The New York Stock Exchange lost more than $500 billion in market capitalization on October 19th, 1987, equivalent to about $1.2 trillion in today’s dollars. The S&P 500 was down 20% on that single day. Some said at the time it was a twenty sigma event.
Wall Street Insiders use the term “sigma” as code for the probability of an event happening. A twenty sigma event should happen about once every “14 plus 85 zeros” years.
Wow. That sounds impossible. If that analyst worked for me, I’d send him back to check his model.
Wall Street Insiders, it seems, have a propensity for being surprised by low probability high magnitude events: those big meaningful events that happen, but only rarely.
Bear Stearns reported value at risk of just $62 million in February of 2008. It lost $9 billion of market capitalization over the subsequent two months. Oops.
Long-Term Capital Management famously lost $4.6 billion in a matter of months in 1998 when a confluence of highly unlikely events happened simultaneously.
In the midst of the global financial crisis, Goldman’s CFO said he had just seen several twenty-five sigma events happen on consecutive days.
In Statistics 101 we learned about flipping coins. We learned that coin flips follow the normal distribution, otherwise known as the bell curve. Statisticians have cleverly determined a metric that explains the distribution of data around the average of normally-distributed data. They call it the standard deviation and refer to it using the Greek letter sigma. When Wall Street Insiders refer to sigma – as in “we just saw a twenty sigma event” - they are referring to standard deviation.
The further a data point lies from the average of a normally-distributed data set, the lower the probability of that event actually happening. Standard deviation, or sigma, is a measure of the distance a data point lies from the average. The higher the sigma, the rarer the event.
The probability distribution of a normally-distributed data set is uniquely defined by just two numbers: its average and its standard deviation. Armed with just those two numbers, we can calculate the likelihood of certain events happening. We can calculate the likelihood of flipping nine heads out of ten flips or five heads out of ten flips or four heads out of ten flips. The calculation is precise and accurate and the results are repeatable, as long as the underlying data set follows the normal distribution.
That ease of quantification – made even easier with modern spreadsheet and database technology – was too much of a temptation for academics and consensus-driven analysts. They went to work calculating the means and standard deviations on all sorts of data sets. They have been doing it for literally the last fifty years.
An alarming number of models, formulas, and theories have emerged over the years that assume market prices follow a normal distribution. The normal distribution assumption, once made, opens up all sorts of opportunities to quantify the unquantifiable.
Nearly all quantitative measures of risk used in the financial markets today assume market prices follow a normal distribution. The value at risk metric once used at places like Bear Stearns and Enron made that assumption. Many trading algorithms are based on it, including the one used at Long-Term Capital Management. The Black-Scholes Formula for pricing options is based on it. Indeed, Modern Portfolio Theory itself hangs together on the assumption that prices follow the normal distribution.
The assumption that prices follow a normal distribution is imbedded in so many financial models, theories, and formulas today that we sometimes forget that we even made it. We forget that the validity of those models, theories, and formulas depend on that one assumption being a good one. We forget that when we actually live through an event that isn’t supposed to happen that perhaps we should take a critical look at our model rather than describing the event as impossible.
There is a reason Wall Street Insiders get blindsided by the impossible. The impossible isn’t actually impossible. We are not experiencing 20 sigma events. We are witnessing the use of bad models based on faulty assumptions.
