The expected rate of return on the market portfolio is 8.50% and the risk–free rate of return

Q2: CAPM and APT:

1. The expected rate of return on the market portfolio is 8.50% and the risk–free rate of return is 2.50%. The standard deviation of the market portfolio is 24%. What is the representative investor’s average degree of risk aversion?

2. Stock A has a beta of 1.45 and a standard deviation of return of 32%. Stock B has a beta of 2.55 and a standard deviation of return of 46%. Assume that you form a portfolio that is 60% invested in Stock A and 40% invested in Stock B. Using the information in question 1, according to CAPM, what is the expected rate of return on your portfolio?


3. Using the information in questions 1 and 2, what is your best estimate of the correlation between stocks A and B?


4. Your forecasting model projects an expected return of 11.75% for Stock A and an expected return of 20.50% for Stock B. Using the information in questions 1 and 2 and your forecasted expected returns, what is your best estimate of the alpha of your portfolio when using CAPM to determine a fair level of expected return?


5. A different analyst uses a two–factor APT model to evaluate expected returns and risk. The risk premiums on the factor 1 and factor 2 portfolios are 4.50% and 2.25%, respectively, while the risk–free rate of return remains at 2.50%. According to this APT analyst, your portfolio formed in question 2 has a beta on factor 1 of 1.30 and a beta on factor 2 of 2.15. According to APT, what is the expected return on your portfolio if no arbitrage opportunities exist?


6. Now assume that your forecasting model of question 4 accurately projects the expected return of Stocks A and B and therefore your portfolio, and that the APT model of question 5 describes the fair rate of return for your portfolio. Do any arbitrage opportunities exist? If yes, would you invest long or short in your portfolio constructed in question 2?