Assume that you manage a risky portfolio with an expected rate of return of 18%
ID: 2616041 • Letter: A
Question
Assume that you manage a risky portfolio with an expected rate of return of 18% and a standard deviation of 34%. The T-bill rate is 4%. 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.) Expected return Standard deviation % per year % per year b. Suppose your risky portfolio includes the following investments in the given proportions: Stock A Stock B Stock C 32% 36% 32% What are the investment proportions of your client's overall portfolio, including the position in T-bills? (Round your answers to 2 decimal places.) Investment Security T-Bills Stock A Stock B Stock C 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.) Reward-to-Volatility Ratio Risky portfolio Client's overall portfolioExplanation / Answer
a). Expected return on portfolio of client = E(R) = w1R1 + w2R2 = 0.85*18 + 0.15*4 = 15.90 % per year.
Standard deviation of portfolio = [w2A*?2(RA) + w2B*?2(RB) + 2*(wA)*(wB)*Cov(RA, RB)]^1/2. Now here as other asset if a T-bill its standard deviation is assumed zero. So portfolio standard deviation = 0.85*34 = 28.9 % per year.
b). In risky portfolio there are 3 stocks with assigned weightage. Now considering the T-bills proportion the weightage of stocks in Client's portfolio are. T-bills investment is 15%.
c). For reward-to-volatility ratio we consider the return to standard deviation ratios for both.
The ratio is higher for Client's overall portfolio as risk is reduced more than returns due to T-bill inclusion.
Stocks Investment in client's portfolio A 32%*0.85 = 27.20% B 36%*0.85 = 30.6% C 32%*0.85 = 27.20%