Assume that you manage a risky portfolio with an expected rate of return of 18%

Question

Assume that you manage a risky portfolio with an expected rate of return of 18% and a standard deviation of 42%. The T-bill rate is 6%. Your client chooses to invest 85% of a portfolio in your fund and 15% in a T-bill money market fund.

a. What is the expected return and standard deviation of your client's portfolio? (Round your answers to 2 decimal places.)

b. Suppose your risky portfolio includes the following investments in the given proportions:

What are the investment proportions of your client’s overall portfolio, including the position in T-bills? (Round your answers to 2 decimal places.)

c. What is the reward-to-volatility ratio (S) of your risky portfolio and your client's overall portfolio? (Round your answers to 4 decimal places.)

Explanation / Answer

Expected return: (0.85 * 18%) + (0.15 * 6%)

Expected Return = 16.2% per year

Standard deviation:

Standard deviation = 0.85 * 42% = 35.7% per year

Part B:

Stock A = 26% * 0.85 = 22.10%

Stock B = 35% * 0.85 = 29.75%

Stock C = 39% * 0.85 = 33.15%

T-bill weight = 15%

Part C

Risky portfolio = (0.18 - 0.06)/ (0.357) = 0.336134

Overall portfolio = (0.162 - 0.06)/ (0.357) = 0.285714

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