Fat Tails and Expecting the Unexpected

“The world we live in is vastly different from the world we think we live in.” – Nassim Taleb

Given enough time, the market will make a fool out of anyone basing their expectations for the future on a normal (or Gaussian) distribution.


Because financial markets do not follow a bell curve. Instead, they operate in the world of fat tails, exhibiting large skewness or kurtosis. This is a fancy way of saying extreme events (high standard deviation or “sigma” moves) are much more likely to occur than a normal distribution would predict.


Let’s run through a real-world example in the U.S. equity market to illustrate this point.

Since 1928, there have been 22,230 trading days in the S&P 500. Based on a normal distribution, one would expect a 3-sigma event (a daily gain of >3.52% or a daily loss of >3.49%) to occur roughly .27% of the time, or in only 60 of those trading days.

What we see in the table below is that they have actually occurred 383 times, or 1.72% of the time.


Probability theory would suggest the likelihood of a 5 or more standard deviation event (a daily gain of >5.86% or a daily loss of >5.83%) is essentially zero but in the real world we have seen such extreme moves 85 times.

The 17-sigma crash that occurred on October 19, 1987 (-20.5% decline, worst in history) was simply not every supposed to happen, in the history of the universe.

But it did. And given enough time, it will happen again.

On, June 24, following the United Kingdom’s vote to leave the European Union, we saw that first hand. Fat tails were evident that day throughout the financial markets. The British Pound crash was the most extreme, declining over 8% (double the prior record) but we also saw the worst declines in history for the Spanish, Italian and Euro Stoxx 50 equity indices. In the U.S., the Volatility Index (VIX) jumped close to 50%, one of the largest spikes in history (for our research on leading indicators of volatility, click here).


Could anyone have predicted the exact timing or magnitude of such an extreme day? No, though with hindsight many have attempted to rationalize these enormous moves as if they could have been expected.

In reality, the best we can do as investors is to understand and accept the fact that fat tails are an inherent part of the game. As an investor, you need to expect the unexpected and be prepared for multiple outcomes. As such, diversification in terms of asset class and strategy is your best defense in dealing with uncertainty and fat tails.

The worst thing you can do as an investor is to react emotionally to such extreme events, taking unwarranted action in your portfolio after the fact with the assumption that an ex-post response will be helpful.

But panic selling is rarely rewarded in the short-run and never an effective strategy in the long-run. Those selling the FTSE 100 (UK’s main equity index) after the Brexit vote would learn that the hard way.


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This writing is for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation regarding any securities transaction, or as an offer to provide advisory or other services by Pension Partners, LLC in any jurisdiction in which such offer, solicitation, purchase or sale would be unlawful under the securities laws of such jurisdiction. The information contained in this writing should not be construed as financial or investment advice on any subject matter. Pension Partners, LLC expressly disclaims all liability in respect to actions taken based on any or all of the information on this writing.



Charlie Bilello is the Director of Research at Pension Partners, LLC, an investment advisor that manages mutual funds and separate accounts.  He is the co-author of four award-winning research papers on market anomalies and investing. Mr. Bilello is responsible for strategy development, investment research and communicating the firm’s investment themes and portfolio positioning to clients. Prior to joining Pension Partners, he was the Managing Member of Momentum Global Advisors and previously held positions as a Credit, Equity and Hedge Fund Analyst at billion dollar alternative investment firms.

Mr. Bilello holds a J.D. and M.B.A. in Finance and Accounting from Fordham University and a B.A. in Economics from Binghamton University. He is a Chartered Market Technician (CMT) and a Member of the Market Technicians Association. Mr. Bilello also holds the Certified Public Accountant (CPA) certificate.

You can follow Charlie on twitter here.


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