Review of CAPM
• CAPM is a model that relates the required return
of a security to its risk as measured by Beta
– Benchmark rate for evaluating investments
– Provides educated estimate for expected return on
assets that have not been traded in the marketplace
– Risk premiums are used to compensate investors for
systematic risk. The risk premium equal to the asset’s
beta times the market risk premium
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CAPM Continued
• An example using Ford Motor Company
– Market risk premium = 8%
– Assume Beta for Ford = .75
– What is market risk premium for Ford?
– Assume same market risk premium of 8%
– Assume following betas
• GM
• Chrysler
• Ford
.9
.6
.75
– Assumer weights of
• GM = ½
Ford = 1/3
Chrysler = 1/6
– What is Beta and expected return on the portfolio?
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CAPM and Alpha
• Graph SML and security in equilibrium
• Alpha: the abnormal rate of return on a security in
excess of what would be predicted by an
equilibrium pricing model like CAPM
• Under-priced securities have a positive alpha
• Over-priced securities have a negative alpha
• Expanded CAPM equation =
E(ri) = rf + B [E(rm) – rf] + alphai + ei
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An Example
• Actual average returns for a 15 year period
–
–
–
–
–
Franklin Income Fund
12.9%
DJIA
11.1%
Salomon’s High Grade Bond 9.2%
Average return on the market 13.0%
Risk free rate
7.0%
• Portfolio Betas
– Franklin Income Fund
1.000
– DJIA
.683
– Salomon’s High Grade Bond .367
• What are the required returns and alphas for the
three portfolios?
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Another Example
• Assume the following
–
–
–
–
The market risk premium is 8%
The risk free rate is 3%
Beta of security X is 1.25
Beta of security Y is .6
• What can you say about security X is th eacutal
return is 15%?
• What if it is 10%?
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A Third Example
• Consider the following table:
Market
Aggressive Defensive
Scenario #1
5.0%
2.0%
3.5%
Scenario #2
20.0%
32.0%
14.0%
• Beta for the Aggressive stock is 2.00 and for the defensive
stock .7
• What is the expected return on each if both scenarios are
equally likely?
• What does the SML look like if the Risk free rate is 8%?
Do the securities have positive or negative alphas?
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Uses of CAPM
• Use CAPM as a hurdle rate for projects
• Use it to determine the cost of capital when
pricing stocks in the Dividend Discount Model
• Use it to determine the discount rate in capital
budgeting problems
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In the Dividend Discount Model
• The equation for determining stock price using the
DDM is
P0 = D0 * (1+g) / k – g
• Consider the following as the markets stood in
1998
–
–
–
–
–
S&P 500 index is a 1229.23
Annual dividend was 16.20
Price/dividend ratio = 75.88
k as derived from CAPM = 12%
What can you say about the growth rate? What is your
required return is 15%
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Capital Investment Decisions
• Consider an investment project with the following cash
flows
– Year 0
– Year 1 through t
•
•
•
•
•
•
•
=
=
-60,000
15,000
Expected market return is 12%
Risk free rate is 8%
Beta of the company is 1.5 and the project is equally risky
t = 7 years
What is the required return based on CAPM?
Would you do the project?
What if the project was riskier by a factor of 1.4?
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Shortcomings in the CAPM Model
• It relies on the theoretical market portfolio
• It relies on expected and not actual returns
How do we get ‘around’ these?
• Use a proxy for the market
• Use actual historical returns
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Note on Estimating Beta
• In theory, over time the value of Beta regresses
towards a value of 1
– High betas one period tend to have lower Betas in the
future
• You can estimate Betas by comparing actual
market returns. Consider the following table:
r - rf
April
May
June
Market
Asset 1
Asset 2
Exc Ret
Exc Ret
Exc Ret
6.0%
12.0%
3.0%
-4.0%
-8.0%
-2.0%
2.0%
4.0%
1.0%
• What is the Beta of each of the two assets?
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