# Convexity

#### Quick Summary of Convexity

Convexity is a measure of the curvature, or the degree of the curve, in the relationship between bond prices and bond yields. Convexity demonstrates how the duration of a bond changes as the interest rate changes.

### What is the dictionary definition of Convexity?

#### Dictionary Definition

1. The state of being convex
2. A convex line or surface
3. A measure of the curvature in the relationship between the prices and yields of bonds

#### Full Definition of Convexity

1. Economics: Situation in which a combination of two or more items is preferable to any one of the individual items. If, for example, someone prefers one slice of bread and half a glass of milk than either a whole bread or a whole glass of milk, he or she has a convex preference. Similarly, if it is easier to make a product using two men and two machines than it is using four machines and no men, it is a convex technology.
2. Mathematics: Characteristic of a set of points in which, for any two points in the set, the points on the curve joining the two points are also in the set.
3. The state of being convex
4. Securities: Tendency (sensitivity) of the changes in the price of interest-bearing bonds (and other fixed-income securities) to accelerate as the price appreciates. Named after the bulging shape of the yield curve, convexity helps explain the difference between the estimated price of a bond and its market price (which is influenced by fluctuations in interest rates). Positive convexity occurs when durations shorten as interest rates rise, or when durations lengthen as interest rates fall. Negative convexity occurs when durations lengthen as interest rates rise, or when durations shorten as interest rates fall. As a general rule, ten-year Treasury bonds have positive convexity whereas mortgage-backed securities have negative convexity.

#### Examples of Convexity in a sentence

It forms an arc of a circle of which the convexity turns slightly to the north; neither bay nor promontory breaks the regularity of its outline.
In all such cases, there is no component to plan convexity, any curvature being entirely orthogonal to the x-y plane.

#### Synonyms For Convexity

projection, convex, protrusion, protruding section, bulge

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#### Definition Sources

Definitions for Convexity are sourced/syndicated and enhanced from:

• A Dictionary of Economics (Oxford Quick Reference)
• Oxford Dictionary Of Accounting
• Oxford Dictionary Of Business & Management

This glossary post was last updated: 2nd February, 2020 | 0 Views.