10.41 There are two stocks in the market, stock A and stock B. The price of stock A today is

$50. The price of stock A next year will be $40 if the economy is in a recession, $55 if the economy is normal, and $60 if the economy is expanding. The attendant probabilities of recession, normal times, and expansion are 0.1, 0.8, and 0.1, respectively. Stock A pays no dividend.

Assume the CAPM is true. Other information about the market includes:

a. If you are a typical, risk-averse investor, which stock would you prefer? Why?

b. What are the expected return and standard deviation of a portfolio consisting of 70 percent of stock A and 30 percent of stock B?

c. What is the beta of the portfolio in part (b)?

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SD(RM) = Standard deviation of the market portfolio = 0.10 SD(R) Standard deviation of stock B's return = 0.12 RB = Expected return on stock B = 0.09 Corr(RA,RM) = The correlation of stock A and the market = 0.8 Corr(RR.RM) = The correlation of stock B and the market = 0.2 Corr(RA,RB) = The correlation of stock A and stock B = 0.6