Surviving by Staying Out of the Fourth Quadrant

Can one survive over the long run in the “wild” Fourth Quadrant, in which many investments appear to reside and for which normal (Gaussian) statistics mislead rather than guide? In his February 2009 draft paper entitled “Errors, Robustness, and The Fourth Quadrant”, Nassim Taleb investigates the (in)tractability of economic and financial series and characterizes approaches to accommodating such fundamental unpredictability. Based on a broad set of worldwide economic data that includes 38 tradable variables with daily price data, he concludes that:

• Economic/financial variables have fat-tailed, power law distributions. Fat-tailedness usually involves a frequency of rare events that is lower than “normal” but a severity of rare events that is much greater than “normal.” Aggregating high-frequency (daily) observations into longer weekly or monthly intervals does not eliminate or suppress the wildness of these distributions.
• These “wild” power law distributions incapacitate conventional statistical methods, including those which assume Gaussian distributions or otherwise depend on variance to describe dispersion. This incapacitation is a consequence of the huge contributions of rare events to statistical measures such as mean and standard deviation.
• It is inherently difficult to estimate the exponential parameter of an empirical power law because power law outputs are extremely sensitive to the value of this parameter.
• Forecasting of economic/financial variables is therefore inherently lame.
• Moreover, small samples and survivorship bias (loss of data “killed” by rare events) work to fool observers into believing that such “wild” distributions are tame.
• Fourth Quadrant environments, described by power law distributions and consequences that scale with the rarity of events, are thus extremely dangerous. Unpredictable rare events in such environments kill.
• Limit exposure to Fourth Quadrant risk by emphasizing margin for forecast error over forecast-based optimization. For example, by keeping a high fraction of a portfolio in very low-variance assets (such as Treasury bills) and a low fraction in very high-variance assets (such as long positions in far out-of-the-money options), one can achieve a medium-variance portfolio while protecting most of the portfolio from rare-event destruction.

In summary, the way to survive the fat-tailedness of investment returns is through limiting exposure to such investments.

Perhaps the wildness of observed power law distributions is an engine of diversity, an enemy of stasis.

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