Assume that you manage a risky portfolio with an expected rate of return of 13%
ID: 1170531 • Letter: A
Question
Assume that you manage a risky portfolio with an expected rate of return of 13% and a standard deviation of 45%. The T-bill rate is 6%. Your client chooses to invest 75% of a portfolio in your fund and 25% 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 % per year _______
Standard deviation % per year _________
b. Suppose your risky portfolio includes the following investments in the given proportions:
Stock A 29%
Stock B 38%
Stock C 33%
What are the investment proportions of your client’s overall portfolio, including the position in T-bills? (Round your answers to 2 decimal places.)
Security Investment Proportions
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 portfolio ___________
Explanation / Answer
a Wp Weight of investment in portfolio 0.75 Wt Weight of investment in T bill 0.25 Rp Return of Portfolio in percentage 13 Rt Return of T- bill in percentage 6 R=Wp*Rp+Wt*Rt Expected return in percentage per year 11.25 Sp Standard Deviation of portfolio in percentage 45 St Standard Deviation of T-bill in percentage 0 V=(Wp^2)*(Sp^2)+(Wt^2)*(St^2) Variance 1139.063 S= Square Root of Variance Standard deviation percentage per year 33.75 Expected return in percentage per year 11.25 Standard deviation percentage per year 33.75 WEIGHT IN PORTFOLIO Wa Stock A 0.29 Wb Stock B 0.38 Wc Stock C 0.33 INVESTMENT PROPORTION OF OVERALL PORTFOLIO Wp*Wa Stock A 0.2175 Wp*Wb Stock B 0.285 Wp*Wc Stock C 0.2475 T-Bill 0.25 T- Bills % 25.00% Stock A% 21.75% Stock B% 28.50% Stock C% 24.75% Rp/Sp Reward to Volatility Ratio of Risky portfolio 0.288889 R/S Reward to Volatility Ratio of Client's overallportfolio 0.333333