What happened? The trick is as follows. The con-operator pulls 10,000 names out of a phone book. He mails a bullish letter to one half of the sample, and a bearish one to the other half. The following month he selects the names of the persons to whom he mailed the letter whose prediction turned out to be right, that is, 5,000 names. The next month he does the same with the remaining 2,500 names, until the list narrows down to 500 people. Of these there will be 200 victims. An investment in a few thousand dollars worth of postage stamps will turn into several million.

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%.

The same logic that applies to the spurious survivor also applies to the skilled person who has the odds markedly stacked in her favour, but who still ends up going to the cemetery. This effect is the exact opposite to the survivorship bias. Consider that all one needs is two bad years in the investment industry to terminate a risk-taking career and that, even with great odds in one's favour, such an outcome is very possible. What do people do to survive? They maximise their odds of staying in the game by taking black-swan risks; those that fare well most of the time, but incur a risk of blowing up.

The most intuitive way to describe the data mining problem to a non- statistician is through what is called the birthday paradox, though it is not really a paradox, simply a perceptional oddity. If you meet someone randomly, there is a one in 365.25 chance of your sharing their birthday, and a considerably smaller one of having the exact birthday of the same year. So, sharing the same birthday would be a coincidental event that you would discuss at the dinner table. Now let us look at a situation where there are 23 people in a room. What is the chance of there being two people with the same birthday? About 50%. For we are not specifying which people need to share a birthday, any pair works.

A similar misconception of probabilities arises from the random encounters one may have with relatives or friends in highly unexpected places. "It's a small world!" is often uttered with surprise. But these are not improbable occurrences - the world is much larger than we think. It is just that we are not truly testing for the odds of having an encounter with one specific person, in a specific location at a specific time.

Rather, we are simply testing for any encounter, with any person we have ever met in the past, and in any place we will visit during the period concerned. The probability of the latter is considerably higher, perhaps several thousand times the magnitude of the former.

When the statistician looks at the data to test a given relationship, say to ferret out the correlation between the occurrence of a given event, like a political announcement, and stock market volatility, odds are that the results can be taken seriously. But when one throws the computer at data, looking for just about any relationship, it is certain that a spurious connection will emerge, such as the fate of the stock market being linked to the length of women's skirts. And just like the birthday coincidences, it will amaze people.

What is your probability of winning the New Jersey lottery twice? One in 17 trillion. Yet it happened to Evelyn Adams, whom the reader might guess should feel particularly chosen by destiny. Using the method we developed above, researchers Percy Diaconis and Frederick Mosteller estimated at 30 to 1 the probability that someone, somewhere, in a totally unspecified way, gets so lucky!

Some people carry their data mining activities into theology - after all, ancient Mediterraneans used to read potent messages in the entrails of birds. Michael Drosnin provides an interesting extension of data mining into biblical exegesis in The Bible Code. Drosnin, a former journalist (seemingly innocent of any training in statistics), aided by the works of a "mathematician," helped "predict" the former Israeli Prime Minister Yitzhak Rabin's assassination by deciphering a bible code. He informed Rabin, who obviously did not take it too seriously. The Bible Code finds statistical irregularities in the Bible; these help predict some such events. Needless to say, the book sold well enough to warrant a sequel predicting with hindsight even more such events.

The same mechanism is behind the formation of conspiracy theories. Like The Bible Code, they can seem perfect in their logic and can cause otherwise intelligent people to fall for them. I can create a conspiracy theory by downloading hundreds of paintings from an artist or group of artists and finding a constant among all those paintings (among the hundreds of thousand of traits). I would then concoct a conspiratorial theory around a secret message shared by these paintings. This is seemingly what the author of the bestselling The Da Vinci Code did.

My favorite time is spent in bookstores, where I aimlessly move from book to book in an attempt to make a decision as to whether to invest the time in reading it. My buying is frequently made on impulse, based on superficial, but suggestive clues. Frequently, I have nothing but a book jacket as appendage to my decision making. Jackets often contain praise by someone, famous or not, or excerpts from a book review. Good praise by a famous and respected person or a well-known magazine would sway me into buying the book.

What is the problem? I tend to confuse a book review, which is supposed to be an assessment of the quality of the book, with the best book reviews, marred with the same survivorship biases. I mistake the distribution of the maximum of a variable with that of the variable itself. The publisher will never put on the jacket of the book anything but the best praise.

Some authors go even a step beyond, taking a tepid or even unfavourable book review and selecting words in it that appear to praise the book. One such example came from one Paul Wilmott (an English financial mathematician of rare brilliance and irreverence) who managed to announce that I gave him his "first bad review," yet used excerpts from it as praise on the book jacket (we later became friends, which allowed me to extract an endorsement from him for my book).

The first time I was fooled by this bias was upon buying, when I was 16, "Manhattan Transfer", a book by the American writer John Dos Passos, based on praise on the jacket by the French writer and "philosopher" Jean-Paul Sartre, who claimed something to the effect that Dos Passos was the greatest writer of our time. This simple remark, possibly blurted out in a state of intoxication or extreme enthusiasm, caused Dos Passos to become required reading in European intellectual circles, as Sartre's remark was mistaken for a consensus estimate of the quality of Dos Passos rather than what it was, the best remark. (In spite of such interest in his work, Dos Passos has reverted to obscurity.)

I am frequently asked the question: when is it truly not luck? There are professions in randomness for which performance is low in luck: Like casinos, which manage to tame randomness. In finance? Perhaps. All traders are not speculative traders: there exists a segment called market makers whose job is to derive, like bookmakers, or even like store owners, an income against a transaction. If they speculate, their dependence on the risks of such speculation remains too small compared to their overall volume. They buy at a price and sell to the public at a more favorable one, performing large numbers of transactions. Such income provides them some insulation from randomness. Such category includes floor traders on the exchanges, bank traders who "trade against order flow," moneychangers in the souks of the Levant. The skills involved are sometimes rare to find: Fast thinking, alertness, a high level of energy, an ability to guess from the voice of the seller her level of nervousness; those who have them make a long career (that is, perhaps a decade). They never make it big, as their income is constrained by the number of customers, but they do well probabilistically. They are, in a way, the dentists of the profession.

Regards,

Nassim Nicholas Taleb
for The Daily Reckoning Australia

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When I was in the employment of the New York office of a large investment house, I was subjected on occasions to the harrying weekly "discussion meeting," which gathered most professionals of the New York trading room to talk about trading stocks.

I do not conceal that I was not fond of such gatherings, and not only because they cut into my gym time. While the meetings included traders, that is, people who are judged on their numerical performance, it was mostly a forum for salespeople (people capable of charming customers), and the category of entertainers called Wall Street "economists" or "strategists," who make pronouncements on the fate of the markets, but do not engage in any form of risk taking; thus having their success dependent on rhetoric, rather than actually testable facts. During the discussion, people were supposed to present their opinions on the state of the world.

To me, the meetings were pure intellectual pollution. Everyone had a story, a theory, and insights that they wanted others to share. I have to confess that my optimal strategy (to soothe my boredom and allergy to confident platitudes) was to speak as much as I could, while totally avoiding listening to other people's replies by trying to solve equations in my head. Speaking too much would help me clarify my mind, and, with a little bit of luck, I would not be "invited" back (i.e, forced to attend) the following week.

I was once asked in one of those meetings to express my views on the stock market. I stated, not without a modicum of pomp that I believed that the market would go slightly up over the next week with a high probability.

How high? "About 70%." Clearly, that was a very strong opinion. But then someone interjected, "But, Nassim, you just boasted being short a very large quantity of SP500 futures, making a bet that the market would go down. What made you change your mind?" I answered, "I did not change my mind! I have a lot of faith in my bet! As a matter of fact, I now feel like selling even more!"

The other employees in the room seemed utterly confused. "Are you bullish, or are you bearish?" the strategist asked me. I replied that I could not understand the words "bullish" and "bearish" outside of their purely zoological consideration. My opinion was that the stock market was more likely to go up ("I would be bullish"), but that it was preferable to short it ("I would be bearish"), because, in the event of its going down, it could go down a lot. Suddenly, the few stock traders in the room understood my opinion and started voicing similar opinions. And I was not forced to come back to the following discussion.

Let us assume that the reader shared my opinion, that the stock market over the next week had a 70% probability of going up and 30% probability of going down. However, let us say that it would go up by 1% on average, while it could go down by an average of 10%. What would the reader do? Is the reader bullish or bearish?

Accordingly, bullish or bearish are terms used by people who do not engage in practicing uncertainty, like the television commentators, or those who have no knowledge in handling risk. Alas, investors and businesses are not paid in probabilities, they are paid in dollars. Accordingly, it is not how likely an event is to happen that matters, it is how much is made when it happens that should be the consideration. How frequent the profit is irrelevant; it is the magnitude of the outcome that counts. It is a pure accounting fact that, aside from the commentators, very few people take home a check linked to how often they are right or wrong. What they get is a profit or loss. As to the commentators, their success is linked to how often they are right or wrong. This category includes the "chief strategists" of major investment banks the public can see on TV, who are nothing better than entertainers. They are famous, seem reasoned in their speech, plow you with numbers, but, functionally, they are there to entertain - for their predictions to have any validity they would need a statistical testing framework. Their fame is not the result of some elaborate test, but rather the result of their presentation skills.

Outside of the need for entertainment in these shallow meetings I have resisted voicing a "market call" as a stock trader, which caused some personal strain with some of my friends and relatives. One day a friend of my father - of the rich and confident variety - called me during his New York visit. He wanted to pick my brain on the state of a collection of financial markets. I truly had no opinion, nor had made the effort to formulate any, nor was I remotely interested in stock markets. The gentleman kept plowing me with questions on the state of economies, on the European central banks; these were precise questions no doubt aiming to compare my opinion to that of some other "expert" handling his account at one of the large New York investment firms. I neither concealed that I had no clue, nor did I seem sorry about it. I was not interested in markets ("Yes, I am a trader") and did not make predictions, period. I went on to explain to him some of my ideas on the structure of randomness and the verifiability of market calls, but he wanted a more precise statement of what the European bond markets would do by the Christmas season.

He came away under the impression that I was pulling his leg; it almost damaged the relationship between my father and his rich and confident friend. For the gentleman called him with the following grievance: "When I ask a lawyer a legal question, he answers me with courtesy and precision.

When I ask a doctor a medical question, he gives me his opinion. No specialist ever gives me disrespect. Your insolent and conceited 29- year-old son is playing prima donna and refuses to answer me about the direction of the stock market!"

The best description of my lifelong business in the stock market is "skewed bets", that is, 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 event, 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.

Why are these events poorly valued? Because of a psychological bias; people who surrounded me in my career were too focused on memorising Section 2 of the Wall Street Journal during their train ride to reflect properly on the attributes of random events when it comes to trading stocks. Or perhaps they watched too many gurus on television. Or perhaps they spent too much time upgrading their PalmPilot. Even some experienced trading veterans do not seem to get the point that frequencies do not matter. Jim Rogers, a "legendary" investor, made the following statement:

"I don't buy options. Buying options is another way to go to the poorhouse. Someone did a study for the SEC and discovered that 90 percent of all options expire as losses. Well, I figured out that if 90 percent of all long option positions lost money, that meant that 90 percent of all short option positions make money. If I want to use options to be bearish, I sell calls."

Visibly, the statistic that 90% of all option positions lost money is meaningless, (i.e., the frequency) if we do not take into account how much money is made on average during the remaining 10%. If we make 50 times our bet on average when the option is in the money, then I can safely make the statement that buying options is another way to go to the palazzo rather than the poorhouse. Mr Jim Rogers seems to have gone very far in life for someone who does not distinguish between probability and expectation (strangely, he was the partner of George Soros, a complex man who thrived on rare events).

One such rare event is the stock market crash of 1987, which made me as a stock trader and allowed me the luxury of becoming involved in all manner of scholarship. Many traders aim to get out of harm's way by avoiding exposure to rare events - a mostly defensive approach. I am far more aggressive than those traders and go one step further; I have organised my career and business in such a way as to be able to benefit from them. In other words, I aim at profiting from the rare event, with my asymmetric bets.

Regards,

Nassim Nicholas Taleb
for The Daily Reckoning Australia

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