Rationalizing away the possibility of extreme events (or surprises) under conditions of probabilistic normality is an interesting behavioral economics phenomenon in society. Such behavior is signaled by attributions of “uncertainty,” “anomalies,” “shocks,” or some other lofty but equally pretentious notion of time-space deception. The truth is that denying the possibility of extreme outcomes defies the logic of normality, as such outcomes are certainly possible (or even imminent) under normal conditions.
Carl Friedrich Gauss (1777–1855) discovered the specific characteristics of what we now know as normality. The conceptual framework for describing normality is the normal frequency distribution, or “bell curve,” also known as a “Gaussian” distribution. Normality is a common assumption of many of nature’s phenomena, and a central concept in probability theory.
Extreme values in the universe (or population) of outcomes occur naturally and more frequently than many presume. Under conditions of normality, 1 in 22 observations will deviate by twice the standard deviation (which is the square root of the variance) from the mean, 1 in 370 will deviate by three times the standard deviation, and up to 5 in 1,000 observations will deviate from the mean by three or more times the standard deviation. Note especially that extreme outcomes can fall well beyond the mean (to infinity).
We as analysts have a duty to educate decision-makers about how to use probability theory to advance the cause of modern finance in society. That includes emphasizing the counter-intuitive possibilities of extreme events in the economy. To assume away the normality of such surprises would be naïve.
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