Assume that you manage a risky portfolio with an expected rate of return of 18%
ID: 2773976 • 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:
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%.
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.)
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.)
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%
Explanation / Answer
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%.
Expected rate of Return of Overall Portfolio = Weight of risky portfolio*Expected Return of Risky Portfolio + (1-Weight of risky portfolio)*Risk free Rate
17 = y*18 + (1-y)*5.5
17 = 18y + 5.5 - 5.5 y
17-5.5 = 12.5 y
y =11.5/12.5
y = 0.92
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 = (1-0.92 ) = 8%
Stock A = 0.92*32% = 29.44%
Stock B = 0.92*36% = 33.12%
Stock C = 0.92*32% = 29.44%
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.)
Since Risk Free asset has zero standard deviation
Standard deviation = Proportion invested in risky portfolio*Standard Deviation of it
Standard deviation = 92%*34%
Standard deviation = 31.28%
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%.