Consider the following two scenarios for the economy and the returns in each sce
ID: 2756299 • 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
Find the beta of each stock. (Round your answers to 2 decimal places.)
If each scenario is equally likely, find the expected rate of return on the market portfolio and on each stock. (Round your answers to 2 decimal places.)
If the T-bill rate is 4%, what does the CAPM say about the fair expected rate of return on the two stocks? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
Which stock seems to be a better buy on the basis of your answers to (a) through (c)?
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.
Explanation / Answer
Expected return (market) = -5 + 12 / 2 = 3.5%
Expected return (stock A) = -9 + 21 / 2 =6%
Expected return (stock B) = -3 + 10 / 2 =3.5%
standard deviation of market = [(-5-3.5)*2 /2 + (12-3.5)*2 * /2]^2 = 8.5%
standard deviation of Stock A = [(-9-6)*2 /2 + (21-6)*2 * /2]^2 = 15%
standard deviation of stock B = [(-3-3.5)*2 /2 + (10-3.5)*2 * /2]^2 = 6.5%
covariance of market and stock A = (-5-3.5)* (-9-6)/2 + (12-3.5) * (21-6)/2 = 127.5
covariance of market and stock B = (-5-3.5)* (-3-3.5)/2 + (12-3.5) * (10-3.5)/2 = 62.9
Beta of stock A = covariance of Market and Stock A / variance of market
= 127.5 / 72.25
=1.76
Beta of stock B = covariance of Market and Stock B / variance of market
= 62.9 / 72.25
= 0.87
c) Expected return = = risk free return + beta * market risk premium
Expected return (stock A) = 4 + 1.76 * (6-4) = 7.52 %
Expected return (stock B) = 4 + 0.87 * (3.5-4) = 3.565 %
d) Stock A