by Jason Voss, CFA
As the U.S. Federal Reserve lays the verbal groundwork for an eventual real-world quantitative easing (QE) taper, bond prices are dropping at an accelerated rate. In order to understand the ramifications of a Federal Reserve taper on the prices of a bond or bond portfolio, what is needed is a bond convexity primer.
In the parlance of those who know calculus, convexity is the second derivative. For the layperson, this is known as the rate of change in change. For convexity to make better sense, let me compare it to driving a car. When you are driving a car, your speed is the rate of change in the car's location. Want to change your speed (i.e., the rate of change)? Then you either give the car more gas with the accelerator or press down on the brakes to slow the car down. Speeding up and slowing down are the second derivative. Speeding up means that there is a positive second derivative, while slowing down means that there is a negative second derivative.
Related to the bond market, the speed of your car is called duration, while the speeding up / slowing down is known as convexity. The higher the convexity, the more dramatic the change in price given a move in interest rates. Whatever you call it, after a while, if you keep braking a car it stops. After a while, if your bond is experiencing negative convexity, it also slows down / loses value. The harder the acceleration or braking, the greater the change in your speed.
So why is the relationship between a bond's yield and its price known as convexity? As yields change, the change in the price of the bond is not linear; it is curved in a convex fashion. To understand convexity more directly, take a
