What is 'Convexity'
Convexity is a measure of the curvature in the relationship between bond prices and bond yields that demonstrates how the duration of a bond changes as the interest rate changes. Convexity is used as a riskmanagement tool, and helps to measure and manage the amount of market risk to which a portfolio of bonds is exposed.
BREAKING DOWN 'Convexity'
As interest rates increase, bond yields increases, and consequently, bond prices decrease. Conversely, as interest rates fall, bond yields fall and bond prices rise. In the example figure shown above, Bond A has a higher convexity than Bond B, which indicates that all else being equal, Bond A will always have a higher price than Bond B as interest rates rise or fall.Convexity and Risk
Convexity is a better measure of interest rate risk, in relation to duration, because the concept of duration assumes that interest rates and bond prices have a linear relationship. Duration can be a good measure of how bond prices may be affected due to small and sudden fluctuations in interest rates. However, the relationship between bond prices and yields is typically more sloped, or convex. Therefore, convexity is a better measure for assessing the impact on bond prices when there are large fluctuations in interest rates.
As convexity increases, the systemic risk to which the portfolio is exposed increases. As convexity decreases, the exposure to market interest rates decreases and the bond portfolio can be considered hedged. In general, the higher the coupon rate, the lower the convexity (or market risk) of a bond. This is because market rates would have to increase greatly to surpass the coupon on the bond, meaning there is less risk to the investor.
Negative and Positive Convexity
If a bond's duration increases as yields increase, the bond is said to have negative convexity. In other words, the shape of the bond is said to be concave. Therefore, if a bond has negative convexity, its price would increase in value as interest rates rise, and the opposite is true. Some examples of bonds that exhibit negative convexity are bonds with a traditional call provision, preferred bonds and most mortgagebacked securities (MBS).
If a bond's duration rises and yields fall, the bond is said to have positive convexity. If a bond has positive convexity, it would typically experience larger price increases if yields fall, in relation to price decreases when yields increase. The typical types of bonds with positive convexity are bonds with makewhole call provisions and noncallable bonds. Under normal market conditions, the higher the coupon rate, the lower a bond's degree of convexity. Consequently, zerocoupon bonds have the highest degree of convexity because they do not offer any coupon payments.

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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 >>