Question 4: There are three stocks in the market, stock A, stock B, and stock C. 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 $95 if the economy is expanding. The probabilities of recession, normal times, and expansion are 0.20, 0.65, and 0.15, respectively. Stock A pays no dividends and has a beta of 0.64. Stock B has an expected return of 6%, a standard deviation of 30%, a beta of 0.42, and a correlation with stock A of 0.52. Stock C has an expected return of 4.739%, a standard deviation of 23%, a beta of 0.26, and correlations with stock A of 0.42 and with stock B of 0.46. Assume the CAPM holds. a) (6 marks) Calculate the expected return and standard deviation of stock A. b) (2 marks) If you are a typical, risk-averse investor with a well-diversified portfolio, which stock would you prefer? c) (6 marks) Calculate the expected return and standard deviation of a portfolio consisting of 45% of stock A, 30% of stock B, and 25% of stock C. d) (6 marks) Calculate the beta of the portfolio in (c). You can use the following formula to calculate the variance of a portfolio of three stocks (securities). XL, XU, and XZ are the weights of these securities in the portfolio. o = x o +x;o; + x?o? + 2x2x, CORR2,0,0, + 2x,x,CORR,,20,02 + 2x, X, CORR2,00 200