The Kromwell Community Bank's asset portfolio has an average duration of 6 years and its liability portfolio has an average duration of 2.5 years.The bank has $500 million in total assets and $450 million in liabilities.The Kromwell Community Bank is thinking about hedging its risk by using a Treasury Bond futures contract whose underlying's duration is 7.5 years and has a price of $98,000.How many futures contracts will it need to hedge its risk?

Question

Quizplus · Accepted Answer

First, we need to calculate the bank's net duration gap:

Net duration gap = (assets' dollar amount x assets' duration) - (liabilities' dollar amount x liabilities' duration)
Net duration gap = ($500 million x 6 years) - ($450 million x 2.5 years) = $3.75 billion

Next, we need to calculate the number of futures contracts needed to hedge the net duration gap:

Number of contracts = Net duration gap / (futures contract multiplier x Treasury Bond futures price)
Number of contracts = $3.75 billion / (1000 x $98,000) = 2,551 contracts

Therefore, the best choice is B, 2,551 contracts.

The Kromwell Community Bank's Asset Portfolio Has an Average Duration