Question

Assume that you manage a risky portfolio with an expected rate of return of 14% and a standard deviation of 38%. The T-bill rate is 5%. 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 22%
Stock B 31%
Stock C 47%
What are the investment proportions of your clientâs 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
Clientâs overall portfolio

Answer 1

Answer and Explanation:

The computation is shown below:

a. The expected return and standard deviation is as follow

Expected Return is

= 85% × 14% + 15% × 5%

= 12.65% per year

Now

Standard Deviation is

= 85% × 38%

= 32.3% per year

b.

The investment proportions are as follows

T bills = 15%

Amount invested Stock A is

= 85% × 22%

= 18.70%

Amount invested Stock B is

= 85% × 31%

= 26.35%

Amount invested Stock C is

= 85% × 47%

= 39.95%

c.

As we know that

Reward-to-variability Ratio = (Return of Risky Portfolio - Return of T-Bills) ÷ Standard Deviation of Risky Portfolio

= (14% - 5%) ÷ 38%

= 0.2368

Client’s Reward-to-variability Ratio = (Client Portfolio return - Return of T-Bills) ÷ Client Portfolio Standard Deviation

= (12.65% - 5%) ÷ 32.3%

= 0.2368