Consider the following balance sheet $($in millions$)$ for an FI:

Assets

Duration $=14$

years

Liabilities

$$1,020$

Duration $=7$

years

Equity

$$960$

$60$

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

Duration gap

$7\mathrm{.}41$

years

b$.$ What is the Fl$\text{'}$s interest rate risk exposure?

The FI would be hurt by increasing

interest rates.

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

The FI could hedge its interest rate risk by futures or forward contracts.

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

Impact on the Fl$\text{'}$s equity value

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$,R.$ Assume that the deliverable Treasury bond has a duration of thirteen years. The bonds underlying the futures contract have a par value of $$100,000.($Negative amount should be indicated by a minus sign. Enter your answer in dollars not in millions.$)$

Change in value per futures contract

$

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.$)$

Number of Treasury

hnnd