FRM Part I · FRM Exam Part I · Interest Rates
A bond portfolio has a modified duration of 8.0 and a convexity of 90. Using both duration and convexity, what is the approximate percentage price change if yields rise by 100 basis points?
The approximate price change is -7.55%. The duration term gives -8.00% for a 1% yield rise, and the positive convexity adjustment of 0.5 × 90 × 0.01² = 0.45% offsets part of the loss. Convexity always adds to the price change for a plain bond.
- A-7.55%Correct
- B-8.45%
- C-7.10%
- D-8.00%
Explanation
ΔP/P ≈ -D×Δy + 0.5×C×(Δy)² = -0.08 + 0.5×90×0.0001 = -0.08 + 0.0045 = -0.0755, or -7.55%. The -8.45% option subtracts the convexity term instead of adding it. The -7.10% option omits the factor 0.5, and -8.00% is the duration-only estimate.
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