Question

You manage a risky portfolio with an expected rate of return of 22% and a standard deviation of 34%. The T-bill rate is 6%. Your risky portfolio includes the following investments in the given proportions: Stock A 31 % Stock B 36 % Stock C 33 % Suppose that your client decides to invest in your portfolio a proportion y of the total investment budget so that the overall portfolio will have an expected rate of return of 18%. a. What is the proportion y? (Round your answer to the nearest whole number.) b. What are your client’s investment proportions in your three stocks and the T-bill fund? (Do not round intermediate calculations. Round your answers to 2 decimal places.) c. What is the standard deviation of the rate of return on your client’s portfolio? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Answer and Explanation:

A.

E(r) = y x R(rp) + (1-y)*rf

0.18 = y * 0.22+(1-y)*0.06

0.18 = 0.22y +0.06 -0.06y

Collect like terms

0.18-0.06 = 0.22y - 0.06y

0.12 = 0.16y

y = 0.12/0.16

= 0.75

= 75%

B.

Stock a = 31% x 0.75

= 0.2325

= 23.25%

Stock b = 36% * 0.75

= 0.27%

Stock c = 33% * 0.75

= 0.2475

= 24.75%

A total of all these stocks gives 100 percent

C.

We have standard deviation = 34%

Y * standard deviation

= 0.75 * 0.34

= 0.255

= 25.5%