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

–5

%

–7

%

–3

%

Boom

27

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 4%, 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

Answer 1

a. Beta of Stock A =Change in Rate of Return/Change in Market return =(35%+7%)/(27%+5%) =1.3125
Beta of Stock B =Change in Rate of Return/Change in Market return =(19%+3%)/(27%+5%) =0.6875

b. Expected Return of Market =(27%-5%)/2 =11%
Expected Return of Stock A =(35%-7%)/2 =14%
Expected return of Stock B =(19%-3%)/2 =8%

c. Fair Rate of Return of Stock A =Risk free Rate+Beta*(Market Return-Risk Free Rate =4%+1.3125*(11%-4%)=13.19%
Fair Rate of Return of Stock B =Risk free Rate+Beta*(Market Return-Risk Free Rate =4%+0.6875*(11%-4%) =8.81%

Stock A is better because expected Return is greater than fair rate of return.