DURATION HEDGING WITH FUTURES
You are concerned about the liabilities of one of your subsidiaries in Pennsylvania. The subsidiary has an outstanding liability in terms of a bond with the face value of $24,000,000 and 3% annual coupon that matures in 3 years. The liability is fully guaranteed by you. You are assured that the subsidiary won't be able to honor the liability and, as a result, you look for a way to hedge your risk.
Assume that there are three zero coupon bonds available for hedging with respective maturities of 1, 2, and 3 years, and each of them has a face value of $1,000. How would you go about constructing a hedging portfolio for both duration and convexity in the term structure? More specifically, how many units of each bond do you need to trade in order to create the hedge?