Standard Deviation and Beta 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 probabilities of recession, normal times, and expansion are .1, .8, and .1, respectively. Stock A pays no dividends and has a correlation of .8 with the market portfolio. Stock B has an expected return of 9 percent, a standard deviation of 12 percent, a correlation with the market portfolio of .2, and a correlation with stock A of .6. The market portfolio has a standard deviation of 10 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)? LO.1