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FRM Part II · FRM Exam Part II · Risk Management for Changing Interest Rates: Asset-Liability Management and Duration Techniques

A bond has modified duration of 6.0 and convexity of 50. Yields rise by 100 bp. Using duration and convexity, the approximate percentage price change is closest to:

The approximate price change is -5.75%. Duration alone gives -6.00% (6.0 times 1%), and the convexity adjustment adds back +0.25% (0.5 times 50 times 0.0001). Convexity reduces the loss from a yield rise, so the duration-only estimate is too pessimistic.

  1. A-6.00%
  2. B-5.75%Correct
  3. C-5.50%
  4. D-6.25%

Explanation

Change = -D*dy + 0.5*C*dy^2 = -6.0*0.01 + 0.5*50*0.0001 = -0.06 + 0.0025 = -5.75%. Ignoring convexity gives -6.00%, which overstates the loss. Subtracting the convexity term gives -6.25%, a sign error.

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