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: Stock A 24 % Stock B 32 Stock C 44 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%. a. What is the proportion y? (Round your answer to 1 decimal places.) b. What are your client's investment proportions in your three stocks and in T-bills? (Round your intermediate calculations and final answers to 2 decimal places.) c. What is the standard deviation of the rate of return on your client's portfolio?

Answer 1

Answer:

a. 87.5%

b. Stock A: 21%; Stock B: 28%; Stock C: 38.5%; T-bill: 12.5%

c. Standard deviation of the client's portfolio: 26.25%

Explanation:

a. y is calculated as:

Risky portfolio return * y +  T-bill return * (1 - y) = Expected return of the portfolio <=> 0.14y + 0.06 ( 1-y) = 0.13 <=> y = 87.5%

b. Client investment in each stock and in T-bills:

Client investment in each stock = 0.875 * percentage of each stock in a risky portfolio ( because the risky portfolio is accounted for 87.5% of the whole investment)

=> Stock A = 24% x 0.875 = 21% ; Stock B = 32% * 0.875 = 28% ; Stock C = 44 * 0.875 = 38.5%

Client investment in T-bill = 1- y = 1 - 0.875 = 12.5%

c. Standard deviation is calculated as: Standard deviation of risky portfolio * y = 30% * 87.5% = 26.25% (because standard deviation of return in T-bill is 0)