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

A trader holds a 10-year zero-coupon bond with face value $50,000,000. The yield is 5% with annual compounding. Which is closest to the DV01 of the position?

About $29,234. The position's market value is roughly $30.70 million and its modified duration is 10/1.05 = 9.52. Multiplying market value by modified duration and by 0.0001 gives the dollar change per basis point. Using Macaulay duration or face value would overstate it.

  1. A$29,234Correct
  2. B$30,696
  3. C$47,619
  4. D$50,000

Explanation

Price = 50,000,000 / 1.05^10 ≈ $30,695,650. Modified duration = 10 / 1.05 = 9.5238. DV01 = 30,695,650 × 9.5238 × 0.0001 ≈ $29,234. The $30,696 option uses Macaulay duration of 10 instead of modified duration. The $47,619 option applies modified duration to face value instead of market value, and $50,000 makes both errors.

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