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 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. 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.