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.

StockE(R)Beta

A15%0.7

B20%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)-0.5A²

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). (7points)