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 16%. 12%

Bond Fund 8% 4%

T-Bill Fund 4% 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 12%.

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)-1/2Asigma^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)