decision at risk

DECISION AT RISK
DECISION-MAKING FROM
THE PERSPECTIVE OF
BEHAVIOURAL FINANCE
BEFORE YOU CONTINUE...
The theory around Behavioural Finance is new and very much in development. The literature on the subject is
therefore still limited and the terminology lacks consistency. We have made a selection from the large number
of (thought) experiments, studies and practical experiences which are available, and added some real-life cases.
Before you turn the page, or just start to leaf through this booklet, I would like to give you a brief explanation of
Not original research, then, but an attempt to give an impression, in an accessible manner, of the current status of
its contents and origin.
this field and the aberrations which people are capable of in a decision-making context. We have summarised the
provenance of the examples, research results and (thought) experiments in a bibliography at the back.
In December 2000, soon after our establishment, Cardano published the booklet ‘On pirates, pointed caps and
paradoxes’. This took a light-hearted look at the influence of complexity in statistics and arithmetic on the decisions,
I hope that the brief introduction provided in this booklet will shed new light on your view of decision-making
which people ultimately make. The enthusiastic responses we got from readers called for a sequel. Hence this
processes. Be warned: seasoned experts have proved just as prone to being deceived as laymen in the field of
compilation on the theme of Behavioural Finance.
decision-making!
It turns out that rationally operating Homo Sapiens goes about things considerably less rationally as Homo
In this publication, we have once again attempted to cast complex, relatively new material in a readable form.
Economicus. During the cognitive thought processes, which precede economic decisions, Homo Economicus, it
I wish you as much pleasure in browsing through and reading this booklet as we had in compiling it!
seems, unconsciously allows himself to be seduced by fallacies. In our previous publication, we already sketched
some examples from Daniel Kahneman and Amos Tversky. They are today generally acknowledged as the
founding fathers of Behavioural Finance. Amos Tversky died in 1996; otherwise he would certainly have shared the
Theo Kocken
Nobel Prize for Economics, which Daniel Kahneman received in 2002. This high international acclaim underlines
the importance of their new discipline. And rightly so. While the economic currents of the past hundred years
invariably assumed reason to be triumphant, research of Kahneman et al. shows that when it comes to economic
CEO
decision-making processes, acting rationally is anything but self-evident.
Cardano
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3
CARDANO
Ever since the early 16th century, probability theory has played a major role in risk modelling. In that era, Girolamo
Cardano (1501 – 1576), one of the founding fathers of statistics, applied the first systematic calculations to the
practice of understanding dice games, thereby building a bridge between academic theory and practice.
Cardano, the company that shares his name, applies quantitative analysis to investment & risk management. In
doing so, we utilise a wide range of modern instruments and techniques, building on the solid basis of our own
research and experience of the financial markets. We act as the bridge between the theory and the practice of
investment & risk management. In particular, we help clients identify and quantify the most significant financial
risks and drivers of investment return and then decide which risks will be best rewarded.
Cardano has emerged as market leader in the investment & risk management field. The teamwork between
professionals from different backgrounds (including risk managers, investment consultants, investment bankers
and academics) produces robust, innovative and practical solutions.
We offer our clients specialist, integrated investment & risk management solutions - ranging from advice to full
implementation and management - in the following areas:
• Solvency Management - Overseeing the management of the assets relative to the liabilities, given a defined objective and risk tolerance
• Risk Management - Identifying and controlling exposure to various risks, including designing and executing derivatives structures
• Investment Management - Manager research and selection as well as portfolio structuring
By offering full implementation and management, moving beyond just advice, we are able to provide our clients
with a single point of contact and to reduce not only the costs but also the operational risks. Equally important,
this integrated approach ensures that our research and advice is based on actual market experience gained, e.g.
the flow we have in derivatives execution for our clients.
Our independence means that we are able to offer the best choice of third party providers, whether derivatives
counterparties or best-of-breed investment managers. This independence means that we work closely with and
exclusively for our clients at all times, creating a strong alignment of interests.
In summary, although the instruments may have changed in the past 500 years, the name Cardano still stands for
building a bridge between theory and practice.
www.cardano.com
5
EMOTIONAL CORNERS
MENTAL ACCOUNTING: ORDERLY FAVOURED
OVER COST-EFFECTIVENESS
It seems we all have a complete banking system in our
heads. With accounts that generate their own credit
and debit valuations, and which may be opened or
closed at given moments. Hence, € 5 may be spent
unnoticed in one situation, whilst the same sum,
debited from a different account, may be experienced
as a heavy burden. This phenomenon is known as
mental accounting. Let’s take a look over the shoulders
of leading researchers in this area.
You better cut the pizza in four pieces
because I’m not hungry enough to eat six
Yogi Berra
Cinema or home?
The following experiment was carried out in 1984. A number
The second case concerns a calculator worth € 125 and a coat costing € 15. Again, the calculator must be paid for
of people were asked what they would do if they discovered that they had lost their cinema ticket – which they
first. The sales assistant tells the customer that the same calculator is temporarily available at another branch (20
had bought in advance for € 10 – when they arrived at the cinema. Would they buy a new one, or would they back
minutes away by car) for € 120. Now it turns out that only 29% would be prepared to take the detour, while 71%
off and return to spend a quiet evening at home? A small minority of 46% said they would buy a new ticket. The
would purchase both the coat and the calculator in the present store. Evidently, the percentage of the reduction is
same group was then presented with another scenario. Imagine, the researchers now said, you are on your way to
more important than the absolute amount.
the cinema to buy a ticket for € 10 at the box office. Before you arrive at the counter, you discover that on the way
there you have lost a € 10 note. But luckily you have enough left to buy a ticket. Do you buy it or do you go home?
In this case, 88% of the people answered that they would still buy a ticket.
A car from the children?
The irrational urge to divide up the money available into
several different ‘pots’ may be carried to some lengths. Many households have taken out loans for the purchase
The (rationally inexplicable) difference in reactions is explained by the two mental accounts which have been
of a car, a washing machine or a fridge. At the same time, they will often also have savings accounts for specific
opened in connection with this situation: a cinema ticket account and a cash account. In the first scenario, the
purposes: to finance the children’s studies when they grow up, to top up a pension or pay for a sabbatical in 10
account for cinema tickets has already been debited by € 10. This sum would be doubled if a second ticket would
years’ time. The difference between the interest they pay and the interest they receive is substantial. Even so, the
be purchased. Evidently, most people don’t consider a movie to be worth that much. In the second scenario,
idea of financing a car with the money set aside for the education of young children is generally taboo. Strange,
the ticket account has not yet been debited, but the budget for the showing has already been reserved on that
because if the same fixed repayment schedule - including the payment of interest - that a bank would expect for
account. The cash account will be debited more heavily as result of the loss. However, since this account generally
the car were followed over the course of 4 years, the savings account would still serve its original purpose and a
has a much larger balance than a single € 10 note, this will be viewed as a minor problem.
significant amount of money would be saved. People apparently like to arrange things so that they are ‘properly
separated’ and will accept a disadvantageous interest rate spread to do so.
As with the phenomenon of sunk costs in Cutting your losses, one ought to consider only the marginal returns
from the investment still to be made. Imagine that the moviegoer sets a value of € 12 on watching the film. When
he reads in the newspaper that a tickets costs € 10, he therefore decides to go to the film. After the incidents (the
Pulling the wool over their eyes loss of a ticket or a € 10 note), buying a ticket is always advisable in this case: after all, the marginal investment will
their own eyes. And the credit card companies are happy to join in. After all, there is a lot of money to be made.
Credit card users seem quite prepared to pull the wool over
always yield € 2 profit!
People do not tend to think of money spent with credit cards as debt. As long as it is paid for each month after the
Another striking fact in this experiment is that if you change the order of the situations, the percentage of people
first bill arrives, there is nothing wrong with that. Credit card companies, however, offer the option of paying the
prepared to buy a second ticket rises. By first presenting the case involving the € 10 loss, people apparently realise
outstanding balance in instalments. It turns out that debt can easily be taken on in this way.
more easily that the loss of a ticket can actually be regarded as lost cash.
Most credit card holders do not intend to let the debt on the card build up. In a study by the University of Michigan
among a large group of American credit card holders, only 27% said they deliberately made use of the credit
facilities available to them; the rest said that they never chose to borrow money, and that they paid everything
Cash desk bargain
A few years earlier, research was carried out into the extent to
straight away. But the figures show that 75% of cardholders regularly pay interest on their cards. So the valuable
which people judge absolute price differences in relation to the cost of an item. The starting point was a person
‘plastic’ leads to debts that are not regarded as such. And at extremely high costs, as credit card companies charge
who goes into a department store to buy a coat and a calculator. In the first case, the calculator costs € 15 and
high interest rates which bear no relation to the rates that cardholders would pay on a normal loan.
the chosen coat costs € 125. The calculator must be paid for first. The cashier tells the customer that the same
calculator is on special offer for € 10 at another branch 20 minutes away by car. A clear majority of 68% would put
the calculator back on the shelf and drive round to the other branch after purchasing the coat.
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Ever noticed that people never say
‘it’s only a game’ when they’re winning
BEING A GOOD LOSER
LOSS AVERSION: UNCERTAINTY HAS A PRICE
Ivern Ball
Everyone has to make choices sometimes, with differing chances of a positive or
negative outcome. In this respect, many people like to take a risk-averse approach as a
matter of course. For them, the possibility of losing outweighs the positive prospect of
potential winnings. Although the degree of risk-aversion differs from person to person,
the phenomenon can be heavily influenced in just about everybody. Events that precede
the decision play a major role.
A bird in the hand is worth...
Risk-averse behaviour is well illustrated by the following study.
prototype. However, there was no commercially attractive and adequately robust production technology. Despite
A group had to choose between the following two options:
this, Ibuka announced Sony’s new product, and put it on display in the showroom. He made the Chromatron
A. 80% chance of winning € 4.000, 20% chance of nothing
technology Sony’s top priority. With 150 people on the production line, the initial failure rate was over 99.7%; only
B. Definitely winning € 3.000
2 or 3 usable picture tubes per 1.000 produced! All Sony Chromatron colour TVs - 13.000 were eventually made -
80% of the people opted for certainty in B. The data used in this study showed that for these people, certainty is
were sold at a large loss.
evidently worth a maximum of € 200. This value is also known as the certainty equivalence. Increase the amount
There was major disagreement about the continuation of this project among the heads of the company. Morita
which can be won under A and the percentage voting for A will increase. The sum at which a person will prefer
wanted to end it, but Ibuka refused. He pressed ahead and threw even more effort into trying to resolve the
the uncertainty of A to the certainty of B will depend on their personal degree of risk aversion. It seems we are
production problems. Only when the financial managers announced Sony’s insolvency in 1966 Ibuka agreed to
prepared to ‘pay’ for certainty, but not any price.
end this project.
Note that this phenomenon manifests itself in decision-making in the most diverse fields: from political to
investment decisions, from determining the further direction of a study to the choice of a particular production
technology. An important factor here is the fact that certainty is generally easier to justify, not least in hindsight.
Pluses and minuses
If both options entail uncertainty, the choice apparently changes. Because when asked to choose between options
the opportunity to immediately compensate a loss incurred. The following studies demonstrate this:
C and D below, 65% of the participants chose option C.
Someone who has just won € 30 is given a choice:
C. 20% chance of winning € 4.000
A. take a fifty-fifty chance of winning € 9 or losing € 9, or
D. 25% chance of winning € 3.000
B. do nothing, hence no further gains or losses.
Risk-averse behaviour may be tempered if someone is given
The degree of uncertainty is of secondary importance. The choice is now being made on the basis of the highest
In this situation, 70% of the participants opt for A. With the € 30 still in their thoughts, they calculate a worst-case
expected value (probability versus winning value).
scenario in which they still make a profit, in this case € 21.
What is striking is the sharp transition from certainty to uncertainty, as the above effect is noticeable even if the
The same experiment is done with people who have just lost € 30. In this case, only 40% choose A. Option A is
probability only changes from 100% to 99%!
now less attractive because there is a substantial probability of losing even more, while in the best case, one is still
left with a loss.
The following question is put to the group which has just lost € 30:
Daredevil The situation in which a person can take a chance to avoid
a possible loss can lead to a switch from risk-averse to risk-taking behaviour. Take a look at the results of the
C. take a 33% chance of winning € 30, with a 67% of winning nothing
D. definitely receive € 10
following study.
If a choice has to be made between:
Now 60% choose C. Although the expected outcomes of C and D are the same, the possibility of completely
E. 80% probability of losing € 4.000, 20% probability of breaking even
compensating for the earlier loss apparently makes this option more attractive.
F. Definitely losing € 3.000
So it turns out that many people become more risk-averse after a loss, unless they are given the opportunity
92% opts for E, despite the worse outcome which may be expected. The avoidance of loss is again the motive.
to completely make up the loss incurred. In that case, risk-averse behaviour may even turn into risk-taking
The small probability of breaking even with option E leads the overwhelming majority to go for this option.
behaviour!
The approach to risk-evaluation can change depending on how one got into a situation in the first place. Business
decision-makers need to be constantly aware of this. Because if, for example, a big loss is reported by one division
Sharp picture, clear thinking?
In the early sixties, Sony took a licence in Chromatron cathode
ray tube technology. Both founders of Sony, Masura Ibuka and Akio Morita, were impressed by the sharpness
and immediately afterwards an investment decision has to be taken about a totally different division, it is important
to realize that the effects as sketched above can colour the decision.
and brightness of this picture tube for televisions. In September 1964, Ibuka’s team managed to develop a single
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CUTTING YOUR LOSSES
SUNK COSTS AND FACING UP TO THE TRUTH
Large projects with rather long lead times are particularly prone to it. Even before their
completion, new information, different market conditions or setbacks along the way
suddenly affect the chances of profitability, or even wipe them out completely. Sometimes,
terminating the project at that time is the only financially justified solution. When coming
to a decision, only the marginal investment, set against the profit still achievable with
that investment, ought to be considered. But what do we observe? The higher the sunk
costs - investments which have already been made and are irreversible - compared to the
investment still required, the less willingness there is to face up to the truth.
In such cases, the final marginal investments may be made even if by then they are not
justified by the marginal profit still achievable - usually because the decision-makers
simply do not want to face up to a large loss, but prefer to put off the problem until the
distant future. So, while they can be quite sure that other solutions will achieve better
results, they are prepared to convince themselves - and others - that the original path
must not be abandoned. This is not fiction but a pitfall whose existence has been proved
by research.
When you find yourself in a hole,
the best thing you can do is stop digging
Warren Buffet
Beyond radar
Above the clouds
A researcher takes as an example a company in the aviation
Another example of how sunk costs can influence the
industry that has started developing an aircraft that will be invisible to radar. A rival firm is engaged in a similar
evaluation of the ‘point-of-no-return’ is the development of the supersonic airliner Concorde. Its eventual
project. After years of working simultaneously, the competitor succeeds: his design meets all the objectives.
development costs were seven times higher than originally budgeted, while the returns turned out to have
Moreover, his aircraft will in all cases be faster and cheaper - both in terms of purchase price and running costs
been seriously overestimated. Such serious errors must have become apparent long before the delivery of the
- than the design that ‘our’ aircraft builder is still working on. So the aircraft builder who is lagging behind will
first Concorde to fly commercially. Nevertheless, the project went ahead. Thanks to large new investments, the
presumably not sell a single plane, and will have to write off his investment.
supersonic aircraft was taken into production. Eventually, only nine aircraft were sold. They were kept in the air
for years, against better judgement. After continued heavy losses, the operational life of this aircraft ended only
recently: Concorde made its final flight in October 2003.
The researcher presents this situation to a group of students and asks them whether, if they were involved in a
project like this, they would continue to pursue it. A large majority of 83% said they would abandon the project
immediately.
Below zero Another well-known example of sunk costs comes from the
The researcher presents the same problem to another group of students. But he also tells them that ‘our’ - lagging
field of lending, and is illustrated by the practical experiences of an adviser. One of his clients is a large, reputable
- aircraft builder has already spent € 90 million of his € 100 million original budget, and will be able to achieve a
banking institution. The adviser is asked to shed light on the way in which loans that are difficult to recover are
prototype on budget. In other words, he only has € 10 million ‘to go’.
dealt with. In order to prevent the situation from worsening, the adviser first analyses the causes of the ‘bad’ loans.
A clear picture emerges. Many of the loans which proved difficult to collect were made to clients who have been
Despite the certainty of loss - after all, the rival company will be the first to market his aircraft, which is better in all-
allocated to a particular account manager for some time. After authorizing an initial loan, the account manager
essential respects - now only 15% of the students say they would end the project. The fact that ‘only’ € 10 million
later granted supplementary loans to those clients. He apparently felt - consciously or unconsciously - obligated to
is needed to complete a project in which € 90 million has already been invested has clouded their judgement.
do so. Due to a good relationship with those clients, perhaps. However, in view of the uncollectable nature of the
They would rather increase a certain loss by € 10 million than accepting the (considerable but smaller) investment
loans it is more likely he was trying to make up for earlier mistakes by granting the subsequent loans. Without the
loss straight away.
subsequent loans, those clients might have ‘collapsed’ and the earlier loans would have to be written off for good.
So matters went from bad to worse.
The adviser suggests the bank to immediately reassign all debtor clients to a different account manager at the
Under water
There are countless practical examples of the consequences
first sign of a problem. The strategy works. The bank still grants additional loans to its clients, but only on objective
of sunk costs. Take the Channel Tunnel, a major project which aimed to re-establish a fixed link between Great
grounds.
Britain and continental Europe for the first time since the last ice age. The ‘chunnel’ was put into use twelve months
late. By then, the costs incurred were double those budgeted for in 1987. Moreover, it emerged early on that the
The dilemma of sunk costs is an issue in many - usually capital-intensive and long-term - projects of diverse kinds.
yield estimates were over-optimistic - even while it was still under construction, it was known that the ‘chunnel’
It applies to investments in ICT, production plants and infrastructure works. The economists involved must keep
would remain unprofitable far into the future. However, the capital invested and prestige prevented the initiators
asking themselves what the marginal contribution will be of the expenditure to be incurred from today onwards.
from admitting to the fiasco. The ‘chunnel’ was therefore completed. Interest repayments were halted, a debt-
If that marginal contribution does not cover the additional investment, the project must be terminated. Sunk costs
restructuring plan launched. Now the ‘chunnel’ is operating marginally, barely capable of generating enough to
should not play a role in the decision.
pay off the remaining interest.
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STAYING PUT...
STATUS QUO EFFECT: ONCE HELD, NOT SOLD
Whether you are young or old, progressive or conservative, everybody has a certain natural
aversion to change. It is a proven psychological phenomenon which has been the cause of
many a decision-making debacle.
People are very open-minded about new things
as long as they’re exactly like the old ones
Charles Kettering
Swap?
The natural urge to prefer an existing situation - of whatever
Cash or a higher share price?
If a business can profitably invest its money in expansion,
kind - over a new one has been studied by psychologists in an experiment which shows how easily the process
improvements or new technology, choosing not to pay out a dividend could be an attractive option for the
of attachment to possessions or to an existing situation comes about. One of the studies concerns two groups of
shareholders as well as the company itself. They could then look forward to a probable rise in the share price and
students and a third control group.
those in need of cash would be able to sell securities at a more attractive price than if a dividend were paid out.
The first two groups have to answer a short list of questions. While completing the list, each participant from the
But dividends have traditionally been favoured by a large group of shareholders in some countries, even at the
first group is handed a mug. The students in the other group each receive a bar of Swiss chocolate.
time when they were still taxable. The reason lies in the fact that the shareholder does not have to take any action
After completing the list, the students with mugs are asked whether they would like to swap them for bars of
to receive a dividend, and regards it as a bonus that can be spent. Consciously placing a sales order, by contrast, is
Swiss chocolate. At the same time, the participants from the other group are given the opportunity to swap their
viewed as a change to the existing situation and therefore inadvertently arouses resistance.
bars of chocolate for mugs. For control purposes, a third group of people are allowed to choose directly: a mug or
a chocolate bar.
Of the control group, 56% choose mugs while 44% opt for the chocolate. This demonstrates that there is no
Making the best of it
extreme preference for one or the other.
new developments is difficult. Even if the new technology turns out to be economically justified and has proved
The results show that of the group of students with mugs, 89% want to keep them; only 11% prefer chocolate bars.
its reliability. History provides numerous examples. For instance, following the invention of the steam engine,
In the other group, the lion’s share (90%) of the participants similarly prefer the existing situation and only 10%
the first steam-powered ships were built as early as the end of the 18th century. They were still rather expensive
trade their chocolate bars for mugs.
in terms of fuel, but less dependent on weather conditions and hence more reliable. Although steam power was
Saying goodbye to existing technology in favour of entirely
increasingly used on inland waterways, the large sailing ships continued to transport freight and passengers to
A similar study, this time with regard to investment decisions, was carried out by renowned researchers from
and from France and Great Britain for a very long time. Even when it became obvious that only steamships had
Harvard University in collaboration with Boston University.
a future, some sailing companies continued to invest in improving sailing ships. Not until a hundred years after
the first steamships, did the last of them change tack – and by then many had gone bankrupt as a result of their
First of all, a group of economics students were asked for their expectations what people, who had previously
technological deficit – and did the steamship win the day on the principal lines with distant destinations too.
invested little due to a lack of serious money, but who were interested in and well-read on financial matters, would
invest in, if a large gift from a distant uncle should come their way. They were given four choices: government
bonds, municipal bonds, moderately risky shares and highly risky shares. The results (18%, 32%, 32% and 18%,
Too late, too slow respectively) were dependent on their attitude to risk and were nothing special in themselves.
Laboratories, which established a position of international technological leadership. In the early ’80s, Wang Labs
In the 1950s, the inventor Dr. An Wang founded his Wang
were among the first in the world to market a desktop word processor. Only some time later did IBM introduce its
However, another group of students was presented with a different case: again they were asked what a not-yet-
Personal Computer. In a short space of time, IBM managed to make its PC the world standard. Even as this signal
moneyed but very interested potential investor would do in terms of their investment mix should he or she inherit
became increasingly hard to ignore, Wang stuck with its own computer architecture. Although Wang later gave
a large sum of money from a distant uncle, but this time the money was already invested in a particular asset
in by accepting IBM’s standard, the term IBM-compatible - which other manufacturers had by then long been
category. They were told to disregard tax and transaction costs. The results were now significantly different. For
successfully using - was still taboo at Wang. Conceding the existing situation so late, so slowly and ultimately only
example, if no investment was known in advance (the previous experiment), 32% opted for municipal bonds,
in part, despite the clear signals from the market, led to catastrophe. The company which in its glory days recorded
but if it was known that municipal bonds was the allocation they had in their portfolios, 47% chose to keep this
a turnover of $ 3 billion (1986) with 30.000 employees went into ‘Chapter Eleven’ in 1992 and was later broken up
allocation. There was now an obviously larger preference to keep whatever category happened to be in one’s
and sold off.
possession, even though there were no rational grounds for doing so.
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FIRMLY ANCHORED
ANCHORING: UNCONSCIOUS BEACONS WHEN ESTIMATING FIGURES
Looking to buy a house? Or thinking of making
an offer on something quite different? Then total
concentration is called for because external factors
influence your judgement of prices, numbers and
other values. Unnoticed, but demonstrably so.
When estimating figures, it turns out that our
reason irrationally starts looking for an ‘anchor’.
And this anchor can take any form, strangely
enough, even a reference that has nothing to do
with the actual valuation. For instance, real estate
agents can be influenced in determining a realistic
asking price for a house. And it works. Because who
would still be prepared to pay money for a UMTS
frequency today? Nevertheless, serious parties put
down billions for them not so long ago, elbowing
each other out of the way in the process!
The painter will produce pictures
of little merit if he takes the works
of others as his standard
Leonardo da Vinci
Research shows that the phenomenon goes much further than many suspect. For example, a random number
Clutching at anchors
was chosen for a group of people using a wheel of fortune. The group was then asked to estimate how many
earnings ratios for dotcom companies which were far higher than the historical average. P/e ratios of dotcom
African countries belonged to the United Nations. The estimate they gave proved highly dependent on the result
companies averaged around 600. Expectations were high for these companies because such p/e ratios imply
produced by the wheel, regardless of its irrelevance to the subject. When the wheel stopped at 10, the estimate
double-digit long-term growth rates. Other sectors such as telecom, media and high-tech start-ups also had very
was 25. When the wheel pointed to 65, the average estimate of African UN countries rose to 45.
high p/e ratios.
At the end of the last century, the market got used to price/
In this period, the introductory prices of promising technology companies were determined more by the size of
In general, the results of estimates are determined not so much by completely irrelevant external figures as by the
previous price/earnings ratios than by fundamental analysis.
starting value of relevant factors. Our previous booklet On Pirates, Pointed Caps and Paradoxes contains a number
of nice examples!
An example of this was the initial public offering of Palm Pilot, the manufacturer of the then-popular Palm
organiser. On March 2nd 2000, its owner, 3COM, floated 6% of Palm Pilot. On the basis of the valuations of other
Who’ll start the bidding?
companies, the CFO of Palm Pilot valued the company at $ 15 billion (p/e ratio of 185, on the basis of operating
Anchoring also works when it comes to the respondents’
income). The investment banks that supervised the launch settled on a valuation of $ 15.6 billion. In the night
own fields of expertise. Take real estate agents: they may be expected to be well-informed about the market
before the eventual introductory price was determined, the CFO came up with a market value of $ 22 billion (p/e
prices of the real estate they are trying to sell. Nevertheless, evidently even these experts are sensitive to the
ratio of 270). The shares were introduced at $ 38 each. The share price of Palm Pilot shot up to $ 165 on March 2nd,
phenomenon. In order to demonstrate this fact, two groups of real estate agents were formed. They all view the
to end the day at $ 95 (p/e ratio of 675).
same house, and have the same information at their disposal, such as sale prices achieved for other properties in
The fact that anchoring also played a role in the minds of buyers is shown by the following. At the end of the day
the neighbourhood. The researcher gives the first group an asking price of € 119.900. He tells the second group
of the stock market launch, the 94% of Palm Pilot owned by 3COM was worth a little under $ 52 billion on the
that the price is € 149.900. The researcher then asks the real estate agents to give him a realistic estimate of the
basis of the share price. However, the market capitalisation of 3Com itself was $ 28 billion at the end of that day. In
expected sale price. The first group comes up with an average price of € 111.454. The other group thinks it can sell
other words: the value of 3Com excluding the shares it held in Palm Pilot would at that moment in time have had
the house for an average of € 123.818. So even experts - unconsciously - latch onto an anchor when it is offered
a negative value of $ 24 billion!
to them!
Ultimately, fundamental considerations prevail. Palm Pilot’s share price sank to $ 20 within 2.5 months. The growth
expectations were not realised. Palm Pilot (now PalmOne) has not made an annual profit since 2000.
Chasing shadows
If everyone thinks they know it all, the auctioneer has an easy
job. Take the UMTS frequencies. Everyone jumped onto the bandwagon, for substantial sums. British telecom
companies started it all off, acquiring frequencies for € 648 per British subject. (Not per projected paying
secondary school pupil, please note!) Soon afterwards, the German frequencies went for € 613 per inhabitant.
This presumably reflects a significant anchor effect because at the time of the auction, no objective value of a
UMTS frequency was calculable. The realisation that these sums were nonsensical came only much later. The
auction results shortly afterwards in Italy and the Netherlands: € 240 and € 171 per inhabitant, respectively.
But these prices too, may be misleading. Because to this day, nobody has yet earned a penny from UMTS. On the
contrary, investments are now being written off even before any turnover has been achieved!
23
24
THE SHADOWS OF OVERESTIMATION
AWARENESS BEST ANTIDOTE TO DRAMATICALLY FLAWED ESTIMATES
Overestimation sooner or later causes problems. This is certainly true if component projects
together determine the probability of success of the overall project. But it is a fact: almost
everybody tends to overestimate under certain conditions.
The phenomenon whereby individuals tend to overestimate themselves has been
demonstrated by means of a test that is as simple as it is convincing. A group of students
was asked how they rated their performance compared to the average performance of
students. No fewer than 82% rated their own performance as above average. It is hardly
possible to formulate clearer proof than this!
Overestimating oneself also plays a role in investment decisions. Researchers have
demonstrated this fact by comparing the actual costs of pioneer process plants with the
costs initially estimated. On average, the actual costs turned out to be 20% higher than those
on which the investment plans were based. It has also been calculated that across a broad
range of industrial sectors, 80% of projects do not achieve the intended market share.
Doubt is uncomfortable,
certainty is ridiculous
François Voltaire
Mergers and acquisitions are often seriously affected by this phenomenon. Many studies have shown that
- it is almost the same as the chances of somebody winning the jackpot in the national lottery three times - that
following acquisitions, the buyer is barely able to raise the yield of the total. The company launching the takeover
the probability of success originally calculated must have been an overestimation. According to the Columbia
bid not only overestimates the influence it can wield on the activities it has purchased, it also underestimates the
Accident Investigation Board (CAIB), one cause of the accident was an accumulation of errors of mental decision-
strengths of the other company compared to those of the managers within its own ranks. It therefore believes that
making which - when added together - resulted in broadly endorsed approval for the launch of the fatal Columbia
by introducing its own managers, it will achieve great improvements. Its own ‘weaknesses’ are suppressed. What
mission.
also emerges very clearly is that in many cases, the synergy which can be achieved by ‘mergers’ is estimated to be
far greater than is ever actually achieved in practice. As a result, the takeover sum will be too high, a fact which is
The fact that people are often too optimistic about a project in which they are themselves involved is the result
often quickly recognized by shareholders, since it has been statistically proved that the shareholder value of the
of the ‘inside view’. They have a lot of knowledge about the project, they think they have a good grip on it and
buyer more often goes down than up after a takeover.
underestimate what they don’t know. There is a remedy: the ‘outside view’. Here, the project is compared to similar
projects in the past (including competitors’ projects), creating an awareness of why projects do or do not succeed.
Self-overestimation in business is sometimes explained with the help of the concept of ‘organizational optimism’.
Practice shows that this helps to considerably sharpen the powers of judgment.
This means that employees tend to give only those estimates which are agreeable to the management - as a form
of loyalty. An additional factor is competition. Imagine cuts are being made within a company. Of the projects
currently underway, it is known that a number will have to go. The management board decides to base its decision
Catch a movie? on which projects are to continue on the presentations made by project managers about the financial future of
wrong at Walt Disney studios, too. Take the - understandable - custom of premiering films at weekends. It would
their projects. The most profitable will be selected. Ironically, the managers who underestimate the costs or risks
regularly be the case that several films - including films made by rival studios - would hit the silver screen in the
of their projects or overestimate the returns have the greatest chance of winning their case. But it is those projects
same weekend. The consumer had to choose, and attendances stagnated for all new movies. A little care and
which offer the least certainty that the objectives set out will actually be achieved!
attention could have prevented this. To quote Walt Disney’s chairman Joe Roth: “Hubris. Hubris. If you only think
In the course of its history, things have occasionally gone
about your own business, you think, “I’ve got a great movie, we’re going to go out and do this.” And you don’t think
Looking back at history, a great many failures have been caused by overestimating one’s own chances of success
that everybody else is thinking the same way.”
- and underestimating a rival. Both individually and in business.
Not even an elephant …
The right well General John Sedgewick - a Union commander during the
American Civil War – was once standing in a trench. He was inspecting the troops during the battle of Spotsylvania
The oil company Shell invests a lot of money in the exploration
of oil wells. After all, starting drilling requires a considerable investment. An investment which will be lost if it turns
out that the ‘well’ is not going to produce any oil.
Court House in 1864. In order to reassure the men, he said: “They couldn’t hit an elephant at this dist...”
The geologists at Shell regularly make estimates of the probability of their predictions failing. It was found that
newly appointed geologists - despite their excellent credentials - consistently and significantly overestimated their
Technical tragedy
When numerous factors together determine the success or
chances of success. Given a 30% probability of success as estimated by themselves, it turned out that only one or
failure of a project, optimistic estimates by individuals can lead to the chances of the overall project succeeding
two out of ten wells they rated as promising were actually viable. Therefore, a training programme was developed.
being drastically overestimated. These are ‘and/and’ situations: if one factor fails, the entire project fails. Each factor
The new geologists were presented with a large number of cases of previously drilled wells along with the factors
taken on its own has a low probability, which often means that little importance is attached to the accumulation of
which determine the probability of oil being present. After they had delivered their estimates, they were given the
small probabilities; but because the project will only succeed if all of a large number of small probabilities do not
actual results of the projects in question. As a result, their powers of judgment improved significantly. Now when
occur, the risk of failure is nonetheless greater than it is generally judged to be, and hence a form of unintended
they estimate a 30% chance of oil being found, in 3 out of 10 cases, oil is actually struck!
overestimation results. The NASA Space Shuttle project is one example. Just before the Challenger shuttle came to
grief, the probability of failure was stated as 1 per 100.000 launches. Seventeen years and less than 150 launches
later, the mission of the Columbia shuttle came to a dramatic end. The probability of two such incidents is so low
27
28
STUMBLING IN STAGES
ISOLATION EFFECT: A DISTORTED VIEW OF ONE’S CHANCES
Many of the decisions people take are based on choices between alternatives. In such
cases, a miraculous effect can be observed. A person’s choice can be influenced without
them noticing by ‘cutting up’ the same problem into several partial alternatives in
different ways. This so-called ‘isolation effect’ plays a role in a large number of everyday
decisions!
It is surely rational to treat
identical problems identically,
but often people do not
Daniel Kahneman & Amos Tversky
Misleading representation
Two rival TV stations are recording a one-off quiz, independently
The isolation tendency is an attempt at simplification (after all, the 75% / 25% probability is the same in both
of each other. The rules of the game are only presented to the participants at the start of recording. At Station
options), but the simplification leads to isolation, which in this case leads to the illusion of security (case A). A factor
Alpha, they first have to answer a number of questions. If they get to answer all the questions right, they go on
which should be accorded due weight, then, certainly if the decision-making process lends itself to being split up
to the final question. If they do not reach the final - the probability is 75% - they go home empty-handed. Before
into successive steps, and decisions are required in subsequent steps before certainty has been achieved in earlier
answering the first-round questions, the participants have to say in advance what they will choose, should they
ones. This is most clearly expressed in the situation described below which occurs only too often!
reach the final: to immediately pocket € 3.000 or to play ‘all or nothing’: an 80% chance of winning € 4.000 or get
nothing at all.
Innovation or tradition?
A CEO who is considering exploiting an oilfield has two hurdles
Station Beta formulates the rules differently. Only one round is played, but the participants can choose in advance
to overcome, along with a number of other matters. A licence is required and he will have to make a decision
between a series of questions with a 25% chance of winning € 3.000 or a series of questions with a 20% chance of
regarding the operating technology to be used. The licence will only be valid for a limited period. So if it is granted,
winning € 4.000. In both cases, if they answer any of the questions wrongly, their trip to the studio has been in vain.
the oilfield must be ready for production as soon as possible. Therefore, he cannot delay his decision regarding
the production technology to be used until he knows whether he will get the licence. He believes there is a 75%
probability that the licence will be awarded to a rival or that no licence will be issued at all. As for the technology,
What do the participants choose, weighing up their risk and expected gain?
he has two options. On the one hand he can follow a risk-free path, based on proven technology. He knows that he
The probabilities at Station Alpha may be summarised as follows:
will then make € 30.000.000 profit. But a most promising and innovative method has just been introduced which
First round: 75% chance of winning nothing therefore 25% chance of:
offers an 80% probability of 33% more profit. He does reflect that this also leaves a 20% of failure, which would
A. 100% certainty of winning € 3.000
mean no profit at all. He has advisers to help him, but he has to make the decision himself.
B. 80% chance of winning € 4.000, 20% chance of winning nothing
His advisers can divide the problem into two steps for him: 25% chance of getting the licence, after which there
is the certainty of a € 30.000.000 profit or 80% chance of a profit of 1.33*30.000.000 = € 40.000.000. In line with
In an experiment, it emerged that given this formulation, 78% of participants opt for A and 22% for B.
the results of the behavioural experiment described, it is likely that he will intuitively choose the first option, that
The chances of winning and losing the Station Beta quiz are as follows:
is the proven technology. But if his advisers - in the conviction that they are giving him the greatest possible
C. 25% chance of winning € 3.000
transparency - decide to condense the situation into a single step, i.e. a 25% probability of € 30.000.000 per
D. 20% chance of winning € 4.000
production unit or a 20% probability of € 40.000.000, the results of the previous experiment show that he may be
more inclined to choose the latter, the latest technology!
Given this description, 65% of participants go for option D.
Situations such as these crop up everywhere.Take proposed corporate acquisitions in which imperfect competition
All the possible outcomes are - ultimately - the same for all participants in both cases. Still people choose different
plays a role. Given the uncertainty about the competition authority’s verdict, should a higher takeover sum be
options when they are formulated differently. Why? There is clearly a lack of transparency among the players. The
offered to make the chances of a successful bid as good as certain (competition rulings notwithstanding), or
first - two-stage - formulation is described in such a way as to create the suggestion of certainty: 100% chance of
do these circumstances argue for a lower figure? In the latter case, the chances of the takeover succeeding are
winning € 3.000, with the players arbitrarily suppressing the thought that before they get to that point, they will
reduced, but if it does happen, a higher yield is assured! A high probability of being blocked by the competition
first have to win the first round. The second formulation gives a considerably clearer picture, presenting the choice
authority once again makes this a choice between two risky alternatives, not between an apparently safe one and
as being between two risky options, which allows a clearer risk-return assessment to be made.
a risky one. What is clear is that the way in which we render the probabilities transparent or instead isolate them
plays a big role in the psychology of the bidding game!
These results show that how people assess their chances of winning depends on how the chances are presented.
31
32
SMALLER PROBABILITY, HIGHER SCORE
REPRESENTATIVENESS PUSHES STATISTICAL KNOWLEDGE TO THE BACKGROUND
It is part of the elementary knowledge that we all share: the probability of an event
A is always greater than or equal to the probability of event A coinciding with event B.
But research shows that we sometimes suddenly lose sight of this self-evident truth. An
important reason for this is representativeness: in brief, assigning more probability to an
event because, in our minds, it better fits a sketched situation.
A great many people think they
are thinking when they are merely
rearranging their prejudices
William James
The best-known study into the influence of representativeness concerns a group of people who were asked to list
And? A son or a daughter?
the most likely characteristics of a certain Bill. Bill was described as 34 years old, highly intelligent but with little
the size of a sample survey. To demonstrate this - in two separate studies - research groups were told about two
imagination. He is a compulsive worker with a rather apathetic nature, good at maths but bad at the social sciences.
hospitals. One was a small regional hospital with 15 births per day, the other a large regional teaching hospital
The group was presented with eight characteristics or combinations of characteristics, including ‘accountant’, ‘jazz
with 45 children born per day. The long-term boy/girl ratio in both hospitals was 50%. The groups were asked to
player in his free time’ and ‘accountant who is a jazz player in his free time’. Each of the group members then had to
indicate in which of the two hospitals the probability was greater that, of the babies born on any one day, more
indicate how probable they thought it that a characteristic or combination of them could be attributed to Bill.
than 60% would be boys.
Representativeness also expresses itself in the act of ignoring
In both groups, roughly as many people choose the small hospital as the large one. A surprising result, because
The characteristic ‘accountant’ proved very popular. The combination of an accountant who plays jazz in his
the smaller the sample, the bigger the chance of deviations from the norm. So the probability that the deviant
free time scored lower, but still quite well. Playing jazz in his free time without any other characteristics being
situation of 60% boys should arise on a single day is greater in the small hospital.
mentioned was rated as very unlikely. But the actual probability of a jazz-playing Bill is, of course, always greater
than the probability that Bill plays jazz and is also an accountant. Unconsciously, the participants forgot to pay
In subsequent studies, the daily percentage was increased to 70 and even 80.Then the preference of the participants
heed to this elementary rule!
for the small hospital increased. Higher percentages, it seems, are increasingly regarded as non-representative, and
as a result, sample size again begins to play a role.
The reason is that ‘accountant’ was seen as being highly representative for Bill as he was described. As a result,
‘accountant who plays jazz’ was still regarded as reasonably probable by the participants. The extreme unlikeliness
of Bill playing jazz was overshadowed by the dominant representativeness of ‘accountant’, and apparently, therefore,
Performance appraisal
easily accepted along with it. When the term ‘accountant’ was not mentioned in a characteristic, that dominance
which both want him to grant a high-risk loan. He has to choose between them. One company is 13 years old,
ceased to play a part in the evaluation of that characteristic, causing jazz playing - hardly representative for Bill - to
the other has been in business for 42 years. Both companies have very good records: they outperform the sector
move into the foreground and being given a very low score.
average for 60% of the time, under performing the sector average for 40% of the time.
The study was extended to two other groups. One contained highly experienced statisticians, the other only
The study described above established that 60% is not yet seen as non-representative. Thus it may be that the
people with an average knowledge of this field. Both groups described the problem as ‘easy’, yet they fell into the
companies are assessed as being equivalent in performance terms. In so judging, the difference in age between
same pitfall as the first group. As soon as Bill was described in statistical terms, the statisticians clearly won ground.
them is overlooked. Wrongly so, because it is that very difference which allows the 42-year-old company to make
This shows that verbal context is capable of pushing statistical knowledge to the background!
a much bigger claim on out performance than its much younger rival! If the value for out performance had been
A banker is approached by two companies in the same sector
70% of the time or more, we may assume on the basis of the previous experiment - the ratio of boys to girls born As a result, the factors which influence particular developments may be given too much or rather too little
that the older company would receive the credit for its performance compared to the newer company.
weight.
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36
illu kans op een kans
CHANCE OF A CHANCE
CONDITIONAL PROBABILITIES ARE OFTEN MISLEADING
It is easy to be wrong-footed when faced with conditional probabilities. For instance,
apparently reliable witnesses can make unreliable witness statements. And despite
qualitatively good advice, a businessman needs to think twice about the value of advice.
A glimpse into the world of Bayesian statistics. Or, to put it another way: the probability of
a probability produces a new probability!
Evaluation of Man’s performance as an
intuitive statistician is far too generous
Paul Slovic & Sarah Lichtenstein
Taxi!
Rain splashing up and dim street lighting give the town centre
a colourless appearance. A man puts the key into the lock of his front door and sees a taxi driving off from the
front of the hotel opposite. Moments later he hears a crash. He looks up: there is a lot of superficial damage, but
no injuries. “They can sort it out between them”, he thinks, and goes inside.
The following morning he reads in the newspaper that the taxi left the scene of the accident and disappeared
without a trace. He comes forward as a witness, although all he remembers is the colour of the taxi: blue. The police
consider that to be useful information because the town has only 15 blue taxis and no fewer than 85 green ones.
Before summoning the drivers of the blue taxis for questioning, the chief of police decides to hold a test: how
reliable are his informer’s powers of observation?
In equivalent conditions, the man is able to correctly identify the colours of blue and green taxis shown to him at
random in no fewer than 80% of cases, which means he names the wrong colour in only 20% of cases.
The description of the taxi accident and the subsequent witness test was presented to a group of people during
a study. The group was asked what the probability was that the taxi involved in the accident really was blue. What
answer did most of the participants give? And what does your own intuition tell you?
For explanation: page 42
Go or No go?
A venture capitalist has a large number of investment projects
to choose from. He knows from experience that only two in every thousand projects result in large profits, the rest
will produce moderate losses. He forms an ‘excellence board’ to select a project for him. This exclusive group has
already proved itself: they will always qualify as ‘good’ projects which are ultimately profitable. Of course there
remains a possibility that a project which is ultimately loss-making will be rated as good by the board. In view of
the excellent qualities of the group, that probability is small: a ‘bad’ project will be recognised as ‘bad’ in 98% of
cases and will not make the investor’s shortlist.
The investor knows that a profitable project will definitely generate € 30 million, while a bad project will make a €
5 million loss. Is his ‘excellence board’ providing good advice? What does your intuition tell you?
For explanation: page 43
40
EXPLANATION
Taxi!
Go or no go
The answer most of the participants gave was 80%. Right? No, the probability that the colour was identified
The probability that a project will be assessed as profitable but will ultimately produce a loss is approximately 90%.
correctly in this case is only 41%. The witness statement is therefore highly unreliable. The reason for this is the
In spite of the great expertise of his ‘excellence board’, the profit expectation of the investor is therefore negative:
large difference between the number of green (85) and blue (15) taxis. The probability that the witness correctly
0.9*(- € 5 million) + 0.1*(€ 30 million) = a loss of € 1.5 million.
perceives the colour may be four times greater than that of him identifying it wrongly, but there are nearly six times
as many green taxis as blue ones. The research group does not fully understand the significance of the condition
The cause of this counter-intuitive outcome lies in the fact that the very high percentage scores of the excellence
(blue/green distribution) connected with the measured (unconditional) probability of identification. They do sense
board are virtually completely negated by the extremely low probability of a project that is actually profitable. Let’s
that it has an effect, because their answers deviate from the 80% quoted. Both upwards and downwards because
go through the figures again.
- independently of each other - they still come to an average of approximately 80%. But that very conditionality
(15/85) significantly alters the actual chances of correct identification. Let’s take a look at the figures.
The probability that a selected project is profitable is 0.2 percent. The probability that the team actually assesses
that project as good is 100% of 0.2%, i.e. 0.2%. On the other hand, there is a 99.8% probability of a loss-making
If a taxi drives off from the front of the hotel at any one time, there is a 15% probability that it will be blue. The
project. The probability that such a project will nevertheless be assessed as good is 2% of 99.8%, in other words
witness correctly identifies the colour in 80% of cases. So the probability of a blue taxi driving off and being
- nearly - 2%. The probability that the team judges positively and the assessed project indeed turns out to be
identified by the man as blue is 80% of 15%, i.e. 12%. By the same reasoning, the probability of a green taxi driving
profitable is approximately 0.2/(0.2+2), so = (only) 9%.
off and being identified by the man as blue is 20% of 85%, or 17%. These probabilities hold as long as the man
has not said what he believes the taxi’s colour to be. However, his opinion has already been clearly recorded in
The formal calculation is as follows:
the police report: he believes that the taxi is blue. This renders the probabilities of the other two possibilities
Define the probability of a successful project as S and an unsuccessful one as S.
(identifying a blue taxi as green and a green taxi as green) to be zero. From this it follows that the probability of the
Define the probability that a project will be designated as successful as A, and that a project will be advised
man getting the colour right is 12/(12+17), or a little over 41%. Hence the probability that he got it wrong is 59%.
against but turn out to be successful as A. The probability of selecting a project that turns out to be unsuccessful is
therefore P(S|A). According to the basic rules of statistics:
The reason why the participants in the study put the probability of correct colour identification at 80% on average
P(S|A) P(A) = P(S A)= P(A|S) P(S) => P(S|A) = P(A|S) P(S)/ P(A) = (0.02*0.998)/P(A)
c
therefore lies in the fact that when reaching a conclusion, they did not take into account the conditions (the
distribution of blue and green taxis) connected with the unconditionally determined probability of identification.
P(A) may in turn be determined as:
You don’t believe it? Below is the formal calculation according to the basic rules of statistics:
Define the probability of a blue taxi as B and a green one as B.
P(A|S) P(S) + P(A|S) P(S) = (0.02*0.998 + 1*0.002)
Define the probability that a taxi is perceived as blue as W. The ‘perception blue’ is therefore the representation of
the actual colour blue.
Hence follows:
The probability of a green taxi being identified as blue is P(B|W). Following the basic rules of statistics:
P(B|W) P(W) = P(B W)= P(W|B) P(B) => P(B|W) = P(W| B) P(B)/ P(W) = (0.2*0.85 )/P(W)
c
P(S|A) = P(A|S) P(S)/P(A) = (0.02*0.998)/(0.02*0.998 + 1*0.002)
P(W) may in turn be determined as P(W|B) P(B) + P(W|B) P(B) = 0.2*0.85+0.8*0.15 = (17+12)/100
This is approximately equal to 0.02/(0.02+0.002) ~
~ 90%.
Hence follows: P(B|W) = P(W|B) P(B)/ P(W) = (0.2*0.85)/(0.2*0.85+0.8*0.15)
The probability that the identification is wrong, in other words that the taxi was really green, is approximately
17/(12+17) ~ 59%.
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43
Girolamo Cardano
(24/9/1501, Pavia - 21/9/1576, Rome)
In Ars Magna (1545), Cardano’s major work, we bear witness to a contest between the age-old mathematical
tradition of Euclid and the Arab world and the new ideas percolating through the sixteenth century. The
Renaissance introduced the idea that the future is not written in stone, but can be shaped by humankind. Cardano
was one of the first to translate this concept into a mathematical application: probability.
Apart from Cardano’s precious contribution to probability, he also made a great number of other scientific
discoveries in mathematics, biology and medicine. One of these is the Cardan suspension, a support on which
an instrument (such as a compass) is hung on gimbals. The Cardan shaft in our automobiles is also based on this
idea.
Cardano’s first mathematical publication was Practica arithmetica et mensurandi singularis (The Practice of
Arithmetic and Simple Mensuration, 1539), followed by Artis magnae sive de regulis algebraicis liber unus or Ars
I have discovered the reason for
a thousand astounding facts
Magna (1545). This later work contained solutions to cubic and quadratic equations. Cardano’s Liber de ludo aleae
(The Book on Games of Chance) - penned in 1525 but not published until 1645 - propounded the first systematic
calculations in the field of probability. In this sense, he can be seen as the father of risk modelling.
Girolamo Cardano
In his own era, Cardano was particularly renowned in the field of medicine. In 1552 he was invited to Scotland
to treat Archbishop Hamilton of Edinburgh, whose asthmatic condition had him on death’s doorstep. Cardano
succeeded in applying his knowledge of allergies to help Hamilton recover, which propelled Cardano to the
pinnacle of European fame.
The highly productive Cardano lectured in Pavia and Bologna and authored as many as 131 published works.
He also left 111 manuscripts to posterity and even claimed to have burned some 170 other works.
45
REFERENCES
Emotional corners (mental accounting)
Staying put... (status quo)
Kahneman, D., & Tversky, A. (2000). Choices, Values,
and Frames. p 12, & 244. Cambridge University Press.
Thaler, R. H. (1993). Advances in Behavioral Finance.
Samuelson, W. & Zeckhauser, R. (1988). Status Quo Bias
The shadows of overestimation (overconfidence)
Other references
Kahneman, D., & Tversky, A. (2000). Choices, Values,
Fang, H., & Moscarini, G. (november 2002).
Baron, J. (2000). Thinking, and Deciding, Third Edition.
and Frames. p 172. Cambridge University Press.
Overconfidence, Morale, and Wage-Setting Policies.
Cambridge University Press.
Working Paper. p 5-6. Department of Economics,
p 562. Russell Sage Foundation.
Yale University.
in Decision Making. Journal of Risk, and Uncertainty,
1, p 7-59.
Slovic, P. (2001). The Perception of Risk. Earthscan
Publications Ltd.
Kahneman, D., & Tversky, A. (2000). Choices, Values,
and Frames. p 409-411. Cambridge University Press.
Being a good loser (loss aversion)
Kahneman, D., & Tversky, A. (2000). Choices, Values, and
Firmly anchored (anchoring)
Bratvold, R. B., Beggs, S. H., & Campbell, J. M. (2002).
Frames. p 21, 260-261, & 271. Cambridge University
Kahneman, D., Slovic P., & Tversky, A. (1982). Judgment
Would you Know a Good Decision if you Saw One?
Press.
under Uncertainty: Heuristics, and Biases. p 14.
p 7. SPE 77509 Society of Petroleum Engineers Inc.
Cambridge University Press.
Nathan J. (1999). Sony: The Private Life. Houghton
Mifflin Company.
Northcraft, G. B., & Neale, M. A. (1987). Experts,
Stumbling in stages (isolation)
Amateurs, and Real Estate: An Anchoring-and-
Kahneman, D. (1979). Prospect Theory: an Analysis of
adjustment
Decision under Risk. Econometrica, 47:2, p 263-291.
Perspective
on
Property
Pricing
Cutting your losses (sunk costs)
Decisions. Organizational Behavior, and Human
Plous, S. (1993). The Psychology of Judgment, and
Decision Processes, 39, p 84-97.
Decision Making. p 244. McGraw-Hill.
Smaller probability, higher score
Van Damme, E. E. C. (november 2000). UMTS Auctions
(representativeness)
Li, C., & Wearing, B. (november 2000). The Financing,
in Europe. Working Paper. Center for Economic
Kahneman, D., Slovic P., & Tversky, A. (1982). Judgment
and Financial Results of Eurotunnel: Retrospect,
Research, Tilburg University.
under Uncertainty: Heuristics, and Biases. p 82, & 92.
and Prospect. Working Paper, 00/13. Department of
Cambridge University Press.
Accounting, Finance, and Management, University of
Shefrin H. (1999). Beyond Greed, and Fear: Under-
Essex.
standing Behavioral Finance, and the Psychology of
Investing. Harvard Business School Press.
Chance of a chance (conditional probabilities)
Kahneman, D., Slovic P., & Tversky, A. (1982). Judgment
under Uncertainty: Heuristics, and Biases. p 156.
Cambridge University Press.
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47
COLOPHON
Final editing:
Marja Koolschijn, Olav Aagaard, Jeroen van der Hoek and Rob Janssen
Editing:
Jaap Streefkerk
Design and lay-out:
Studio Goosen graphic design, Goirle
Full colour illustrations:
Rob Plante, Roberts’ creative
Printing:
PlantijnCasparie, Capelle aan den IJssel
Translation:
The Language Lab Talenservice, Amsterdam
Special thanks to:
Paul Vogels, Michel Kuiters, Vincent van Antwerpen,
Huub van Capelleveen and Theo Kocken
48