise their prepayment
nificance). The nominal rate could be defined as the sum of the
option as ruthlessly as the model we have elaborated implies
real rate and the expected inflation rate, and these compo-
and/or there are transaction costs, observable and unobserv-
nents could be viewed as being governed by separate process-
able, that make exercise more complicated than is depicted.
es, requiring two state variables [Richard, (1978)].
Many researchers have developed ad hoc prepayment functions, fancier versions of the one in the warmup model, that
148
Alternately, and equivalently, in their two-state variable model
allow prepayments for reasons other than hitting the bound-
Brennan and Schwartz (1985) assume different mean-revert-
ary condition. These models are typically option-based in the
ing processes for the short rate and the rate on a long-term
sense that they use the same sorts of variables that the rig-
consol bond. Adding a state variable changes the equilibrium
orous, frictionless models used, but they allow for a wider
20 Indeed, from (4) there is a choice in use of the risk adjustment term. You can, as
above, bias the mean change in rates by deducting λδ from it and discount at the
risk free rate, or you can project at the true mean and discount at the risk-adjusted rate r + λδMr/M. The former is often easier because r – λδ can be inferred from
the Treasury yield curve.
21 Note though that we do not need to know u or λ separately. Only u – λδ matters
and that can be inferred from market prices. We do need to know δ.
range of response elasticities. In the context of continuous
In all cases, however, the basic structure of the model and the
time models, Dunn and McConnell (1981) and Brennan and
ultimate solutions are the same:
Schwartz (1985) added random prepayments, which they
modeled as Poisson processes, to rational prepayments,
■ The value of the mortgage is the expected present value
given by the boundary condition (7). If ρ is the probability of
of the cash flows, discounted at a risk-adjusted rate that is
a random prepayment, then the expected cash flow (C in (4))
revealed by market prices.
is increased by ρ(M-PAR). Boundary conditions are as before.
■ The cash flows come from optimal exercise, which comes
from wealth maximization and in general involves tanWhile much empirical work on default and prepayment has
been proprietary, several studies have been published. Foster
and Van Order (1985) estimate models of default and prepayment using aggregate data, which allows them to use ordinary
gency conditions.
■ There is in general no closed form solution. Solution
requires converting into discrete values and backwardsolving.
least regression techniques to obtain estimates, and Deng et
■ Practical modelers and traders use more complicated but
al. (2000) use a proportional hazard model to estimate both
less elegant behavioral models. The models are option-
prepayment and default models that allow for unobserved
based but not explicitly value-maximizing, and Monte Carlo
heterogeneity among borrowers. The basic structure of both
techniques are typically applied to obtain solutions.
models is option-based, using the extent to which the options
are in the money as key explanatory variables. An advantage
References
of the more behavioral models, like Deng et al., which do not
• Barter, R., and R. Rendleman, 1979, “Fee based pricing of fixed rate loan commitments,” Financial Management, Spring, 13-20
• Black, F., and M. Scholes, 1973, “The pricing of options and corporate liabilities,”
Journal of Political Economy, 81, 637-59
• Brennan, M., and E. Schwartz, 1977, “Savings bonds, retractable bonds and callable
Bonds,” Journal of Financial Economics, 5, 67-88
• Brennan, M., and E. Schwartz, 1985, “Determinants of GNMA mortgage prices,”
Journal of AREUEA, 13:1, 209-228
• Cox, J., J. Ingersoll, and S. Ross, 1985, “A theory of the term structure of interest
rates,” Econometrica, 53, 302-407
• Deng, Y., J. Quigley, and R. Van Order, 2000, “Mortgage terminations, heterogeneity
and the exercise of mortgage options,” Econometrica, 68:2, 275-307
• Dunn, K. and J. McConnell, 1981, “Valuation of GNMA mortgage-backed securities,”
Journal of Finance, 36, 613-623
• Foster, C. and R. Van Order, 1985, “FHA terminations: A prelude to rational mortgage
pricing,” Journal of AREUEA, 13:1, 273-291
• Hendershott, P., and R. Van Order, 1987, “Pricing mortgages: An interpretation of
models and results,” Journal of Financial Services Research, 1:1, 77-111
• Kau, J., and D. Keenan, 1995, “An overview of option-theoretic pricing of mortgages,” The Journal of Housing, 6:2, 217-244
• Malliaris, A., and W. Brock, 1981, “Stochastic methods in economics and finance,”
North Holland
• Merton, R., 1973, “The theory of rational option pricing,” Bell Journal of Economics,
4, 141-183
• Merton, R., 1995, “Continuous time finance,” Blackwell, Cambridge MA
• Richard, S., 1978, “An arbitrage model of the term structure of interest rates,”
Journal of Financial Economics, 6:1, 33-57
• Sargent, T., 1987, “Dynamic macroeconomic theory,” Harvard University Press,
Cambridge MA
explicitly model optimal exercise, is that they are easier to
use for pricing because they do not require backward solving
techniques to calculate model prices. Backward-solving models are often costly to solve, especially if there are many state
variables.22 With models that are not explicitly optimizing simulation or ‘Monte-Carlo’ techniques can be used to estimate
expected present value. This allows much greater flexibility in
modeling and appears to be the main tool used by traders.
Conclusion
This paper describes the option-based approach to pricing
fixed rate, prepayable mortgages using techniques used to
price callable bonds. It is relatively straightforward to extend
the model to analyze default in the same option framework
[Hendershott and Van Order (1987) and Kau and Keenan
(1995)] with default as a put option, selling the house back to
the lender at a price equal to the value of the mortgage. More
complicated is analysis of the two options together [Kau and
Keenan (1995)]. In that case exercising one option means foregoing the right to exercise the other, which greatly complicates the analysis.
22 For instance, if there are lagged values of variables, such as in analyzing
adjustable rate mortgages [Kau and Keenan (1995)] or delayed reaction, they need
to be modeled as separate state variables in optimizing models.
149
150 - The
Assets
Efficient pricing of
default risk:
Different approaches
for a single goal
Damiano Brigo
Head of Credit Models, Banca IMI
Massimo Morini
University of Milan Bicocca
Abstract
With the rapid development of the credit derivatives market,
efficient pricing of default has become an extremely important issue for the credit risk management of banks and other
investors. We consider here some of the opportunities and
problems that the development of this market poses to quantitative research in academia and industry. We describe different modeling choices pointing out the practical pros and cons
of the different frameworks. For all different frameworks, we
present innovative solutions allowing both computational efficiency and high consistency with the increasingly liquid credit
reference market, the market of credit default swaps.
151
Efficient pricing of default risk: Different approaches for a single goal
The last few years have been described by many as a period of
outstanding increased from U.S.$170 billion in 1997 to almost
downturn for the financial markets, or at least of increased
U.S.$1,400 billion in 2001. At the same time, the range of
worry and lack of confidence. Crises have struck investors in
products is growing, in particular in portfolio credit derivatives
different markets, starting from the collapse of the LTCM
and options on existing credit derivatives. Besides represent-
hedge fund in 1998, to the burst of the Internet equity bubble
ing an important contribution to the stability of the financial
in 2000, and to the debt crisis of both sovereigns (Russia
market as a whole, the increasing liquidity of this market is
1998, Argentina 2001) and major industrial worldwide players
opening up unmissable opportunities for credit risk manage-
(Enron 2001, WorldCom 2002). These events have pushed
ment of banks and other investors.
many investors out of different sectors of the financial market.
In the following section, we will explain the structure of the
However, a closer look at the situation reveals that the context
most common credit derivatives. Then we consider the rele-
is twofold. While a proportion of investors were actually pushed
vance of the development of a liquid market for credit risk for
out by the recent crises, those who remained started to devel-
reliable relative value pricing through quantitative modeling.
op instruments to strengthen and defend themselves for the
We describe the general features of the major modeling
future. This process includes the development of a substantial-
frameworks, and present innovative solutions for exploiting
ly new market, the credit derivatives market, which has been
the opportunities and reducing the problems of the different
growing dramatically even when most other financial markets
approaches.
have been stagnating. Credit derivatives are mostly over-thecounter derivative securities whose final payout depends on
Credit default swaps (CDS)
the default of a reference entity. Default has several meanings,
Since the market is experiencing a fast evolution, it is not yet
including the risk that one counterparty will not honor some of
possible to give a precise or definitive taxonomy of credit
its obligations. While the types of structures that are being
derivatives. However, an important feature of these instru-
developed are quite complex and varied the common purpose
ments, pointed out for instance by Bielecki and Rutkowski
of these products remains the same, to allow market partici-
(2001), is the precise extent of credit risk that a product
pants to single out, transfer, and trade separately credit and
allows to be transferred, namely the intrinsic definition of
default risk, namely the part of the risk in a contract which is
credit risk. We have securities that allow the entire risk asso-
related to the credit reliability of an obligor.
ciated with a transaction vulnerable to credit risk to be transferred, such as ‘total rate of return swaps’ and ‘equity return
In parallel, the development of this market has been fueled by
swaps.’ We also have products that transfer the risk related to
the increased attention of regulatory agencies to exposures in
changes in the value of an agreement due to movements of
OTC derivatives by many of the world’s major financial institu-
the credit quality (financial reliability) of one or more oblig-
tions. Regulations, such as Basel I and II, made the advantages
ors, such as credit spreads swaps and options. Finally, there
of an efficient credit risk market even more apparent, in par-
are products precisely focused on separating and transfer-
ticular to major banks. The market for credit derivatives was
ring only the risk directly involved with a default event. This
created in parallel in Europe and in the U.S. during the 1990’s,
last category appears to be most attractive to market partic-
and it has recently experienced the highest growth rate of all
ipants. Credit default swaps (CDS) and similar products, for
derivatives markets. The vitality of this market is revealed
example, represented over two thirds of the entire credit
both in terms of quantitative expansion and qualitative devel-
derivatives business in 2002.
opment and financial innovation. According to a Risk magazine survey in 2002, the notional value of credit derivatives
152 - The
A credit default swap is a contract between two parties, called
the protection buyer and the protection seller, designed to
ance contracts and could not be traded separately from the
transfer the financial loss that the protection buyer would
reference obligation. This system did not favor efficiency, con-
suffer if a particular default event happened to a third party,
sistency, and competition in evaluating credit risk, and strong-
called the reference entity. Usually, the reference entity is a
ly limited the possibilities for credit risk management. Instead,
debtor of the protection buyer. The protection buyer agrees
the creation of an increasingly liquid market allowing investors
to pay a periodic amount R (less frequently an upfront fee) to
to trade credit risk separately as any other tradable asset was
the seller in exchange for a single protection payment, made
a real major financial innovation, since it led to a strong
by the seller only in case the pre-specified feared default
increase in attention, competition, and precision in evaluating
event happens. The CDS are quoted on the market though a
credit risk.
fair R, often called CDS spread, making the current price of
the contract equal to zero, like in interest rate swaps.
From a quant’s perspective, it allowed for the extension of the
advanced techniques for pricing and management that had
In spite of all possible variations, the basic structure of the
been developed for different markets, such as equity, interest-
product is always the simple one described. This structure
rate, and FX derivatives, to credit risk.
allows for a protection similar to an insurance contract, but a
CDS is an autonomous security traded on a financial market
The increasing liquidity of the CDS market, in particular, has
like any other derivative. The relevance of this feature in a sit-
played an important role in shaping credit modeling, making it
uation of increasing liquidity will be further pointed out in the
more similar to those typical in other markets. The CDS, aimed
next section, with particular attention to its consequences on
at transferring only the risk directly involved with a default
quantitative valuation and risk management.
event, are the most interesting category also from a quant’s
point of view. In fact, their evaluation poses in a clean way the
CDS and other credit derivatives from a quant’s
perspective
problem of modeling and pricing the financial consequences
Traditional models for pricing and hedging contingent claims
quotations embed fundamental information on the market
written on equity or on the term structure of interest rates
assessment of the risk neutral default probabilities for the ref-
do not include a specific consideration for credit risk. The
erence obligor.
of the central specific event, the default. Consequently, CDS
increased attention of market participants and regulators to
credit risk, and the growing amount of complex structured
Since, as is well known, pricing of contingent claims is cor-
products for which default risk could not be overlooked, called
rectly performed by expectation under risk neutral probabili-
for increased attention to credit risk also from quants in aca-
ties, this is actually what we are interested in for valuation of
demia and industry. In particular, because of the contempo-
default-dependent payoffs. Obviously this information is not
rary development of the credit derivatives market, giving the
transparent and requires setting a precise modeling frame-
possibility to transfer default risk through an OTC contract,
work for being assessed quantitatively (although we will see
the focus moved to the development of specific models for the
that default probabilities in CDS appear quite robust to the
valuation of these new contracts. In fact the agreements used
choice of the model). The procedure for determining the
for transferring credit risk needed to be correctly priced for
parameters of a model in such a way that it gives answers con-
making the transfer effective.
sistent with known reference market prices is called calibration. When the model has been calibrated to the basic prod-
Previous financial agreements which were used to protect
ucts, it can be used for pricing consistently more advanced
investors from credit risk had features often similar to insur-
default-risky payoffs.
153
However, before CDS reached a critical liquidity, the market
Structural models
price of credit risk expressed by them was not a reliable rep-
The first important contribution to quantitative credit model-
resentation of the market expectations or risk premia.
ing dates back to the seminal paper of Black and Scholes
Therefore modeling concentrated on explaining default risk
(1973), which introduced the principles of modern option pric-
based on information ‘external’ to its specific market. With the
ing. In this paper the valuation of company liabilities was indi-
increase in liquidity and diffusion of the CDS, the precise
cated as a possible application of the pricing technique intro-
information on the price of credit risk they provide, deter-
duced (later known as the Black and Scholes formula), and the
mined by a reliable level of demand and supply, becomes a
underlying idea was a structural explanation of default.
fundamental benchmark for fair valuations. This moved the
Although the distinction is at times rather subtle, financial
attention of quants to building models that are able to regis-
research labels as structural those models containing a styl-
ter efficiently, through calibration, the information provided
ized description of the economic causes for a market value or
by the reference CDS market. Such models are then reliable
event; they are opposed to those models, at times called
enough to be used for required applications.
reduced form models, based on a quite general mathematical
framework to be specified consistently with historical or cross-
This last development set a context for relative value pricing
section data. In the Black and Scholes (1973) and then Merton
similar to that of traditional derivatives markets, but many
(1974) default model, a company defaults if, at maturity T of its
technical modeling problems posed by valuation of credit risk
debts, the value of the company is lower than the reimburse-
are peculiar. Most of them had been paid little attention to in
ment to be made. Based on this interpretation and by assum-
the past, since possible applications were less necessary and
ing a geometric Brownian Motion (GBM, also called lognormal
relevant. The possible structural causes of credit risk, or on
diffusion) dynamics for the value of the company, all the math-
the other hand the sudden consequences of a default event,
ematics required for computing default probabilities is that
are both examples of specific features making this risk inher-
typical of plain vanilla equity option pricing.
ently different from that involved in modeling the underlying
asset of more traditional derivatives. Another distinctive fea-
Black and Cox (1976) also remain in this framework for explain-
ture, not treated in this work, is the fundamental incongruence
ing default based on balance sheet notions, but increase real-
between the nature of default interdependency and the con-
ism by introducing the so-called first passage time models.
cept of interdependency comfortably used for interest rate
Here the value of a company is again a GBM, and default still
and equity markets. Therefore, although many techniques and
happens if the value of this process is lower than the level of
models previously used have turned out to be useful for this
its debts, but now this event is not limited to an unrealistic sin-
new application, the extension of the quantitative apparatus
gle maturity time. Here the debt level is a barrier Dt, possibly
to this new market has called for a massive work on model
time varying, and the value of the company can fall below Dt
innovation and development of new techniques.
at any time, causing default. For first time passage models the
mathematics required was already in use for equity barrier
The alternative models for credit risk pricing do not differ
options. The model was tractable (easy to make computations
simply due to technical details. The main modeling frame-
with) in case the underlying was assumed to have constant
works stem from different views on fundamental issues, such
parameters, in this case the explicit probability distribution for
as the choice of the variables to model or the correct descrip-
the first time that a GBM hit a barrier is known.
tion of a default event. We briefly review some of these frameworks in the next three sections.
One may be unconvinced by the hypothesis on the firm value
underlying these approaches, but the ultimate reason that led
154 - The
to the development of alternative approaches was a practical
credit spreads, but not for their volatility. For this one has to
one. Structural models appeared empirically unable to
allow for continuous stochastic variation of intensity. In this
describe real market expectation of defaults. The gradual
case we move to Cox Processes. In this setting, conditional on
description of default implied by these structural approaches
the information on the path followed by intensity, default hap-
was not consistent with market expectation of default as a
pens at first jump time of an inhomogeneous Poisson process
sudden event, not fully predictable by observing book values
with this time-varying intensity. Thus survival probability is
of a company. In particular structural models tend to imply
P(τ > t) = E[P(τ > t | { λ(s): 0 ≤ s ≤ t})] = E[e–∫λ(s)ds]
unrealistically low default probability in the short-term.
This approach can exploit many results and well-known modLater we will describe some possibilities to overcome these
els typical of stochastic modeling of the short interest rate
practical problems of structural models without leaving the
(instantaneous spot rate), already in use for interest rate
structural representation of default. In the next section,
derivatives. Notice in fact that the expressions for survival
instead, we see a radically different framework.
probabilities are analogous to the functions expressing bond
prices in terms of the dynamics of the short rate. Advanced
Intensity models
intensity models [Duffie and Singleton (1999)] are more flexi-
The direct way to take into account the sudden nature of the
ble than structural models. However, depending on the dynam-
default event in the real word is modeling directly default as
ics chosen for the intensity, here too there can be differences
an unpredictable, exogenous event. This leads to reduced form
in terms of tractability and calibration power. We will see later
models, also called intensity models, where default happens at
a model designed with specific attention to both aspects.
the time of the first jump of a stochastic (jump) Poisson
process with intensity λ. This means that the time of default τ
Market models
is exponentially distributed with a probability of survival for t
Intensity models, although developed for increasing consis-
years given by P(τ > t) =
e–λt,
with expected time to default 1/λ.
tency with the market, are based on modeling theoretical,
In such models there is no attempt made to model the eco-
non-observable quantities and lead to option formulas quite
nomic causes for default. Default is simply a random variable
different from those traders are used to. Traders on the inter-
with a distribution parameter λ to be determined consistently
est rates market are used to price options with the Black for-
with market evidence.
mula, developed originally for commodity futures. This formula is based on modeling the underlying as a lognormal
Also in this framework many extensions have been put for-
process under the pricing measure. Without this structure,
ward to increase realism and flexibility. A model with constant
even the typical concept of implied volatility cannot be used
default intensity is neither realistic nor flexible enough to
consistently. To recover the features of classic option formu-
embed market information about default probabilities on dif-
las in credit, the first step is modeling directly the underlying
ferent interims. As a solution, the intensity can be supposed to
rates in credit derivatives payoffs. So default is not to be
vary deterministically in time, also continuously (given some
explicitly modeled, neither as a predictable nor as a structur-
technical conditions). In this case, the default happens at the
al event.
first jump of an inhomogeneous Poisson process with intensity λ(t), leading to a survival probability P(τ > t) = e–∫λ(s)ds. The
In interest rate modeling, recent developments in probability
shape of this survival probability hints at the fundamental fact
made it possible to give a rigorous probabilistic foundation to
that the intensity can be interpreted as an instantaneous cred-
the aforementioned market standard of pricing most liquid
it spread. This model can account for the term structure of
options via heuristically derived Black-like formulas. This led
155
to the so-called market models, such as the Libor and the
enough flexibility to be calibrated to a term structure of CDS
Swap Market Models.
rates, and thus to the embedded default probability.
Generalizing the definition, in a market model we model
Is it possible to enrich the calibration power of structural mod-
directly market observables underlying common options, and
els while keeping tractability, namely consistent with the
they are assumed to follow the so-called standard market
mathematics of barrier options? Thanks to recent advances in
model, namely a lognormal diffusion under the reference pric-
this last field, the answer is now affirmative. Lo et al (2003)
ing measure. This allows us to price options with Black-like for-
show that, assuming a specific shape for the barrier, one can
mulas. Hull and White (2003) outline that a market model
have explicit formulas also when the underlying is modeled as
approach, which makes it possible to detect the implied volatil-
a GBM with time-varying parameters. For credit risk, this
ities in option quotations, can be useful also in a credit setting,
means that we can have a tractable structural model even if
in order to make option quotations more standard, and there-
allowing for time-varying volatility of the underlying. Such a
fore transparent and understandable. This would help enhance
model and its calibration to CDS are described in Brigo and
liquidity in some growing markets for credit options, such as
Tarenghi (2004).
options on CDS. But there are some relevant issues to be considered, ranging from detecting the correct specification of
Assuming that the volatility of the firm value is piecewise con-
the state variables helping to price real world derivatives, to
stant (a step function), the model can be easily calibrated to
technical issues in the definition of the reference probability
CDS quotes using both volatility and the debt barrier. In Brigo
measure.
and Tarenghi (2004) diagnostic tests are performed to verify
that this is not only a formal consistency due to the many
A tractable structural model consistent with
market implied default probabilities
parameters, but corresponds to an increased capability to pick
Typically credit models were specified according to credit
bilities are computed and compared with those implied by a
spreads or balance sheets information. However credit
standard intensity model (the framework designed for this
spreads appear to be largely determined by causes different
exact purpose). Surprisingly enough, the probabilities found
from default probabilities, for instance liquidity. On the other
are nearly the same. This evidence confirms two hypotheses.
hand, some recent major defaults (Enron, Parmalat) suggest
Firstly, that CDS information on default probabilities is robust.
that default often happens in conjunction with particularly
If the level of fitting power is kept equivalent, it is not highly
unreliable balance-sheets information, so that book values can
dependant on modeling assumptions. Secondly, that the
be even more misleading for assessing default probabilities.
tractable structural model of Brigo and Tarenghi (2004) also
out relevant implied market structures. Implied default proba-
matches, besides the CDS quotes, the whole structure of
Therefore, it seems that nowadays, even when using a struc-
default probabilities as determined by intensity models.
tural model, it may be appropriate to refer to the credit deriv-
156 - The
atives market to extract default probabilities, and in particular
A recent development that is currently under investigation
to CDS. Indeed, the CDS market is becoming an increasingly
concerns the possibility to calibrate the CDS quotes via an
reliable and liquid source of information for market default
uncertain debt barrier, using the barrier scenarios and proba-
probabilities, and is rapidly updated when new information on
bilities as calibrating parameters and keeping the value of the
the real financial situation of a debtor is disclosed, sometimes
firm volatility as an exogenous input from the equity market.
even anticipating it. However, there are technical problems in
Among other issues, the work of Brigo and Tarenghi (2004)
implementing this approach. Structural models have not
suggests that practical problems of standard structural mod-
els in pricing are not an unavoidable consequence of the
an intensity) has the form dyt = k(μ – yt)dt + v(ytdWt)1/2, where
hypothesis made, but depend a lot on the data used for
the vector β = (k, μ, v, y0) has positive components. All param-
expressing these assumptions in quantitative terms, and on
eters have a clear and intuitive role in determining the dynam-
the fitting capability of the structural model to these data.
ics of the process.
Brigo and Tarenghi (2004) also show applications of the
The condition 2kμ>v2 ensures the process remains positive,
model. Firstly, they analyze a concrete default case, the
and Brigo and Alfonsi (2005) present a scheme to enforce this
Parmalat case, showing how the model can efficiently embed
property also when the model is discretized for simulation.
increasing proximity to default as information on the wors-
This process features a non-central chi-square distribution
ened credit quality of a company is disclosed in time. Secondly,
and is highly tractable, featuring closed-form formulas for
they consider the pricing of a claim embedding counterparty
pricing.
risk, and show how in this setting default correlation can be
accounted for in a rather natural way, exploiting the proximity
CIR has often been used in interest rate derivatives pricing,
between the underlying being modeled and the equity market.
and also for the pricing of credit derivatives. With the development of the interest rate derivatives, it soon appeared
A positive intensity model with increased
calibration power
strongly limited by the low number of parameters. In fact
We mentioned earlier that not all possible specifications of the
interest rates.
these models cannot fit exactly the initial term structure of
intensity dynamics are equivalent for applications. We can
recall at least three different orders of problems. Firstly, the
As we noticed also in the last section, an increased calibration
intensity has to be strictly positive (thus forbidding Gaussian
power is now desirable in the credit market too. When a refer-
models) for default probabilities to be meaningful. Secondly,
ence market for a source of risk becomes reliable enough,
not all candidate intensity processes have the same calibration
using models fully consistent with that market price becomes
power. If the range of products considered increases, even in a
a necessary requisite for giving a fair price to more advanced
reasonable range, basic common processes can become inad-
products. Furthermore, increased liquidity reduces the risk of
equate. This was already revealed in interest rate modeling.
perfectly fitting unreliable quotations. Using a technique
Thirdly, computational times and complexity are extremely
developed on the interest rate market, one can extend the CIR
important in pricing. Models allowing for closed form formulas
dynamics above to fit a full term structure of CDS. This is done
(not requiring simulation) are usually preferred, in particular
in Brigo and Alfonsi (2005), where references are given, and
when a model has to be calibrated both to credit and interest
in the resulting ‘CIR++’ model they set the intensity to λt = yt
rate products.
+ ψ(t,β), where y has the dynamics seen before and ψ is a
deterministic function. If ψ is determined consistently with the
In Brigo and Alfonsi (2005) a model is proposed that aims to
default probabilities extracted from the CDS market (say via a
give a more complete answer to these requirements than in
deterministic-intensity model), the model is exactly calibrated
preceding models. To ensure positive intensity, the family of
to CDS. And we are left with parameters β for calibrating dif-
stochastic processes considered are the square-root diffu-
ferent products, although this feature will probably show its
sions, introduced by Feller (1951) for application in the field of
usefulness when options in the credit market become more
genetics. In finance this process is usually called the CIR
liquid. More importantly, the model extended this way inherits
process, after the application to short interest rate modeling
the tractability of CIR.
of Cox, Ingersoll and Ross (1985). The process y (for instance
157
When building the general model, Brigo and Alfonsi (2005)
ferent variations of the payoff in the market are analyzed in
assume extended CIR dynamics in parallel to the default inten-
detail, and in particular one CDS payoff structure is singled
sity and the short interest rate, with the instantaneous corre-
out, realistic enough for application to the market but simple
lation between the two Brownian drivers set to ρ. This model
enough to allow for the construction of a market model. This
has the potential to be fully consistent with interest rates and
CDS structure is shown to lead to a CDS option equivalent to
CDS default probabilities, and parameters are left to include
a simplified callable defaultable floating rate note. Since this is
information on both credit and interest rate option markets. In
another relevant payoff in credit options, this latter CDS struc-
addition, when ρ is set to zero, the calibration of the full model
ture is taken as the central one for building the market model
is automatic due to the tractability of the extended CIR cou-
(although the derivation is outlined also for alternative speci-
pled with the interesting feature of separability. The latter
fications).
means that the credit derivatives desk of a bank can ask for
interest rate parameters from the interest rates desk and add
Setting the price of the CDS to zero and deriving the spread
them in a model to be calibrated to CDS, keeping full consis-
R one finds the correct underlying of the option. Denote by
tency in valuation procedures.
Ta+1, …,Tb the payment dates of the CDS, with time intervals αi.
Denote by Q the risk neutral probability and by D(t,Ti) the sto-
When ρ ≠ 0 this is no longer true, but Brigo and Alfonsi (2005)
chastic discount factor. The correct definition of CDS rate
show empirically that the implications of ρ on CDS prices is
turns out:
bounded by a small fraction of the market bid-ask spread, and
is thus negligible. So one can keep the efficient zero-correla-
Ra,b (t) = [Σbi=a+1 E[D(t,Ti)1{Ti-1<τ≤Ti} | Ft]]/ [Σbi=a+1 αiQ(τ > t | Ft)
tion calibration and then set ρ to the desired value in pricing.
P (t,Ti)],
Approximated formulas are introduced for different payoffs,
including CDS options, namely options to enter a CDS at a
with P (t,Ti) = [E[D(t,Ti)1{τ >Ti} |Ft]]/[ Q(τ > t | Ft)]
future time. And with deterministic interest rates and stochastic intensity an exact analytical pricing formula is derived.
Here τ is default time, while E[·| Ft)] represents expectation
These formulas have a particular use for detecting the capa-
conditional on all information (up to t) except the default time.
bility of this model to interpret and replicate the smile phe-
1A represents the indicator function for set A. The protection
nomenon. But for this we first have to see how the smile can
payment is set to 1. The corresponding CDS option, to enter
be detected on the CDS option market.
a CDS with fixed rate K at time Ta, has discounted payoff
1{τ >Ta} D(t,Ta) [Σbi=a+1 αiP(Ta,Ti)](Ra,b (ta) – K)+ and taking risk
A market model for real world credit payoffs with
non-vanishing numeraire
neutral expectation one finds the price. The technical tools
We already described how a market model approach might be
Rutkowski (2001).
are omitted here and can be found for example in Bielecki and
useful for the development of the credit options market, and
which issues should receive particular attention. Accordingly,
The technical tool to develop market models is the change of
rather than starting from an abstract definition, Brigo (2004)
numeraire theory. To put it in a nutshell, this allows us to com-
focuses on a specific payoff, the options on CDS, since they
pute a price, expressed by a risk neutral expectation, as the
are written on the most liquid single-name credit derivative,
expectation of a related quantity under a different probability
and their market is likely to expand in the future. In order to
measure (equivalent to the risk neutral one).
detect the most convenient state variable to be modeled,
Brigo (2004) starts from the real world CDS payoff. The dif-
158 - The
The purpose of market models is to detect a suitable probabil-
ity measure under which both the underlying is a martingale
results, and the application of a model approximation to the
and the price expression reduces to a Black formula. In our
derivation of a pricing formula for Constant Maturity CDS, a
case, this implies that all but (Ra,b (ta) –
K)+
should get out of
payoff receiving increasing attention in the market, are given
the expectation.
in Brigo (2004).
In Brigo (2004) a probability measure is considered, individua martingale. In addition, if Ra,b(t) is assumed to follow a log-
Understanding the smile and the parameters
from a comparison of intensity and market
models
normal process under this measure, through the change of
Another advantage of having obtained a rigorous market
numeraire the price of the option reduces, before default, to
model is that we can detect the implications of the use of a dif-
the simple formula
ferent model (for instance the CIR++ intensity model) on
ated by its so-called associated numeraire, such that Ra,b(t) is
options implied volatility. This means first of all understanding
Σbi=a+1 αiP(t,Ti)(Ra,b(t)Φ(d1) – KΦ(d2)), where Φ(·) is the cumu-
the effects of the model parameters (i.e. β in CIR++) on implied
late Normal probability and d1 and d2 are as in the Black for-
volatility. Secondly, it means understanding the pattern of the
mula, with reference to the underlying Ra,b(t) at valuation
smile effect intrinsic in the model dynamics. As is well known,
time t.
the smile effect can be interpreted as a deviation from the lognormality assumption for underlying market observables
It is interesting to notice that, in this derivation of Brigo
which, when market quotations are made through a lognormal
(2004), the chosen numeraire cannot drop to zero, in the
model, is revealed by a non-flat shape of the graph of implied
spirit of Jamshidian (2002), thus ensuring equivalence of the
volatilities plotted against strike prices. From the perspective
pricing measures.
of a trader, a clear understanding of these implications is
of fundamental importance,
Rk,b(0)
K
Price
Volatility
often influencing the choice
Option 1
61
60
32.5
62.16%
of a model at least as much
Option 2
43.4
43
24.5
63.71%
as the technical advantages
Figure 1
of the model itself. For the
CIR++ stochastic intensity
Parameter
K↑
μ↑
ν↑
y0↑
K↑ ρ = 0
K↑ ρ = –1
K↑ ρ = 1
ρ↑
Implied volatility
↓
↑
↑
↑
↑/flat
↑/↓/ flat
↑/flat
↓
As long as the market has not yet reached a critical level of liq-
and interest rate model, this
uidity, this model would be hard to calibrate to reliable implied
kind of analysis is done in
volatilities for pricing different products. However, it plays a
Brigo and Cousot (2003).
very important role. It makes it possible to consistently trans-
Among other issues, they
late the prices of different options into implied volatilities,
obtain the following format, as presented in Figure 2, where K
helping to understand different implications of market options
is the option strike. Smile patterns implied by explicit intensity
quotations. Let us look at the quotations in Figure 1. It is hard
models such as CIR++ might be considered unsatisfactory
to compare them based on the Price column, provided by the
when this phenomenon is clearly established on the CDS
market. If we move to the Volatility column, provided by the
option market. In this case one can obtain more flexible pat-
model just presented, the information provides a much more
terns modeling directly the market observable R under the rel-
effective understanding and comparison. The specification of
evant measure, similarly to what we have described above, but
a general model, including the dynamics of R under a range of
replacing lognormality with a tractable dynamics allowing for
probability measures, is currently under investigation. Initial
smile (displaced diffusion, CEV, mixture dynamics, SABR).
Figure 2
159
Conclusion
References
In this work we have outlined some general features of
• Bielecki T., and M. Rutkowski, 2001, “Credit risk: Modeling, valuation and hedging,”
Springer Verlag
• Black F., and M. Scholes, 1973, “The pricing of options and corporate liabilities,”
Journal of Political Economy, 81, 637-654
• Black, F., and J. C. Cox, 1976, “Valuing corporate securities: Some effects of bond
indenture provisions,” Journal of Finance, 31, 351-367
• Brigo, D., 2004, “Constant maturity credit default swap pricing with market models,”
available at ssrn.com
• Brigo, D., 2005a, “Market models for CDS options and callable floaters,” Risk
Magazine, January 2005. Extended version available at damianobrigo.it
• Brigo, D., and A. Alfonsi, 2005, “Credit default swaps calibration and derivatives
pricing with the SSRD stochastic intensity model,” Available at damianobrigo.it.
Finance and Stochastics, Vol. X (1).
• Brigo, D., and L. Cousot, L., 2003, “A comparison between the SSRD Model and a
market model for CDS options pricing,” Bachelier 2004 Conference
• Brigo, D., and M. Tarenghi, 2004, “Credit default swap calibration and equity swap
valuation under counterparty risk with a tractable structural model,” Paper presented at the 2004 FEA conference at MIT
• Duffie D., K. Singleton, 1999, “Modeling term structures of defaultable bonds,”
Review of Financial Studies, 12, 687-720
• Hull, J., and A. White, 2003, “The valuation of credit default swap options,” Rothman
school of management working paper
• Lo C. F., H. C. Lee, and C. H. Hui, 2003, “A simple approach for pricing barrier
options with time-dependent parameters,” Quantitative Finance, 3
• Merton, R., 1974, “On the pricing of corporate debt: The risk structure of interest
rates,” Journal of Finance, 29, 449-470
quantitative modeling for relative value pricing in the field of
credit derivatives. In doing so, we had to address different
approaches to modeling, pointing out pros and cons of different frameworks. Then, although avoiding most technical
details, we presented three different models in different
frameworks, all designed to overcome possible limitations
and inadequacies typical of earlier solutions.
A final remark on some of the results summarized here is in
order. It may seem that some of the solutions presented here
are actually ahead of the market, in that they would require a
further development in liquidity of certain markets for being
fully exploited. However, it has sometimes happened that
financial markets have developed only when sufficiently
sound technical tools for dealing with such developments had
been provided by research. This research typically required a
lot of analysis and attempts before reaching a level which,
associated to different external factors, allowed the market to
take some steps forward in terms of efficiency and stability.
160 - The
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Pricing

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