Assume that you manage a risky portfolio with an expected rate of return of 14%
ID: 2651446 • Letter: A
Question
Assume that you manage a risky portfolio with an expected rate of return of 14% and a standard deviation of 30%. The T-bill rate is 6%.
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 13%.
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.)
References
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Assume that you manage a risky portfolio with an expected rate of return of 14% and a standard deviation of 30%. The T-bill rate is 6%.
Explanation / Answer
a. Proportion Y = y, then proportion of T-Bill = 1-y
13% = 14y + 6*(1-y) = 14y + 6 -6y
y = 0.875
Thus, Proportion Y = 0.875 or 87.5%
b. T-Bills = 100 - 87.5 = 12.5%
Stock A = 87.5 x 24% = 21%
Stock B = 87.5 x 32% = 28%
Stock C = 87.5 x 44% = 38.5%
c. Standard Deviation = 30 x 0.875 = 26.25%