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

A bank manager uses modified duration to estimate the price change of a long-dated bond portfolio after a very large, sudden rise in yields. Compared with the actual price change, the duration-only estimate will most likely:

The duration-only estimate overstates the price decline. Duration is a linear approximation, but the price-yield relationship of a standard bond is convex, so for a large yield increase the actual price falls less than the linear estimate predicts.

  1. AUnderstate the price decline because the price-yield relationship is convex
  2. BOverstate the price decline because the price-yield relationship is convexCorrect
  3. CBe exact, because duration is a first-order measure that captures the full change
  4. DBe exact only if the yield curve is upward sloping

Explanation

Duration is a linear approximation of a convex price-yield curve. For a large yield rise, the actual price falls by less than the linear estimate, so duration overstates the decline. Option A has the direction reversed for a yield increase.

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