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

A bond trades at a price of 105 with a modified duration of 7 and a convexity of 60. If its yield falls by 100 basis points, what is the approximate price change using both duration and convexity?

The price rises by about 7.67. The duration effect is 7% and the convexity adjustment is 0.5 × 60 × 0.0001 = 0.3%, giving 7.3% of 105. Duration alone gives 7.35, and convexity adds to the gain when yields fall.

  1. A+7.04
  2. B+7.35
  3. C+7.67Correct
  4. D+7.98

Explanation

ΔP/P ≈ -D×Δy + 0.5×C×Δy² = 0.07 + 0.5×60×0.0001 = 0.07 + 0.003 = 0.073. Multiplying by 105 gives +7.665, about +7.67. Option B uses duration only. Option A subtracts the convexity term. Option D omits the factor of one half.

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