A $200 million bond portfolio currently has a modified duration of 6.53. In anticipation of a decline in interest rates, the portfolio manager seeks to increase the modified duration of the portfolio to 9.5 by using a Treasury bond futures contract priced at 95,650. The futures contract has an implied modified duration of 12.65. The portfolio manager has estimated the yield beta of her portfolio to be 1 relative to the implied yield on the futures contract. You must show all your work in Excel to receive credit for any of the questions in this problem

1. Will she purchase or sell contracts?

2. How many contracts will be needed to change the duration of the portfolio as intended?

Without regard to your answer to (2), assume that the number of contracts needed is 550. Also assume, that the implied yield on the contract increased by .30%, your portfolio decreased in value by 3,929,754, and the futures contract decreased in value to 92,616.

3. What is the profit or loss on the futures contract?

4. What is the overall change in the value of the portfolio with the futures position?