Assume that you manage a risky portfolio with an expected rate of return of 18%
ID: 2640113 • Letter: A
Question
Assume that you manage a risky portfolio with an expected rate of return of 18% and a standard deviation of 34%. The T-bill rate is 5.5%. Your risky portfolio includes the following investments in the given proportions: Stock A 32 % Stock B 36 % Stock C 32 % 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 17%. 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.) Security Investment Proportions T-Bills % Stock A % Stock B % Stock C % 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
Explanation / Answer
Assume that you manage a risky portfolio with an expected rate of return of 18% and a standard deviation of 34%. The T-bill rate is 5.5%. Your risky portfolio includes the following investments in the given proportions: Stock A 32 % Stock B 36 % Stock C 32 % 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 17%.
a. What is the proportion y? (Round your answer to 2 decimal places.)
overall portfolio will have an expected rate of return = expected rate of return of risky portfolio * Proportion y + expected rate of return of risk free * (1-Proportion y )
17 = 18* Proportion y + 5.5*(1- Proportion y)
17 = 18 Proportion y + 5.5 - 5.5 Proportion y
Proportion y =( 17-5.5)/(18-5.5)
Proportion y = 0.92 or 92%
Answer
Proportion y = 0.92 or 92 %
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.)
Security Investment Proportions T-Bills = 1- 0.92 = 0.08 = 8%
Stock A = 32% * 92 = 29.44%
Stock B = 36% * 92 = 33.12%
Stock C = 32% * 92 = 29.44%
Answer
Security Investment Proportions T-Bills 8 %
Stock A 29.44%
Stock B 33.12%
Stock C 29.44%
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 of the rate of return on your client's portfolio = standard deviation of risky portfolio * Proportion y + standard deviation of risk free * (1-Proportion y )
standard deviation of the rate of return on your client's portfolio = 34*92% + 0*8%
standard deviation of the rate of return on your client's portfolio = 31.28%
Answer
Standard deviation 31.28 % per year