Problem 5(40 marks).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 7%. 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.

a)What is the expected value and standard deviation of the rate of return on your client's portfolio? [4 marks]

b)What is the reward-to-volatility ratio (Sharpe ratio) of your risky portfolio? What is the reward-to-volatility ratio (Sharpe ratio) of your client's risky portfolio? Comment on the relationship between these two Sharpe ratio calculated and explain the intuition

behind. [8 marks]

c) Draw the Capital Allocation Line (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. [6 marks]

d)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 16%.

(i) What is the proportion y? [2 marks]

(ii) What is the standard deviation of the rate of return on your client's portfolio? [3 marks]

e)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? [2 marks]

(ii) What is the expected value and standard deviation of the rate of return on your client's optimized portfolio? [4 marks]

f) If your client's degree of risk aversion increases fromA= 3.5 toA= 4.5.

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

fund? [2 marks]

(ii) Comparing your answers to d)(i) and e)(i), what do you conclude about the relationship between the proportion y invested in the your fund and your client's attitude toward risk? [3 marks]

(iii) Given that the optimal proportion of the risky asset in the complete portfolio is given by the equationy=E(rp)rf/Ap2, whereris the risk-free rate, E(r) is theexpected return of the risky portfolio,p^2is variance of returns, andAis the risk

aversion coefficient. For each of the variables on the right side of the equation, dis- cuss the impact of the variable's effect onyand why the nature of the relationship makes sense intuitively. Assume the investor is risk averse.