Expected Returns. Consider the following two scenarios for the economy, and the

Question

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)?

Explanation / Answer

(a) The beta is the sensitivity of the stock return to the market return movements. Let A be the aggressive stock and D be the defensive one. Then beta is the change in the stock return per change in the market return. Therefore, we compute each stock’s beta by calculating the difference in its return across the two scenarios divided by the difference in the market return.

A = (10 - 38)/(8 - 32) = 2.00

       = -28 / -24

       = 1.16

D = (6 - 24)/(8- 32) = 0.70

        = -18 / -24

        = 0.75

You should not ask more then one question in single post but i answering

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