Tail events are events with a low probability of realization but with tremendous consequences. In investment theory, future outcomes are often assumed to follow a normal distribution, but empiric market data shows that this assumption seldom holds true. Contrary, financial returns often experience distributions much “fatter” than normal curves meaning that tail events are much more frequent than many investors realize.
The “tail” in tail risk refers to the end sections of the bell‐shaped curve that illustrates the Normal probability distribution of events. In the context of investments, the extreme left‐hand side of the bell‐shaped distribution represents the lowest returns, whereas the right‐hand side represents the highest returns. The art of tail‐risk protection is to asymmetrically protect against left‐hand events (losses) while maintaining participation in those events on the right (profits).
The Normal Distribution
In order to understand the significance of tail risks, it is important to understand the notion of a normal distribution and its shortcomings. A normal distribution assumes that, given enough observations, all values in the sample will be distributed equally above and below the mean. About 99.7% of all variations falls within three standard deviations of the mean and therefore there is only a 0.3% chance of an extreme event occurring. This property is important because many financial models such as Modern Portfolio Theory, Efficient Markets and the Black-Scholes option pricing model all assume normality. However, the financial markets are less than perfect and largely influenced by unpredictable human behavior, which leaves us with fat tail risks. The Normal distribution together with two heavy-tailed distributions are displayed in exhibit 1.
[Inset tail risk graph] Exhibit 1: Financial returns usually experience negatively skewed distributions, which means that extreme events are more probably than judged by the Normal distribution. Hence, financial returns are subject to tail risk.
By definition, a distribution with a fat tail is a collection of potential future outcomes, where the probability of the occurrence of an extreme event exceeds three standard deviations. The aftermath of the 2008 Financial Crisis highlighted the shortcomings of conventional financial theory, which has only been further emphasized by the continuation of smaller and larger economic shocks e.g. 2001 Dot-Com crisis, 2008 Financial Crisis, 2011 European Debt crisis, 2014 Russian Financial Crisis, 2015 Chinese Stock Market Crash. Hence, the assumption of the normal distribution in financial risk management can pose an inherent threat to invested capital as the consideration of tail risk has shown to be of paramount importance.