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Assume that you manage a risky portfolio with an expected rate of return of 16% and a standard deviation of 32%. The T-bill rate is 6%. Your risky portfolio includes the following investments in the given proportions: Stock A 28 % Stock B 34 Stock C 38 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 15%. a. What is the proportion y

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Answer: 0.90 or 90%

Explanation:

The risky portfolio gives a return of 16% and the T-bill gives a 6% return.

Assume that proportion y is going into the risky portfolio and x is going into the T-bill.

The expected return for the overall portfolio = 15%

Use simultaneous equation:

x + y = 1

0.16y + 0.06x = 0.15

y = 1 - x

0.16 (1 - x) + 0.06x = 0.15

0.16 - 0.16x + 0.06x = 0.15

-0.1x = 0.15 - 0.16

x = -0.01/0.1

x = 10%

y = 1 - x

= 1 - 10%

= 90%

= 0.90

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