Negative Convexity

When the shape of a bond's yield curve is concave. A bond’s convexity is the rate of change of its duration, and is measured as the second derivative of price with respect to yield.

Most mortgage bonds are negatively convex.  



|||Callable bonds are negatively convex at lower yields than the yield at which the bond is likely to be called. 

One property of a non-callable bond is that as interest rates fall, its price will increase. However, with a callable bond, as interest rates fall, the incentive for the issuer to call the bond at par increases; therefore, its price will not rise as quickly as the price of a non-callable bond. 

The price of a callable bond might actually drop as the likelihood that the bond will be called increases. This is why the shape of a callable bond's curve of price with respect to yield is concave or "negatively convex."