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

A portfolio manager holds a bond portfolio worth $50 million with a modified duration of 6.0. She wants to hedge against a parallel rise in yields using a Treasury bond futures contract priced at $100,000 per contract, whose underlying has a modified duration of 8.0. Which position implements the duration-based hedge?

The hedge is to short 375 contracts. The number of contracts equals portfolio value times portfolio duration divided by futures price times futures duration, which is 300 million over 800,000. Futures are shorted because they gain when yields rise and bond prices fall.

  1. AShort 375 contractsCorrect
  2. BLong 375 contracts
  3. CShort 500 contracts
  4. DShort 667 contracts

Explanation

N = (P x Dp) / (F x Df) = (50,000,000 x 6.0) / (100,000 x 8.0) = 300,000,000 / 800,000 = 375. A rise in yields lowers bond prices, so the hedger must short futures, which gain when yields rise. Short 500 ignores the duration ratio (6/8), and short 667 inverts it.

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