Lecture 2

Transcription

Lecture 2

c 2015 Juliusz Jablecki: Equity and Fixed Income
Equity and Fixed Income
Juliusz Jabłecki
Banking, Finance and Accounting Dept.
Faculty of Economic Sciences
University of Warsaw
[email protected]
and
Head of Monetary Policy Analysis Team
Economic Institute, National Bank of Poland
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Lecture 2:
Approaches to equity valuation
Total market capitalization of global equity markets is ca. USD
55 tn (65% world GDP) with some 46 ths listings. Equity markets
have changed a lot over the past century.
Source: Credit Suisse Global Investment Returns Yearbook 2013
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From an investment point of view equities form one of the main
asset classes
Source: Credit Suisse Global Investment Returns Yearbook 2013
There are several approaches to valuing equity. In what follows
we first describe basic rules of thumb, before introducing the
Bloomberg Discounted Dividend Model (DDM) and the JP Morgan fair value model for equities.
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Heuristic #1: Price-to-earnings ratio is a gauge of overconfidence. Stocks with low P/E are attractive.
Investors who buy stocks with low PE ratios think
they’re getting a bargain. Generally, they believe that
when a stock’s PE ratio is high, investors have unrealistic expectations for the earnings growth of that stock.
High hopes, the low PE investor reasons, are usually
dashed, along with the price of the stock. Conversely,
they believe the prices of low PE stocks are unduly discounted and, when earnings recover, the price of the
stock will follow.
Source: J. O’Shaughnessy, What Works on Wall Street, 2005
The strategy of selecting low P/E stocks hasn’t performed spectacularly well...
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Heuristic #2: Look at price-to-book ratio which is not susceptible to earnings manipulation
...investors who buy stocks with low price-to-book
ratios believe they are getting stocks at a price close to
their liquidating value, and that they will be rewarded
for not paying high prices for assets.
Over the long haul, buying low P/B stocks has actually performed
reasonably well...
Source: J. O’Shaughnessy, What Works on Wall Street, 2005
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There is no fundamental theoretical reason why we should care
about these heuristics other than that others might as well...
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We now look at a simple, yet powerful valuation model. DDM
is based on a simple idea that stock price should be equal to the
present value of forecasted dividends:
∞
D2
D1
Di
X
+
+
...
=
PV =
(1 + r) (1 + r)2
i=1 (1 + r)i
DDM looks deceptively simple. In fact, there are some obvious
problems with applying it in practice:
• we don’t know future earnings: E1, E2, ...
• we don’t know future payout ratios, and hence, dividends
D1, D2, ...
• we don’t know which discount rate r to apply
A useful starting point is to assume e.g. constant dividend or
dividend growing at a constant rate. But how sensible is that?
Practitioners have a way of using DDM and it is worth looking
at how they do it.
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Implementation step 1: determine the discount rate using CAPM
Each investor demands compensation for investing in a (risky)
stock S instead of a risk-free bond
rs = rf (risk-free rate) + Π(equity risk premium) =
= rf + β × (rM − rf ) =
cov(rM , rS )
(rM − rs)
= rf +
var(rM )
The “knowns” in this equation are:
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• the risk-free rate which can be approximated e.g. by 10Y
US Treasury bond yield;
• the beta which can be found by regressing stock’s return on
the market index (S&P 500)
But how to determine rM ? We could simply calculate historical
average return on S&P 500, but that would be backward-looking.
Instead, Bloomberg uses a forward-looking approach:
• find out analysts’ expectations of dividends for all companies
in the market
• calculate capitalization-weighted dividend return one would
obtain by holding the market
• use market prices of all stocks to find out capitalizationweighted price of the “market”
• find out rM as implied by expected dividends and current
prices
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This is how the market risk premium has behaved in the US:
Beta for Apple ≈ 0.9
Apple risk premium ≈ 0.9 × (0.10 − 0.026) = 6.7%
Implementation step 2: determine model stages and companies’
growth rates
In FY1, FY2 dividend forecasts are readily available for most
tickets.
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From that point on, Bloomberg assumes each company develops
in three stages: growth, transition and mature. The length of
the growth and transition periods depends on whether the equity
is classified as explosive growth, high growth, average growth, or
slow/mature growth.
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• Growth stage: varies from 3Y to 9Y; during the first year
of the growth stage, if there is an explicit EPS forecast for
FY3, use that forecast; if there is no explicit forecast for FY3,
the EPS in FY3 is set as FY2×(1 + long-term growth rate);
during the remaining years of the growth stage earnings per
share (EPS) grow at the long-term growth rate.
• Transition stage: following the growth stage, the model
assumes that the earnings growth rate for the firm approaches
the rate that applies to the general market for all mature issues.The model applies the same linear increase or decrease
to the payout ratio to arrive at the mature stage payout
ratio, which defaults to 45%.
• Mature stage: After the transition stage, the model assumes that all issues have the same earnings growth rate
and payout rate. The payout rate defaults to 45%. The
mature growth rate equals: retention rate × rM
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$
'
Example: Assume that a U.S. equity has per share earnings estimates of $0.50 in the first year and $1.00 in the second year
with an indicated annual dividend of $0.10. Also assume that the
firm has an annual growth rate of 15% and that its growth and
transition stages are each two years. The firm’s current payout
ratio is then 20% as a result of its current annual dividend and
first year earnings of $0.50 per share (0.10/0.50 = 20%). Assume that the current 10-year Treasury bond rate is 6% and that
the equity risk premium is 4%. Theoretical value of the equity
equals $10.2.
&
%
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The second model we analyze is the JP Morgan Fair Value Model
for Equities.
The model assumes that the equity price is equal to the expected
future cash flows (i.e. dividends) discounted to the present using
an equity discount rate (EDR):
kE0(1 + g)i
P =
,
i
(1
+
EDR)
i
X
where E0 denotes current earnings, g is earnings growth rate and
k the payout ratio. To implement the model, k, g and EDR
need to be specified.
• dividend payout ratio is assumed to equal the long-term average for S&P 500, k = 50%;
• earnings are assumed to grow accoring to a two-stage model;
the first stage lasts 5 years over which g is estimated using a
backward-looking econometric model (as analysts’ forecasts
were found to be systematically over-optimistic); in the second stage g reverts to the long-run average since 1950s of
gLT = 2.2%
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With these assumptions:
P =
kE0
(1 + gLT + 5(gE − gLT ))
EDR − gLT
Given market price, implied EDR can be determined:
Market price → implied EDR → econometric model
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The full model is parameterized as follows
The EDR model has worked reasonably well in practice...
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These coefficients may be already outdated. We will try to see how the model performs
using current data.
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Exam-like problems
1. Determine the formula for the price of a stock in DDM
assuming:
(a) constant dividend;
(b) dividend growing at a constant rate g;
(c) what condition does g and r have to satisfy for the discounted dividend series to converge (and hence for price
to exist).
2. The stock market is composed of three companies A, B, and
C, each with a share of 1/3 in total capitalization. Analysts
expect A to pay a perpetual dividend of 10; B to pay a
divided of 3 next year and to grow by 5% forever; C to pay
a dividend of 2 and grow by 8% forever. The market prices
of stocks A, B, C are 100, 105 and 110 respectively. Find
the implied market rate of return.
3. Assume that a U.S. equity has per share earnings estimates
of $0.50 in the first year and $1.00 in the second year with
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an indicated annual dividend of $0.10. Also assume that the
firm has an annual growth rate of 15% and that its growth
and transition stages are each two years. The firm’s current
payout ratio is then 20% as a result of its current annual dividend and first year earnings of $0.50 per share (0.10/0.50
= 20%). Assume that the current 10-year Treasury bond
rate is 6% and that the equity risk premium is 4%. Calculate the theoretical value of the equity using the Bloomberg
dividend discount model.
4. Show that in a two-stage JP Morgan fair equity valuation
kE0
(1 + gLT + 5(gE − gLT )), where
model P = EDR−g
LT
gE is the earnings growth rate in the first five-year stage,
and gLT is the long-term earnings growth rate.
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Lecture 2

Transcription

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