Question

An investor wants to form a two asset portfolio with proportion y of available funds invested in a risky portfolio with an expected return of 11% and a standard deviation of 15% and the remaining proportion (1 - y) of available funds invested in treasury bills with a return of 1%, so that the standard deviation of the complete portfolio will not exceed 10%.

a. What is the proportion y?

b. What is the expected return for the complete portfolio?

Correct answer is below. Please show how you get to the answer clearly for a great score. Thanks!

a: y = 0.667

b: E(rC) = 7.67%

Answer 1

Risky portfolio with weight y

Expected rate of return = 11%

Standard Deviation = 15%

T-Bill rate = 1%, weight (1-y)

Maximum portfolio's deviation required = 10%

a). So, proportion of risky portfolio y = 10/15 = 0.667

Proportion of risk free T-bill = 0.333

b). Expected return of the complete portfolio = 0.667*11 + .333*1 = 7.67%