Fat-Tailed Distribution

The tails of a distribution are its far ends, representing extreme outcomes. In a normal distribution, the probability of extreme events falls off very quickly. In a fat-tailed distribution, extreme events are much more likely than the normal distribution predicts.

Financial returns are widely observed to be fat-tailed. For example, under a normal distribution, a daily fall in a stock market index of more than five standard deviations should happen so rarely that it might be expected only once in many thousands of years. In reality, such falls have happened several times within a few decades, including the 1987 crash and moves during the 2008 financial crisis.

Fat tails have important consequences for risk management. Models that assume normal distributions can seriously underestimate the probability of large losses, giving a false sense of security. Statisticians describe fat tails using measures such as kurtosis, which captures how heavy the tails are.

To address fat tails, risk managers use stress tests, historical worst-case scenarios, distributions that allow for more extreme outcomes and measures such as expected shortfall, which look at the size of losses in the tail rather than just the threshold.