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Bond Convexity Calculator

Quick answer

ΔP ≈ −MD·Δy + ½·C·Δy²: with modified duration 4.21 and convexity 24.9, a +1% rate move prices −4.09%, not −4.21%.

  • Formula and worked example included.

Figures are estimates from this calculator’s standard formula — adjust the inputs in the tool below for your exact number.

How the Convexity Calculator Calculates Results

ΔP% ≈ −ModDur × Δy + ½ × Convexity × Δy²

Convexity measures the curvature of the bond price-yield relationship. It corrects duration's linear approximation, especially for large rate moves. The computation rests on ΔP% ≈ −ModDur × Δy + ½ × Convexity × Δy². A bond with modified duration 4.21 and convexity 24.9 facing a +1% yield move prices at −4.21% + 0.5 × 24.9 × 0.01² ≈ −4.09% — the convexity term claws back 0.12 points. Each input you type is substituted the instant you release the key, and the result is expressed in exactly the units or currency you chose.

  1. 1

    Step 1

    Start with the primary figures the Convexity Calculator asks for.

  2. 2

    Step 2

    Your values are substituted into ΔP% ≈ −ModDur × Δy + ½ × Convexity × Δy².

  3. 3

    Step 3

    Read off the computed result.

  4. 4

    Step 4

    Vary one input at a time to see its effect.

Use Cases

Large rate-shock pricing

Improving on duration for ±2%+ moves

Callable bond analysis

Detecting negative convexity zones

Portfolio construction

Barbells add convexity versus bullets

Risk reporting

Adding curvature to linear duration limits

Common Mistakes

  • Mixing signs

  • Stale convexity

  • Overkill for small moves

FAQs

Why is convexity valuable to investors?

Prices fall less and rise more than duration predicts: positive convexity is a free cushion that widens with rate swings.

When does convexity mislead?

Negative convexity: callable bonds and mortgage paper lose it as rates fall — refinancing caps the upside.

What is the math behind the Convexity Calculator?

The Convexity Calculator applies ΔP% ≈ −ModDur × Δy + ½ × Convexity × Δy², where the second term corrects duration's straight-line estimate.

Do I need an account or app?

No account and no app — the Convexity Calculator is a web tool that keeps working even on a slow connection.