Convexity

Written By
Paul Tracy
Updated August 5, 2020

What is Convexity?

In the bond world, convexity refers to the shape of the yield curve and  how sensitive bond prices are to changes in interest rates.

How Does Convexity Work?

The degree to which a bond's price changes when interest rates change is called duration, which often is represented visually by a yield curve. Convexity describes how much a bond's duration changes when interest rates change, meaning that investors can learn a lot not just from the direction of the yield curve but the curviness of the yield curve. Accordingly, convexity helps investors anticipate what will happen to the price of a particular bond if market interest rates change.

Generally, when interest rates fall, bond prices rise. But a bond with negative convexity loses value when interest rates fall. This is often the case for mortgage-backed securities because they rely on underlying mortgage loans, which are typically refinanced (and thus paid off early) when interest rates fall. Prepayment repays the lenders and mortgage-backed security investors off early, leaving them stuck with reinvesting their money at the market's current lower rates. Just the opposite would happen with bonds that have positive convexity.

Why Does Convexity Matter?

Convexity is a price-predicting tool for bonds. It also reveals the interest rate risk of a bond and helps investors consider whether a bond's yield is worth the underlying risk.

Most mortgage bonds are negatively convex, largely because they can be prepaid. An issuer's incentive to call a callable bond at par also increases as interest rates decrease; therefore, the prices of instruments with negative convexity do not rise as quickly as the prices of noncallable bonds, whose convexity is different.