Problem:
There are two stocks in the market, stock A and stock B. The price of stock A today is $75. The price of stock A next year will be $63 if the economy is in a recession, $83 if the economy is normal, and $96 if the economy is expanding. The probabilities of recession, normal times, and expansion are .2, .6, and .2 respectively. Stock A pays no dividends and has a correlation of .8 with the market portfolio. Stock B has an expected return of 13%, a standard deviation of 34%, a correlation with the market portfolio of .25, and a correlation with stock A of .48. The market portfolio has a standard deviation of 18%. Assume CAPM holds.
a. If you are a typical, risk adverse investor with a well-diversified portfolio, which of the stocks would you prefer to hold? Why?
b. What are the expected return and standard deviation of a portfolio consisting of 70% stock A and 30% of stock B?
c. What is the beta of the portfolio in part b.?