The Normal Distribution

An Illustration of Basic Probability

The normal (or Gaussian) distribution is one of the most commonly observed and is the starting point for modeling many natural processes. It usually is found in events that are the aggregation of many smaller, but unobservable events. A good example is the motion of small particles of dust in water. When viewed in a microscope they perpetually move back and forth from the random impacts of water molecules. If one were to plot the distance traveled by dust particles over a given time interval and repeat the measurement several times, the resulting distribution would be normal. The path followed by the dust particles is referred to as Brownian motion. In this case, the movement of the dust is the aggregation of several random shocks from the water molecules.

The exhibit below illustrates a more simple process that gives rise to the familiar "bell curve" of the normal distribution. In this case balls are dropped from the top and pass through a series of pins until they hit the bottom. Once at the bottom, they stack up to record the number that have hit that point. At first there does not seem to be any pattern but after a few minutes the stacks conform to the superimposed curve.

Asset returns closely follow the normal distribution in part because they are the aggregation (or average) of random shocks of information. The news that affects future cash flows takes the place of water molecules in the aforementioned Brownian motion.

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