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.)

Expected return	% per year
Standard deviation	% per year

b. Suppose your risky portfolio includes the following investments in the given proportions:

Stock A	24%
Stock B	32%
Stock C	44%

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

Answer 1

a) Expected Return = W1 * R1 + W2 * R2

Expected return = (85% * 14%) + (15% * 6%) = 11.9% + 0.9% = 12.80%

Standard deviation of portfolio is calculated using the mathematical relation:

Correlation coefficienct between T- bond fund and any portfolio = 0. Also, standard deviation of T-bonds is 0.

Standard deviation = 25.5%

b) Proportion in client's portoflio, where 15% is for T-bill fund.

T-bills: 15%

Stock A: 85% of portolio * 24% = 20.40%

Stock B: 85% of portolio * 32% = 27.20%

Stock C: 85% of portolio * 44% = 37.40%

c) Rewards to Volatility ratio, also known as, Sharpe's ratio is mathematically written as:

Risk free rate = 6% (return on T-bills)

Risky portfolio = (14% - 6%)/30% = 0.27

Client portfolio = (12.80% - 6%)/25.5% = 0.27