What bond convexity measures
Duration provides a linear approximation. Convexity captures the curvature.
Positive convexity means the bond gains more when rates fall than it loses when rates rise. Negative convexity means the opposite.
Bond Convexity Calculator
Calculate bond convexity from price observations under shifted yield scenarios, then estimate the second-order price adjustment beyond duration's linear approximation.
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Bond Analytics
Bond convexity explained: formula, calculation, and why it matters beyond duration
Bond convexity measures the curvature of the price–yield relationship beyond duration's linear approximation.
Convexity formula
Estimated from three price observations under parallel yield shifts.
Convexity = (P− + P+ − 2 × P₀) / (P₀ × (Δy)²)
P− = price when yield decreases, P+ when it increases, P₀ = current price, Δy = yield change as decimal.
Price Change ≈ −Duration × Δy + ½ × Convexity × (Δy)²
Combined duration-convexity approximation.
Positive vs negative convexity
Option-free bonds have positive convexity. Zero-coupon bonds have the highest.
Callable bonds can exhibit negative convexity near the call strike.
Worked example
Bond at 100, repriced at 102.50 (−50 bps) and 97.80 (+50 bps). Convexity = 0.30 / 0.000025 = 12,000.
Limitations
Requires pre-computed prices. Does not perform bond valuation.
Frequently asked questions
Duration alone underestimates gains when rates fall and overestimates losses when rates rise.
Generally yes, but bonds with higher convexity command a price premium.
Yes — callable bonds and MBS exhibit negative convexity near option strikes.
25–50 basis points is standard. CFA curriculum uses 50 bps.
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