37. Standard Deviation and Beta There are two stocks in the market: stock A and stock B. The price of stock A today is $52. The price of stock A next year will be $40 if the economy is in a recession, $59 if the economy is normal, and $68 if the economy is expanding. The probabilities of recession, normal times, and expansion are .1, .65, and .25, respectively. Stock A pays no dividends and has a correlation of .45 with the market portfolio. Stock B has a standard deviation of 51 percent, a correlation with the market portfolio of .40, and a correlation with stock A of .50. The market portfolio has a standard deviation of 20 percent. The risk-free rate is 4 percent and the market risk premium is 7.5 percent. Assume the CAPM holds.

a. If you are a typical, risk-averse investor with a well-diversified portfolio, 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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