CFA Level I · CFA Level I Exam · Fixed-Income Bond Valuation: Prices and Yields
A bond has a price of 100.00, a modified duration of 7.20, and a convexity of 70. If its yield falls by 100 bps, the percentage price change using both duration and convexity is closest to:
The estimated price change is about +7.55%. Duration contributes +7.20% for the 100 bp decline, and the convexity adjustment adds 0.5 x 70 x 0.0001 = 0.35%. Using duration alone understates the gain, while doubling the convexity term overstates it.
- A+7.20%
- B+7.55%Correct
- C+7.90%
Explanation
Duration effect: -7.20 x (-0.01) = +7.20%. Convexity effect: 0.5 x 70 x (0.01)^2 = 0.00350 = +0.35%. Total is +7.55%. Duration alone gives 7.20%, and 7.90% wrongly doubles the convexity term.
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