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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 a modified duration of 7.0 and a convexity of 70. Yields rise by 2.0%. Using the duration-plus-convexity approximation, what is the estimated percentage price change?

The estimated price change is -12.6%. The duration effect is -7.0 × 2% = -14.0%, and the convexity adjustment is 0.5 × 70 × (0.02)² = +1.4%. Adding them gives -12.6%; convexity reduces the loss from a yield rise.

  1. A-13.3%Correct
  2. B-14.0%
  3. C-14.7%
  4. D-12.6%

Explanation

Duration term = -7.0 × 0.02 = -14.0%. Convexity term = 0.5 × 70 × 0.02² = 0.5 × 70 × 0.0004 = 0.014 = +1.4%. Total = -12.6%. So the correct value is -12.6%, and -14.0% omits convexity while -14.7% subtracts the convexity term in error.

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