Convexity

1. Broadly, convexity measures the curvature of the line representing the relationship between an instrument’s yield and its value. Duration and Modified duration can be used as the basis for straight line estimates of the rate of change of price/present value. Convexity is an estimate of the rate of change of duration. This is often visualised as the degree of 'curviness' of the line representing value versus yield. Convexity is calculated as: Sum [PV x t x (t+1)]/Sum(PV).
2. More 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.
3. More loosely, the terms Convexity and Modified convexity are often used interchangeably. Obviously this can lead to potential confusion, so it is important to clarify whether convexity or modified convexity is intended in any particular context.

See also

• Duration
• Modified convexity
• Modified duration