How the Normal Distribution Keeps Crashing The Global Financial System

The only normal people are the ones you don’t know very well.
— Alfred Adler

What is normal? Normal is conforming to a standard; usual, typical, expected. And what could be more normal than the humble normal distribution?

The normal distribution, also called Gaussian distribution after German mathematician Carl Friedrich Gauss (the Duke of Mathematicians) is everywhere, from the social sciences to the natural sciences to machine learning.

So it was only natural for Charles S. Peirce, writing in the late 19th century, to call it normal, referring to its widespread use and usefulness.

When the normal distribution is not explicitly used, it implicitly inhabits the core of many scientific models: significance tests in psychology, such as T-tests, make Gaussian assumptions about model residuals. Many financial models, such as the Black-Scholes model, crucially depend on the assumption of “normality”.

Normal distributions, crashing markets, and an old man that, according to DALL-E, is supposed to be Gauss.

But what is normal in this context, really? As we will see later, assuming normality in places where things are far from the normal, such as the global financial system, can lead to disastrous outcomes.

Still, the normal distribution is too widespread to easily get replaced. Its popularity rests on several…