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

A $80 million portfolio has a modified duration of 5.25. The hedger uses a DV01-based hedge with futures whose DV01 is $70 per basis point per contract, and shorts the number of contracts that matches the portfolio DV01. Later, the portfolio's yields rise by 10 bp while the yield implied by the futures rises only 8 bp. What is the approximate net P&L of the combined position?

The net result is a loss of about $84,000. The portfolio loses $420,000 on a 10 bp rise, while 600 short futures gain only $336,000 on an 8 bp rise. The shortfall arises because the yield shifts were not parallel, which is basis or yield-beta risk.

  1. ALoss of $84,000Correct
  2. BGain of $84,000
  3. CLoss of $420,000
  4. DGain of $336,000 only

Explanation

Portfolio DV01 = 80,000,000 × 5.25 × 0.0001 = $42,000, so the hedge is 42,000/70 = 600 short contracts. Portfolio loss = 42,000 × 10 = $420,000. Futures gain = 600 × 70 × 8 = $336,000. Net = −$84,000. The −$420,000 option ignores the hedge. The $336,000 option counts only the futures leg. The gain of $84,000 has the wrong sign.

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