Convexity

Duration gives a straight-line estimate of how much a bond's price will change when yields change. In reality, the relationship between price and yield is curved. Convexity measures that curve.

For a typical bond, the curve works in the investor's favour. When yields fall, the price rises a little more than duration predicts. When yields rise, the price falls a little less than duration predicts.

Take a ten-year bond with a 5% coupon priced at 1,000, with a modified duration of about 7.7. Duration alone suggests that a one-percentage-point rise in yield would lower the price to about 923, and a one-point fall would raise it to about 1,077. The actual prices are about 926 and 1,081. The small extra gain in both cases comes from convexity.

Convexity matters more for large rate changes and for long-term bonds. Bonds with higher convexity are generally more valuable, all else equal. Some bonds, such as callable bonds, can have negative convexity, meaning their price gains are limited when rates fall because the issuer is likely to repay them early.