Q2: CAPM and APT:

1. The expected rate of return on the market portfolio is 9.75% and the risk-free rate of return is 1.50%. The standard deviation of the market portfolio is 19.75%. What is the representative investor's average degree of risk aversion?

2. Stock A has a beta of 1.50 and a standard deviation of return of 35%. Stock B has a beta of 4.25 and a standard deviation of return of 85%. 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 13.25% for Stock A and an expected return of 41.50% 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 4.25% and 2.95%, respectively, while the risk-free rate of return remains at 0.75%. According to this APT analyst, your portfolio formed in question 2 has a beta on factor 1 of 3.70 and a beta on factor 2 of 2.60. 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?