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	% per year
Standard deviation	% per year

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

Stock A	32%
Stock B	36%
Stock C	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.)

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

Solution:

a. The expected value for the client = (T-bill money x bill rate) + (invest x expected rate of return)

Mean = (0.15 x 4%) + (0.85 x 18%)

= 0.006 + 0.153

=0.159

The expected value on the client’s portfolio = 15.9% per year

Standard deviation= invest x Standard deviationStandard deviation

= 0.85 x 34% = 0.85 x 0.34

= 0.289

The standard deviation on the client’s portfolio =28.9% per year

b.  Since portfolio c is 85 percent invested in p, this means

.85 × .32 = 27.2% in Stock A,

.85 × .36 = 30.6% in Stock B,

.85 × .32 = 27.2% in Stock C.

The fraction invested in T-bills is 15%

c. The reward-to-variability ratio of your fund is given by

[E (rp) - rf]/σp

[18 - 4]/34 = 41.1765%

Your client’s portfolio offers the same reward-to-variability ratio, that is

[E (rc) - rf]/σc

[15.9 - 4]/28.9 = 41.1765%