Book Summary & Highlights: Statistical Consequences Of Fat Tails By Nassim Taleb

Book Summary & Highlights: Statistical Consequences Of Fat Tails By Nassim Taleb



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Amazon Summary

The book investigates the misapplication of conventional statistical techniques to fat tailed distributions and looks for remedies, when possible. Switching from thin tailed to fat tailed distributions requires more than “changing the color of the dress.” Traditional asymptotics deal mainly with either n=1 or n=∞, and the real world is in between, under the “laws of the medium numbers”–which vary widely across specific distributions. Both the law of large numbers and the generalized central limit mechanisms operate in highly idiosyncratic ways outside the standard Gaussian or Levy-Stable basins of convergence. A few examples: - The sample mean is rarely in line with the population mean, with effect on “naïve empiricism,” but can be sometimes be estimated via parametric methods. - The “empirical distribution” is rarely empirical. - Parameter uncertainty has compounding effects on statistical metrics. - Dimension reduction (principal components) fails. - Inequality estimators (Gini or quantile contributions) are not additive and produce wrong results. - Many “biases” found in psychology become entirely rational under more sophisticated probability distributions. - Most of the failures of financial economics, econometrics, and behavioral economics can be attributed to using the wrong distributions. This book, the first volume of the Technical Incerto, weaves a narrative around published journal articles.

About Author: Nassim Taleb

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Consequences Of Applying Statistics In Extremistan

Here are some consequences of moving out of the yellow zone, the statistical comfort zone:
1. The law of large numbers, when it works, works too slowly in the real world.
2. The mean of the distribution will rarely correspond to the sample mean; it will have a persistent small sample effect (downward or upward) particularly when the distribution is skewed (or one-tailed). Rare events determine the mean, and these, being rare, take a lot of data to show up. Consider that some power laws (like the one described as the “80/20” in common parlance have 92 percent of the observations falling below the true mean.
3. Metrics such as standard deviation and variance are not useable They fail out of sample-even when they exist; even when all moments exist. It is a scientific error that the notion of standard deviation (often mistaken for average deviation by its users) found its way as a measure of variation as it is very narrowly accuate in what it purports to do, in the best of circumstances.
4. Beta, Sharpe Ratio and other common hackneyed financial metrics are uninformative Practically every single economic variable and financial security is thick tailed. Of the 40,000 securities examined, not one appeared to be thin-tailed. This is the main source of failure in finance and economics.
5. Robust statistics is not robust and the empirical distribution is not empirical.
6. Linear least-square regression doesn’t work (failure of the Gauss-Markov theorem)
7. Maximum likelihood methods can work well for some parameters of the distribution (good news)
8. The gap between disconfirmatory and confirmatory empiricism is wider than in in situations covered by common mistakes (ie, the difference between absence of evidence and evidence of absence becomes larger). What is called “evidence based” science, un less rigorously disconfirmatory, is usually interpolative, evidence-free, and unscientific.
9. Principal component analysis (PCA) and factor analysis are likely to produce spurious factors and loads.
10. The method of moments (MoM) fails to work . higher moments are uninformative or do not exist.
11. There is no such thing as a typical large deviation.
12. The Gini coefficient ceases to be additive.
13. Large deviation theory fails to apply to thick tails. I mean, it really doesn’t apply.
14. Risks of financial options are never mitigated by dynamic hedging.
15. Forecasting in frequency space diverges from expected payoff.
16. Much of the claims in the psychology and decision making literature concerning the “overestimation of tail probability” and irrational behavior with respect of rare events comes from misunderstanding by researchers of tail risk, conflation of probability and expected payoffs, misuse of probability distributions, and ignorance of extreme value theory (EVT).
17. Ruin problems are more acute and ergodicity is required under thick tails.



(Epistemelogy: the invisibility of the generator) * We do not observe probability distributions, just realizations. * A probability distribution cannot tell you if the realization belongs to it. * You need a meta-probability distribution to discuss tail events (i.e., the conditional probability for the variable to belong to a certain distributions vs. others).


Though shalt not compare a multiplicative fat-tailed process in Extremistan in the subexponential class to a thin-tailed process from mediocristan, particularly one that has Chernoff bounds.


Simply, it is the opinion of the author, that it is not rigorous to talk about “probability” as a final product, or event as a “foundation” of decisions. In the real world one is not paid in probability, but in dollars (or in survival). The fatter the tails, the more one needs to worry about payoff space—the saying goes: ”payoff swamps probability” One can be wrong very frequently if the cost is low, so long as one is convex to payoff (ie make large gains when one is right). Further, one can be forecasting with 99.99% accuracy and still go bust (in fact, more likely to go bust: funds with impeccable track records were those that went bust during the 2008-2009 rout).