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FRM Part I · FRM Exam Part I · Applying Duration, Convexity, and DV01

A portfolio has two positions: a long USD 20 million market value position with modified duration 4.0, and a short USD 12 million market value position with modified duration 7.5. Yields move in parallel. By how much does the portfolio value change if yields rise by 10 basis points, using DV01 approximations?

The portfolio gains USD 10,000. The long position has DV01 of USD 8,000 and the short position USD 9,000 in the opposite direction, so net exposure is short USD 1,000 per basis point. A 10bp rise in yields therefore produces a USD 10,000 gain.

  1. AGain of USD 10,000Correct
  2. BLoss of USD 10,000
  3. CGain of USD 17,000
  4. DLoss of USD 17,000

Explanation

Long DV01 = 20,000,000 × 4.0 × 0.0001 = USD 8,000. Short DV01 = 12,000,000 × 7.5 × 0.0001 = USD 9,000. Net DV01 = 8,000 − 9,000 = −1,000 (loses value when yields fall by 1bp, gains when rising). For +10bp: gain = 10 × 1,000 = USD 10,000. Adding the DV01s gives 17,000, ignoring the short sign.

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