An investor holds a bond portfolio with principal value $10,000,000 whose price and modied 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 futures price of the contract is 105.2. The contract size is $100,000. The conversion factor for the cheapest-to-deliver is equal to 98.1%. The cheapestto-deliver has a modied duration equal to 8.

1. Give a proof of the hedge ratio f as obtained in equation (11.4).

2. Determine the number of contracts f he has to sell.