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

A portfolio manager holds a bond portfolio worth $10,000,000 with a modified duration of 6.0. She wants to fully hedge against small parallel yield changes using Treasury bond futures. Each contract has a contract value (futures price times size) of $100,000 and an underlying duration of 8.0. Which position minimizes the interest rate exposure?

The hedger should short 75 contracts. The hedge ratio equals portfolio value times portfolio duration divided by futures contract value times futures duration, which is 60,000,000 divided by 800,000. A bond portfolio loses when yields rise, so futures must be sold short to offset.

  1. AShort 75 contractsCorrect
  2. BLong 75 contracts
  3. CShort 100 contracts
  4. DShort 133 contracts

Explanation

The duration-based hedge ratio is N = (P x D_P)/(F x D_F) = (10,000,000 x 6.0)/(100,000 x 8.0) = 60,000,000/800,000 = 75. The portfolio loses value when yields rise, so the hedger must short futures. Short 133 inverts the duration ratio, and short 100 ignores duration differences.

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