Question

Consider the following two scenarios for the economy and the expected 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 % –11 % –6 %
Boom 33 40 18
Find the beta of each stock. 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 5%, 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 on the basis of your answers to (a) through (c)?

Answer 1

Answer: The answer is provided below

Explanation:

Beta of a stock is sensitivity of a stock return to the market return. Beta of a stock is the change in stock return per change in market return.

a. Beta of Stock A = (-11-40)/(-8-33)

= (-51)/(-41) = 1.24

Beta of Stock D = (-6-18)/(-8-33)

= (-24)/(-41) = 0.59

b. The expected market return will be:

= (0.5 × -8) + (0.5 × 33)

= -4 + 16.5

= 12.5%

c. Now using CAPM, fair expected return of the stocks will be:

Stock A = 5 + 1.24(12.5 - 5)

= 5 + 1.24(7.5)

= 5 + 9.3

= 14.3%

Stock D = 5 + 0.59(12.5 - 5)

= 5 + 0.59(7.5)

= 5 + 4.43

= 9.43%

Stock A is the better buy