PLEASE SHOW ALL WORK

5. Suppose a Bank of Texas (BoT) has an average asset duration of 4 years, an average liability duration of two years, total assets of $500 million, and liabilities of $450 million at a given point in time. Suppose, too, that the firm plans to trade in Treasury bond futures contracts. The T-bonds named in the futures contracts have a duration of 10 years, and the T-bonds' current price is S99,700 per $100,000 contract How many futures contracts does a BoT need to cover a given size risk exposure? What is the change in net worth of BoT, if interest rate increases from 2% to 5% As we notice that BoT have positive duration gap (indicating its assets have longer average maturity than its liabilities). What sort of hedging strategy should BoT adopt if interest rate declines? a. Required Futures contracts are 1103, Change in NW 550 millions, long hedge b. Required Futures contracts are 2005, Change in NW 700 millions , short hedge c. Required Futures contracts are 1000, Change in NW 905 millions , long hedge d. Required Futures contracts are 1553, Change in NW 100 millions , long hedge e Required Futures contracts are 1300, Change in NW 50 millions, short hedge