Convexity
Definition
Convexity measures the curvature of a bond’s price–yield relationship. It adjusts the duration estimate so price changes are more accurate for larger yield moves.
Key Takeaways
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Plain vanilla (non-callable) bonds have positive convexity → prices fall less when yields rise and rise more when yields fall (vs duration-only).
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Callable bonds can show negative convexity when the call is likely.
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Use Duration + Convexity together for better price-change estimates.
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Higher convexity is usually valuable (all else equal).
Price change approximation (plain text)
%ΔPrice ≈ −(Modified Duration × ΔYield) + 0.5 × (Convexity × ΔYield²)
Nigeria Example (illustrative)
If a bond has Modified Duration = 5.0 and Convexity = 45, and yields rise by +1.00% (0.01):
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Duration effect ≈ −5.0 × 0.01 = −5.00%
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Convexity effect ≈ 0.5 × 45 × 0.01² = +0.225%
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Estimated total ≈ −4.78% (less severe drop than duration alone).
When it matters
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Bigger yield moves or long-duration bonds.
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Callable/structured bonds (watch for negative convexity).
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Risk reports and scenario testing.
Common Pitfalls
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Using duration alone for large rate shocks.
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Ignoring call risk (negative convexity) on callable bonds.
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Comparing convexity across bonds without aligning yield basis and frequency.
Mini-FAQ
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Is higher convexity always better? Generally yes for non-callables; for callables, rising convexity can flip negative near the call zone.
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Do I need convexity for small moves? Duration is often enough for small Δy; add convexity for bigger moves.
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Where do I get it? From your broker, term sheet analytics, or a calculator.
Related Terms
Duration · Callable Bond · Yield to Maturity (YTM) · Yield to Worst (YTW)
