Assume that you manage a risky portfolio with an expected rate of return of 14%
ID: 2817359 • Letter: A
Question
Assume that you manage a risky portfolio with an expected rate of return of 14% and a standard deviation of 30%. The T-bill rate is 6%. Your client chooses to invest 85% of a portfolio in your fund and 15% in a T-bill money market fund.
a. What is the expected return and standard deviation of your client's portfolio? (Round your answers to 2 decimal places.)
b. Suppose your risky portfolio includes the following investments in the given proportions:
What are the investment proportions of your client’s overall portfolio, including the position in T-bills? (Round your answers to 2 decimal places.)
c. What is the reward-to-volatility ratio (S) of your risky portfolio and your client's overall portfolio? (Round your answers to 4 decimal places.)
Expected return 12.8% per year Standard deviation 25.5 % per yearExplanation / Answer
a. Expected return = 0.85*14 +0.15*6 = 12.8%
Expected standard deviation = 0.85*30 + 0.15* 0 = 25.5% (Since T-bills have 0 Standard deviation)
b. T bills = 15% (Given)
Stock A = 24% *0.85 = 20.4%
Stock B = 32%*0.85 = 27.2%
Stock C = 44% *0.85 = 37.4%
Total =15% + 20.4% + 27.2% + 37.4 % = 100%
c. Reward to volatility ratio is the Sharpe ratio which is given by (Portfolio return - risk free return) /Std. deviation of portflio
Reward to volatility ratio of risky portfolio = (14%-6%)/ 30% = (0.14-0.06)/0.30 = 0.2667
Reward to volatility ratio of Client’s overall portfolio = (12.8%-6%)/25.5% = (0.128-0.06)/0.255 = 0.2667
(Both have the same reward-to-volatility ratio)