CFA Level I · CFA Level I Exam · Yield-Based Bond Convexity and Portfolio Properties
A bond portfolio's effective duration is 7.0 and its convexity is 80. Yields fall by 100 bps in a parallel shift. Using the duration-plus-convexity approximation, the portfolio's percentage price change is closest to:
The portfolio price rises about 7.4%. The duration effect gives 7.0% for a 100 bp fall in yields, and the convexity adjustment adds 0.5 × 80 × 0.0001, or 0.4%. Using duration alone understates the gain.
- A+7.0%
- B+7.4%Correct
- C+7.8%
Explanation
Change = -7.0×(-0.01) + 0.5×80×(0.01)^2 = 7.0% + 0.4% = 7.4%. Duration alone gives 7.0%. Subtracting the convexity term or doubling it gives other values, which are wrong.
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