Suppose a bank has an asset duration of 5 years and a liability duration of 2.5 years. This bank has $1,000 million in assets and $750 million in liabilities. They plan on hedging with a Treasury bond futures contract which has an underlying 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?

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The correct answer is A.The bank needs to hedge its interest rate risk by matching the duration of its assets and liabilities. The bank has $1,000 million in assets with a duration of 5 years and $750 million in liabilities with a duration of 2.5 years. The bank plans on hedging with a Treasury bond futures contract which has an underlying duration of 8.5 years and which is selling right now for $99,000 for a $100,000 contract.To calculate the number of futures contracts needed, we can use the following formula:Number of contracts = (Asset duration * Asset value - Liability duration * Liability value) / (Futures contract duration * Futures contract value)Plugging in the values, we get:Number of contracts = (5 years * $1,000 million - 2.5 years * $750 million) / (8.5 years * $99,000)Number of contracts = $2,500 million / $841,500Number of contracts = 3,714 contractsTherefore, the bank needs to purchase 3,714 futures contracts to fully hedge itself against interest rate risk.

Suppose a Bank Has an Asset Duration of 5 Years