The Black Swan

by Nassim Nicholas Taleb

  Finally, I got something out of my debates: the evidence that Black Swan events are largely caused by people using measures way over their heads, instilling false confidence based on bogus results. In addition to my befuddlement concerning why people use measures from Mediocristan outside those measures’ applicability, and believe in them, I had the inkling of a much larger problem: that almost none of the people who worked professionally with probabilistic measures knew what they were talking about, which was confirmed as I got into debates and panels with many hotshots, at least four with “Nobels” in economics. Really. And this problem was measurable, very easily testable. You could have finance “quants,” academics, and students use and write papers and papers using the notion of “standard deviation,” yet not understand intuitively what it meant, so you could trip them up by asking them elementary questions about the nonmathematical, real conceptual meaning of their numbers. And trip them up we did. Dan Goldstein and I ran experiments on professionals using probabilistic tools, and were shocked to see that up to 97 percent of them failed elementary questions.* Emre Soyer and Robin Hogarth subsequently took the point and tested it in the use of an abhorrent field called econometrics (a field that, if any scientific scrutiny was applied to it, would not exist)—again, most researchers don’t understand the tools they are using.

  Now that the book’s reception is off my chest, let us move into more analytical territory.

  * In Latin: “pearls before swine.”

  * Most intellectuals keep attributing the black swan expression to Popper or Mill, sometimes Hume, in spite of the quote by Juvenal. The Latin expression niger cygnus might even be more ancient, possibly of Etruscan origin.

  † One frequent confusion: people believe that I am suggesting that agents should bet on Black Swans taking place, when I am saying that they should avoid blowing up should a Black Swan take place. As we will see in section IV, I am advocating omission, not commission. The difference is enormous, and I have been completely swamped by people wondering if one can “bleed to death” making bets on the occurrence of Black Swans (like Nero, Giovanni Drogo, or the poor scientist with a rich brother-in-law). These people have made their choice for existential reasons, not necessarily economic ones, although the economics of such a strategy makes sense for a collective.

  * If most of the people mixed up about the message appear to be involved in economics and social science, while a much smaller share of readers come from those segments, it is because other members of society without such baggage get the book’s message almost immediately.

  * For instance, one anecdote that helps explain the crisis of 2008. One Matthew Barrett, former Chairman of Barclays Bank and Bank of Montreal (both of which underwent blowups from exposures to Extremistan using risk management methods for Mediocristan) complained, after all the events of 2008 and 2009, that The Black Swan did not tell him “what should I do about that?” and he “can’t run a business” worrying about Black Swan risks. The person has never heard of the notion of fragility and robustness to extreme deviations—which illustrates my idea that evolution does not work by teaching, but destroying.

  * So far, about fourteen scholarly (but very, very boring) articles. (They are boring both to read and to write!) The number keeps growing, though, and they are being published at a pace of three a year. Taleb (2007), Taleb and Pilpel (2007), Goldstein and Taleb (2007), Taleb (2008), Taleb (2009), Taleb, Goldstein and Spitznagel (2009), Taleb and Pilpel (2009), Mandelbrot and Taleb (2010), Makridakis and Taleb (2010), Taleb (2010), Taleb and Tapiero (2010a), Taleb and Tapiero (2010b), Taleb and Douady (2010), and Goldstein and Taleb (2010).

  * Although his is a bit extreme, this phoniness is not uncommon at all. Many intellectually honest people I had warned, and who had read my book, later blamed me for not telling them about the crisis—they just could not remember it. It is hard for a newly enlightened pig to recall that he has seen a pearl in the past but did not know what it was.

  * Dan Goldstein and I have been collaborating and running experiments about human intuitions with respect to different classes of randomness. He does not walk slowly.

  IV

  ASPERGER AND THE ONTOLOGICAL BLACK SWAN

  Are nerds more blind to swans? Social skills in Extremistan—On the immortality of Dr. Greenspan

  If The Black Swan is about epistemic limitations, then, from this definition, we can see that it is not about some objectively defined phenomenon, like rain or a car crash—it is simply something that was not expected by a particular observer.

  So I was wondering why so many otherwise intelligent people have casually questioned whether certain events, say the Great War, or the September 11, 2001, attack on the World Trade Center, were Black Swans, on the grounds that some predicted them. Of course the September 11 attack was a Black Swan to those victims who died in it; otherwise, they would not have exposed themselves to the risk. But it was certainly not a Black Swan to the terrorists who planned and carried out the attack. I have spent considerable time away from the weight-lifting room repeating that a Black Swan for the turkey is not a Black Swan for the butcher.

  The same applies to the crisis of 2008, certainly a Black Swan to almost all economists, journalists, and financiers on this planet (including, predictably, Robert Merton and Myron Scholes, the turkeys of Chapter 17), but certainly not to this author. (Incidentally, as an illustration of another common mistake, almost none of those—very few—who seemed to have “predicted” the event predicted its depth. We will see that, because of the atypicality of events in Extremistan, the Black Swan is not just about the occurrence of some event but also about its depth and consequences.)

  ASPERGER PROBABILITY

  This consideration of an objective Black Swan, one that would be the same to all observers, aside from missing the point completely, seems dangerously related to the problem of underdevelopment of a human faculty called “theory of mind” or “folk psychology.” Some people, otherwise intelligent, have a deficiency of that human ability to impute to others knowledge that is different from their own. These, according to researchers, are the people you commonly see involved in engineering or populating physics departments. We saw one of them, Dr. John, in Chapter 9.

  You can test a child for underdevelopment of the theory of mind using a variant of the “false-belief task.” Two children are introduced. One child puts a toy under the bed and leaves the room. During his absence, the second child—the subject—removes it and hides it in a box. You ask the subject: Where, upon returning to the room, will the other child look for the toy? Those under, say, the age of four (when the theory of mind starts developing), choose the box, while older children correctly say that the other child will look under the bed. At around that age, children start realizing that another person can be deprived of some of the information they have, and can hold beliefs that are different from their own. Now, this test helps detect mild forms of autism: as high as one’s intelligence may be, it can be difficult for many to put themselves in other people’s shoes and imagine the world on the basis of other people’s information. There is actually a name for the condition of a person who can be functional but suffers from a mild form of autism: Asperger syndrome.

  The psychologist Simon Baron-Cohen has produced much research distinguishing between polar extremes in people’s temperament with respect to two faculties: ability to systematize, and ability to empathize and understand others. According to his research, purely systematizing persons suffer from a lack of theory of mind; they are drawn to engineering and similar occupations (and when they fail, to, say, mathematical economics); empathizing minds are drawn to more social (or literary) professions. Fat Tony, of course, would fall in the more social category. Males are overrepresented in the systematizing category; females dominate the other extreme.

  Note the unsurprising, but very consequential fact that people with Asperger syndrome are highly averse to ambiguity.

  Research shows that academics are overrep
resented in the systematizing, Black-Swan-blind category; these are the people I called “Locke’s madmen” in Chapter 17. I haven’t seen any formal direct test of Black Swan foolishness and the systematizing mind, except for a calculation George Martin and I made in 1998, in which we found evidence that all the finance and quantitative economics professors from major universities whom we tracked and who got involved in hedge fund trading ended up making bets against Black Swans, exposing themselves to blowups. This preference was nonrandom, since between one third and one half of the nonprofessors had that investment style at the time. The best known such academics were, once again, the “Nobel”-crowned Myron Scholes and Robert C. Merton, whom God created so that I could illustrate my point about Black Swan blindness.* They all experienced problems during the crisis, discussed in that chapter, that brought down their firm Long Term Capital Management. Note that the very same people who make a fuss about discussions of Asperger as a condition not compatible with risk-bearing and the analysis of nonexplicit off-model risks, with its corresponding dangers to society, would be opposed to using a person with highly impaired eyesight as the driver of a school bus. All I am saying is that just as I read Milton, Homer, Taha Husain, and Borges (who were blind) but would prefer not to have them drive me on the Nice–Marseilles motorway, I elect to use tools made by engineers but prefer to have society’s risky decisions managed by someone who is not affected with risk-blindness.

  FUTURE BLINDNESS REDUX

  Now recall the condition, described in Chapter 12, of not properly transferring between past and future, an autism-like condition in which people do not see second-order relations—the subject does not use the relation between the past’s past and the past’s future to project the connection between today’s past and today’s future. Well, a gentleman called Alan Greenspan, the former chairman of the U.S. Federal Reserve Bank, went to Congress to explain that the banking crisis, which he and his successor Bernanke helped cause, could not have been foreseen because it “had never happened before.” Not a single member of congress was intelligent enough to shout, “Alan Greenspan, you have never died before, not in eighty years, not even once; does that make you immortal?” The abject Robert Rubin, the bankster I was chasing in Section II, a former secretary of the Treasury, used the same argument—but the fellow had written a long book on uncertainty (with, ironically, my publisher and the same staff used for The Black Swan).*

  I discovered (but by then I was not even surprised) that no researcher has tested whether large deviations in economics can be predicted from past large deviations—whether large deviations have predecessors, that is. This is one of the elementary tests missing in the field, as elementary as checking whether a patient is breathing or whether a lightbulb is screwed in, but characteristically nobody seems to have tried to do it. It does not take a lot of introspection to figure out that big events don’t have big parents: the Great War did not have a predecessor; the crash of 1987, in which the market went down close to 23 percent in a single day, could not have been guessed from its worst predecessor, a one-day loss of around 10 percent—and this applies to almost all such events, of course. My results were that regular events can predict regular events, but that extreme events, perhaps because they are more acute when people are unprepared, are almost never predicted from narrow reliance on the past.

  The fact that this notion is not obvious to people is shocking to me. It is particularly shocking that people do what are called “stress tests” by taking the worst possible past deviation as an anchor event to project the worst possible future deviation, not thinking that they would have failed to account for that past deviation had they used the same method on the day before the occurrence of that past anchor event.*

  These people have PhDs in economics; some are professors—one of them is the chairman of the Federal Reserve (at the time of writing). Do advanced degrees make people blind to these elementary notions?

  Indeed, the Latin poet Lucretius, who did not attend business school, wrote that we consider the biggest objeect of any kind that we have seen in our lives as the largest possible item: et omnia de genere omni / Maxima quae vivit quisque, haec ingentia fingit.

  PROBABILITY HAS TO BE SUBJECTIVE†

  This raises a problem that is worth probing in some depth. The fact that many researchers do not realize immediately that the Black Swan corresponds mainly to an incomplete map of the world, or that some researchers have to stress this subjective quality (Jochen Runde, for instance, wrote an insightful essay on the Black Swan idea, but one in which he felt he needed to go out of his way to stress its subjective aspect), takes us to the historical problem in the very definition of probability. Historically, there have been many approaches to the philosophy of probability. The notion that two people can have two different views of the world, then express them as different probabilities remained foreign to the research. So it took a while for scientific researchers to accept the non-Asperger notion that different people can, while being rational, assign different probabilities to different future states of the world. This is called “subjective probability.”

  Subjective probability was formulated by Frank Plumpton Ramsey in 1925 and Bruno de Finetti in 1937. The take on probability by these two intellectual giants is that it can be represented as a quantification of the degree of belief (you set a number between 0 and 1 that corresponds to the strength of your belief in the occurrence of a given event), subjective to the observer, who expresses it as rationally as he wishes under some constraints. These constraints of consistency in decision making are obvious: you cannot bet there is a 60 percent chance of snow tomorrow and a 50 percent chance that there will be no snow. The agent needs to avoid violating something called the Dutch book constraint: that is, you cannot express your probabilities inconsistently by engaging in a series of bets that lock in a certain loss, for example, by acting as if the probabilities of separable contingencies can add up to more than 100 percent.

  There is another difference here, between “true” randomness (say the equivalent of God throwing a die) and randomness that results from what I call epistemic limitations, that is, lack of knowledge. What is called ontological (or ontic) uncertainty, as opposed to epistemic, is the type of randomness where the future is not implied by the past (or not even implied by anything). It is created every minute by the complexity of our actions, which makes the uncertainty much more fundamental than the epistemic one coming from imperfections in knowledge.

  It means that there is no such thing as a long run for such systems, called “nonergodic” systems—as opposed to the “ergodic” ones. In an ergodic system, the probabilities of what may happen in the long run are not impacted by events that may take place, say, next year. Someone playing roulette in the casino can become very rich, but, if he keeps playing, given that the house has an advantage, he will eventually go bust. Someone rather unskilled will eventually fail. So ergodic systems are invariant, on average, to paths, taken in the intermediate term—what researchers call absence of path dependency. A nonergodic system has no real long-term properties—it is prone to path dependency.

  I believe that the distinction between epistemic and ontic uncertainty is important philosophically, but entirely irrelevant in the real world. Epistemic uncertainty is so hard to disentangle from the more fundamental one. This is the case of a “distinction without a difference” that (unlike the ones mentioned earlier) can mislead because it distracts from the real problems: practitioners make a big deal out of it instead of focusing on epistemic constraints. Recall that skepticism is costly, and should be available when needed.

  There is no such thing as a “long run” in practice; what matters is what happens before the long run. The problem of using the notion of “long run,” or what mathematicians call the asymptotic property (what happens when you extend something to infinity), is that it usually makes us blind to what happens before the long run, which I will discuss later as preasymptotics. Different functions have differ
ent preasymptotics, according to speed of convergence to that asymptote. But, unfortunately, as I keep repeating to students, life takes place in the preasymptote, not in some Platonic long run, and some properties that hold in the preasymptote (or the short run) can be markedly divergent from those that take place in the long run. So theory, even if it works, meets a short-term reality that has more texture. Few understand that there is generally no such thing as a reachable long run except as a mathematical construct to solve equations; to assume a long run in a complex system, you need to also assume that nothing new will emerge. In addition, you may have a perfect model of the world, stripped of any uncertainty concerning the analytics of the representation, but have a small imprecision in one of the parameters to input in it. Recall Lorenz’s butterfly effect of Chapter 11. Such minutely small uncertainty, at the level of the slightest parameter, might, because of nonlinearities, percolate to a huge uncertainty at the level of the output of the model. Climate models, for instance, suffer from such nonlinearities, and even if we had the right model (which we, of course, don’t), a small change in one of the parameters, called calibration, can entirely reverse the conclusions.

  We will discuss preasymptotics further when we look at the distinctions between different classes of probability distributions. I will say for now that many of these mathematical and philosophical distinctions are entirely overblown, Soviet-Harvard-style, top-down, as people start with a model and then impose it on reality and start categorizing, rather than start with reality and look at what fits it, in a bottom-up way.

  Probability on a Thermometer

  This distinction, misused in practice, resembles another deficient separation discussed earlier, between what economists call Knightian risk (computable) and Knightian uncertainty (uncomputable). This assumes that something is computable, when really everything is more or less incomputable (and rare events more so). One has to have a mental problem to think that probabilities of future events are “measurable” in the same sense that the temperature is measurable by a thermometer. We will see in the following section that small probabilities are less computable, and that this matters when the associated payoffs are consequential.