Fat Tails: An Untrustworthy Friend

Abstract

The term fat tails appears quite often in popular literature, but precise definitions and their quantitative consequences are frequently absent. In this article, I aim to correct this. I state some mathematical definitions and investigate some of their important (and surprising) consequences. I attempt to give a characterization of fat tail distributions that is useful; dispels common misconceptions; and ensures that in the real world, the reader will not be caught off guard by the misleading nature of these distributions. It is assumed that the reader is familiar with only the basic idea of a probability distribution, and many of the ideas are presented visually by using graphs and figures. Finally, I apply these concepts to a simple data set from the 2008 financial crisis to illustrate that, far from being an academic exercise, these ideas are relevant in the real world.

TOPICS: Fixed income and structured finance, financial crises and financial market history

Key Findings

• ▪ Fat tail distributions are written about popularly but rarely understood quantitatively.

• ▪ Fat tail distributions have surprising characteristics (moodiness and deceitfulness are two described here).

• ▪ Fat tail distributions govern many real-world phenomena, and understanding their properties has real consequences.