Assume that you manage a risky portfolio with an expected rate of return of 18% and a standard deviation of 28%. The T-bill rate (risk-free rate) is 8%. Your client chooses to invest 70% in the risky portfolio in your fund and 30% in a T-bill money market fund. We assume that investors use mean-variance utility:U=E(r)0.5A2, where E(r)is the expected return, A is the risk aversion coefficient and2is the variance of returns.

[20 marks]

a)What is the expected value and standard deviation of the rate of return on your client's portfolio?

b)Your client's degree of risk aversion isA=3.5.

(i) What proportion, y, of the total investment should be invested in your risky fund?

(ii) What is the expected value and standard deviation of the rate of return on your client's optimized portfolio?

Provethattheoptimalproportionoftheriskyassetinthecompleteportfolioisgivenby the equationy=E(rp)rf/Ap2, whereris the risk-free rate, E(r)is the expected return

of the risky portfolio,p2is variance of returns, andAis the risk aversion coefficient. For each of the variables on the right side of the equation, discuss the impact of the variable's effect onyand why the nature of the relationship makes sense intuitively. Assume the investor is risk averse.