a. Question 4 (20 marks) You are considering constructing a portfolio that consists of one risky (asset A) and one riskless asset. From the historical data you know that the standard deviation on asset A is oa = 10%, expected returns on the asset A and riskless asset are ra= 12.5% and rRF 3%, respectively. Suppose that your utility function is given by U(rp, o%) = rp op, with risk preference value, y of 0.18. Find the optimal weight of asset which corresponds to the portfolio and the expected return of the portfolio to maximize your utility: (10 marks) Max U(Tp, o) = rp - op subject to = lrf + wa(ra - PRF) Op = WAA b. Suppose that the risk-free rate of return is 3.8% and the expected rate of return on the market is 12%. Asset X, Q, Y, and Z have the following beta: Bx = 0.8, Be =-1.2, By = 2.3, and Bz= 1.8. From the historical data we know that the expected returns on the assets are rx= 5.8%, ro = -3.5%, ry= 28%, and rz 12%. Calculate the alpha of each asset and make your investment decisions. (10 marks) a. Question 4 (20 marks) You are considering constructing a portfolio that consists of one risky (asset A) and one riskless asset. From the historical data you know that the standard deviation on asset A is oa = 10%, expected returns on the asset A and riskless asset are ra= 12.5% and rRF 3%, respectively. Suppose that your utility function is given by U(rp, o%) = rp op, with risk preference value, y of 0.18. Find the optimal weight of asset which corresponds to the portfolio and the expected return of the portfolio to maximize your utility: (10 marks) Max U(Tp, o) = rp - op subject to = lrf + wa(ra - PRF) Op = WAA b. Suppose that the risk-free rate of return is 3.8% and the expected rate of return on the market is 12%. Asset X, Q, Y, and Z have the following beta: Bx = 0.8, Be =-1.2, By = 2.3, and Bz= 1.8. From the historical data we know that the expected returns on the assets are rx= 5.8%, ro = -3.5%, ry= 28%, and rz 12%. Calculate the alpha of each asset and make your investment decisions. (10 marks)