# Convexity

From ACT Wiki

Convexity measures the curvature of the profile representing the relationship between an instrument’s or a portfolio's yield and its value.

Convexity is normally calculated as:

Sum(PV x t x (t + 1) ) / Sum(PV).

Where:

PV = Present Value of individual cash flows.

t = timing of cash flows.

Strictly defined, convexity is the rate of change of duration, and modified convexity is the rate of change of modified duration, for small changes in yield from the given starting yield.

More loosely, the terms *Convexity* and *Modified convexity* are sometimes used interchangeably.

Obviously this can lead to confusion, so it is important to clarify whether convexity or modified convexity is intended.