Question 5. (12 Points) You are saving money and have determined that you want to have a total return
on your account of 13%. While you are willing to take some risk, you would like to minimize the risks
that you are taking. Your savings can be invested into three different funds: a risk-free US Treasury Fund,
a U.S. Stock Fund, and an International 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 11.00% 0.37
International Stock Fund 16.00% 0.45
The correlation between the U.S. Stock Fund and the International Stock Fund is 0.6.
(a) If you invest only in the US Stock Fund and the International Fund to achieve a rate of return on
13%, what percentage of your portfolio would you have in US Stock Fund? What will your
standard deviation of your portfolio be? What will be the Sharpe ratio of your portfolio?
(b) If instead you are able to invest in the all three funds (the risk free US Treasury fund, US Stock
fund, and the International Stock fund), what is the highest Sharpe ratio you can achieve? (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 International
Stock Fund in this optimal risky portfolio?
(c) Using your answer in part b, how much will you need to have invested in the risky assets (the
combination of U.S. Stock Fund and to the International Stock Fund you found in part b) and the
U.S. treasury fund to achieve your goal of a 13% rate of return with the lowest possible standard
deviation? What will be the standard deviation of your portfolio?
Question 5. (12 Points) You are saving money and have determined that you want to have a total return
on your account of 13%. While you are willing to take some risk, you would like to minimize the risks
that you are taking. Your savings can be invested into three different funds: a risk-free US Treasury Fund,
a U.S. Stock Fund, and an International 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 11.00% 0.37
International Stock Fund 16.00% 0.45
The correlation between the U.S. Stock Fund and the International Stock Fund is 0.6.
(a) If you invest only in the US Stock Fund and the International Fund to achieve a rate of return on
13%, what percentage of your portfolio would you have in US Stock Fund? What will your
standard deviation of your portfolio be? What will be the Sharpe ratio of your portfolio?
(b) If instead you are able to invest in the all three funds (the risk free US Treasury fund, US Stock
fund, and the International Stock fund), what is the highest Sharpe ratio you can achieve? (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 International
Stock Fund in this optimal risky portfolio?
(c) Using your answer in part b, how much will you need to have invested in the risky assets (the
combination of U.S. Stock Fund and to the International Stock Fund you found in part b) and the
U.S. treasury fund to achieve your goal of a 13% rate of return with the lowest possible standard
deviation? What will be the standard deviation of your 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 | % |
