A $300 million bond portfolio currently has a modified duration of 12.5. The port-

folio manager would like to reduce the modified duration of the bond portfolio to 8,

by using a futures contract priced at $105,250. The futures contract has an implied

modified duration of 9.25. The portfolio manager has estimated that the yield on

the bond portfolio is about 8% more volatile than the implied yield on the futures

contract. Should he enter a long or a short futures position? Calculate the number

of contracts needed to change the duration of the bond portfolio