Definition
Convexity captures the non-linear relationship between bond prices and yields that duration's linear approximation misses. Positive convexity is desirable: bond prices rise more for a rate decrease than they fall for an equal rate increase. Convexity is more important for larger yield changes and longer-duration portfolios.
functions Formula
ΔPrice ≈ −Duration × Δy + ½ × Convexity × (Δy)²
lightbulb Example
A bond has modified duration of 7 and convexity of 60. For a 1% rate increase: Price change ≈ -7% + ½×60×(0.01)² = -7% + 0.3% = -6.7%. Duration alone predicted -7%.
verified_user Key Points
- Captures non-linear price-yield relationship
- Positive convexity benefits bondholders
- More important for larger yield changes
- Callable bonds have negative convexity near call price