Convexity measures how a bond's duration itself changes as interest rates move — it refines the linear duration estimate to account for the fact that bond prices react to large rate moves in a curved, not straight-line, way.
Why It Matters
Duration alone understates gains on rate declines and overstates losses on rate increases for anything beyond a small rate move; convexity is the correction that makes large-scenario risk estimates usable for actual portfolio and hedging decisions, which is exactly why fixed-income risk teams never rely on duration by itself for stress scenarios.
How It Works in Practice
- 1Positive convexity (most option-free bonds) means price gains from falling rates exceed price losses from an equivalent rise in rates — a favorable asymmetry
- 2Negative convexity (callable bonds, mortgage-backed securities) means the opposite: upside is capped (bonds get called or prepaid) while downside isn't, a distinctly unfavorable asymmetry
- 3Convexity is added to the duration-based price estimate as a second-order correction, especially important for larger rate moves
- 4Long-duration, low-coupon bonds (like zero-coupon bonds) exhibit the highest positive convexity
Common Pitfalls
Ignoring negative convexity in mortgage-backed and callable bonds is a well-documented way portfolios have been surprised by losses that a duration-only model didn't predict
Convexity is a second-order effect — for small rate moves, duration alone is usually an adequate approximation, and adding convexity analysis everywhere can be more complexity than the decision requires