What is a fat tail distribution and why it matters?

What is a fat tail distribution and why it matters?

What Is A Fat-tailed distribution And Why It Matters In Business Fat-tailed distributions are graphical representations of the probability of extreme events being higher than normal. In many domains fat tails are significant, as those extreme events have a higher impact and make the whole normal distribution irrelevant.

Is the Sigma of a fat tailed distribution undefined?

Fat-tailed distributions such as the Cauchy distribution (and all other stable distributions with the exception of the normal distribution) have “undefined sigma” (more technically, the variance is undefined).

Why do some bell curves have fat tails?

Some bell curves have fatter tails with a higher prevalence of data significantly different to the mean. Fat-tailed distributions are said to decay more slowly, allowing more room for outlier data to exist sometimes 4 or 5 standard deviations above the mean. As a result, extreme events are more likely to occur.

Why are hedging strategies have fatter tails?

Hedging strategies can often have some short term costs, but over time they are designed to mitigate losses and provide liquidity during crises. In the post crisis era, it is becoming accepted that financial asset returns exhibit fatter tails than normal distributions.

Are there two tails in a normal distribution?

Note that there are two tails: right and left. If we want to describe the ‘right’ tail of the distribution from the one standard deviation from the mean, for example, then the shaded part refers to the right tail of the normal distribution. Formally, we can describe the tail as follows:

Is the behavior of the tail quantifiable?

If you want “ the behavior of the tail” to describe the characteristics of the pdf when ‘x’ gets large, then bounded distributions do not have tails. Nevertheless, some features of tails can be quantified. In particular, by using limits and asymptotic behavior you can define the notion of heavy tails. SAS blog

When does an asset return have a fat tail?

If an asset return simply is governed by high- and low-variance regimes (with normal distributions) the combination will have fat tails. “ [ For] a class of distributions that is not fat-tailed… the probability of two 3-standard deviations events occurring is considerably higher than the probability of one single 6-standard deviations event…

Where does the tail start in a normal distribution?

There are several reasons why a formal definition of “tail” is challenging: Where does the tail start? The tail is “far away from the mean,” but how far away? For the standard normal distribution, should the tail start three standard deviations from the mean? Five? Not all distributions are as well-behaved as the normal distribution.