Your client chooses to invest 40% in your portfolio (p) and 60% (f) in the risk-free asset. What is the standard deviation of your client’s portfolio?

You are a manager of a risky portfolio (consists of bonds and stocks) with an expected return E(rp) = 8% and standard deviation stdevp = 12%. The risk free rate rf = 2% and the standard deviation of the risk free asset is stdevf = 0% 7. Your client chooses to invest 40% in your portfolio (p) and 60% (f) in the risk-free asset. What is the expected return?

1. Your client chooses to invest 40% in your portfolio (p) and 60% (f) in the risk-free asset. What is the standard deviation of your client’s portfolio?

2. Your client chooses to invest 40% in your portfolio (p) and 60% (f) in the risk-free asset. What is the Sharpe ratio of your client’s portfolio?

3. Calculate the utility investors realize from investing 40% of their capital in your portfolio (p) and 60% (f) in the risk-free asset. Assume the following utility function: U = E(r) − 1 × A × stdev2, where A 2 (client’s risk aversion)=5.

4. Calculate the weight in the risky portfolio (p) that maximizes the utility of the client.

Solutions

Expert Solution

1.
=proportion in risky portfolio*standard deviation of risky portfolio
=40%*12%=0.048

2.
=(Expected returns-risk free rate)/standard deviation
=(proportion in risky portfolio*returns of risky portfolio+proportion in riks free asset*returns of risk free asset-rsik free rate)/(proportion of risky portoflio*standard deviation of risky portfolio)
=(40%*8%+60%*2%-2%)/(40%*12%)=0.50

3.
=40%*8%+60%*2%-0.5*5*(40%*12%)^2=0.03824

4.
=(returns of risky portfolio-risk free rate)/(A*standard deviation of risky portfolio^2)
=(8%-2%)/(5*12%*12%)=0.833333333333333

jeff jeffy answered 2 years ago

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