You are a portfolio manager of an investment company in Canada, and you are presented with the following information of two stocks, A & B. The stock information contains only the expected returns E(R) and systematic risk (Beta) of each stock. Stock E(R) Beta A 15% 0.7 B 20% 1.10 1) If the CAPM holds and both stocks A and B are correctly priced accordingly, what is the risk-free interest rate in this economy? What is the expected return on the market portfolio? Show your calculations. (6 marks) 2) Now you have collected more information regarding the two stocks: the correlation between the two stocks is 0.10; the standard deviations for stock A and B are 18% and 24%, respectively. An investor X's risk preferences are characterized by the following utility function: U=E(r)-0.5A02 Assume that for the investor X: A=4. The investor is considering building a portfolio consisting of the two stocks and the risk-free asset. The investor is willing to spend $10,000 on this portfolio. Based on the information you have, how would you allocate the $10,000 in the stocks and risk-free assets to best serve X's welfare? (Assume risk-free rate is 6.25% if you cannot find it from part 1). (10 points) 3) Now there is another investor Y with the same utility function and risk aversion level as the investor X. Investor Y is considering investing $10,000 in a portfolio consisting of the market portfolio and the risk- free assets. The market portfolio has a standard deviation of 15%. How would you allocate the $10,000 in the market portfolio and the risk-free assets to best serve Y's welfare? Compared to your answer in part 2), which investor's strategy is better, X or Y? Why? (Assume the return for the market portfolio is 18.75% if you cannot find it from part 1). (7 points) You are a portfolio manager of an investment company in Canada, and you are presented with the following information of two stocks, A & B. The stock information contains only the expected returns E(R) and systematic risk (Beta) of each stock. Stock E(R) Beta A 15% 0.7 B 20% 1.10 1) If the CAPM holds and both stocks A and B are correctly priced accordingly, what is the risk-free interest rate in this economy? What is the expected return on the market portfolio? Show your calculations. (6 marks) 2) Now you have collected more information regarding the two stocks: the correlation between the two stocks is 0.10; the standard deviations for stock A and B are 18% and 24%, respectively. An investor X's risk preferences are characterized by the following utility function: U=E(r)-0.5A02 Assume that for the investor X: A=4. The investor is considering building a portfolio consisting of the two stocks and the risk-free asset. The investor is willing to spend $10,000 on this portfolio. Based on the information you have, how would you allocate the $10,000 in the stocks and risk-free assets to best serve X's welfare? (Assume risk-free rate is 6.25% if you cannot find it from part 1). (10 points) 3) Now there is another investor Y with the same utility function and risk aversion level as the investor X. Investor Y is considering investing $10,000 in a portfolio consisting of the market portfolio and the risk- free assets. The market portfolio has a standard deviation of 15%. How would you allocate the $10,000 in the market portfolio and the risk-free assets to best serve Y's welfare? Compared to your answer in part 2), which investor's strategy is better, X or Y? Why? (Assume the return for the market portfolio is 18.75% if you cannot find it from part 1). (7 points)
