a bank wishes to hedge its $30 million face value bond portfolio (currently priced at 99 percent of par). the bond portfolio has a duration of 9.75 years. it will hedge with t-bond futures ($100,000 face) priced at 98 percent of par. the duration of the t-bonds to be delivered is nine years. how many contracts are needed to hedge? should the contracts be bought or sold? ignore basis risk.
