Is *The Black Swan: The Impact of the Highly Improbable* gimmicky or profound? In his October 2009 paper entitled “Common Errors in Interpreting the Ideas of *The Black Swan* and Associated Papers”, Nassim Taleb seeks to clarify the import of this book and related publications, *with some key points as follows:*

“The problem, simply stated…is about the degradation of knowledge when it comes to rare events (“tail events”), with serious consequences in some domains I call “Extremistan” (where these events play a large role, manifested by the disproportionate role of one single observation, event, or element, in the aggregate properties). …this is a severe and consequential statistical and epistemological problem as we cannot assess the degree of knowledge that allows us to gauge the severity of the estimation errors.”

“A more compact summary: theories fail most in the tails; some domains are more vulnerable to tail events.”

“The central idea in

The Black Swanis that: rare events cannot be estimated from empirical observationsince they are rare. …the rarer the event, the less we know about its role and the more we need to make up such deficiency with an extrapolative, generalizing theory. It will lack in rigor in proportion to claims about the rarity of the event. Hence model error is more consequential in the tails…this error is more severe in what I call Extremistan, where rare events are more consequential…all measures using squares like “variance”, “linear regression”, “standard deviation”, and other parts of the toolkit fail in Extremistan…”“Given a set of observations, plenty of statistical distributions can correspond to the exact same realizations each would extrapolate differently

outside the set of events on which it was derived. [This] inverse problem is more acute when more theories, more distributions can fit a set a data…“

The small sample properties of rare events[make the inverse problem more acute]. It is also acute in the presence of nonlinearities as the families of possible models/parametrization explode in numbers.“

The survivorship bias effect of high impact rare events[makes the problem of inference more acute]… Clearly, catastrophic events will be necessarily absent from the data… Thus such distributions will let the observer become prone to the overestimation of the stability and underestimation of the potential volatility and risk.”“…most of what students of statistics do is assume a structure similar to the closed ones of games, typically with

a prioriknown probability. Yet the problem we have is not so much making computations once you know the probabilities, but finding the true distribution.”“In fat-tailed domains, there is no such thing as a

typicalevent. …in fat tailed domains, discussing, predicting, hedging an event are not well defined operations, as these events can take a large scale.“…there is the mistake of thinking that the message is that these Black Swans are necessarily more probable than assumed by conventional methods. They are mostly less probable. …in a fat-tailed environment, rare events can be less frequent (their probability is lower), but they are so effective that their contribution to the total pie is more substantial.

“…complexity implies Extremistan…”

“…rationalism crashes in the tails.”

In summary, *investors may want to ponder whether the fat tails of financial asset return distributions (and those for the outputs of many other complex systems) present risks that “normal” statistical methods cannot mitigate.*