You manage a risky portfolio with expected rate of return of 10% and standard deviation of 20%. The T-bill rate is 2%.

(1) Your client chooses to invest 60% of a portfolio in your fund and 40% in a T-hill money market fund. What is the expected value and standard deviation of the rate of return on his portfolio?

(2) Draw the CAL of your portfolio on an expected return-standard deviation diagram. What is the slope of the CAL? Show the position of your client on your fund's CAL.

(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 8%, what is the proportion y?

(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 16%, what is the investment proportion y?

(5) Your client's degree of risk aversion is A = 4, 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?