Suppose that you have an obligation to make payments of $5 million in five years and $5 million in ten years. The yield on a five-year zero coupon bond is 5% and the yield on a ten-year zero coupon bond is 7%.

1. What is the value of this obligation?

2. Suppose you want to hedge the obligation against level movements in yields with a two-year zero coupon bond. The yield on a two-year zero-coupon bond is 2%. How many dollars of the two-year zero-coupon bond do you need to buy? (You can use modified duration without convexity.)

3. Suppose that the yields on zero-coupon bonds change to:

y2 = 3%, y5 = 6%, y10 = 8%

How well did your hedge do? In particular, how much did the value of your portfolio change with this level shift in yields?