Can someone help me solve this question and please show all work

1. You are an advisor for a large pension fund. Real pension funds have liabilities (pensions) due at many dates in the future. For simplicity suppose that the pension fund you are advising has liabilities of $15 million coming due in 5 years and $25 million coming due in 15 years. Suppose that the yield curve is flat and all bonds have yields to maturity of 5% annually. (a) What is the modified duration of the liabilities of the fund? (b) Design an investment in a single zero coupon bond that shields the pension fund from small parallel shifts in the yield curve. Invest so that the pension fund is fully funded. (You are allowed to use a zero coupon bond that has a maturity that is not a whole number.) (c) Consider the asset position you constructed in part 1b. What are the Macaulay and modified durations of this position? What risk exposure is measured by the quantity "duration"? Does the fund face any of this risk? Why? (d) Suppose that the pension fund is instead underfunded." This means that the fund's assets do not cover the discounted value of the liabilities. In response, the managers of the pension fund would like to do some active management to increase returns. In particular they have no view on the direction of change in the Trea- sury yield curve but feel that corporate bonds are underpriced. In words only how might you design an active bond strategy to take advantage of the opportunities reflected in this view? 1. You are an advisor for a large pension fund. Real pension funds have liabilities (pensions) due at many dates in the future. For simplicity suppose that the pension fund you are advising has liabilities of $15 million coming due in 5 years and $25 million coming due in 15 years. Suppose that the yield curve is flat and all bonds have yields to maturity of 5% annually. (a) What is the modified duration of the liabilities of the fund? (b) Design an investment in a single zero coupon bond that shields the pension fund from small parallel shifts in the yield curve. Invest so that the pension fund is fully funded. (You are allowed to use a zero coupon bond that has a maturity that is not a whole number.) (c) Consider the asset position you constructed in part 1b. What are the Macaulay and modified durations of this position? What risk exposure is measured by the quantity "duration"? Does the fund face any of this risk? Why? (d) Suppose that the pension fund is instead underfunded." This means that the fund's assets do not cover the discounted value of the liabilities. In response, the managers of the pension fund would like to do some active management to increase returns. In particular they have no view on the direction of change in the Trea- sury yield curve but feel that corporate bonds are underpriced. In words only how might you design an active bond strategy to take advantage of the opportunities reflected in this view