Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets

by Nassim Nicholas Taleb

If you engaged in a Russian roulette–type strategy with a low probability of large loss, one that bankrupts you every several years, you are likely to show up as the winner in almost all samples—except in the year when you are dead.

Like Pascal, I will therefore state the following argument. If the science of statistics can benefit me in anything, I will use it. If it poses a threat, then I will not. I want to take the best of what the past can give me without its dangers. Accordingly, I will use statistics and inductive methods to make aggressive bets, but I will not use them to manage my risks and exposure. Surprisingly, all the surviving traders I know seem to have done the same. They trade on ideas based on some observation (that includes past history) but, like the Popperian scientists, they make sure that the costs of being wrong are limited (and their probability is not derived from past data). Unlike Carlos and John, they know before getting involved in the trading strategy which events would prove their conjecture wrong and allow for it (recall that Carlos and John used past history both to make their bets and to measure their risk). They would then terminate their trade. This is called a stop loss, a predetermined exit point, a protection from the black swan. I find it rarely practiced.

Janet feels that her husband is a failure, by comparison, but she is miscomputing the probabilities in a gross manner—she is using the wrong distribution to derive a rank. As compared to the general U.S. population, Marc has done very well, better than 99.5% of his compatriots. As compared to his high school friends, he did extremely well, a fact that he could have verified had he had time to attend the periodic reunions, and he would come at the top. As compared to the other people at Harvard, he did better than 90% of them (financially, of course). As compared to his law school comrades at Yale, he did better than 60% of them. But as compared to his co-op neighbors, he is at the bottom! Why? Because he chose to live among the people who have been successful, in an area that excludes failure. In other words, those who have failed do not show up in the sample, thus making him look as if he were not doing well at all. By living on Park Avenue, one does not have exposure to the losers, one only sees the winners. As we are cut to live in very small communities, it is difficult to assess our situation outside of the narrowly defined geographic confines of our habitat. In the case of Marc and Janet, this leads to considerable emotional distress; here we have a woman who married an extremely successful man but all she can see is comparative failure, for she cannot emotionally compare him to a sample that would do him justice.

Aside from the misperception of one’s performance, there is a social treadmill effect: You get rich, move to rich neighborhoods, then become poor again. To that add the psychological treadmill effect; you get used to wealth and revert to a set point of satisfaction. This problem of some people never really getting to feel satisfied by wealth (beyond a given point) has been the subject of technical discussions on happiness.

The mistake of ignoring the survivorship bias is chronic, even (or perhaps especially) among professionals. How? Because we are trained to take advantage of the information that is lying in front of our eyes, ignoring the information that we do not see. At the time of writing, pension funds and insurance companies in the United States and in Europe somehow bought the argument that “in the long term equities always pay off 9%” and back it up with statistics. The statistics are right, but they are past history. My argument is that I can find you a security somewhere among the 40,000 available that went up twice that amount every year without fail. Should we put the social security money into it? A brief summing up at this point: I showed how we tend to mistake one realization among all possible random histories as the most representative one, forgetting that there may be others. In a nutshell, the survivorship bias implies that the highest performing realization will be the most visible. Why? Because the losers do not show up.

Remember that nobody accepts randomness in his own success, only his failure.

It is not uncommon for someone watching a tennis game on television to be bombarded by advertisements for funds that did (until that minute) outperform others by some percentage over some period. But, again, why would anybody advertise if he didn’t happen to outperform the market? There is a high probability of the investment coming to you if its success is caused entirely by randomness. This phenomenon is what economists and insurance people call adverse selection. Judging an investment that comes to you requires more stringent standards than judging an investment you seek, owing to such selection bias. For example, by going to a cohort composed of 10,000 managers, I have 2/100 chances of finding a spurious survivor. By staying home and answering my doorbell, the chance of the soliciting party being a spurious survivor is closer to 100%.

What am I doing? The exact same task of looking for the survivor within the set of rules that can possibly work. I am fitting the rule on the data. This activity is called data snooping. The more I try, the more I am likely, by mere luck, to find a rule that worked on past data. A random series will always present some detectable pattern. I am convinced that there exists a tradable security in the Western world that would be 100% correlated with the changes in temperature in Ulan Bator, Mongolia.

To get technical, there are even worse extensions. An outstanding recent paper by Sullivan, Timmerman, and White goes further and considers that the rules that may be in use successfully today may be the result of a survivorship bias. Suppose that, over time, investors have experimented with technical trading rules drawn from a very wide universe—in principle thousands of parameterizations of a variety of types of rules. As time progresses, the rules that happen to perform well historically receive more attention and are considered “serious contenders” by the investment community, while unsuccessful trading rules are more likely to be forgotten…. If enough trading rules are considered over time, some rules are bound by pure luck, even in a very large sample, to produce superior performance even if they do not genuinely possess predictive power over asset returns. Of course, inference based solely on the subset of surviving trading rules may be misleading in this context since it does not account for the full set of initial trading rules, most of which are unlikely to have underperformed.

Our brain is not cut out for nonlinearities. People think that if, say, two variables are causally linked, then a steady input in one variable should always yield a result in the other one. Our emotional apparatus is designed for linear causality. For instance, you study every day and learn something in proportion to your studies. If you do not feel that you are going anywhere, your emotions will cause you to become demoralized. But reality rarely gives us the privilege of a satisfying linear positive progression: You may study for a year and learn nothing, then, unless you are disheartened by the empty results and give up, something will come to you in a flash. My partner Mark Spitznagel summarizes it as follows: Imagine yourself practicing the piano every day for a long time, barely being able to perform “Chopsticks,” then suddenly finding yourself capable of playing Rachmaninov. Owing to this nonlinearity, people cannot comprehend the nature of the rare event. This summarizes why there are routes to success that are nonrandom, but few, very few, people have the mental stamina to follow them. Those who go the extra mile are rewarded. In my profession one may own a security that benefits from lower market prices, but may not react at all until some critical point. Most people give up before the rewards.

Unless something moves by more than its usual daily percentage change, the event is deemed to be noise. Percentage moves are the size of the headlines. In addition, the interpretation is not linear; a 2% move is not twice as significant an event as 1 %, it is rather like four to ten times. A 7% move can be several billion times more relevant than a 1 % move! The headline of the Dow moving by 1.3 points on my screen today has less than one billionth of the significance of the serious 7% drop of October 1997.

I am just intelligent enough to understand that I have a predisposition to be fooled by randomness—and to accept the fact that I am rather emotional. I am dominated by my emotions—but as an aesthete, I am happy about that fact. I am just like every single character whom I ridiculed in this book. Not only that, but I may be even worse than them because there may be a negative correlation between beliefs and behavior (recall Popper the man). The difference between me and those I ridicule is that I try to be aware of it. No matter how long I study and try to understand probability, my emotions will respond to a different set of calculations, those that my unintelligent genes want me to handle. If my brain can tell the difference between noise and signal, my heart cannot.

What is the mechanism that should convince authors to avoid reading comments on their work, except for those they solicit from specified persons for whom they have intellectual respect? The mechanism is a probabilistic method called conditional information: Unless the source of the statement has extremely high qualifications, the statement will be more revealing of the author than the information intended by him. This applies, of course, to matters of judgment. A book review, good or bad, can be far more descriptive of the reviewer than informational about the book itself. This mechanism I also call Wittgenstein’s ruler: Unless you have confidence in the ruler’s reliability, if you use a ruler to measure a table you may also be using the table to measure the ruler. The less you trust the ruler’s reliability (in probability called the prior), the more information you are getting about the ruler and the less about the table.

This problem has a more worrying extension; we are not made to view things as independent from each other. When viewing two events A and B, it is hard not to assume that A causes B, B causes A, or both cause each other. Our bias is immediately to establish a causal link. While to a budding trader this results in hardly any worse costs than a few pennies in cab fare, it can draw the scientist into spurious inference. For it is harder to act as if one were ignorant than as if one were smart; scientists know that it is emotionally harder to reject a hypothesis than to accept it (what are called type I and type II errors)—quite a difficult matter when we have such sayings as felix qui po¨tuit cognoscere causas (happy is he who understands what is behind things). It is very hard for us to just shut up. We are not cut out for it. Popper or not, we take things too seriously.

My lesson from Soros is to start every meeting at my boutique by convincing everyone that we are a bunch of idiots who know nothing and are mistake-prone, but happen to be endowed with the rare privilege of knowing it.

The scientist’s behavior while facing the refutation of his ideas has been studied in depth as part of the so-called attribution bias. You attribute your successes to skills, but your failures to randomness. This explains why these scientists attributed their failures to the “ten sigma” rare event, indicative of the thought that they were right but that luck played against them. Why? It is a human heuristic that makes us actually believe so in order not to kill our self-esteem and keep us going against adversity.

The attribution bias has another effect: It gives people the illusion of being better at what they do, which explains the findings that 80 to 90% of people think that they are above the average (and the median) in many things.

In the “quant” world, the designation empty suit applies to the category of persons who are good at looking the part but nothing more. More appropriately, what they have is skill in getting promoted within a company rather than pure skills in making optimal decisions—we call that “corporate political skill.” These are people mostly trained at using PowerPoint presentations.

SECOND THOUGHT: ON SOME ADDITIONAL BENEFITS OF RANDOMNESS Uncertainty and Happiness

The difference between satisficers and optimizers raises a few questions. We know that people of a happy disposition tend to be of the satisficing kind, with a set idea of what they want in life and an ability to stop upon gaining satisfaction. Their goals and desires do not move along with the experiences. They do not tend to experience the internal treadmill effects of constantly trying to improve on their consumption of goods by seeking higher and higher levels of sophistication. In other words, they are neither avaricious nor insatiable. An optimizer, by comparison, is the kind of person who will uproot himself and change his official residence just to reduce his tax bill by a few percentage points. (You would think that the entire point of a higher income is to be free to choose where to live; in fact it seems, for these people, wealth causes them to increase their dependence!) Getting rich results in his seeing flaws in the goods and services he buys. The coffee is not warm enough. The cook no longer deserves the three stars given to him by the Michelin guide (he will write to the editors). The table is too far from the window. People who get promoted to important positions usually suffer from tightness of schedules: Everything has an allotted time. When they travel, everything is “organized” with optimizing intent, including lunch at 12:45 with the president of the company (a table not too far from the window), the Stairmaster at 4:40, and opera at 8:00.

Causality is not clear: The question remains whether optimizers are unhappy because they are constantly seeking a better deal or if unhappy people tend to optimize out of their misery. In any case, randomness seems to operate either as a cure or as Novocain!

I came to this conclusion when, about a decade ago, I stopped using an alarm clock. I still woke up around the same time, but I followed my own personal clock. A dozen minutes of fuzziness and variability in my schedule made a considerable difference. True, there are some activities that require such dependability that an alarm clock is necessary, but I am free to choose a profession where I am not a slave to external pressure. Living like this, one can also go to bed early and not optimize one’s schedule by squeezing every minute out of one’s evening. At the limit, you can decide whether to be (relatively) poor, but free of your time, or rich but as dependent as a slave.

Another way to see the beastly aspect of schedules and rigid projections is to think in limit situations. Would you like to know with great precision the date of your death? Would you like to know who committed the crime before the beginning of the movie? Actually, wouldn’t it be better if the length of movies were kept a secret?