investment

1. The expected rate of return on the market portfolio is 12.50% and the risk–free rate of return is 3.75%. The standard deviation of the market portfolio is 21.25%.  What is the representative investor’s average degree of risk aversion?

1. Stock A has a beta of 1.95 and a standard deviation of return of 44%. Stock B has a beta of 3.75 and a standard deviation of return of 77%.  Assume that you form a portfolio that is 70% invested in Stock A and 30% invested in Stock B.  Using the information in question 1, according to CAPM, what is the expected rate of return on your portfolio?

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

1. Your forecasting model projects an expected return of 21.95% for Stock A and an expected return of 39.50% 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?

1. 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 2.75%, respectively, while the risk–free rate of return remains at 3.75%.  According to this APT analyst, your portfolio formed in question 2 has a beta on factor 1 of 3.95 and a beta on factor 2 of 3.25.  According to APT, what is the expected return on your portfolio if no arbitrage opportunities exist?

1. 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?