Convexity measures the curvature in the relationship between bond prices and interest rates. Since duration assumes a linear price-yield relationship, convexity corrects for the actual curved (convex) nature of this relationship.
Why convexity matters: - Duration underestimates the price increase when rates fall. - Duration overestimates the price decrease when rates rise. - Convexity adds a second-order correction that makes the estimate more accurate.
Price change formula with convexity: > ΔP/P ≈ −Duration × Δy + ½ × Convexity × (Δy)²
Positive vs. negative convexity:
| Bond Type | Convexity | Why | |---|---|---| | Typical bond | Positive | Price rises more than duration predicts when rates fall | | Callable bond | Negative (at low rates) | Call option caps price appreciation; price rises less when rates fall | | MBS (prepayable) | Negative | Prepayments accelerate when rates fall, shortening duration |
Two bonds with the same duration: The bond with higher convexity is more valuable — it outperforms in both falling and rising rate environments (less price drop when rates rise, more price gain when rates fall).
Investor preference: All else equal, investors prefer positive convexity and will accept a lower yield for it (negative convexity bonds trade at a higher yield to compensate).
> Exam tip: Convexity is a "good" property for bondholders. Callable bonds and MBS have negative convexity — prices don't rise as much when rates fall because of the call/prepayment risk. Know this for the Series 7 and CFP®.