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

A fund holds a bond portfolio worth $60 million with a modified duration of 5.0. It wants to hedge fully against small parallel yield shifts using Treasury bond futures priced at $120,000 per contract, with a futures duration of 8.0. Which position, rounded to the nearest whole contract, implements the duration-based hedge?

The hedge is to short about 313 futures contracts. The hedge ratio equals portfolio value times portfolio duration divided by futures price times futures duration, which is 312.5. A short position gains when yields rise, offsetting the portfolio's loss.

  1. AShort 313 contractsCorrect
  2. BLong 313 contracts
  3. CShort 500 contracts
  4. DShort 195 contracts

Explanation

N = (P × D_P)/(F × D_F) = (60,000,000 × 5.0)/(120,000 × 8.0) = 300,000,000/960,000 = 312.5, so 313 contracts. The portfolio loses value when yields rise, so the hedger must short futures. Long 313 has the wrong sign. Short 500 ignores the duration ratio. Short 195 inverts the duration ratio.

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