Consider the following table, which gives a security analysts expected returns o
ID: 2801353 • Letter: C
Question
Consider the following table, which gives a security analysts expected returns on the two stocks for the two particular market returns
a) What are the betas of the stocks?
b) What is the expected return on each stock if the market return is equally likely to be 5% and 20%?
c) What are the alphas of the each stock?
d) What should be cost of capital of all equity financed project by the aggressive firm for a project with the risk characteristics of defensive firm’s stock?
Market return Aggressive stock Defensive stock 5% -20% 3% 20% 60% 15% Risk-free rate 5%Explanation / Answer
a)
beta of aggressive*(20%-5%)=60%-20%
=>beta of aggressive stock=2.666
beta of defensive stock*(20%-5%)=15%-3%
=>beta of defensive stock=0.8
b)
Expected return on aggressive stock=0.5*-20%+0.5*60%=20%
Expected return on defensive stock=0.5*3%+0.5*15%=9%
c)
Expected market return=0.5*5%+0.5*20%=12.5%
Required return on aggressive stock=5%+2.66*(12.5%-5%)=24.95%
Required return on defensive stock=5%+0.8*(12.5%-5%)=11%
Hence,
alpha of defensive stock=20%-24.95%=-4.95%
alpha of aggressive stock=9%-11%=-2%
d)
11%