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CFA Level I · CFA Level I Exam · Yield-Based Bond Convexity and Portfolio Properties

A bond has a modified duration of 7.5 and a convexity of 60. If its yield-to-maturity falls by 100 bps, the estimated percentage price change using both duration and convexity is closest to:

The estimated price increase is about 7.80%. Duration contributes 7.50% and the convexity adjustment of one-half times 60 times 0.0001 adds 0.30%. The convexity term is always positive for an option-free bond, so it is added regardless of the direction of the yield change.

  1. A7.20%
  2. B7.50%
  3. C7.80%Correct

Explanation

Duration effect = -7.5 x (-0.01) = +7.50%. Convexity adjustment = 0.5 x 60 x (0.01)^2 = +0.30%. Total = 7.80%. Using duration alone gives 7.50%, and subtracting the convexity term gives 7.20%, which is the wrong sign.

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