Consider the following two scenarios for the economy and the returns in each sce
ID: 2654136 • Letter: C
Question
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
Scenario
Bust: Market -7 / Aggressive Stock A -9 / Defensive Stock D -5
Boom: Market 28 / Aggressive Stock A 35 / Defensive Stock D 20
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%, 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)?
Explanation / Answer
(a) Beta of Stock A = [35% - (-9%)] / [28% - (-7%)]
= 1.26
Beta of Stock D = [20% - (-5%)] / [28% - (-7%)]
= 0.71
(b) In case of equally likely scenario,
Expected market return = [(-7%) + 28%] / 2
= 10.50%
Expected return of Stock A = [(-9%) + 35%] / 2
= 12.00%
Expected return of Stock D = [(-5%) + 20%] / 2
= 7.50%
(c) Expected return of Stock A = Risk free rate + Beta of Stock A * Market premium
= 4% + 1.26 * (10.50% - 4%)
= 12.19%
Expected return of Stock D = Risk free rate + Beta of Stock D * Market premium
= 4% + 0.71 * (10.50% - 4%)
= 8.62%
(d) Based on the above information, Stock A seems to be the better buy as its expected return is closer to that of the CAPM model which incorporates the risk borne by the stock.
Scenario Market Aggressive Stock A Defensive Stock D Bust -7% -9% -5% Boom 28% 35% 20%