What Duration and Convexity Measure
Duration measures the approximate percentage change in a bond’s price for a 1 percentage point change in interest rates, functioning as a linear, first-order estimate of interest rate sensitivity. A bond with a duration of 7 would be expected to fall roughly 7% in price if rates rise by 1 percentage point.
Convexity measures the curvature of the relationship between bond prices and interest rates — in other words, how much duration itself changes as rates move. Because the actual price-yield relationship is curved rather than a straight line, duration alone becomes less accurate for larger rate changes.
Why Convexity Improves the Estimate
Duration’s linear approximation error
Duration assumes a constant, linear relationship between price and yield changes, which works reasonably well for small rate moves but increasingly understates gains and overstates losses as the size of the rate change grows.
Adding the convexity adjustment
By adding a convexity term to the duration-based price change estimate, analysts can more accurately capture the actual curved price-yield relationship, especially useful for larger rate moves or bonds with embedded options.
Why Convexity Is a Desirable Trait
Because positive convexity means a bond’s price rises more than duration predicts when rates fall, and falls less than duration predicts when rates rise, investors generally prefer bonds with higher convexity for the same duration — it provides an asymmetric benefit that becomes more valuable in a volatile rate environment.
Duration vs. Convexity
| Aspect | Duration | Convexity |
|---|---|---|
| Measures | First-order (linear) price sensitivity | Second-order (curvature) sensitivity |
| Best for | Small rate changes | Refining estimates for larger rate changes |
| Investor preference | Lower for less rate risk | Higher is generally more desirable |
Frequently Asked Questions
Can two bonds have the same duration but different convexity?
Yes, and this is a key reason investors look at both metrics — a bond with higher convexity will perform better in both rising and falling rate scenarios compared to a lower-convexity bond with identical duration.
Do callable bonds have positive or negative convexity?
Callable bonds often exhibit negative convexity in certain price ranges because the issuer’s ability to call the bond limits price appreciation when rates fall, unlike a plain vanilla bond’s typical positive convexity.
Why does duration change as interest rates change?
As rates move, the present value weighting of a bond’s future cash flows shifts, which changes its effective duration — this changing sensitivity is precisely what convexity captures.
Is convexity more important for long-term or short-term bonds?
Convexity tends to be more significant for long-term bonds, since their prices are more sensitive to interest rate changes overall, making the curvature effect more pronounced.
Key Takeaways
Duration provides a linear approximation of how much a bond’s price will move for a given change in interest rates, while convexity corrects for the curvature in that relationship, especially important for larger rate moves. Together, the two metrics give a fuller picture of a bond’s interest rate risk than either alone. This article is for informational purposes only and does not constitute investment advice.
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