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

A bond trades at 100 with modified duration of 7.5 and convexity of 70. Yields rise by 100 basis points in a parallel shift. Using the duration-plus-convexity approximation, what is the estimated percentage price change?

The estimated price change is -7.15%. Duration alone gives -7.5% (7.5 × 1%), and the convexity adjustment adds back 0.5 × 70 × (0.01)² = 0.35%. Convexity always raises the value relative to the linear estimate, so the loss is smaller than the duration-only figure.

  1. A-7.50%
  2. B-7.85%
  3. C-7.15%Correct
  4. D-6.80%

Explanation

Duration effect = -7.5 × 0.01 = -7.50%. Convexity effect = 0.5 × 70 × 0.01² = +0.35%. Total = -7.15%. Subtracting the convexity term gives -7.85%, and omitting the 0.5 factor gives -6.80%.

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