Suppose a bank has an asset duration of 5 years and a liability duration of 2.5 years. This bank has $1000 million in assets and $750 million in liabilities. They are planning on trading in a Treasury bond future which has a duration of 8.5 years and which is selling right now for $99,000 for a $100,000 contract. How many futures contracts does this bank need to fully hedge itself against interest rate risk?

Question

Quizplus · Accepted Answer

The bank's net duration is 5 - 2.5 = 2.5 years. To fully hedge against interest rate risk, the bank needs to trade in futures contracts with a total duration of 2.5 years. The duration of each futures contract is 8.5 years, so the bank needs to trade in 2.5 / 8.5 = 0.2941 futures contracts. Since futures contracts are traded in multiples of $100,000, the bank needs to trade in 0.2941 * 100,000 = $29,410 worth of futures contracts. This is closest to choice A, 3714 contracts.

Suppose a Bank Has an Asset Duration of 5 Years