Understanding convexity

Convexity is a mathematical concept used to compare a bond’s upside price potential with its downside risk. A bond has positive convexity when the price increase resulting from a given decline in interest rates is greater than the price decrease that would result from an equivalent rise in rates. As a general rule, noncallable bonds have positive convexity, while many bonds that can be redeemed prior to maturity have negative convexity.

Why do we start with duration?

To understand convexity, we must first understand duration, which is a metric used to estimate how much the price of a bond will change in response to a change in its yield. Modified duration is a particular version of duration, which, when multiplied by the change in yield, approximates the expected percentage change in price.

However, using duration to estimate price changes assumes a linear relationship between the change in yield and the change in price. In other words, the percentage change in price from an increase in yield is presumed to be the same as the change in price from a decrease in yield.