pension fund manager is considering three mutual funds. The first is a stock fund, the second is a bond fund, and the third is a T-bill risk-free fund that yields a sure rate of 5%. Like any other rational investor, the fund manager likes higher expected return and lower risk. The probability distributions of the risky funds are:

Expected Return Standard Deviation Stock funds (S) 13% 18% Bond funds (B) 7% 9% The correlation between the stock and bond fund returns is -0.35

a) The fund manager has $1000 of cash available for investment. The fund manager can invest in the T- bill fund and only one of the other two funds (either stock or bond).

i. Which fund should she choose? ii. If she has to invest in the T-bill and the fund you answered in part (i) above, how should she invest the $1000 to generate an expected portfolio return of 20%? (remember, negative portfolio weight on an asset is possible!) iii. What is the portfolio standard deviation? (b) Now assume that the fund manager can invest in all three funds. She has $1000 of cash available for investment. The fund manager needs to generate a portfolio expected return of 10% while having as low a portfolio standard deviation as possible to achieve the desired expected return. iv. To achieve her objective, the fund manager will combine the risk-free T-bill fund with the two risky funds. As a first step, she will create the risky portfolio by combining the Stock and the Bond funds. In what proportion should she combine the two funds? (remember, there is one

Page 3 of 3 best combination) What is the expected return and the standard deviation of this risky portfolio? v. In the second step, she will combine the risky portfolio created above with the T-bill to achieve the 10% expected portfolio return. In what proportion should she combine the T-bill and the risky portfolio? What is the resulting dollar allocation to each of the three funds? vi. What is the portfolio standard deviation?