Instead, market outcomes are distributed according to the Pareto distribution*, also known by its far more famous and catchy name, the 80/20 Rule. The 80/20 Rule was the brainchild of Viflredo Pareto, and differs from the normal distribution due to its fat tails.

Fat tails, in a probability distribution, simply signify a higher probability of extreme events occurring (relative to a less fat tail).

Extreme, in this case, meaning life changing.

Covid turning into a global pandemic was (and at the time of writing, still is) an extreme event. The many people who lost jobs, especially in Tourism and Aviation, had their lives severely disrupted almost overnight.

On a less gloomy note, rare life changing events can happen to the upside as well. Entrepreneurial success stories are a good example of this, as well as people who manage to, through some combination of luck and skill, profit from rare events that catch everyone else off guard.

A good instance of this is the people who made money shorting US housing and/or investment banks in the lead up to 2008.

Both Covid and 2008 also demonstrate how we live in a Paretian world. The Covid induced stock market plunge in early 2020 was about a 5 sigma (standard deviation) move, assuming  it followed a normal distribution. 5 sigma moves are “supposed” to occur once every 14,000 years.

Later on in 2020, amid murmurings that Covid vaccines were close to being a reality, stock markets reacted wildly. As traders/investors rushed to reposition portfolios to take into account the possibility of a faster than expected return to normalcy, momentum stocks were sold heavily.

So heavily that their move lower constituted a 15 sigma event, only ~8 months after a 5 sigma event.

That’s a 1 in 1.090e+048 (1 with 48 zeros behind) years event happening a mere 8 months after a 1 in 14,000 year event!

Furthermore, during the height of the credit crunch in 2008, the moves in markets were so extreme that David Viniar, then CFO of Goldman, commented that:

We were seeing things that were 25-standard deviation moves, several days in a row.

25 sigma moves, in a normally distributed world, are “supposed” to occur once every 1.309e+135 years. That’s once in, 1 with 135 zeros behind it, years. And not just for one day, but for “several days in a row”!!

As such, headlines or arguments that claim some rare event will not happen again, or was inconceivable because of it being an X Sigma event, are meaningless. This is because mean and standard deviation, crucial to a normal distribution, are meaningless in Pareto realities.

Furthermore, the normal distribution is reliant on independent outcomes. This means that, in a bell curve world, events have nothing to do with one another – getting heads on the first coin flip does not affect the outcome of the second flip.

On the other hand, Pareto distributions reflect the financial market reality of dependent outcomes. People buy when they see others buying, and they sell when they see others selling; both emotions and paradigms matter.

Clearly the financial markets (and world, and life) are not normally distributed! 

To be concluded…

*of the more general Power Law family of probability distributions