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 % –13 % –6 %

Boom 26 35 19 Required:

a. 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

Beta is the slope of the stock return with that of market returns

Expected return is the Summation of probability times the Expected return in that scenario

	Rate of return
Scenario	Market	Aggressive stock A	Defensive Stock D
Bust	-8%	-13%	-6%
Boom	26%	35%	19%
Beta		1.411764706	0.735294118
Expected return	9.00%	11.00%	6.50%

a.

Beta of Stock A = 1.42

Beta of Stock B = 0.74

b.

Expected return on the market portfolio = 9.00%

Expected return on Stock A = 11.00%

Expected return on Stock B = 6.50%

c.

The required rate of return R(e) is calculated by CAPM model

R(e) = r(f) + Beta*(R(m) - r(f))

R(m) is the market return =9%

r(f) is the risk-free rate = 5%

For Stock A

R(e) = 0.05+1.42*(0.09-0.05)

R(e) = 0.1068= 10.68%

For Stock B

R(e) = 0.05+0.74*(0.09-0.05)

R(e) = 0.0796= 7.96%

d.

Stock A seems to be a better buy since the fair expected return using CAPM is lower than the expected return. In short, Stock A seems to be under-valued and hence a better buy.