Fat tails are anomalies in normal distributions that, quite honestly, are tough to explain in hypothetical terms. Simply put, it’s a skewness or *kurtosis*, which identifies whether the tails of a distribution contain extreme values compared to that of either a normal distribution or an exponential distribution. Since markets move based on human psychology, under-and overreactions to various data, coupled with the herding instincts of traders, this will sometimes push prices to escape velocity. Although the extremes are infrequently, they do happen.

A normal distribution has a defined mean and standard deviation [Standard Deviation for Finance Illiterates]. To define a range of data points under a normal distribution, place brackets where most of the data will likely fall. Two standard deviations captures 95% of where those data points will hang out; the 5% of the data outside the bands (*Shoutout Bollinger bands*) are the fat tails.

From an options trading perspective, that little 5% is where the big money can be made. It’s that sweet spot where price acceleration really kicks in and stocks in the fat tails can surge in the direction of the trend. The more fear, the less participation. The more greed, the greater the participation. Compared to fat-tailed distributions, in the normal distribution events that deviate from the mean by five or more standard deviations (“*5-sigma events*“) have lower odds, meaning that in the normal distribution extreme events are less likely than for fat-tailed distributions.

Hot shots like Benoit Mandelbrot and Nassim Taleb have noted the shortcomings of the normal distribution model and have proposed that fat-tailed distributions such as the stable distributions govern asset returns frequently found in finance. The Black Scholes model [The Black Scholes Model: How Ed Thorp Made It Cool] of option pricing is based on a normal distribution. If the distribution is actually a fat-tailed one, then the model will under-price options that are far out-of-the-money (OTM), since a 5- or 7-sigma event is much more likely than the normal distribution would predict.

Sometimes fat tails occur but are undesirable due to the added risk they imply. For example, an investment strategy may have an expected return, after one year, that is five times its standard deviation. Assuming a normal distribution, the likelihood of a negative return is less than one in a million. Normal distributions that emerge in finance generally do so because the factors that shape an asset’s price are “*well-behaved*“. However, traumatic “*real-world*” events are seldom well-behaved.