Fooled By Randomness by Nassim Nicholas Taleb


Aut tace aut loquele meliora solencio (only when the words outperform silence).

Solon: The observation of the numerous misfortunes that attend all conditions forbids us to grow insolent upon our present enjoyments, or to admire a man’s happiness that may yet, in course of time, suffer change. For the uncertain future has yet to come, with all variety of future; and him only to whom the divinity has guaranteed continued happiness until the end we may call happy.


Such tendency to make and unmake prophets based on the fate of the roulette wheel is symptomatic of our ingrained inability to cope with the complex structure of randomness prevailing in the modern world. 

People do not like to insure against something abstract; the risk that merits their attention is always something vivid. 

Age is beauty, almost always, and the new and the young are generally toxic. 

When I think of Monte Carlo mathematics, I think of a happy combination of the two: The Monte Carlo man’s realism without the shallowness, combined with the mathematician’s intuition with the excessive abstraction. 

Monte Carlo methods consist of creating artificial history using the sample path concepts. 

The word sample stresses that one sees only one realization among a collection of possible ones. 

A mistake is not something to be determined after the fact, but in the light of the information until that point. 

Distilled Thinking: thinking based on information around us that is stripped of meaningless but diverting clutter. 

A journalist should view matters like a historian, and play down the value of the information he is providing, such as by saying: “Today the market went up, but this information is not too relevant as it emanates mostly from noise.”

A preference for distilled thinking implies favoring old investors and traders, that is, investors who have been exposed to markets the longest, a matter that is counter to the common Wall Street practice of preferring those that have been the most profitable, and preferring the youngest whenever possible.

The wise man listens to meaning; the fool only gets the noise.

Cavafy: For the gods perceive things in the future, ordinary people things in the present, bu the wise perceive things about to happen. 

I reckon that I am not immune to such emotional defect. But I deal with it by having no access to information, except in rare circumstances. Again, I prefer to read poetry. If an event is important enough, it will find its way to my ears.

People who look to closely at randomness burn out, their emotions drained by the series of pangs they experience. Regardless of what people claim, a negative pan is not offset by a positive one (some psychologists estimate the negative effect for an average loss to be up to 2.5 the magnitude of a positive one); it will lead to an emotional deficit.

Science lies in the rigor of the inference, not in random references to such grandiose concepts as general relativity or quantum indeterminacy. Such rigor can be spelled out in plain English. Science is a method and rigor; it can be identified in the simplest of prose writings. 

At a given time in the market, the most successful traders are likely to be those that are best fit to the latest cycle.

Loyalty to ideas is not a good thing for traders, scientists - or anyone.

The difference between a trader and an investor lies in the duration of the bet, and the corresponding size. There is absolutely nothing wrong with investing “for the long haul,” provided one does not mix it with short-term trading - it is just that many people become long-term investors after they lose money, postponing their decision to sell as part of their denial. 

Both bought more bonds after the market declined sharply, but not in response to a predetermined plan.

Darwinian ideas are about reproductive fitness, not about survival. 

I try to benefit from rare events, events that do not tend to repeat themselves frequently, but, accordingly, present a large payoff when they occur. I try to make money infrequently, as infrequently as possible, simply because I believe that rare events are not fairly valued, and that the rarer the vent, the more undervalued it will be in price. In addition to my own empiricism, I think that the counterintuitive aspect of the trade (and the fact that our emotional wiring does not accommodate it) gives me some form of advantage. 


I started to label a rare event as any behavior where the adage “beware of calm waters” can hold. 

I associate rare events with any misunderstanding of the risks derived from a narrow interpretation of past time series. 

No amount of observations of white swans can allow the inference that all swans are white, but the observance of a single black swan is sufficient to refute that conclusion.

In spite of my being a voracious reader, I have rarely been truly affected in my behavior (in any durable manner) by anything I have read. A book can make a strong impression, but such an impression tends to wane after some newer impression replaces it in my brain (a new book). I have to discover things by myself. These self-discoveries last. 

There are only two types of theories: 1. Theories that are known to be wrong, as they were tested and adequately rejected (labeled falsified); and 2. Theories that have not yet been known to be wrong, not falsified yet, but are exposed to be proved wrong. 

A theory cannot be verified. It can only be provisionally accepted. A theory that falls outside of these two categories is not a theory. A theory that does not present a set of conditions under which it would be considered wrong would be termed charlatanism - it would be impossible to reject otherwise. Why? Because the astrologist can always find a reason to fit the past event, by saying that Mars was probably in line but not too much so (likewise to me a trader who does not have a point that would make him change his mind is not a trader). 

I speculate in all of my activities on theories that represent some vision of the world, but with the following stipulation: No rare event should harm me. In fact, I would like all conceivable rare events to help me. 

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 statics and inductive methods to make aggressive bests, but I will not use them to manage my risks and exposure. Trade on ideas based on some observation (that includes past history) but make sure that the costs of being wrong are limited.  Know before getting involved in the trading strategy which events would prove their conjecture wrong and allow for it.

How much can past performance be relevant in forecasting future performance? 

These biases can be outlined as follows: (a) the survivorship biases arising from the fact that we see only winners and get a distorted view of the odds, (b) the fact that luck is most frequently the reason for extreme success and (c) the biological handicap of our inability to understand probability.

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. 

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 no show up.

Even a broken clock is right twice a day.

Time will eliminate the annoying effects of randomness. 

Nobody accepts randomness in his own success, only his failure. 

A random series of runs need not exhibit a pattern to look random; as a matter of fact, data that is perfectly patternless would be extremely suspicious and appear to be man-made. A single random run is bound to exhibit some pattern - if one looks hard enough.

I prefer to remain a skeptic. I never said that every rich man is an idiot and every unsuccessful person unlucky, only that in absence of much additional information it is preferable to reserve one’s judgement. It is safer.

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.

It is better to have a handful of enthusiastic advocates than hordes of people who appreciate your work - better to be loved by a dozen than liked by the hundreds.

Researchers divide the activities of our mind into the following two polarized parts, called System 1 and System 2. System 1 is effortless, automatic, associative, rapid, parallel process, opaque (i.e. we are not aware of using it), emotional, concrete, specific, social, and personalized. System 2 is effortless, controlled, deductive, slow, serial, self aware neutral, abstract, sets, asocial, and depersonalized.

One cannot make a decision without emotion. Mathematics gives the same answer: If one were to perform an optimizing operation across a large collection of variables, even with a brain as large as ours, it would take a very long time to decide on the simplest of tasks. So we need a shortcut; emotions are there to prevent us from temporizing. It seems that the emotions are the ones doing the job. Psychologists call them “lubricants of reason.”

One-dimensional means that we are looking at one sole variable, not a collection of separate events. 

A simplified (but sufficient) explanation of what an option means. Say a stock trades at $100 and that someone gives me the right (but not the obligation) to buy it at $110 one month ahead of today. This is dubbed a call option. It makes sense for me to exercise it, by asking the seller of the option to deliver me the stock at $110, only if it trades at a higher price than $110 in one month’s time. If the stock goes to $120, my option will be worth $10, for I will be able to buy the stock at $110 from the option writer and sell it to the market at $120, pocketing the difference. But this does not have a very high probability. It is called out-of-the-money, for I have no gain from exercising it right away.

I noticed that very few option traders can maintain what I call a “long volatility” position, namely a position that will most likely lose a small quantity of money at expiration, but is expected to make money in the long run because of occasional spurts. I discovered very few people who accepted losing $1 for most expirations and making $10 once in a while, even if the game were fair (i.e., they made the $10 more than 9.1% of the time).

We think with our emotions and there is no way around it.

Too many people read explanations. We cannot instinctively understand the nonlinear aspect of probability. 

My activity in the market (and other random variable) depends far less on where I think the market or the random variable is going so much as it does on the degree of error I allow around such a confidence level. 

The epiphany I had in my career in randomness came where I understood that I was not intelligent enough, nor strong enough, to even try to fight my emotions. Besides, I believe that I need my emotions to formulate my ideas and get the energy to execute them. 

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.

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. 

Our bias is immediately to establish a causal link. 

There is difference between noise and signal, and noise needs to be ignored while a signal needs to be taken seriously. 

Carneades was not merely a skeptic; he was a dialectician, someone who never committed himself to any of the premises from which he argued, or to any of the conclusions he drew from them. He stood all his life against arrogant dogma and belief in one sole truth. 

He does not feel obligated to explain it. 

What characterizes real speculators from the rest is that their activities are devoid of path dependence. They are totally free from their past actions. Every day is a clean slate. 

Many people get married to their ideas all the way to the grave. Beliefs are said to be path dependent if the sequence of ideas is such that the first one dominates. 

Certainly, the odds in games where the rules are clearly and explicitly defined are computable and the risks consequently measured. But not in the real world. For mother nature did not endow us with clear rules. The game is not a deck of cards (we do not even know how many colors there are). But somehow people “measure” risks, particularly if they are paid for it.

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 stoic’s prescription was precisely to elect what one can do to control one’s destiny in front of a random outcome. At the end, one is allowed to choose between no life at all and what one is given by destiny; we always have an option against uncertainty. 

Having control over randomness can be expressed in the manner in which one acts in the small and the large. Recall that epic heroes were judged by their actions, not by the results. No matter how sophisticated our choices, how good we are at dominating the odds, randomness will have the last word. We are left only with dignity as a solution - dignity defined as the execution of a protocol of behavior that does not depend on the immediate circumstance. It may not be the optimal one, but it certainly is the one that makes us feel best. Grace under pressure,  for example. 

The poem addresses Antony, now defeated and betrayed. It asks him to bid her farewell, Alexandria the city that is leaving him. It tells him not to mourn his luck, not to enter denial, not to believe that his ears and eyes are deceiving him. Antony, do no degrade yourself with empty hopes, Antony, Just listen while shaken by emotion but not with the coward’s implication and complaints. While shaken with emotion. No stiff upper lip. There is nothing wrong and undignified with emotions - we are cut to have them. What is wrong is not following the heroic or, at least, the dignified path. That is what stoicism truly means. It is the attempt by man to get even with probability. 

Start stressing personal elegance at your next misfortune. Exhibit sapere vivere (“know how to live”) in all circumstances. 

Dress your best on your execution day (shave carefully); try to leave a good impression on the death squad by standing erect and proud. Try not to play victim when diagnosed with cancer (hide it from others and only share the information with the doctor - it will avert the platitudes and nobody will treat you like a victim worth of their pity; in addition, the dignified attitude will make both defeat and victory feel equally heroic). Be extremely courteous to your assistant when you lose money (instead of taking it out on him as many of the traders whom I scorn routinely do). Try not to blame others for your fate, even if they deserve blame. Never exhibit any self-pity, even if your significant other bolts with the handsome ski instructor or the younger aspiring model. Do not complain. If you suffer from a benign version of the “attitude problem,” like one of my childhood friends, do not start playing nice guy if your business dries up (he sent a heroic email to his colleagues informing them “less business, but same attitude”). The only article Lady Fortuna has no control over is your behavior. Good luck.

I am convinced that we are not made for clear-cut, well-delineated schedules. We are made to live life firemen, with downtime for lounging and meditating between calls, under the protection of protective uncertainty. 

For writing to be agreeable to me, the length of the piece needs to remain unpredictable. 

Besides the effect on well-being, uncertainty presents tangible informational benefits, particularly with the scrambling of potentially damaging, and self-fulling, messages. 

A mild degree of unpredictability in your behavior can help you to protect yourself in situations of conflict.