Here's what today is looking like in financial markets thanks to the surprise Brexit vote results last night. Suffice it to say, it's not pretty with markets crashing -5% to -12% overnight. As we said in our post about the Brexit being Binary Bollocks, these types of shocks can concentrate weeks to months' worth of market movement into a single day's trading session. Those with a little statistical knowledge call these types of moves mutli-sigma events, which is an abbreviated way of saying prices moved many standard deviations (sigma) above or below their means. Here's technician Charlie Biello weighing in just that way today:

Now, that bit about this type of move "supposed to happen" about 1 in every 4 million days is the result of some statistical tables assigning probabilities to different values on a normally distributed data set. Normally distributed is a statistical term meaning that any observations we see in a data set will be in a bell curve shape, with roughly 68% of the data points being 1 standard deviation above or below the average, and 95% being within 2 standard deviations of the average, and virtually no data points outside of 3 standard deviations above or below the average (just .027%).

Problem is - financial market returns are not normally distributed. If 2008 didn't teach us that, consider the double-digit sigma move during the Flash Crash in 2011, or the mother of all normal distribution killing moves - Black Monday in October of 1987. Using a normal distribution curve, there was a 1 in a trillion chance of prices being down more than 6% on 10/21/87, yet they fell -20% in a single session.

Nassim Taleb, author of the fabulous book, Black Swan, separates normally distributed and non-normally distributed by saying that which belongs to normally distributed curves exists in mediocristan, and everything else exists in a place called extremistan. Unfortunately for the efficient frontier and any financial models assuming a normal curve - we live in extremistan!

Take the distribution of wealth as compared to the distribution of human height as an example. Consider that the tallest human ever recorded was 8' 11", or about 1.6 times the average, and 10 standard deviations outside of the average.

Now consider Bill Gates and his net worth of about $54 billion. How tall do you think a person would have to be so that they are as much over the average in height, as Bill Gates is over the average in wealth? 10ft tall? 50? 1,000? Would you believe 1.6 million feet, or 303 miles, tallâ€¦ which is about the length of Lake Michigan. That is how much greater Bill Gates' wealth is than the average American. He should literally not exist in a world which is normally distributed, being thousands of standard deviations above the average. But he does exist, and those $54 billion are really his, making it painfully obvious for those of us down there within a few standard deviations of the mean that we are in fact in extremistan.