# Financial Fat Tail Definition

Fat tails are basically a statistical distribution phenomena. Most people who are familiar with the well-known ‘bell curve’ will be able to visualize the fat tails as a bell curve with the opening of the bell stretched out – making the opening fatter. Fat tails graphs are seen whenever there are a lot of events or values that stray widely from the average giving more frequent high and low values. As most statistical distributions are expected to be “normal” distributions – or bell curve in shape; the fait tails phenomena is most often an unexpected result.

For an example of fat tails we could examine a case where you had a population of people where the average height was 1.75 meters. A fat tails distribution would be observed if the proportion of people who were over 2.1 meters tall or less than 1.5 meters high was larger than the normal bell curve distribution would predict. The fat tails phenomena would also imply that the number of people in the normal range of 1.5 meters to 2.1 meters would be less than the bell curve distribution would predict. If you were ordering jackets for this population and based your choice of jacket sizes on a normal distribution of people’s height, you would find many of the jackets did not fit as a result of the fat tails distribution.

Another way of looking at fat tails is to consider that when events with a low probability actually do occur, people will tend to overestimate the likelihood that they will occur again. So if an earthquake strikes in a certain area, the number of people who buy earthquake insurance goes up even though the likelihood of another earthquake happening remains unchanged. Here again the normal distribution of what a bell curve would predict is replaced by a fat tails distribution. The normal bell curve of prediction is skewed into a fat tails distribution model showing the increased feeling of people that the low-probability event (another earthquake) will happen more often.

In economic markets, as in other social phenomena, classical theories generally expect some form of normal distribution. However, in the marketplace, the distribution is less perfect as human behavior can often differ from expected predictions leaving us with a fat tails of distribution situation. For instance, the distribution of monthly or daily market returns, including risks and volatilities, do not always follow the normal law. When observed in a graph form, the curve becomes flatter and less bell shaped – giving the fat tails distribution; and with it more lower and higher instances of extreme values.

Being aware of extreme events that are depicted by fat tails is not enough to protect yourself from unexpected market events. Investors must also understand the interrelated aspects of the market. Recognizing the causes of fat tails situations and their impact in the marketplace is a good first step. However, being able to understand why the distribution ended up that way is critical if you want to avoid getting caught in a fat tails situation.

Copyright (c) John A. Robb 2008. Just for fun: Anklet Theory