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FRM Part I · FRM Exam Part I · Interest Rate Futures

A manager holds a $50,000,000 bond portfolio with modified duration 7.2 and wants to cut it to 3.0 using Treasury bond futures. Each contract has a price of $125,000 and the cheapest-to-deliver bond has a duration of 9.0. Using the duration-based hedge ratio, what position should be taken?

Short about 187 contracts. To lower duration from 7.2 to 3.0, the position is (3.0 − 7.2) × $50 million divided by ($125,000 × 9.0), which equals about −186.7. The negative sign means selling futures. Hedging to zero duration would need 320 contracts.

  1. AShort about 320 contracts
  2. BShort about 187 contractsCorrect
  3. CShort about 133 contracts
  4. DLong about 187 contracts

Explanation

N = (D_target − D_portfolio) × P / (F × D_F) = (3.0 − 7.2) × 50,000,000 / (125,000 × 9.0) = −210,000,000 / 1,125,000 = −186.7, so short about 187. Short 320 is the full hedge to zero duration. Short 133 uses the target duration alone (3.0 × 50m / 1.125m), which is the wrong calculation.

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