Question

The average duration of the loans is 10 years. The average duration of the deposits is 3 years.
  

Consumer loans	$50 million	Deposits	$235 million
Commercial Loans	$200 million	Equity	$15 million
Total Assets	$250 million	Total Liabilities & Equity	$250 million

What is the number of T-bond futures contracts necessary to hedge the balance sheet if the duration of the deliverable bonds is 9 years and the current price of the futures contract is $96 per $100 face value?

		1,475 contracts.
		1,900 contracts.
		1,630 contracts.
		3,225 contracts.
		2,078 contracts.

Answer 1

Given that,

Duration of Loans = 10 years

Total loans = $250 million

Duration of deposits = 3 years

Total deposits = $235

Average duration = Duration of Loans*Total loans - Duration of deposits*Total deposits = 10*250 - 3*235 = 1795 million

To hedge its, 9 years future contracts of $96 price are available with contract size of 1000

So, Number of future contracts required = Average duration/(duration of future*price*contract size) = 1795000000/(9*96*1000) = 2078 contracts.

Option E is correct.