A portfolio manager plans to use a Treasury bond futures contract to hedge a bond portfolio over the next three months. The portfolio is worth $100 million and will have a duration of 4.0 years in three months. The futures price is 122, and each futures contract is on $100,000 of bonds. The bond that is expected to be the cheapest to deliver will have a duration of 9.0 years at the maturity of the futures contract. (20 pts)

a)The manager should take a____ position in the T-bond future.

b)The number of contracts the manager needs to take is ____

c)Case 1: What adjustments to the hedge are necessary if after one month the bond that is expected to be cheapest to deliver changes to one with a duration of 7 years, assuming the futures price, portfolio value, and portfolio duration remain the same? The manager needs to ____ (long/short) ____ number of contracts

d)Case 2: What adjustments to the hedge are necessary if after one month the bond that is expected to be cheapest to deliver changes to one with a duration of 11 years, assuming the futures price, portfolio value, and portfolio duration remain the same? The manager needs to ____ (long/short) ____ number of contracts