5. Assume that you manage a risky portfolio with an expected rate of return of 16% and a standard deviation of 25%. The T-bill rate (risk-free rate) is 5%. Your client chooses to invest 75% in the risky portfolio in your fund and 25% in a T-bill money market fund. We assume that investors use mean-variance utility: U = E(r)-0.5x Ag?, where E(r) is the expected return, A is the risk aversion coefficient and op is the variance of returns. [20 marks) a) What is the expected value and standard deviation of the rate of return on your client's complete portfolio? [6 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 complete portfolio? [6 marks) c) Your client's degree of risk aversion is A = 3.5. (1) What proportion, y*, of the total investment should be invested in your risky fund? [3 marks] (ii) If your client's degree of risk aversion increases from A = 3.5 to A = 4.5. What proportion, y*, of the total investment should be invested in your risky fund? [3 marks] (iii) What do you conclude about the relationship between the proportion y* and your client's attitude toward risk? [2 marks] 6. Answer the following questions briefly. [10 marks) a) Explain the differences between the short and long positions in call options transaction. [5 marks) b) Two bonds, Bond A and Bond B, have identical times to maturity, coupon rates and face value. Bond A is callable at $105. Bond B is a straight bond that has no special features compared to callable or forwardable bonds with embedded options. Bond B is selling for $110. Which bond should have a higher yield to maturity? Why? [5 marks)