Question

4) Assume that you manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 43%. The T-bill rate is 4%. Your client chooses to invest 70% of a portfolio in your fund and 30% 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	27	%
Stock B	36
Stock C	37

What are the investment proportions of your client’s overall portfolio, including the position in T-bills? (Round your answers to 1 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

Answer 1

a. Expected return = weight in risky portfolio * return of risky portfolio + weight in T-Bill Market * return of T-Bill

Expected return = 0.70 * 0.17 + 0.30 * 0.04

Expected return = 13.10%

Standard Deviation = weight in risky portfolio * SD of risky portfolio

Standard Deviation = 0.70 * 0.43

Standard Deviation = 30.10%

b. Proportion of T-Bill = 30.0%

Proportion of Stock A = Weight of risky portfolio * Weight of Stock A = 70% * 27% = 18.9%

Proportion of Stock B = Weight of risky portfolio * Weight of Stock B = 70% * 36% = 25.2%

Proportion of Stock C = Weight of risky portfolio * Weight of Stock C = 70% * 37% = 25.9%

c. Reward to Volatility ratio

Risky Portfolio = (Expected return - Risk Free) / Standard Deviation = 17%-4%) / 43% = 0.3023

Client's Portfolio = (Expected return - Risk Free) / Standard Deviation = 13.10%-4%) / 30.10% = 0.3023