what is negative convexity 
negative convexity exists when the shape of a bond s yield curve is concave a bond s convexity is the rate of change of its duration and it is measured as the second derivative of the bond s price with respect to its yield most mortgage bonds are negatively convex and callable bonds usually exhibit negative convexity at lower yields understanding negative convexitya bond s duration refers to the degree to which a bond s price is impacted by the rise and fall of interest rates convexity demonstrates how the duration of a bond changes as the interest rate changes typically when interest rates decrease a bond s price increases however for bonds that have negative convexity prices decrease as interest rates fall for example 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 convexity calculation examplesince duration is an imperfect price change estimator investors analysts and traders calculate a bond s convexity convexity is a useful risk management tool and is used to measure and manage a portfolio s exposure to market risk this helps to increase the accuracy of price movement predictions while the exact formula for convexity is rather complicated an approximation for convexity can be found using the following simplified formula convexity approximation p p 2 x p 0 2 x p 0 x dy 2 