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The Probability of a Rare Event

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Nov. 03, 2009

 - The Probability Of A Rare Event

Author:

William J. DeRosa, Jr., CFA



If one hasn’t had the opportunity to do so, I highly recommend Nassim Taleb’s Fooled by Randomness. The book describes an incredibly important concept for successful investment which includes subjects such as probability distribution and outlier (fat tail) events.

The chance of a rare event happening is dependent on one’s perspective. First, we need to understand exactly what is rare? We often hear a familiar phrase- “It was a once in a 100 year event”. Isn’t it amazing how often these so called events occur? We only need to go back over the past thirty years or so to identify many of these situations. What we discover is that these rare events happen with relative frequency. Whether its 9/11, the Russian debt crisis, the Asian currency crisis, or some other unexpected occurrence- the isolated events may be rare, but the frequency of some shock happening is relatively predictable.

Why are we consistently surprised when something unusual happens? Why are we unable to build these six-sigma events into our models? It seems as though humans simply are not conditioned to expect extreme events. This probably isn’t so unusual. After all, we don’t like to anticipate terrible outcomes. It would be highly unproductive to always contemplate disaster. However, there is a deeper cause to this oversight.

The following is an excerpt which discusses the very principle of unexpected fat-tail events;


{It's amazing to me that Amaranth seems to have relied on the same "principle" as did the disgraced managers of Long-Term Capital, "stewards" of what was (until Amaranth) the biggest blow-up in hedge-fund history. Simply put, this "principle" holds that various historical relationships between various markets will "mean revert" once they begin to diverge significantly from the norm. The mean reversion principle has become an article of faith among many of the major hedge funds. Given the alleged sophistication of these supposedly risk-savvy players, it is shocking that a principle that thumbs its nose at the "fat tail" events that are far, far more common than any modeling ever suggests continues to have holy-grail status. And then, when funds like Long-Term Capital and Amaranth blow up, the ready excuse is "who would have thought such a 'highly remote' event would ever occur?"

The lesson here is that these models that are so avidly followed by those who should know better have been dead wrong and continue to be dead wrong about the odds of so-called rare events. The equity markets have been in a derivatives-induced coma for several years now, and my sense is that the upcoming fourth quarter is about as ripe a period as I can imagine for this coma to come to an abrupt end. An upside breakout can blow away those who've been heavily overwriting calls; a downside break creates potentially huge liability for those who have sold a massive quantity of very low delta puts that have thus far been "free money," month after month. In other words, market moves may begin to feed on themselves rather than mean revert, and some players will pay - big time - for this.}


Returning to our previous question- the answer is the phrase ‘free money’. As long as a stable, profitable, and risk-free situation exists, managers will attempt to exploit it for as long as possible with little regard for alternative consequences.



William J. DeRosa, Jr. is the General Partner of Anthem Asset Management, LLC is an independent investment management company. He has also served as Director of Equity Research and Senior Portfolio Manager at various buy-side asset management firms. Mr. DeRosa is a Chartered Financial Analyst and is a member of The CFA Institute.

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