What Is Bond Convexity?

Bond convexity is closely associated with duration but takes the concept one step further. While duration estimates how a bond's price can be expected to react to changes in market interest rates, convexity measures how the bond's duration—and by implication, its price—will change depending on how much interest rates change.

Taken together, both duration and convexity show how a bond or bond portfolio can be expected to perform when interest rates change. This helps investors understand the price risk of owning fixed-income securities under different interest rate scenarios. In general, the higher a bond's coupon rate, the lower its convexity, or market risk.

Positive And Negative Convexity

Convexity can be both positive and negative. In general, most "plain vanilla" bonds have a positive convexity. As interest rates fall, the price of the bond will rise at an increasing rate, but when rates increase, the price will fall at a declining rate.

In other words, a bond with positive convexity will gain more in price when yields fall than it will lose when yields rise. That is, the bondholder gains more when yields fall than is lost when yields rise.

However, there are some bonds that exhibit negative convexity. In a rising interest rate environment, their price doesn't increase as fast as bonds with positive convexity, or their price may actually go down.

This often occurs with callable bonds, in which the issuer is more likely to call, or buy back, bonds with higher coupon rates. It also occurs with mortgage-backed securities, which are more likely to be prepaid because mortgage borrowers can be expected to refinance their loans into lower rates. In both cases, the investor will get his or her money back faster than anticipated, making them less valuable.

By the same token, if rates were to rise, bonds with negative convexity would be more likely to increase in price—or lose less—than bonds with positive convexity, because there is less risk they will be called or paid off early.

Summary

Convexity measures how much a bond's duration will increase or decrease depending on a change in interest rates. Bonds with positive convexity will gain more in price when yields fall than they will lose when yields rise. Bonds with negative convexity will rise in price when yield rises, because they can be expected to pay off earlier than expected.