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?