Problem 1.7. A portfolio manager plans to use a Treasury bond futures contract to hedge a bond portfolio over the next four months. The portfolio is worth $23 million and will have a duration of 8.8 years in five months. The futures price is 127, 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 19 years at the maturity of the futures contract.

(a) What position in futures contracts is required? (b) Suppose that all rates decrease over the four months, but long-term rates decrease less than short-term and medium-term rates. What is the effect of this on the performance of the hedge?