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

A fund manages a $100 million bond portfolio with a modified duration of 7.0. The manager wants to reduce the portfolio duration to 3.0 using futures priced at $125,000 per contract, with a duration of 9.0 for the underlying bond. Which trade achieves the target?

Short about 356 contracts. To cut duration from 7 to 3 the manager needs a duration change of minus 4 on $100 million, divided by the futures value times duration of 1.125 million per contract. That gives roughly negative 355.6, so a short position of 356.

  1. AShort 356 contractsCorrect
  2. BShort 267 contracts
  3. CShort 622 contracts
  4. DLong 356 contracts

Explanation

N = (D* - D) x P / (F x Df) = (3 - 7) x 100,000,000 / (125,000 x 9) = -400,000,000 / 1,125,000 = -355.6, so short about 356. Short 267 uses the target duration of 3 instead of the change in duration. Short 622 uses the full duration of 7, which would take the duration to zero. Long 356 has the wrong sign.

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