There are two stocks in the market, Stock A and Stock B . The price of Stock A today is $65. The price of Stock A next year will be $56 if the economy is in a recession, $73 if the economy is normal, and $91 if the economy is expanding.
The probabilities of recession, normal times, and expansion are 0.1, 0.65, and 0.25, respectively. Stock A pays no dividends and has a correlation of 0.55 with the market portfolio. Stock B has an expected return of 14 percent, a standard deviation of 38 percent, a correlation with the market portfolio of 0.60, and a correlation with Stock A of 0.45. The market portfolio has a standard deviation of 20 percent. The risk free rate is 6 percent and the market risk premium is 7.5 percent - Assume the CAPM holds.
a. Which stock would you prefer? Why?
b. What are the expected return and standard deviation of a portfolio at 70% od stock A and 30% of stock B?
c. What is the beta of the portfolio (for part b)