Please help me check my work!

Problem 2 (37 marks): There are two stocks in the market, stock A and stock B. The price of stock A today is $70. The price of stock A next year will be $60 if the economy is in a recession, $82 if the economy is normal, and $86 if the economy is expanding. The probabilities of recession, normal times, and expansion are 0.2, 0.6, and 0.2, respectively. Stock A pays no dividends and has a correlation of 0.9 with the market portfolio. Stock B has an expected return of 10 percent, a standard deviation of 52 percent, a correlation with the market portfolio of 0.3, and a correlation with stock A of 0.25. The market portfolio has a standard deviation of 14 percent. Assume the two stocks are not necessarily correctly priced (i.e., the CAPM may not hold for each of the two stocks).

a) What are the expected return, standard deviation, variance, and beta of stock A?

b) What is the beta of stock B?

c) If you are a typical, risk-averse investor with a well-diversified portfolio, which stock would you prefer? Why?

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

e) What is the beta of the portfolio in part (d)?