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%

Bond Fund(B) 10% 5%

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)