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Intermediate Investments F303 1
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
Intermediate Investments F303 2
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 .9• Chrysler .6• Ford .75
– Assumer weights of • GM = ½ Ford = 1/3 Chrysler = 1/6
– What is Beta and expected return on the portfolio?
Intermediate Investments F303 3
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
Intermediate Investments F303 4
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?
Intermediate Investments F303 5
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%?
Intermediate Investments F303 6
A Third Example
• Consider the following table:
• 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?
Market Aggressive DefensiveScenario #1 5.0% 2.0% 3.5%Scenario #2 20.0% 32.0% 14.0%
Intermediate Investments F303 7
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
Intermediate Investments F303 8
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%
Intermediate Investments F303 9
Capital Investment Decisions
• Consider an investment project with the following cash flows– Year 0 = -60,000
– Year 1 through t = 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?
Intermediate Investments F303 10
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
Intermediate Investments F303 11
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:
• What is the Beta of each of the two assets?
Market Asset 1 Asset 2
r - rf Exc Ret Exc Ret Exc Ret
April 6.0% 12.0% 3.0%May -4.0% -8.0% -2.0%June 2.0% 4.0% 1.0%