A portfolio manager plans to use a Treasury bond futures contract to hedge a bond portfolio over the next six months. The portfolio is worth $50 million and will have a duration of 3.0 years in six months. The futures price is 112, and each futures contract is on $100,000 of bonds. The bond that is expected to be cheapest to deliver will have a duration of 7.0 years at the maturity of the futures contract.

What position in futures contracts is required?

Suppose that all rates fall over the six months, but long-term rates fall less than short-term rates, then?