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 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 1 decimal places.)

c. What is the standard deviation of the rate of return on your client's portfolio? (Round your intermediate calculations and final answer to 1 decimal places.)

Answer 1

Rate of return on risky portfolio = 15% T- Bills rate = 5% Expected return from clients portfolio = 13% Let's say the client invested in the risky portfolio the 1-y would be the investment in Tbilis Y* 15 + 5*(1-Y) = 13 15Y+5 - 5Y = 13 10Y = 13-5 Y = =8/10 =0.8 So he choose to invest 80% in risky portfolio and 20% in Tbilis

b) Since he choose to invest 80% in risky asset so the proportion would be (%) T Bills 20.0 19.2 26.4 34.4 24*0.8 33*0.8 43*0.8 Stock B Stock C The risk would be only on the risky portfolio and T bills standard deviation w So the standard deviation of the risky portfolio is 40% and the client invested 80% of his asset in that So = 40%*0.8 32 %