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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 portfolio worth 100 million has modified duration 6.0 and convexity 50. Yields rise by 100 bps in parallel. Using duration plus convexity, the estimated change in value is closest to:

The estimated change is about -5.75 million. Duration gives -6.0% and the convexity adjustment adds 0.5 times 50 times 0.0001, or 0.25%, producing -5.75% on 100 million. Ignoring convexity would give -6.00 million.

  1. A-6.00 million
  2. B-5.75 millionCorrect
  3. C-6.25 million
  4. D-5.50 million

Explanation

Percentage change = -6.0*0.01 + 0.5*50*(0.01)^2 = -0.06 + 0.0025 = -0.0575. On 100 million this is -5.75 million. Option A omits the convexity term; option C subtracts it instead of adding.

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