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

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

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

The FI would be hurt by increasing

interest rates.

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

The Fl 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 $95.$ 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

bond