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# CAPM

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Problem 11. (Section Four) Expected Returns. Consider the following two scenarios for the economy, and the returns in each scenario for the market portfolio, an aggressive stock A, and a defensive stock D.

Rate of Return

Scenario Market Aggressive Stock A Defensive Stock D
Bust -8% -10% -6%
Boom 32 38 24

a. Find the beta of each stock. In what way is stock D defensive?
b. If each scenario is equally likely, find the expected rate of return on the market portfolio and on each stock.
c. If the T-bill rate is 4 percent, what does the CAPM say about the fair expected rate of return on the two stocks?
d. Which stock seems to be a better buy based on your answers to (a) through (c)?

#### Solution Preview

Problem 11. (Section Four) Expected Returns. Consider the following two scenarios for the economy, and the returns in each scenario for the market portfolio, an aggressive stock A, and a defensive stock D.

Rate of Return

Scenario Market Aggressive Stock A Defensive Stock D
Bust -8% -10% -6%
Boom 32 38 24

a. Find the beta of each stock. In what way is stock D defensive?
b. If each scenario is equally likely, find the expected rate of return on the market portfolio and on each stock.
c. If the T-bill rate is 4 percent, what does the CAPM say about the fair expected rate of return on the two stocks?
d. Which stock seems to be a better buy based on your answers to (a) through (c)?

Rate of Return
Scenario Market Aggressive Stock A Defensive Stock D
Bust -8% -10% -6%
Boom 32% 38% 24%

a. Find the beta of each stock. In what way is stock D defensive?

We can use regression to calculate the value of beta.
Beta is the slope of the line with market return on the X axis and the stock return on the Y axis

Stock A
Market (X) Stock A (Y) XY X2
-8 -10 80 64
32 38 1,216 1,024
Total 24 28 1,296 1,088

N= number of observations= 2
summation of X= 24
summation of Y= 28
summation of XY= 1,296
summation of X2= ...

#### Solution Summary

Calculates the beta of each stock, the expected rate of return on the market portfolio and on each stock, the fair expected rate of return on the two stocks as per CAPM

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