Bond Convexity Calculator
Measure a bond’s convexity and see how it sharpens the duration-only estimate of price change for a given yield move.
How it works
Convexity = Σ [CFₜ × t(t+1) ÷ (1+y)ᵗ] ÷ [price × (1+y)²] · %ΔPrice ≈ −modified duration × Δy + ½ × convexity × Δy²
Convexity measures the curvature of a bond’s price-yield relationship — the reason duration alone under- or over-states price changes for larger yield moves. Because the true curve bends toward the investor, adding the convexity term always improves the estimate: it softens the loss when yields rise and boosts the gain when they fall. Higher convexity is generally desirable, as it provides a better payoff profile for the same duration.
Worked example
A 5-year, 5% bond at par has a convexity near 24 and a modified duration of about 4.33. For a +1% yield move, duration predicts −4.33%, and the convexity term adds ½ × 24 × 0.01² ≈ +0.12%, giving roughly −4.21% — closer to the true price change.
Sources: Bond convexity (Wikipedia)
Frequently asked questions
Why does convexity always help the bondholder?
The price-yield curve is convex, so actual prices are higher than the straight-line duration estimate at both ends. That means smaller losses than predicted when yields rise and larger gains when they fall — a favourable asymmetry.
When does convexity matter most?
For large yield swings and for long-maturity or low-coupon bonds, where the price-yield curve bends the most. For tiny changes, duration alone is already accurate and the convexity term is negligible.
What units is convexity in?
It is a pure number used inside the ½ × convexity × Δy² term, where Δy is in decimal form. Larger convexity values mean a more curved, more favourable price response.
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Educational estimate, not investment advice. Options and leveraged positions carry substantial risk.