Problem 5 (40 marks). Assume that you manage a risky portfolio with an expected rate of...

 

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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) – 0.5 x Ao?, where E(r) is the expected return, A is the risk aversion coefficient ando? 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? [3 marks] 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) – 0.5 x Ao?, where E(r) is the expected return, A is the risk aversion coefficient ando? 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? [3 marks]

Answer rating: 100% (QA)

Risky Portfolio expected return 18 Risky Portfolio standard deviation 28 Tbill rate 7 Clients Proportion in risky portfolio 70 Clients Proportion in Tbills 30 a Expected value and standard deviation o... View the full answer