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 × Aσ2 , where E(r) is the expected return, A is the risk aversion coefficient and σ 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? 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. c) Draw the Capital Allocation Line (CAL) of your portfolio on an expected returnstandard deviation diagram. What is the slope of the CAL? Show the position of your client on your fund’s CAL. 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? (ii) What is the standard deviation of the rate of return on your client’s portfolio?
. Assume that you manage a risky portfolio with an expected
return
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 × Aσ2
,
where E(r) is the expected return, A is the risk aversion coefficient and σ
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?
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.
c) Draw the Capital Allocation Line (CAL) of your portfolio on an expected returnstandard deviation diagram. What is the slope of the CAL? Show the position of
your client on your fund’s CAL.
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?
(ii) What is the standard deviation of the rate of return on your client’s portfolio?
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