Question 3. (10 Points) You have just graduated from Champlain College and have started a job which
offers to match your contributions into your retirement account up to 6% of your annual salary. You have
decided you want to deposit 6% of your salary each year into your retirement savings account. Your
retirement savings can be invested into three different funds: a risk-free US Treasury Fund, a U.S. Stock
Fund, and an Emerging Markets Stock Fund. The information regarding the three funds is below.
Investment Expected Return Standard Deviation
of Return
U.S. Treasury Fund 3.00% 0.00
U.S. Stock Fund 9.00% 0.25
Emerging Markets Stock Fund 15.00% 0.40
The correlation between the U.S. Stock Fund and the Emerging Markets Stock Fund is 0.51.
(a) If you invest 40% of your money in the U.S. Treasury Fund and 60% in the U.S. Stock Fund,
what will be the expected return on your portfolio? What will be the standard deviation of your
portfolio? What is the Sharpe Ratio of this portfolio?
(b) Rather than only investing in the U.S. market, you would like to invest in the Emerging Markets
Stock Fund as well. What is the highest Sharpe ratio you can achieve using both the U.S. Stock
Fund and the Emerging Markets Stock Fund in your portfolio? (Hint: Use solver in Excel and do
not allocate any money to the U.S. Treasury Fund) How much money, in percentage of the total
portfolio, is allocated to the U.S. Stock Fund and to the Emerging Markets Stock Fund in this
optimal risky portfolio?
Question 3. (10 Points) You have just graduated from Champlain College and have started a job which
offers to match your contributions into your retirement account up to 6% of your annual salary. You have
decided you want to deposit 6% of your salary each year into your retirement savings account. Your
retirement savings can be invested into three different funds: a risk-free US Treasury Fund, a U.S. Stock
Fund, and an Emerging Markets Stock Fund. The information regarding the three funds is below.
Investment Expected Return Standard Deviation
of Return
U.S. Treasury Fund 3.00% 0.00
U.S. Stock Fund 9.00% 0.25
Emerging Markets Stock Fund 15.00% 0.40
The correlation between the U.S. Stock Fund and the Emerging Markets Stock Fund is 0.51.
(a) If you invest 40% of your money in the U.S. Treasury Fund and 60% in the U.S. Stock Fund,
what will be the expected return on your portfolio? What will be the standard deviation of your
portfolio? What is the Sharpe Ratio of this portfolio?
(b) Rather than only investing in the U.S. market, you would like to invest in the Emerging Markets
Stock Fund as well. What is the highest Sharpe ratio you can achieve using both the U.S. Stock
Fund and the Emerging Markets Stock Fund in your portfolio? (Hint: Use solver in Excel and do
not allocate any money to the U.S. Treasury Fund) How much money, in percentage of the total
portfolio, is allocated to the U.S. Stock Fund and to the Emerging Markets Stock Fund in this
optimal risky 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 sure rate of 5.8%. The probability distributions of the risky funds are: |
| Expected Return | Standard Deviation | |||
| Stock fund (S) | 19 | % | 48 | % |
| Bond fund (B) | 9 | % | 42 | % |
| The correlation between the fund returns is .0762. |
| Suppose now that your portfolio must yield an expected return of 17% and be efficient, that is, on the best feasible CAL. |
| a. | What is the standard deviation of your portfolio? (Do not round intermediate calculations. Round your answer to 2 decimal places.) |
| Standard deviation | % |
| b-1. | What is the proportion invested in the T-bill fund? (Do not round intermediate calculations. Round your answer to 2 decimal places.) |
| Proportion invested in the T-bill fund | % |
| b-2. | What is the proportion invested in each of the two risky funds? (Do not round intermediate calculations. Round your answers to 2 decimal places.) |
| Proportion Invested | |
| Stocks | % |
| Bonds | % |
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