Assume that you manage a risky portfolio with an expected rate of return of 16%
ID: 2738023 • Letter: A
Question
Assume that you manage a risky portfolio with an expected rate of return of 16% and a standard deviation of 32%. The T-bill rate is 6%. Stock A 28 % Stock B 34 % Stock C 38 %
Stock A @ 28%
Stock B @ 34%
Stock C @ 38%
A client prefers to invest in your portfolio a proportion (y) that maximizes the expected return on the overall portfolio subject to the constraint that the overall portfolio's standard deviation will not exceed 30%.
a. What is the investment proportion, y?
b. What is the expected rate of return on the overall portfolio?
Explanation / Answer
(a) Portfolio standard deviation = y x 32%. If your client wants a standard deviation of 30%, then
y = (30%/32%) = 0.9375= 93.75% in the risky portfolio.
(b) Mean return = 6% + (16% - 6%)y = 6% + 10% (0.9375) = 6% + 9.375% = 15.375 %.