The Crash of 1987 and the 300 Mile Tall Man

There’s lots of good stuff out there this week on the crash of 1987, so called Black Monday, including these interesting stats from Michael Harris talking about how it was a 25 Sigma event. As a reminder, a standard deviation is quoted with the Greek Symbol Sigma, thus moves more than xx standard deviations above/below their average move is often quoted as xx Sigma moves.

Note that the standard deviation of daily returns before the crash was 0.809%. Not that it makes a fundamental difference but many refer to 1987 crash, a -20.5% daily drop., as a 20-sigma event based on a returns series that includes it. However, if one uses the series of returns before the crash, then it turns out it was 25-sigma event, as shown below.

That 25 sigma event means the “odds” of a -20.5% drop in a single day happening were something on the order of 1 in a trillion, on a normally distributed data set. Now, 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 – as the 1987 crash showed us plainly.

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? 1000?  Would you believe 1.6 million feet, or 303 miles, tall… 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.

So if you take anything away from the 1987 crash, let it be that your algorithms and machine learning and quant based risk and all the rest need to know that financial markets aren’t part of mediocristan. The odds of another single day 20% drop are much greater than the 1 in a Trillion the 25 Sigma would have your believe.


The performance data displayed herein is compiled from various sources, including BarclayHedge, and reports directly from the advisors. These performance figures should not be relied on independent of the individual advisor's disclosure document, which has important information regarding the method of calculation used, whether or not the performance includes proprietary results, and other important footnotes on the advisor's track record.

Benchmark index performance is for the constituents of that index only, and does not represent the entire universe of possible investments within that asset class. And further, that there can be limitations and biases to indices such as survivorship, self reporting, and instant history.

Managed futures accounts can subject to substantial charges for management and advisory fees. The numbers within this website include all such fees, but it may be necessary for those accounts that are subject to these charges to make substantial trading profits in the future to avoid depletion or exhaustion of their assets.

Investors interested in investing with a managed futures program (excepting those programs which are offered exclusively to qualified eligible persons as that term is defined by CFTC regulation 4.7) will be required to receive and sign off on a disclosure document in compliance with certain CFT rules The disclosure documents contains a complete description of the principal risk factors and each fee to be charged to your account by the CTA, as well as the composite performance of accounts under the CTA's management over at least the most recent five years. Investor interested in investing in any of the programs on this website are urged to carefully read these disclosure documents, including, but not limited to the performance information, before investing in any such programs.

Those investors who are qualified eligible persons as that term is defined by CFTC regulation 4.7 and interested in investing in a program exempt from having to provide a disclosure document and considered by the regulations to be sophisticated enough to understand the risks and be able to interpret the accuracy and completeness of any performance information on their own.

RCM receives a portion of the commodity brokerage commissions you pay in connection with your futures trading and/or a portion of the interest income (if any) earned on an account's assets. The listed manager may also pay RCM a portion of the fees they receive from accounts introduced to them by RCM.

See the full terms of use and risk disclaimer here.