The Black Swan

Notes

1

The spread of camera cell phones has afforded me a large collection of pictures of black swans sent by traveling readers. Last Christmas I also got a case of Black Swan Wine (not my favorite), a videotape (I don’t watch videos), and two books. I prefer the pictures.

2

The highly expected not happening is also a Black Swan. Note that, by symmetry, the occurrence of a highly improbable event is the equivalent of the nonoccurrence of a highly probable one.

3

Recursive here means that the world in which we live has an increasing number of feedback loops, causing events to be the cause of more events (say, people buy a book because other people bought it), thus generating snowballs and arbitrary and unpredictable planet-wide winner-take-all effects. We live in an environment where information flows too rapidly, accelerating such epidemics. Likewise, events can happen because they are not supposed to happen. (Our intuitions are made for an environment with simpler causes and effects and slowly moving information.) This type of randomness did not prevail during the Pleistocene, as socioeconomic life was far simpler then.

4

It is also naïve empiricism to provide, in support of some argument, series of eloquent confirmatory quotes by dead authorities. By searching, you can always find someone who made a well-sounding statement that confirms your point of view – and, on every topic, it is possible to find another dead thinker who said the exact opposite. Almost all of my non-Yogi Berra quotes are from people I disagree with.

5

It is remarkable how fast and how effectively you can construct a nationality with a flag, a few speeches, and a national anthem; to this day I avoid the label “Lebanese”, preferring the less restrictive “Levantine” designation.

6

Benoît Mandelbrot, who had a similar experience at about the same age, though close to four decades earlier, remembers his own war episode as long stretches of painful boredom punctuated by brief moments of extreme fear.

7

The historian Niall Ferguson showed that, despite all the standard accounts of the buildup to the Great War, which describe “mounting tensions” and “escalating crises”, the conflict came as a surprise. Only retrospectively was it seen as unavoidable by backward-looking historians. Ferguson used a clever empirical argument to make his point: he looked at the prices of imperial bonds, which normally include investors’ anticipation of government’s financing needs and decline in expectation of conflicts since wars cause severe deficits. But bond prices did not reflect the anticipation of war. Note that this study illustrates, in addition, how working with prices can provide a good understanding of history.

8

We will see in Chapter 10 some clever quantitative tests done to prove such herding; they show that, in many subject matters, the distance between opinions is remarkably narrower than the distance between the average of opinions and truth.

9

I then realized that the great strength of the free-market system is the fact that company executives don’t need to know what’s going on.

10

I specialized in complicated financial instruments called “derivatives”, those that required advanced mathematics – but for which the errors for using the wrong mathematics were the greatest. The subject was new and attractive enough for me to get a doctorate in it.

11

Her third husband was an Italian philosopher.

12

To those readers who Googled Yevgenia Krasnova, I am sorry to say that she is (officially) a fictional character.

13

I emphasize possible because the chance of these occurrences is typically in the order of one in several trillion trillion, as close to impossible as it gets.

14

What I call “probability distribution” here is the model used to calculate the odds of different events, how they are distributed. When I say that an event is distributed according to the “bell curve”, I mean that the Gaussian bell curve (after C. F. Gauss; more on him later) can help provide probabilities of various occurrences.

15

I am safe since I never wear ties (except at funerals).

16

Since Russell’s original example used a chicken, this is the enhanced North American adaptation.

17

Statements like those of Captain Smith are so common that it is not even funny. In September 2006, a fund called Amaranth, ironically named after a flower that “never dies”, had to shut down after it lost close to $7 billion in a few days, the most impressive loss in trading history (another irony: I shared office space with the traders). A few days prior to the event, the company made a statement to the effect that investors should not worry because they had twelve risk managers – people who use models of the past to produce risk measures on the odds of such an event. Even if they had one hundred and twelve risk managers, there would be no meaningful difference; they still would have blown up. Clearly you cannot manufacture more information than the past can deliver; if you buy one hundred copies of The New York Times, I am not too certain that it would help you gain incremental knowledge of the future. We just don’t know how much information there is in the past.

18

The main tragedy of the high impact-low probability event comes from the mismatch between the time taken to compensate someone and the time one needs to be comfortable that he is not making a bet against the rare event. People have an incentive to bet against it, or to game the system since they can be paid a bonus reflecting their yearly performance when in fact all they are doing is producing illusory profits that they will lose back one day. Indeed, the tragedy of capitalism is that since the quality of the returns is not observable from past data, owners of companies, namely shareholders, can be taken for a ride by the managers who show returns and cosmetic profitability but in fact might be taking hidden risks.

19

Neither Peirce nor Popper was the first to come up with this asymmetry. The philosopher Victor Brochard mentioned the importance of negative empiricism in 1878, as if it were a matter held by the empiricists to be the sound way to do business – ancients understood it implicitly. Out-of-print books deliver many surprises.

20

This confirmation problem pervades our modern life, since most conflicts have at their root the following mental bias: when Arabs and Israelis watch news reports they see different stories in the same succession of events. Likewise, Democrats and Republicans look at different parts of the same data and never converge to the same opinions. Once your mind is inhabited with a certain view of the world, you will tend to only consider instances proving you to be right. Paradoxically, the more information you have, the more justified you will feel in your views.

21

Clearly, weather-related and geodesic events (such as tornadoes and earthquakes) have not changed much over the past millennium, but what have changed are the socioeconomic consequences of such occurrences. Today, an earthquake or hurricane commands more and more severe economic consequences than it did in the past because of the interlocking relationships between economic entities and the intensification of the “network effects” that we will discuss in Part Three. Matters that used to have mild effects now command a high impact. Tokyo’s 1923 earthquake caused a drop of about a third in Japan’s GNR Extrapolating from the tragedy of Kobe in 1994, we can easily infer that the consequences of another such earthquake in Tokyo would be far costlier than that of its predecessor.

22

The word the is written twice.

23

The Parisian novelist Georges Perec tried to break away from narrative and attempted to write a book as large as the world. He had to settle for an exhaustive account of what happened on the Place Saint-Sulpice between October 18 and October 20, 1974. Even so, his account was not so exhaustive, and he ended up with a narrative.

24

Such tests avoid both the narrative fallacy and much of the confirmation bias, since testers are obliged to take into account the failures as well as the successes of their experiments.

25

The best noncharlatanic finance book I know is called What I Learned Losing a Million Dollars, by D. Paul and B. Moynihan. The authors had to self-publish the book.

26

Doctors are rightfully and vigorously skeptical of anecdotal results, and require that studies of drug efficacy probe into the cemetery of silent evidence. However, the same doctors fall for the bias elsewhere! Where? In their personal lives, or in their investment activities. At the cost of being repetitive, I have to once again state my amazement at the aspect of human nature that allows us to mix the most rigorous skepticism and the most acute gullibility.

27

My colleague Mark Spitznagel found a martial version of the ludic fallacy: organized competitive fighting trains the athlete to focus on the game and, in order not to dissipate his concentration, to ignore the possibility of what is not specifically allowed by the rules, such as kicks to the groin, a surprise knife, et cetera. So those who win the gold medal might be precisely those who will be most vulnerable in real life. Likewise, you see people with huge muscles (in black T-shirts) who can impress you in the artificial environment of the gym but are unable to lift a stone.

28

What Nietzsche means by this term are the dogma-prone newspaper readers and opera lovers who have cosmetic exposure to culture and shallow depth. I extend the term here to the philistine hiding in academia who lacks in erudition out of lack of curiosity and is closely centered on his ideas.

29

Note that these sayings attributed to Yogi Berra might be apocryphal – it was the physicist Niels Bohr who came up with the first one, and plenty of others came up with the second. These sayings remain, however, quintessential Berraisms.

30

The book you have in your hands is approximately and “unexpectedly” fifteen months late.

31

While forecast errors have always been entertaining, commodity prices have been a great trap for suckers. Consider this 1970 forecast by U.S. officials (signed by the U.S. Secretaries of the Treasury, State, Interior, and Defense): “the standard price of foreign crude oil by 1980 may well decline and will in any event not experience a substantial increase”. Oil prices went up tenfold by 1980. I just wonder if current forecasters lack in intellectual curiosity or if they are intentionally ignoring forecast errors.

32

I owe the reader an answer concerning Catherine’s lover count. She had only twelve.

33

Most of the debate between creationists and evolutionary theorists (of which I do not partake) lies in the following: creationists believe that the world comes from some form of design while evolutionary theorists see the world as a result of random changes by an aimless process. But it is hard to look at a computer or a car and consider them the result of aimless process. Yet they are.

34

Recall from Chapter 4 how Algazel and Averroës traded insults through book titles. Perhaps one day I will be lucky enough to read an attack on this book in a diatribe called The White Swan.

35

Such claims are not uncommon. For instance the physicist Albert Michelson imagined, toward the end of the nineteenth century, that what was left for us to discover in the sciences of nature was no more than fine-tuning our precisions by a few decimal places.

36

There are more limits I haven’t even attempted to discuss here. I am not even bringing up the class of incomputability people call NP completeness.

37

This idea pops up here and there in history, under different names. Alfred North Whitehead called it the “fallacy of misplaced concreteness”, e.g., the mistake of confusing a model with the physical entity that it means to describe.

38

These graphs also illustrate a statistical version of the narrative fallacy – you find a model that fits the past. “Linear regression” or “R-square” can ultimately fool you beyond measure, to the point where it is no longer funny. You can fit the linear part of the curve and claim a high R-square, meaning that your model fits the data very well and has high predictive powers. All that off hot air: you only fit the linear segment of the series. Always remember that “R-square” is unfit for Extremis­tan; it is only good for academic promotion.

39

Yogi Berra might have a theory of epilogism with his saying, “You can observe a lot by just watching”.

40

While looking at the past it would be a good idea to resist naïve analogies. Many people have compared the United States today to Ancient Rome, both from a military standpoint (the destruction of Carthage was often invoked as an incentive for the destruction of enemy regimes) and from a social one (the endless platitudinous warnings of the upcoming decline and fall). Alas, we need to be extremely careful in transposing knowledge from a simple environment that is closer to type 1, like the one we had in antiquity, to today’s type 2, complex system, with its intricate webs of casual links. Another error is to draw casual conclusions from the absence of nuclear war, since, invoking the Casanova argument of Chapter 8, I would repeat that we would not be here had a nuclear war taken place, and it is not a good idea for us to derive a “cause” when our survival is conditioned on that cause.

41

This chapter provides a general conclusion for those who by now say, “Taleb, I get the point, but what should I do?” My answer is that if you got the point, you are pretty much there. But here is a nudge.

42

Dan Gilbert showed in a famous paper, “How Mental Systems Believe”, that we are not natural skeptics and that not believing required an expenditure of mental effort.

43

Make sure that you have plenty of these small bets; avoid being blinded by the vividness of one single Black Swan. Have as many of these small bets as you can conceivably have. Even venture capital firms fall for the narrative fallacy with a few stories that “make sense” to them; they do not have as many bets as they should. If venture capital firms are profitable, it is not because of the stories they have in their heads, but because they are exposed to unplanned rare events.

44

There is a finer epistemological point. Remember that in a virtuous Black Swan business, what the past did not reveal is almost certainly going to be good for you. When you look at past biotech revenues, you do not see the superblockbuster in them, and owing to the potential for a cure for cancer (or headaches, or baldness, or bad sense of humor, etc.), there is a small probability that the sales in that industry may turn out to be monstrous, far larger than might be expected. On the other hand, consider negative Black Swan businesses. The track record you see is likely to overestimate the properties. Recall the 1982 blowup of banks: they appeared to the naïve observer to be more profitable than they seemed. Insurance companies are of two kinds: the regular diversifiable kind that belongs to Mediocristan (say, life insurance) and the more critical and explosive Black Swan-prone risks that are usually sold to reinsurers. According to the data, reinsurers have lost money on underwriting over the past couple of decades, but, unlike bankers, they are introspective enough to know that it actually could have been far worse, because the past twenty years did not have a big catastrophe, and all you need is one of those per century to kiss the business good-bye. Many finance academics doing “valuation” on insurance seem to have missed the point.

45

These scalable laws were already discussed in the scriptures: “For onto everyone that hath shall be given, and he shall have abundance; but from him that hath not shall be taken away even that which he hath”. Matthew (Matthew 25:29, King James Version).

46

Much of the perception of the importance of precocity in the career of researchers can be owed to the misunderstanding of the perverse role of this effect, especially when reinforced by bias. Enough counterexamples, even in fields like mathematics meant to be purely a “young man’s game”, illustrate the age fallacy: simply, it is necessary to be successful early, and even very early at that.

47

The Web’s bottom-up feature is also making book reviewers more accountable. While writers were helpless and vulnerable to the arbitrariness of book reviews, which can distort their messages and, thanks to the confirmation bias, expose small irrelevant weak points in their text, they now have a much stronger hand. In place of the moaning letter to the editor, they can simply post their review of a review on the Web. If attacked ad hominem, they can reply ad hominem and go directly after the credibility of the reviewer, making sure that their statement shows rapidly in an Internet search or on Wikipedia, the bottom-up encyclopedia.

48

As if we did not have enough problems, banks are now more vulnerable to the Black Swan and the ludic fallacy than ever before with “scientists” among their staff taking care of exposures. The giant firm J. P. Morgan put the entire world at risk by introducing in the nineties RiskMetrics, a phony method aiming at managing people’s risks, causing the generalized use of the ludic fallacy, and bringing Dr. Johns into power in place of the skeptical Fat Tonys. (A related method called “Value-at-Risk”, which relies on the quantitative measurement of risk, has been spreading.) Likewise, the government-sponsored institution Fanny Mae, when I look at their risks, seems to be sitting on a barrel of dynamite, vulnerable to the slightest hiccup. But not to worry: their large staff of scientists deemed these events “unlikely”.

49

The nontechnical (or intuitive) reader can skip this chapter, as it goes into some details about the bell curve. Also, you can skip it if you belong to the category of fortunate people who do not know about the bell curve.

50

I have fudged the numbers a bit for simplicity’s sake.

51

One of the most misunderstood aspects of a Gaussian is its fragility and vulnerability in the estimation of tail events. The odds of a 4 sigma move are twice that of a 4.15 sigma. The odds of a 20 sigma are a trillion times higher than those of a 21 sigma! It means that a small measurement error of the sigma will lead to a massive underestimation of the probability. We can be a trillion times wrong about some events.

52

My main point, which I repeat in some form or another throughout Part Three, is as follows. Everything is made easy, conceptually, when you consider that there are two, and only two, possible paradigms: nonscalable (like the Gaussian) and other (such as Mandebrotian randomness). The rejection of the application of the non-scalable is sufficient, as we will see later, to eliminate a certain vision of the world. This is like negative empiricism: I know a lot by determining what is wrong.

53

Note that variables may not be infinitely scalable; there could be a very, very remote upper limit – but we do not know where it is so we treat a given situation as if it were infinitely scalable. Technically, you cannot sell more of one book than there are denizens of the planet – but that upper limit is large enough to be treated as if it didn’t exist. Furthermore, who knows, by repackaging the book, you might be able to sell it to a person twice, or get that person to watch the same movie several times.

54

As I was revising this draft, in August 2006, I stayed at a hotel in Dedham, Massachusetts, near one of my children’s summer camps. There, I was a little intrigued by the abundance of weight-challenged people walking around the lobby and causing problems with elevator backups. It turned out that the annual convention of NAFA, the National Association for Fat Acceptance, was being held there. As most of the members were extremely overweight, I was not able to figure out which delegate was the heaviest: some form of equality prevailed among the very heavy (someone much heavier than the persons I saw would have been dead). I am sure that at the NARA convention, the National Association for Rich Acceptance, one person would dwarf the others, and, even among the superrich, a very small percentage would represent a large section of the total wealth.

55

The nontechnical reader can skip from here until the end of the chapter.

56

By using symmetry we could also examine the incidences below the number.

57

Source: M.E.J. Newman(2005) and the author’s own calculations.

58

Clearly, you do not observe 100 percent in a finite sample.

59

This is a simple illustration of the general point of this book in finance and economics. If you do not believe in applying the bell curve to social variables, and if, like many professionals, you are already convinced that "modern" financial theory is dangerous junk science, you can safely skip this chapter.

60

Granted, the Gaussian has been tinkered with, using such methods as complementary “jumps”, stress testing, regime switching, or the elaborate methods known as GARCH, but while these methods represent a good effort, they fail to address the bell curve’s fundamental flaws. Such methods are not scale-invariant. This, in my opinion, can explain the failures of sophisticated methods in real life as shown by the Makridakis competition.

61

More technically, remember my career as an option professional. Not only does an option on a very long shot benefit from Black Swans, but it benefits disproportionately from them – something Scholes and Merton’s “formula” misses. The option payoff is so powerful that you do not have to be right on the odds: you can be wrong on the probability, but get a monstrously large payoff. I’ve called this the “double bubble”: the overpricing of the probability and that of the payoff.

62

I am selecting Merton because I found him very illustrative of academically stamped obscurantism. I discovered Merton’s shortcomings from an angry and threatening seven-page letter he sent me that gave me the impression that he was not too familiar with how we trade options, his very subject matter. He seemed to be under the impression that traders rely on “rigorous” economic theory – as if birds had to study (bad) engineering in order to fly.

63

Medieval medicine was also based on equilibrium ideas when it was top-down and similar to theology. Luckily its practitioners went out of business, as they could not compete with the bottom-up surgeons, ecologically driven former barbers who gained clinical experience, and after whom a-Platonic clinical science was born. If I am alive, today, it is because scholastic top-down medicine went out of business a few centuries ago.

64

I lost his business card, but would like to warmly thank a scientist traveling to Vienna aboard British Airways flight 700 on December 11, 2003, for suggesting the billiard ball illustration in Chapter 11. All I know about him is that he was fifty-two, gray-haired, English-born, wrote poetry on yellow notepads, and was traveling with seven suitcases since he was moving in with his thirty-five-year-old Viennese girlfriend.

65

It is impossible to go very deep into an idea when you run a business, no matter the number of hours the occupation entails – simply put, unless you are insensitive, the worries and feelings of responsibility occupy precious cognitive space. You may be able to study, meditate, and write if you are an employee, but not when you own a business – unless you are of an irresponsible nature. I thank my partner, Mark Spitznagel, for allowing me – thanks to the clarity of his mind and his highly systematic, highly disciplined, and well engineered approach – to gain exposure to high-impact rare events without my having to get directly involved in business activities.