CFA Level I · CFA Level I Exam · Curve-Based and Empirical Fixed-Income Risk Measures
A callable bond has an effective duration of 4.0 and an effective convexity of -60. If the benchmark yield curve shifts down in parallel by 100 bps, the estimated percentage price change is closest to:
The estimated price change is about +3.70%. The duration effect adds 4.00% for a 100 bps fall, and negative convexity subtracts 0.5 times 60 times 0.0001, or 0.30%, leaving 3.70%. Adding the convexity term instead would wrongly give 4.30%.
- A+3.40%
- B+3.70%Correct
- C+4.30%
Explanation
Change = -D x Δy + 0.5 x C x Δy^2 = -4.0 x (-0.01) + 0.5 x (-60) x 0.0001 = 0.04 - 0.003 = 0.037, i.e. +3.70%. Ignoring convexity gives 4.00%, and adding the convexity term gives +4.30%, which is a sign error.
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