Problem 13-31 Using CAPM (LO1, 4)

There are two stocks in the market, stock A and stock B. The price of stock A today is $77. The price of stock A next year will be $65 if the economy is in a recession, $85 if the economy is normal, and $97 if the economy is expanding. The probabilities of recession, normal times, and expansion are 0.2, 0.6, and 0.2, respectively. Stock A pays no dividends and has a beta of 0.80. Stock B has an expected return of 13%, a standard deviation of 34%, a beta of 0.57, and a correlation with stock A of 0.48. The market portfolio has a standard deviation of 14%. Assume the CAPM holds.

a. What are the expected return and standard deviation of stock A? (Do not round intermediate calculations. Round the final answers to 2 decimal places.)

	Stock A
Expected return	%
Standard deviation	%

b. If you are a typical, risk-averse investor with a well-diversified portfolio, which stock would you prefer?

multiple choice

• Stock A

• Stock B

c. What are the expected return and standard deviation of a portfolio consisting of 55% of stock A and 45% of stock B? (Do not round intermediate calculations. Round the final answers to 2 decimal places.)

Expected return	%
Standard deviation	%

d. What is the beta of the portfolio in (c)? (Do not round intermediate calculations. Round the final answer to 3 decimal places.)

Beta of the portfolio