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)

0.5 A2,

where E(r) is the expected return, A is the risk aversion coeffiffifficient and 2 is 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?