Convexity Calculator

Work out convexity instantly with clear inputs, formula shown and shareable results.

About Convexity Calculator

Convexity measures the curvature of the price-yield relationship, computed from the second moment of the discounted cash flows. Positive convexity means prices rise more than duration predicts when yields fall and fall less when they rise.

Formula

Convexity

C = Σ t(t+1)·PV(CFₜ) / [Price·(1+y)²]

Worked example

With the default values below, Convexity Calculator returns Convexity of 120.4415. Change any input above and every figure here is recalculated in your browser.

Inputs used

Annual Coupon Rateaccepts 0–100 %: 6 %
Yield To Maturityaccepts 0–100 %: 7 %
Years To Maturityaccepts 1–40: 15

Results

Convexity: 120.4415
Modified Duration: 9.3877 years
Convexity Adjustment For 1% Move: 0.6022%
Estimated Price Change For A 1% Rise: -8.7855%

Step by step

1Values used
2Convexity
3Convexity= 120.4415
4Modified Duration= 9.3877 years
5Convexity Adjustment For 1% Move= 0.6022
6Estimated Price Change For A 1% Rise= -8.7855

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax or fees or charges into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
Figures are estimates for planning only. Market returns are not guaranteed, and rates, limits and tax rules change. This is not financial or tax advice — speak to a qualified adviser before acting.
This is an estimate for general information and not professional financial, tax or legal advice. See the full disclaimer for the limits that apply to this kind of calculator.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Figures are estimates for planning only. Market returns are not guaranteed, and rates, limits and tax rules change. This is not financial or tax advice — speak to a qualified adviser before acting.

Frequently Asked Questions

Which bonds have the most convexity?

Long-dated, low-coupon bonds — their cash flows are furthest away and most sensitive to discounting.

Is convexity always desirable?

Positive convexity is. Mortgage-backed securities can show negative convexity because prepayments accelerate when rates fall.