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

A bond has a price of 100, a modified duration of 7.0 and a convexity of 60. Its yield rises by 100 basis points. Using the second-order (duration plus convexity) approximation, what is the estimated percentage change in price?

The estimated price change is -6.7%. Duration alone gives -7.0%, and the convexity adjustment of 0.5 times 60 times 0.0001, or +0.3%, is added because convexity is positive and reduces the loss from a yield rise.

  1. A-7.0%
  2. B-6.7%Correct
  3. C-7.3%
  4. D-6.4%

Explanation

Percentage change = -D*Δy + 0.5*C*(Δy)^2 = -7*0.01 + 0.5*60*0.0001 = -0.07 + 0.003 = -0.067, or -6.7%. The -7.0% option is the duration-only estimate. The -7.3% option subtracts the convexity term instead of adding it. The -6.4% option leaves out the 0.5 factor.

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