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CFA Level I · CFA Level I Exam · Interest Rate Risk and Return

A bond has a modified duration of 8.00 and a convexity of 90.0. If its yield rises by 50 bps, the estimated percentage price change using duration and convexity is closest to:

The estimated change is about -3.89%. Duration alone gives -4.00% (8 × 0.5%), while convexity adds back 0.5 × 90 × 0.000025 = 0.1125%. Convexity reduces the loss from a yield rise, so the net decline is smaller than duration implies.

  1. A-3.89%Correct
  2. B-3.78%
  3. C-4.00%

Explanation

Duration effect = -8 × 0.005 = -4.00%. Convexity effect = 0.5 × 90 × (0.005)^2 = 0.5 × 90 × 0.000025 = 0.1125%. Total = -4.00% + 0.1125% = -3.89%. The duration-only estimate of -4.00% overstates the loss.

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