A bank with total assets of $271 million and equity of $31 million has a leverage adjusted duration gap of +0.21 years.Use the following quotation from the Wall Street Journal to construct an at-the-money futures option hedge of the bank's duration gap position.

$\text { TREASURY BULS (IMMM)-\$1 }$
$\text { million; 91-day (\$25.28 ea.) }$

$\begin{array}{ccc}
\text { Strike Price} & \text {Calls-Settle} & \text {Putesettle}\
96.00 & 28 \text { basis points } & 63 \text { basis points } \
96.25 & 19 \text { basis points } & 78 \text { basis points } \
96.50 & 12 \text { basis points } & 96 \text { basis points }
\end{array}$

If 91-day Treasury bill rates increase from 3.75 percent to 4.75 percent,what will be the profit/loss per contract on the bank's futures option hedge?

Question

A bank with total assets of $271 million and equity of $31 million has a leverage adjusted duration gap of +0.21 years.Use the following quotation from the Wall Street Journal to construct an at-the-money futures option hedge of the bank's duration gap position.

$\text { TREASURY BULS (IMMM)-\$1 }$
$\text { million; 91-day (\$25.28 ea.) }$

$\begin{array}{ccc}
 \text { Strike Price} & \text {Calls-Settle} & \text {Putesettle}\
96.00 & 28 \text { basis points } & 63 \text { basis points } \
96.25 & 19 \text { basis points } & 78 \text { basis points } \
96.50 & 12 \text { basis points } & 96 \text { basis points }
\end{array}$

If 91-day Treasury bill rates increase from 3.75 percent to 4.75 percent,what will be the profit/loss per contract on the bank's futures option hedge?

Quizplus · Accepted Answer

The bank has a positive duration gap, which means that its assets are more sensitive to interest rate changes than its liabilities. As a result, the bank is exposed to interest rate risk. To hedge this risk, the bank can use a futures option hedge.The bank can buy a put option on Treasury bills with a strike price of 96.25. This option will give the bank the right to sell Treasury bills at a price of 96.25, even if interest rates increase. If interest rates do increase, the value of the Treasury bills will decrease, and the bank will be able to exercise its put option and sell the Treasury bills at a profit.The profit on the put option will be equal to the difference between the strike price and the market price of the Treasury bills. If interest rates increase from 3.75 percent to 4.75 percent, the market price of the Treasury bills will decrease by 0.25 percent. This means that the bank will make a profit of $556.10 per put option contract.

A Bank with Total Assets of $271 Million and Equity TREASURY BULS (IMMM)-$1 \text { TREASURY BULS (IMMM)-\$1 } TREASURY BULS (IMMM)-$1

A Bank with Total Assets of $271 Million and Equity $\text { TREASURY BULS (IMMM)-\$1 }$