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

A bond has a modified duration of 7.5 and a convexity of 80. Its price is 100. Using both duration and convexity, what is the estimated percentage price change if yield rises by 100 basis points?

The estimated price change is -7.10%. Duration contributes -7.5 times 1%, or -7.5%, and convexity adds 0.5 times 80 times (0.01 squared), or +0.4%. Combined, the bond loses about 7.10%, less than the duration-only estimate.

  1. A-7.10%Correct
  2. B-7.50%
  3. C-7.90%
  4. D-8.30%

Explanation

Percentage change = -D*Δy + 0.5*C*Δy² = -7.5*0.01 + 0.5*80*0.0001 = -0.075 + 0.004 = -0.071, i.e. -7.10%. The option -7.90% subtracts the convexity term instead of adding it, and -7.50% ignores convexity.

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