Question

Check Assume that you manage a risky portfolio with an expected rate of return of 15% and a standard deviation of 31%. The T-bill rate is 5% Your risky portfolio includes the following investments in the given proportions: 125 points Stock A Stock 8 Stock C Your client decides to invest in your risky portfolio a proportion 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 14%. Punt a. What is the proportion ? (Round your answer to 1 decimal places.) Proportion y References 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.) Investment Proportions Security T-Bills StockA Stocks Stock C

Answer 1

return portfolio = y x (retur n risky) + (1 - y) x (returnTbill)

14 = y x 15+ (1 - y) x 5

14 = 15y +5 — 5y

9 = 104

y = 0.9 or 90%

Therefore the proportion of risky portfolio is 90% and the proportion of T bill is 10%

Further portfolio proportion of the assets is as follows:

Asset	Original %	Portfolio %	Final %
Tbill	100.00%	10.00%	100% x 10% = 10.00%
Stock A	26.00%	90.00%	90% x 26% = 23.40%
Stock B	33.00%	90.00%	90% x 33% = 29.70%
Stock C	41.00%	90.00%	90% x 41% = 36.90%
		Total portfolio	10+23.40+29.70+36.90 = 100%

Standard deviation of the portfolio will be the weighted standard deviation of the risky portfolio as the Tbill has no standard deviation:

Portfolio standard deviation = 0.90 x 31 = 27.90%