You wish to use a Treasury bond futures contract to hedge a bond portfolio over the next 6 months. The portfolio is worth $100 million and has have a duration of 5 years. The futures price is 105, and each futures contract is on $100,000 of bonds. The bond that is expected to be cheapest is a 2.5% coupon 2-year bond. Coupons are paid semi-annually. The term structure of interest rates is currently flat at 2% per annum.

1. What is the price of the cheapest to deliver bond?
2. What is its duration?
3. What position in futures contracts is required to hedge your portfolio?