Please solve the below question step wise...
Portfolio optimisation (10 marks) A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market. The probability distribution of the funds is as follows: Expected Return Standard Deviation Stock Fund(s) 20% 15% 10% 5% Bond Fund(B) T-bill Fund(T) 5% 0% The correlation between the stock fund and bond bund is 0.3. The correlation between the T-bill money market fund and the other funds is 0. (a) The manager chooses to invest 70% of a portfolio in stock fund (S) and 30% in bond fund (B). What is the expected value and standard deviation of the rate of return on his portfolio? (2 marks) (b) Suppose that the manager decides to invest in a proportion of the total investment budget in stock fund (S) and all other in T- bill market fund (T), so that the overall portfolio will have an expected rate of return of 15%. i. What is the proportion? (2 marks) ii. What is the standard deviation of the rate of return on the manager's portfolio? (2 marks) (c) The manager has the utility function, U = E(r)-1/2A sigma^2. His degree of risk aversion is A = 2. If the manager is going to invest in the stock fund (S) and the T-bill money market fund (T) only. What proportion of the total investment should he invest in stock fund (S) and T-bill money market fund (T) to maximise his utility? (4 marks) Portfolio optimisation (10 marks) A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market. The probability distribution of the funds is as follows: Expected Return Standard Deviation Stock Fund(s) 20% 15% 10% 5% Bond Fund(B) T-bill Fund(T) 5% 0% The correlation between the stock fund and bond bund is 0.3. The correlation between the T-bill money market fund and the other funds is 0. (a) The manager chooses to invest 70% of a portfolio in stock fund (S) and 30% in bond fund (B). What is the expected value and standard deviation of the rate of return on his portfolio? (2 marks) (b) Suppose that the manager decides to invest in a proportion of the total investment budget in stock fund (S) and all other in T- bill market fund (T), so that the overall portfolio will have an expected rate of return of 15%. i. What is the proportion? (2 marks) ii. What is the standard deviation of the rate of return on the manager's portfolio? (2 marks) (c) The manager has the utility function, U = E(r)-1/2A sigma^2. His degree of risk aversion is A = 2. If the manager is going to invest in the stock fund (S) and the T-bill money market fund (T) only. What proportion of the total investment should he invest in stock fund (S) and T-bill money market fund (T) to maximise his utility? (4 marks)
