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

The bank’s manager expects a 1 percent increase in interest rates from the current rates of 10 percent. Given such expectations, 1) what is the number of T-bond futures contracts necessary to hedge the balance sheet if the duration of the deliverable bonds tied to the futures contracts is 9 years and the current price of the futures contract is $96 per $100 face value?

Answer 1

Given information is:

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

The bank’s manager expects a 1 percent increase in interest rates from the current rates of 10 percent.

To determine:

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

Solution:

Step 1:

To calculate number of T bond future contracts, we have to find out first leverage adjusted duration gap of bank's portfolio which is equal to:

LADG = DA - DL K = 10 - (3*235/250) = 7.18 years

Step 2:

Number of T-bond future contracts = -((LADG) A)/ DF * PF

= -(7.18*250000000)/(9*0.96*100000)

= - 2077.5463 = 2077 contracts

Answer:

2077 T-bond futures contracts are necessary to hedge the balance sheet if the duration of the deliverable bonds tied to the futures contracts is 9 years and the current price of the futures contract is $96 per $100 face value