What is '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.
BREAKING DOWN 'Negative Convexity'
Callable bonds are negatively convex at lower yields than the yield at which the bond is likely to be called.
One property of a noncallable 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 noncallable 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
A measure of the curvature in the relationship between bond prices ... 
Convexity Adjustment
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Call Risk
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A bond that can be redeemed by the issuer prior to its maturity. ... 
European Callable Bond
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How is convexity used in risk management?
Learn how convexity is used for risk management for bond portfolios, and understand the difference between duration and convexity ... Read Answer >> 
You currently are holding a portfolio of bonds. Interest rates are expected to increase ...
The correct answer is c. Bonds with high convexity are less affected by changes in interest rates than bonds with lower convexity. ... Read Answer >> 
How do I use the principles of convexity to compare bonds?
Read a brief overview of bond duration and bond convexity and why bondholders should take these into consideration when deciding ... Read Answer >> 
What is the correlation between a coupon rate and the convexity of a given bond?
Read about the relationship between the coupon rate of a bond, its yield and its convexity, and why zerocoupon bonds tend ... Read Answer >> 
How can I calculate convexity in Excel?
Learn how to approximate the effective convexity of a bond using Microsoft Excel using a modified and simpler version of ... Read Answer >> 
How can I calculate convexity in MATLAB?
Learn about convexity of the bonds and how to calculate it in MATLAB with function "bndconvy" after specifying necessary ... Read Answer >>