Consider the following balance sheet $($in millions$)$ for an FI: Assets: Duration $=12$ years $ $860$ Liabilities: Duration $=3$years $ $780$ Equity $80$

a$.$ What is the FI$$s duration gap? $($Do not round intermediate calculations. Round your answer to $2$ decimal places. $($e$.$g$.,32\mathrm{.}16))$

b$.$ What is the FI$$s interest rate risk exposure?

c$.$ How can the FI use futures and forward contracts to create a macrohedge?

d$.$ What is the impact on the FI$$s equity value if the relative change in interest rates is an increase of $1$ percent? That is$,\backslash$Delta R$/(1+$ R$)=0\mathrm{.}01.($Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Enter your answer in dollars not in millions.$)$

e$.$ Suppose that the FI in part $($c$)$ macrohedges using Treasury bond futures that are currently priced at $94$ What is the change in value per futures contract used to hedge if the relative change in all interest rates is an increase of $1$ percent? That is$,\backslash$Delta R$/(1+$ R$)=0\mathrm{.}01.$ Assume that the deliverable Treasury bond has a duration of eleven years. The bonds underlying the futures contract have a par value of $$100,000.($Negative amount should be indicated by a minus sign. Enter your answer in dollars not in millions.$)$

f$.$ If the FI wants to macrohedge, how many Treasury bond futures contracts does it need? $($Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Round down your answer to the nearest whole number.$)$