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

A fund holds a $50,000,000 bond portfolio with a duration of 7.2. The manager wants to reduce the portfolio duration to 4.0 using interest rate futures. Each futures contract has a contract value of $125,000 and a duration of 6.4. What position achieves the target duration?

The manager should short 200 contracts. Moving duration from 7.2 to 4.0 requires a change of minus 3.2 on a $50 million portfolio, which is minus 160 million, divided by futures duration times value of 800,000. The negative result means a short position of 200.

  1. AShort 200 contractsCorrect
  2. BLong 200 contracts
  3. CShort 450 contracts
  4. DShort 313 contracts

Explanation

N = (D* - D)P/(D_F x F) = (4.0 - 7.2) x 50,000,000/(6.4 x 125,000) = -160,000,000/800,000 = -200, so short 200. Short 450 would be the full hedge to zero duration (7.2 used), which overshoots the target. Short 313 wrongly uses the target duration of 4.0 as the change in duration.

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