Question

You are holding two stocks: Stock A and Stock B. Assume the following information:

Realized return: R_A = 0.20, R_B = 0.10

Standard deviation: SD(R_A) = 0.30, SD(R_B) = 0.20

Beta_A = 0.87, Beta_B = 1.46

r_f = 0.03; the expected return on the market portfolio is 12%

a. Which stock has a higher level of total risk? Which stock has a higher level of systematic risk? Explain your answer.

b. What is the risk premium for Stock A and Stock B? What is the risk premium on the market portfolio?

c. What is the required return for Stock A and Stock B based on CAPM?

d. Calculate Jensen's Alpha, Sharpe Ratio and Treynor Ratio for Stock A and Stock B. Which stock provides better investment opportunity based on each criterion?

Answer 1

1.
Stock A has higher level of total risk as measured by standard deviation
Stock B has higher level of systematic risk as measured by beta

2.
Risk premium for Stock A=0.87*(12%-3%)=7.83%
Risk premium for Stock B=1.46*(12%-3%)=13.1400%
Risk premium for market=(12%-3%)=9%

3.
Required return for Stock A=3%+7.83%=10.83%
Required return for Stock B=3%+13.14%=16.14%

4.

Jensen's alpha

Jensen's alpha for Stock A=20%-10.83%=9.17%

Jensen's alpha for Stock B=10%-16.14%=-6.14%

Stock A is better

Sharpe Ratio

Sharpe Ratio for Stock A=(20%-3%)/0.30=0.5666

Sharpe Ratio for Stock B=(10%-3%)/0.20=0.35

Stock A is better

Treynor Ratio

Treynor Ratio for Stock A=(20%-3%)/0.87=0.195402

Treynor Ratio for Stock A=(10%-3%)/1.46=0.047945

Stock A is better