6.31. A portfolio manager plans to use a Treasury bond futures contract to hedge a bon portfolio over the next 3 months. The porifolio is worth S100 million and will have duration of 4.0 years in 3 months. The futures price is 122, and each futures contract is o S100,000 of bonds. The bond that is expected to be cheapest to deliver wl have duration of 9.0 years at the maturity of the futures contract. What position in future contracts is required? (a) What adjustments to the hedge are necessary if after month the bond thati expected to be cheapest to deliver changes to one with a duration of 7 years? (b) Suppose that all rates increase over the next 3 months, but long-term rates increa less than short-term and medium-term rates. What is the effect of this on th performance of the hedgel