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

Question

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

Quizplus · Accepted Answer

To calculate the number of T-bond futures contracts required to hedge the balance sheet, we need to use the duration matching approach.
The duration of the loans is 10 years, and the duration of the deposits is 3 years. Therefore, the duration gap is 7 years (10 - 3 = 7). This means that the bank is exposed to interest rate risk due to the difference between the duration of assets and liabilities.
To hedge this risk, the bank needs to buy T-bond futures contracts such that the duration of the deliverable bonds matches the duration gap. Here, the duration of the deliverable bonds is given as 9 years.
The formula to calculate the number of futures contracts required is:
Number of contracts = (Duration gap * Portfolio value) / (Duration of the deliverable bonds * Futures contract price)
Let's assume the portfolio value is $100 million. Then,
Number of contracts = (7 * 100,000,000) / (9 * 96) = 2,078
Therefore, the bank needs to buy 2,078 T-bond futures contracts to hedge the balance sheet. The answer is D) 2,078 contracts.

The Average Duration of the Loans Is 10 Years