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 4%. 

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 25%.

a. What is the investment proportion, y ? (Do not round Intermediate calculations. Round your answer to 2 decimal places.)

b. What is the expected rate of return on the overall portfolio? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Given for risky portfolio,

E(p) = 14%

SD(p) = 38%

rf = 4%

Max Standard deviation = 25%

a). So at standard deviation of 25%, investment in y = 0.25/0.38 = 0.6579 or 65.79%

So, y = 65.79%

and investment in risk free rate = 1-0.6579 = 0.3421 or 34.21%

b). Expected return of overall portfolio is weighted average return of its assets

So, Rate of return = 0.6579*14 + 0.3421*4 = 10.58%