An investor holds a bond portfolio with principal value $10,000,000 whose price and modified

duration are respectively 112 and 9.21. He wishes to be hedged against a rise in interest rates by

selling futures contracts written on a bond. Suppose the price of the cheapest-to-deliver issue is

105.2. The nominal amount of the futures contract is $100,000. The conversion factor for the

cheapest-to-deliver is equal to 0.981. The cheapest-to-deliver has a modified duration equal to 8.

Additionally, assume that if the yield of portfolio changes by 25 basis points, the yield of

cheapest-to-deliver issue changes by 70 basis points. What is the number of futures contracts

that the investor has to sell to hedge against a rise in interest rates?