Mr. Madoff is a portfolio manager who is responsible for a $350 million portion of the bond portfolio of Affluent.com’s pension fund. The current investment guidelines specify that the duration for the portfolio can be in a range of minus one and plus one of the duration benchmarks. Currently, the duration benchmark is 3.2 and the duration for the portfolio is 4.0. Mr. Madoff expects that rates will rise. He wants to reduce the duration of the portfolio to the lower end of the duration benchmark’s range, 3, by using Treasury bond futures contracts, which he is authorized to use by the pension fund’s investment guidelines. 

a. What position (long or short) should Mr. Madoff take in Treasury bond futures to reduce the duration from 5 to 3? 

b. Suppose that the dollar duration per Treasury bond futures contract (based on the cheapest-to-deliver issue) for a 25 basis point change in rates is $2,400. How many Treasury bond futures contracts must be bought or sold?