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FRM Part I · FRM Exam Part I · Applying Duration, Convexity, and DV01

A portfolio manager uses only modified duration to estimate the price change of an option-free, fixed-coupon bond after a large parallel fall in yields. Compared with the bond's actual price change, the duration-only estimate will most likely:

The duration-only estimate understates the price increase. The price-yield curve of an option-free bond is convex, so the straight-line duration approximation lies below it. For a large fall in yields, the actual gain is larger than duration predicts, and ignoring convexity creates this error.

  1. AOverstate the price increase because the price-yield relationship is concave
  2. BUnderstate the price increase because the price-yield relationship is convexCorrect
  3. CEqual the actual price increase because duration is exact for parallel shifts
  4. DUnderstate the price increase only if the bond is trading at a premium

Explanation

Duration is a linear approximation to a convex price-yield curve. The tangent line lies below the curve, so for a large yield fall the actual price gain exceeds the duration estimate. For a large yield rise the duration estimate overstates the loss. Duration is exact only for infinitesimal yield changes.

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