Convexity
Measures the curvature of the price-yield relationship — how duration itself changes.
Convexity captures the smile curve in bond pricing: the price-yield relationship isn't a straight line (duration's assumption), it's curved. When yields rise, prices fall less than duration predicts; when yields fall, prices rise more than duration predicts. This asymmetry is valuable — convexity is a 'good' thing. Including convexity improves price estimates for larger yield moves: ΔP/P ≈ −Dur×Δy + 0.5×Conv×(Δy²). For example, with duration 6 and convexity 50, a 1% yield rise causes ~5.5% price drop (not 6%), while a 1% yield fall causes ~6.5% price gain (not 6%). Higher convexity means the bond exhibits less downside and more upside, all else equal.
Formula