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?