Duration alone gives only a straight-line estimate of how a bond’s price moves with yield — convexity is the correction that captures the actual curve in that relationship.
How it works
The estimated percentage price change combines a linear duration effect (negative modified duration times the yield change) with a convexity correction (half the convexity times the yield change squared).
What this does not include
This does not include option-adjusted convexity for callable or mortgage-backed bonds, whose price-yield relationship can behave very differently (sometimes negative convexity) from the option-free bonds this simple formula assumes.
How to use this calculator
- Enter modified duration, convexity, and the expected yield change.
A worked example
A bond with modified duration 7, convexity 80, facing a 1% yield increase: price change = −6.6% — convexity adjusts the simple duration-only estimate (which alone would predict −7%) for the curvature in the price-yield relationship.
What the variables mean
| Variable | Meaning |
|---|---|
| Modified duration | The bond’s sensitivity to yield changes, in linear terms |
| Convexity | A second-order correction accounting for the actual curved relationship |
| Yield change | The assumed change in yield, as a percentage |
Edge cases worth knowing
Convexity makes bond price changes asymmetric — a bond typically gains more in price from a yield decrease than it loses from an equal yield increase, and this calculator’s convexity term captures that curvature that duration alone misses.
A negative modified duration has no standard meaning for typical bonds, so the calculator declines to show a result for that input.
Frequently asked questions
Why does convexity matter more for large yield changes?
The duration-only estimate is a straight-line approximation to a curve — the further the yield moves, the more that straight line diverges from the actual curved price-yield relationship, which convexity corrects for.
Is convexity always a benefit to bondholders?
For an option-free bond, yes — positive convexity means the bond gains more when yields fall than it loses when yields rise by the same amount, an advantage duration alone doesn’t capture.
How is convexity calculated in practice?
It’s typically derived from a bond’s full cash flow schedule discounted at different yields — this calculator takes convexity as a given input rather than deriving it from cash flows directly.
