Problem 1.

Suppose that you have decided to fund a three-year liability with a portfolio consisting of positions in a two- year zero-coupon bond (2YR) and a four-year zero-coupon bond (4YR). The current interest rate level is 10%.

1. a) Compute the price of both bonds.

2. b) Since our liability is a three-year liability, we want to immunize our portfolio by duration matching.

   Set up the portfolio, describing how many dollars you have to invest into each bond.

3. c) Immediately after you make your initial purchases, rates fall to 8%. If you do not rebalance your

   portfolio, what is your realized yield after three years?

4. d) What is the duration of the portfolio after the drop in interest rates without rebalancing?

5. e) How would you have to rebalance your portfolio?