Question

Assume that you manage a risky portfolio with an expected rate of return of 15% and a standard deviation of 40%. The T-bill rate is 5%.

Your risky portfolio includes the following investments in the given proportions:

Stock A	24	%
Stock B	33	%
Stock C	43	%

Your client decides to invest in your risky portfolio a proportion (y) of his total investment budget with the remainder in a T-bill money market fund so that his overall portfolio will have an expected rate of return of 13%.

a. What is the proportion y? (Round your answer to 2 decimal places.)

Proportion y            

b. What are your client's investment proportions in your three stocks and the T-bill fund? (Round your intermediate calculations and final answers to 2 decimal places.)

Security	Investment   Proportions
T-Bills		%
Stock A		%
Stock B		%
Stock C		%

c. What is the standard deviation of the rate of return on your client's portfolio? (Round your intermediate calculations and final answer to 2 decimal places.)

Standard deviation             % per year

Answer 1

a) Expected return is given by mathematical relation:

If y proportion is invested in risky fund, amount invested in T-bill would be 1-y

0.13 = 0.15y + 0.05(1-y)

0.13 = 0.15y + 0.05 - 0.05y

0.08 = 0.1y

y = 80%

b) Proportion of investment

20% of portfolio in T-Bills and 80% in risky portfolio.

So, proportion of T-bills = 20%

Proportion of stock A = 80% * 24% = 12.88%

Proportion of stock B = 80% * 33% = 17.92%

Proportion of stock C = 80% * 43% = 25.20%

c. Standard deviation for client portfolio

Expected standard deviation is given by mathematical relation:

But, Standard deviation of a T-bill is zero. So standard deviation of portfolio is, using the formula above is:

SD = 80% * 40% = 32%