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FRM Part I · FRM Exam Part I · Interest Rates

For a plain-vanilla option-free bond, the yield falls by 100 basis points. How does the price increase estimated by modified duration alone compare with the actual price increase?

Duration alone understates the actual price increase. Positive convexity means the true price-yield curve lies above the linear duration approximation, so a yield fall produces a larger gain than duration predicts. Adding the convexity term corrects this shortfall.

  1. AIt understates the actual increase because of positive convexityCorrect
  2. BIt overstates the actual increase because of positive convexity
  3. CIt equals the actual increase for any size of yield change
  4. DIt understates the actual increase only if the bond is callable

Explanation

The price-yield curve of an option-free bond is convex, lying above its tangent line (the duration estimate) on both sides. When yields fall, the actual price gain is therefore larger than the duration estimate. The overstating option describes what happens when yields rise and the estimate of the loss is too large. The callable case involves negative convexity, which works differently.

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