Convexity

This concept is best described with respect to a bond. Consider a graph of the bonds price (y-axis) and the bond yield (x-axis). If this graph was a straight line (downward sloping), there would be no convexity. It would be a simple linear relationship between bond price and yield (yield up, price down). However, bonds are non-linear functions of yields partly because irrespective of their how high their yield is, they cannot have negative price. Hence, the bond price is not a straight line, but a curve that is upward (like a bowl). So, if rates increase, the simple linear straightline will tell you (incorrectly) that the bond price drops too much). Essentially, the convexity is the second derivative whereas the linear relationship is the first-derivative (of bond price with respect to yield). If the asset price drops less than predicted by the linear relationship, it is known to have positive convexity (commonly referred in the bond market simply as ‘convexity’). However, if the asset price drops by more than predicted by the linear relationship, it is known to have negative convexity (rather than the common usage in mathematics of concavity). Convexity is also associated with options which (by definition) have non-linear payoffs.