Question

Assume that you manage a risky portfolio with an expected rate of return of 15% and a standard deviation of 29%. The T-bill rate is 5%.

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

Stock A	22	%
Stock B	31
Stock C	47

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 12%.

a. What is the proportion y? (Round your answer to 1 decimal places.)

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

c. What is the standard deviation of the rate of return on your client's portfolio?

Answer 1

c. Calculation of Standard dviatuion of rate of return on Client's portfolio.

WE KNOW THAT

where p1 = proportion of investment in risky portfolio

p2 = proportion of investment in T-Bills

1= Standard deviation of Risky portfolio

2= Standard deviation of T-Bills.

r = Correlation coefficient between risky portfolio and T-Bills.

We know that Standard deviation of T-Bills (2) is Zero (0).

Given that p1 = proportion of investment in risky portfolio = 70%

   p2 = proportion of investment in T-Bills = 30%

   1= Standard deviation of Risky portfolio = 29%

On substituting given values in the above formula we get

SO STANDARD DEVIATION OF CLIENT"S PORTFOLIO = 20.30%.

Hope you understood the solution. If you have any doubt please leave your doubt in the comment section so that I can clarify your doubt.

Thank You.