Assume that you manage a risky portfolio with an expected rate of return of 17%
ID: 2738955 • Letter: A
Question
Assume that you manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 33%. The T-bill rate is 7%.
Your risky portfolio includes the following investments in the given proportions:
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 16%.
a. What is the proportion y? (Round your answer to 2 decimal places.)
Proportion y = ?
b. What are your client's investment proportions in your three stocks and the T-bill fund? (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? (Round your intermediate calculations and final answer to 2 decimal places.)
Standard deviation ? % per year
Stock A 30 % Stock B 35 % Stock C 35 %Explanation / Answer
Solution:
a. What is the proportion y? (Round your answer to 2 decimal places.) Mean return on portfolio = Rf+ (Rp- Rf)y Y = (15% - 7%)/10% y = .8 b. What are your client's investment proportions in your three stocks and the T-bill fund? (Round your intermediate calculations and final answers to 2 decimal places.) T-bills = 30% Stock A 0.3*0.7 = 0.210 21.0% Stock B 0.35*0.7 = 0.245 24.5% Stock C 0.35*0.7 = 0.245 24.5% c. What is the standard deviation of the rate of return on your client's portfolio? (Round your intermediate calculations and final answer to 2 decimal places.) Standard deviation ? % per year Expected return: (0.30 x 7%) + (0.7 x 17%) = 14% per year Standard deviation: 0.70 x 33% = 23.1% per year 0.210 21.0% 0.245 24.5% 0.245 24.5%