A second-order sensitivity; it is a tool that measures of the sensitivity of a bond or portfolio’s duration to a change in its yield. It is the second derivative of the price/ yield relationship. A decrease in bond yield causes an increase in the bond’s convexity, and vice versa. A bond’s convexity is positively correlated to the dispersion (spectrum of distribution) of its cash flows: in general, a bond with cash flows that are more dispersed or spread out in time than another bond (that does not feature the same) will have a higher convexity, and vice versa.

Positive convexity is a situation in which the price increase that would be caused by a decrease in yield is greater than the price decrease that would be caused by a yield increase of an equal proportion. Negative convexity represents the opposite situation and does not appeal to bond investors.

For example, callable bonds have negative convexity in an environment of low interest rate.