You manage a risky portfolio with expected rate of return of 7% and standard deviation of 15%. The T-bill rate is 4%. (25 marks)

(3) Suppose that your client decides to invest in your portfolio a proportion y of the total investment budget so that the overall portfolio will have an expected rate of return of 5%, what is the proportion y? (5 marks)

(4) Suppose that your client prefers to invest in your fund a proportion y that maximizes the expected return on the complete portfolio subject to the constraint that the complete portfolio's standard deviation will not exceed 10%, what is the investment proportion y? (5 marks)

(5) Your client's degree of risk aversion is A = 3, what proportion, y, of the total investment should be invested in your fund? What is the expected value and standard deviation of the rate of return on your client's optimized portfolio? (5 marks)