Assume that you manage a risky portfolio with an expected rate of return of 14% and a standard deviation of 38%. The T-bill rate is 5%. 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.)
Expected return % per year Standard deviation % per year
b. Suppose your risky portfolio includes the following investments in the given proportions:
Stock A 22% Stock B 31% Stock C 47%
What are the investment proportions of your clientâs overall portfolio, including the position in T-bills? (Round your answers to 2 decimal places.)
Security Investment
Proportions T-Bills % Stock A % Stock B % Stock C %
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.)
Reward-to-Volatility Ratio Risky portfolio Clientâs overall portfolio
Assume that you manage a risky portfolio with an expected rate of return of 14% and a standard deviation of 38%. The T-bill rate is 5%. 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.)
| Expected return | % per year |
| Standard deviation | % per year |
b. Suppose your risky portfolio includes the following investments in the given proportions:
| Stock A | 22% |
| Stock B | 31% |
| Stock C | 47% |
What are the investment proportions of your clientâs overall portfolio, including the position in T-bills? (Round your answers to 2 decimal places.)
| Security | Investment Proportions | |
| T-Bills | % | |
| Stock A | % | |
| Stock B | % | |
| Stock C | % | |
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.)
| Reward-to-Volatility Ratio | |
| Risky portfolio | |
| Clientâs overall portfolio | |
Related questions
A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a rate of 4.8%. The probability distribution of the risky funds is as follows:
| Expected Return | Standard Deviation | |
| Stock fund (S) | 18% | 38% |
| Bond fund (B) | 9 | 32 |
The correlation between the fund returns is 0.14.
Solve numerically for the proportions of each asset and for the expected return and standard deviation of the optimal risky portfolio. (Do not round intermediate calculations and round your final answers to 2 decimal places. Omit the "%" sign in your response.)
| Portfolio invested in the stock | % |
| Portfolio invested in the bond | % |
| Expected return | % |
| Standard deviation | % |
A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a rate of 5.0%. The probability distribution of the risky funds is as follows:
| Expected Return | Standard Deviation | |
| Stock fund (S) | 11% | 40% |
| Bond fund (B) | 6 | 20 |
The correlation between the fund returns is 0.16.
Solve numerically for the proportions of each asset and for the expected return and standard deviation of the optimal risky portfolio. (Do not round intermediate calculations and round your final answers to 2 decimal places. Omit the "%" sign in your response.)
| Portfolio invested in the stock | % |
| Portfolio invested in the bond | % |
| Expected return | % |
| Standard deviation | % |
| Assume that you manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 29%. The T-bill rate is 8%. Your clientâs degree of risk aversion is A = 2.9, assuming a utility function U = E(r) - ½Aϲ. |
| a. | What proportion, y, of the total investment should be invested in your fund? (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "%" sign in your response.) |
| Investment proportion y | % |
| b. | What is the expected value and standard deviation of the rate of return on your clientâs optimized portfolio? (Do not round intermediate calculations. Round your answers to 2 decimal places. Omit the "%" sign in your response.) |
| Expected return | % | |
| Standard deviation | % | |
