2. Assume that you manage a risky portfolio with an expected rate of return of 18% and a standard deviation of 28%. The T-bill rate (risk-free rate) is 8%. Your client chooses to invest 70% in the risky portfolio in your fund and 30% in a T-bill money market fund. We assume that investors use mean-variance utility: U-: E(r)-0.5 Ad', where E(r) is the expected return, A is the risk aversion coefficient and 2 is the variance of returns [25 marks] a) What is the expected value and standard deviation of the rate of retum on your client's portfolio? 4 marks] b) What is the reward-to-volatility ratio (Sharpe ratio) of your risky portfolio? What is the reward-to-volatility ratio (Sharpe ratio) of your client's risky portfolio? Comment on the relationship between these two Sharpe ratio calculated [6 marks] c) Your client's degree of risk aversion is A 3.5. What proportion, y, of the total invest ment should be invested in the risky fund that you manage? 3 marks] d) If your client's degree of risk aversion increases from A = 3.5 to A = 4.5 (i) What proportion, y, of the total investment should be invested in the risky fund that you manage? 13 marks] (ii) Comparing your answers to c) and d) i), what do you conclude about the relation ship between the proportion y invested in the your fund and your client's attitude toward risk? 3 marks] e) Briefly explain the factors that can affect the proportion of the total investment in the risky portfolio [6 marks]