CFA Level I · CFA Level I Exam · Curve-Based and Empirical Fixed-Income Risk Measures
A bond has a modified duration of 6.00 and a convexity of 50.0. If its yield to maturity falls by 100 bps, the percentage price change is closest to:
The price change is about +6.25%. The duration effect contributes 6.00% (6.00 × 1%), and the convexity adjustment adds 0.5 × 50 × (0.01)² = 0.25%. Duration alone understates the price gain when yields fall.
- A+6.25%Correct
- B+6.50%
- C+6.75%
Explanation
Percent change ≈ -ModDur×Δy + 0.5×Convexity×(Δy)². With Δy = -0.01: +6.00% + 0.5×50×0.0001 = +6.00% + 0.25% = +6.25%. Using duration alone gives 6.00%, which understates the gain.
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