Prologue

The Probable and the Certain

Does your next door neighbor drive a better car than you? Is he more prominent than you? Now the real question: is he smarter than you –or merely luckier? Could it be that he is doing very well precisely because he is stupid? This book is about luck disguised and perceived as non-luck (that is, skills) and, more generally, randomness disguised and perceived as non-randomness (that is, determinism). It manifests itself in the business world in the shape of the lucky idiot –but we see it everywhere else, though not in such an accentuated and obvious manner. In politics, it can be encountered in the shape of a country’s president discoursing on the jobs that "he" created, "his" recovery, and "his predecessor’s" inflation –though these discourses generally only fool one segment of the public. For instance, on December 19, 1998, Vice President Al Gore stood up in the rose garden and declared, from the authority of his podium, that President Clinton eliminated the federal deficit. No statement can more convincingly illustrate the need for better understanding of randomness in our society. The reason we have something called scientific standards is precisely to prevent people from making such type of statement –by forcing them to present evidence showing that these two elements (Clinton’s election and the budget deficit) are linked by more than mere coincidence.

For we are genetically still very close to our ancestor who roamed the Savannah. The formation of our beliefs is fraught with superstitions—even today (I might say, especially today). Just as one day some primitive tribesman scratched his nose, saw rain falling, and developed an elaborate method of scratching his nose, we link economic prosperity to some rate cut by the Federal Reserve Board , or the success of a company with the appointment of the new president "at the helm". Bookstores are full of biographies of successful men and women presenting their specific explanation on how they made it big in life (we have an expression, "the right time and the right place" to weaken what conclusion can be inferred from them). This confusion strikes people of different persuasions: the literature professor invests a deep meaning into a mere coincidental occurrence of word patterns, while the financial statistician proudly detects "regularities" and "anomalies" in data that is plain random.

At the cost of appearing biased, I have to say that the literary mind can be intentionally prone to the confusion between noise and meaning. However, this causes little harm; few claim that art is a tool of investigation of the Truth—rather than an attempt to escape it or make it more palatable. Symbolism is the child of our inability and unwillingness to accept randomness; we give meaning to all manner of shapes; we detect human figures in inkblots. I saw mosques in the clouds claimed Arthur Rimbaud the 19th century French symbolic poet. This interpretation took him to "poetic" Abyssinia (in East Africa), where he was brutalized by a Christian Lebanese slave dealer, contracted syphilis, and lost a leg to gangrene. Although he gave up poetry in disgust at the age of 19, he ended up dying anonymously in a Marseilles hospital ward while still in his thirties. But it was too late: European intellectual life developed what seems to be an irreversible taste for symbolism –we are still paying its price, with psychoanalysis and other fads.

Regrettably, some people play the game too seriously; they are paid to read too much into things. This feeling is not be shared by those who sat spellbound for hours in a literature class listening to some tweeded professor splitting hairs in a Pushkin poem, with his incomprehensible Russian-Cambridge accent (his name is Vladimir Nabokov and he was capable of interpreting anything in about everything). The French poet Paul Valery was surprised to listen to a commentary of his poems that found meanings that had until then escaped him (of course, it was pointed out to him that these were intended by his subconscious). Perhaps the mother of all over-interpretations is a biography of the writer Gustave Flaubert (the author of Madame Bovary) by the French "philosopher" Jean-Paul Sartre. In it, Sartre dumped the kitchen sink of his imaginative mind, using what psychoanalysis and existentialism can bring to bear.

More generally, we underestimate the share of randomness in about anything, a point that may not merit a book –except when it is the specialist who is the fool of all fools. Disturbingly, science has only recently been able to handle randomness. Probability theory is a recent arrival in mathematics.

Consider the left and the right columns of Table 1-1. The best way to summarize the major thesis of this book is that it addresses situations (many of them tragicomical) where the left column is mistaken for the right one.

Table -1 Humbling Differences. This table presents the central distinctions used in the book. It will be referred to continuously, with an emphasis on elements of the left columns mistaken for the corresponding right one.

General

Luck

Skills

Randomness

Determinism

Probability

Certainty

Belief, conjecture

Knowledge, certitude

Theory

Reality

Anecdote, coincidence

Causality, law

Market Performance

Lucky idiot

Good trader

Survivorship bias

Market out-performance

Finance

Volatility

Return

(or drift)

Guess the risks (but realize it is a guess)

Measure (as in quantitative finance)

Stochastic variable

Deterministic variable

Physics and Engineering

Noise

Signal

Literary Criticism

None (literary critics do not seem to have a name for things they do not understand)

Symbol

Philosophy of Science

Epistemic probability

Physical probability

Induction

Deduction

The reader may wonder whether the opposite case might not deserve some attention: that is, the situations where non-randomness is mistaken for randomness. Shouldn’t we be concerned with situations where patterns and messages may have been ignored? I have two answers. First, I am not overly worried about the existence of undetected patterns. We have been reading lengthy and complex messages in just about any manifestation of nature that presents jaggedness (such as the palm of a hand, the residues at the bottom of Turkish coffee cups, etc.). Armed with home supercomputers and chained processors, and helped by complexity and "chaos" theories, the scientists, semi-scientists, and pseudoscientists will be able to find portents. Second, we need to take into account the costs of mistakes; in my opinion, mistaking the right column for the left one is not as costly as an error in the opposite direction. Even popular opinion warns that bad information is worse than no information at all.

However interesting these areas could be, their discussion would be a tall order. In addition, they are not my current professional specialty. Mine is the application of rigor to financial randomness. Accordingly, this book focuses on the business world. In addition, business presents the best (and most entertaining) laboratory for the understanding of these differences. For it is the are the area of human undertaking where the confusion is greatest and its effects the most pernicious. For instance, we often have the mistaken impression that a strategy is an excellent strategy, or an entrepreneur a person endowed with "vision", or a trader an excellent trader, only to realize that 99.9% of their past performance is attributable to chance, and chance alone. Ask a profitable investor to explain the reasons for his success: he will offer some deep and convincing interpretation of the results. Frequently, these delusions are intentional and deserve to bear the name charlatanism.

If there is one and only cause for this confusion between the left and the right side of our table, it is our inability to think critically –we may enjoy propounding conjectures as truth. We are just built like that. We will see that our mind is not equipped to handle probabilities; such infirmity even strikes the expert, sometimes just the expert. A critical mind, on the other hand, is someone who leaves room, when confronting a given set of information, to attribute a large share of its possible cause to the left column.

Monsieur Prud’homme carried around a large sword with a double intent: primarily to defend the Republic against its enemies, and secondarily to attack it should it stray from its course. In the same manner, this book has two purposes: to defend science, but to attack it when it goes too far. The first part of the book explains why we need better understanding of probability and causality. The second warns us from falling into the other extreme, and, in the name of science, making worse blunders than those caused by ignorance —as a Wall Street trader I have seen more of my share of snake oil salesmen dressed in the garb of scientists.

[Book Description, chapter by chapter]

Part 1: Solon's Warning

Croesus, King of Lydia, was considered the richest man of his time. To this day Romance languages use the expression "rich as Croesus" to describe a person of excessive wealth. He was said to be visited by Solon, the Greek legislator known for his dignity, reserve, upright morals, humility, frugality, wisdom, intelligence, and courage. However, Solon did not display the smallest surprise at the wealth and splendor surrounding his host, nor the tiniest admiration for their owner. Croesus was so irked by the manifest lack of impression on the part of this illustrious visitor that he attempted to extract from him some acknowledgment. He asked him if he had known a happier man than him. Solon cited the life of a man who led a noble life and died while in battle. Prodded for more, he gave similar examples of heroic but terminated lives, until Croesus, irate, asked him pointblank if he was not to be considered the happiest man at all. Solon answered: "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 continued happiness until the end we may call happy." [Dryden translation]

The modern equivalent has been no less eloquently voiced by the baseball coach Yogi Bera, who seems to have translated Solon’s outburst from the pure Attic Greek into no less pure Brooklyn English with "it ain’t’ over until it’s over", or, in a less dignified manner, with "it ain’t over until the fat lady sings". In addition, aside from his use of the vernacular, the Yogi Bera quote presents an advantage of being true, while the meeting between Croesus and Solon was one of these historical facts that took place in the mind of the chronicler, as it was chronologically impossible for the two men to have been in the same location.

The policy of this book is to reserve some element of surprise to the reader, and avoid too dry and academic an outline (this author hates books that can be easily guessed from the table of contents) --but a hint of what comes next seems in order. Part I is concerned with the degree to which a situation may yet, in the course of time, suffer change. For we can be tricked by situations involving mostly the activities of the Goddess Fortuna --Jupiter’s firstborn daughter. Solon was wise enough to get the following point: that which came with the help of luck could be taken away by luck (and often rapidly and unexpectedly at that). The flip side, which deserves to be considered as well (in fact it is even more of our concern), is that things that come with little help from luck are more resistant to randomness. Solon also had the intuition of a problem that has obsessed science for almost three centuries. It is called the problem of induction; it even has an acronym, P. of I.; it is the most important problem in the social sciences. We call it in this book the black swan or the rare event. He even understood another linked problem that many people my generation do not seem comprehend, which we call the skewness issue: it does not matter how frequently something succeeds if failure is too costly to bear.

Yet the story of Croesus has another twist. Having lost a battle to the redoubtable Persian king Cyrus, he was about to be burned alive when he started calling Solon's name and shouting something like "Solon, you were so right, you were so wise" (again this is pure legend). As Cyrus inquired about the nature of such unusual invocations, he informed him about Solon's warning. This impressed Cyrus to the point of his sparing Croesus' life as he reflected on the possibilities as far as his own fate was concerned. People were thoughtful at that time.

The Millionaire Across the Street

NERO

Hit by Lightning

Nero Tulip became obsessed with trading after witnessing a strange scene one spring day as he was visiting the Chicago Mercantile Exchange. A red convertible Porsche, driven at several times the city speed limit, abruptly stopped in front of the entrance, its tires emitting the sound of slaughtered pigs. A visibly demented athletic man in his thirties, his face flushed red, emerged and ran up the steps as if he were chased by a tiger. He left the car double-parked, its engine running, provoking a angry fanfare of horns. After a long minute, a bored young man clad in a yellow jacket (yellow was the color reserved for clerks) came down the steps, visibly untroubled by the traffic commotion. He drove the car into the underground parking garage—perfunctorily as if it were his daily chore.

That day Nero Tulip was hit with what the French call a coup de foudre, a sudden intense (and obsessive) infatuation that strikes like lightning. "This is for me!", he screamed enthusiastically --he could not help comparing the life of a trader to the alternatives. Academia conjured up the image of a silent university office with rude secretaries; business inspired him a quiet office staffed with slow thinkers and semi-slow thinkers who express themselves in full sentences.

Temporary Sanity

Unlike a coup de foudre, the infatuation triggered by the Chicago scene had not left him at the time of writing, close to a decade-and-a-half after the incident. For Nero swears that no other lawful profession in our times could be as devoid of boredom as that of the demented trader who seemed chased by a tiger. Furthermore, although he has not yet practiced the profession of high-sea piracy, he is now convinced that even the occupation of pirate would present more dull moments than that of the trader.

Nero is a fictional character, though no overly so, as he is a composite of persons I have encountered in my career in randomness. He could best be described as someone who randomly (and abruptly) swings between the deportment and speech manners of a church historian and the verbally abusive, demented intensity of a Chicago pit trader. But Nero has other traits: he can commit hundreds of millions of dollars in a transaction without a blink or a shadow of second thoughts yet agonize between two appetizers on the menu, changing his mind back and forth and wearing out the most patient of waiters.

Nero holds an undergraduate degree in ancient literature and mathematics from Cambridge. He enrolled in a Ph.D. program in statistics at the University of Chicago but, after completing the prerequisite coursework, as well as the bulk of his doctoral research, he switched to the philosophy department. He called the switch "a moment of temporary sanity", adding to the consternation of his thesis director who warned him against philosophers and predicted his return back to the fold. He finished writing his thesis in philosophy –not the Derrida continental style of incomprehensible philosophy (that is incomprehensible to anyone outside of their ranks, like myself). It was quite the opposite: his thesis was on the methodology of statistical inference in its application to the social sciences. In fact, his thesis was indistinguishable from a thesis in mathematical statistics –it was just a bit more thoughtful (and twice lengthier).

It is often said that philosophy cannot feed its man –but that was not the reason Nero left. He left simply because philosophy cannot entertain its man. At a first stage, it started looking futile; he then recalled his thesis director's warnings. Then, suddenly, it started to look like work. As he became tired of writing papers on some arcane details of his earlier papers, he gave up the academy. These academic debates bored him to tears, particularly that very small minute points invisible to the non-initiated were at stake. Action is what Nero wanted. The problem with Nero is that he selected the academy in the first place in order to kill what he detected was the flatness and tempered submission of employment life.

After the scene of the trader chased by a tiger, Nero rapidly found a trainee spot on the Chicago Mercantile Exchange, working for a prestigious (but eccentric) local, who trained him in the Chicago style, in return for Nero solving his mathematical equations. He rapidly graduated to the rank of self-employed trader. Then, when he got tired of standing on his feet in the crowd, and straining his vocal cords, he decided to seek employment "upstairs", that is, trading from a desk. He moved to the New York area and took a position with an investment house.

Nero specialized in quantitative financial products, in which he had an early moment of glory, became famous and in demand. Many investment houses in New York and London flashed huge guaranteed bonuses to him. But Nero went into hiding; he rapidly pulled back to anonymity --the Wall Street stardom track did not quite fit his temperament. To stay a "hot trader" required some organizational ambitions and a power hunger that he felt lucky not to possess. He was only in it for the fun -and his idea of fun did not include administrative and managerial work. He was susceptible to conference room boredom and was incapable of talking to businessmen, particularly those run-of-the-mill variety. Nero is allergic to the vocabulary of business talk, not just on plain esthetic grounds. Words like "game plan", "bottom line", "how to get there from here", "we provide our clients with solutions", "our mission" and some such hackneyed expressions that dominate meetings lack both the precision and the coloration that he preferred to hear. Whether people populate silence with hollow sentences, or if such meetings present any true merit, he did not know; at any rate he did not want to be part of it. Indeed Nero's extensive social life included almost no businessman.

Nero switched career to what is called proprietary trading; traders are set up as independent entities, internal funds with their own allocation of capital. They are left alone to do as they please, provided of course that their results satisfy the executives. The name proprietary comes from the fact that they trade the company's own money. At the end of the year one receives between 7% and 12% of the profits thus generated. The proprietary trader has all the benefits of self employment, can work any hour he likes, can travel at a whim, and engage in all manner of personal pursuits. Nero has been doing that for the past ten years, in the employment of two different trading firms.

Trading Style

A word on Nero's trading style. He is as conservative a trader as one can be in such a business. In the past he has had good years and less than good years –but virtually no truly "bad" years. Over these years he slowly built for himself a stable nest egg, thanks to an income ranging between $300,000 and (at the peak) $2,200,000. On average, he manages to accumulate $400,000 a year in after-tax money (from an average income of about $800,000); these go straight into his savings account. In 1993, he had a flat year and was made to feel uncomfortable in his company. Other traders made out much better, so the capital at his disposal was severely reduced, and he was made to feel undesirable at the institution. He then went to get an identical job, down to an identically designed workspace, but in a different firm that was friendlier. In the fall of 1994 the traders who had been competing for the great performance award blew up in unison during the worldwide bond market crash that resulted from the unexpected tightening by the Federal Reserve Bank of the United States. They are all currently out of the market, performing a variety of tasks… This business has a high mortality rate.

Why didn’t Nero make more money? Because of his trading style –or perhaps his personality. His risk aversion is extreme. Nero’s objective is not to maximize his profits, so much as it is to avoid having this entertaining money machine called trading taken away from him. Blowing up meant returning to the tedium of the university or the non-trading life. Every time his risks increase, he conjures up the image of the quiet hallway at the university, the long mornings at his desk spent in revising a paper, kept awake by bad coffee. No, he did not want to have to face the solemn university library where he was bored to tears! "I am shooting for longevity", he is wont to say.

Nero has seen many traders blow up, and does not want to get into that situation. He rapidly exits trades after a predetermined loss. He never sells naked options. He never puts himself in a situation where he can lose more than, say, $1,000,000 –regardless of the probability of such an event. That amount has always been variable; it depends on his accumulated profits for the year. This risk aversion prevented him from making as much money as the other traders on Wall Street who are often called "Masters of the Universe". The firms he worked for generally allocate more money to other traders with a different style, like John we will encounter further down.

Nero's temperament is such that he does not mind losing small money. "I love taking small losses", he says. "I just need my winners to be large". In no circumstances did he want to be exposed to these rare events, like panics and sudden crashes that wipe a trader out in a flash. To the contrary, he wanted to benefit from them. When people ask him why he does not to hold on to losers, he invariably answers that he was trained by "the most chicken of them all", the Chicago trader Stevo who taught him the business. This was not true; the real reason is his training in probability and his innate skepticism.

There is another reason Nero is not as rich as others in his situation. His skepticism does not allow him to invest any of his money outside of treasury bonds. He therefore missed out on the great bull market. The reason he offered is that it could have turned out to be a bear market and a trap. The difference with people around him who were enriched by the stock-market was that he was cash-flow rich, but that his assets did not inflate at all along with the rest of the world. He contrasted himself with one of those startup technology companies that were massively cash-flow negative, but for which the hordes developed some infatuation. This allowed the owners to become rich from their stock valuation, thus depending on the randomness of the market's election of the winner. The difference with his friends of the investing variety was that he did not depend on the bull market, and, accordingly, would not have to worry about the bear market at all. His net worth was not a function of the investment of his savings --he did not want to depend on his investments, but on his cash earnings, for his enrichment. He took not an inch of risk with his savings, which he invested in the safest possible vehicles. Treasury bonds were safe; they are issued by the United States Government, and governments can hardly go bankrupt since they can freely print their own currency to pay back their obligation.

Today, at 39, after 14 years in the business, he can consider himself comfortably settled. His personal portfolio contains several million dollars in medium maturity Treasury Bonds, enough to eliminate any worry about the future. What he likes most about proprietary trading is that it requires considerably less time than other high paying professions; in other words it is perfectly compatible with his non-middle-class work ethics. Trading forces someone to think hard; those who merely work hard generally lose their focus and intellectual energy.

This free time has allowed him to carry on a variety of personal interests; recall that he reads voraciously and cannot have a lawyer or a doctor’s schedule. Nero found the time to go back to the statistics department where he started his doctoral studies and finished the "harder science" doctorate in statistics, by rewriting his thesis in more concise terms. Nero now teaches, once a year, a half-semester seminar called History of Probabilistic Thinking in the mathematics department of New York University, a class of great originality that draws excellent graduate students. He has saved enough money to be able to maintain his lifestyle in the future and has contingency plans perhaps to retire into writing popular essays of the scientific-literary variety, with themes revolving around probability and indeterminism –but only if some event in the future causes the markets to shut down.

John the High Yield Trader

Across the street from Nero’s house stands John’s –a much larger one. John is a high yield trader, but he is not a trader in the style of Nero. A brief professional conversation with him would reveal that he presents the intellectual depth and sharpness of mind of an aerobics instructor (though he does not have the physique). A purblind man could see that he has been doing markedly better than Nero (or, at least, feels compelled to show it). He parks two top of the line German cars in his driveway (his and hers), in addition to two convertibles (one of which is a collectible Ferrari), while Nero drives less ostentatious vehicles.

The wives of John and Nero are acquaintances, of the health-club type of acquaintance, but Nero’s wife feels extremely uncomfortable in the company of John’s. She feels that the lady is not merely trying to impress her, but is treating her like someone inferior. While Nero is inured to the sight of traders getting rich (and try too hard to become sophisticated by turning into wine collectors and opera lovers), his wife had rarely encountered repressed new wealth --the type of people who have felt the sting of indigence at some point in their lives and want to get even by exhibiting their wares. The only dark side of being a trader, Nero often says, is the sight of money being showered on unprepared people who are suddenly taught that Vivaldi's Four Seasons is "refined" music. But it is hard for his spouse to be exposed almost daily to the neighbor who keeps boasting of the new decorator they just hired, not the least uncomfortable with the fact that their library came with the leather-bound books (her readings at the health club are limited to People Magazine but her shelves include a selection of untouched books by dead American authors). She also keeps discussing unpronounceable exotic locations where they repair during their vacations without so much as knowing the smallest thing about the place and would be hard put to explain in which continent the Seychelles Islands were located. Nero's wife is all too human: although she keeps telling herself that she does not want to be in the shoes of John's wife, she feels as if she has been somewhat swamped in the competition of life. Somehow words and reason become ineffectual in front of an oversized diamond, a monstrous house, and a sports car collection.

An Overpaid Hick

Nero also suffers the same ambiguous feeling towards his neighbors. He is quite contemptuous of John, who represents about everything he is not and does not want to be --but there is the social pressure that is starting to weigh in on him. In addition, he too would like to sample such excessive wealth. Intellectual contempt does not control personal envy. That house across the street keeps getting bigger, with addition after addition --and Nero's discomfort keeps apace. While Nero has succeeded beyond his wildest dreams, both personally and intellectually, he is starting to consider himself as having missed a chance somewhere. In the pecking order of Wall Street, the arrival of such types as John causes him to no longer be a significant trader –but while he did not care before he is starting to worry about it. All would have been well if he did not have this stupid large house across the street from him judging him with this superficial standard every morning. Is it the genetic pecking order at play, with John's house size making him a beta male? Worse even, John is about 5 years his junior, and, despite a shorter career, makes at least 10 times his income.

When they run into each other Nero has a clear feeling that John tries to put him down --with barely detectable but no less potent signs of condescension. Some days John ignores him totally. Had John been a remote character, one Nero could read about in the papers, the situation would have been different. But here John is in flesh and bones and he is his neighbor. The mistake Nero made was to start talking to him, as the rule of pecking order immediately emerged. Nero tried to soothe his discomfort by recalling the behavior of Swann, the character in Proust's Search of Time Lost, a refined art dealer and man of leisure who was at ease with such men as his personal friend the then-Prince of Wales, but acted like he had to prove something in the presence of the middle class. It was much easier for Swann to mix with the aristocratic and well established set of Guermantes than it was for the social-climbing one of the Verdurins, no doubt because he was far more confident in their presence. Likewise Nero can exact some form of respect from prestigious and prominent people. He regularly takes long meditative walks in Paris and Venice with an erudite Nobel prize-caliber scientist (the kind of people who no longer have to prove anything) who actively seeks his conversation. A very famous billionaire speculator has called him a few times to ask him his opinion on the valuation of some derivative securities. But here he is obsessively trying to gain the respect of some overpaid hick with a cheap New Jersey "Noo-Joyzy" accent.

Clearly, John is not as well educated, well bred, physically fit, or perceived as being intelligent as Nero –but that is not all: he is not even as street-smart as him! Nero has met true street-smart people in the pits of Chicago; these exhibit a rapidity of thinking that he could not detect in John. Nero is convinced that the man was a confident retard who did well because he never made an allowance for his vulnerability. But Nero could not, at times, repress his envy --he wondered whether it was an objective evaluation of John, or if it was his feeling slighted that made him have such assessment of John. Perhaps it was Nero who was not quite the best trader. Maybe he did not push himself too hard, or seek the right opportunity --instead of "thinking", writing articles and reading complicated papers. Perhaps he should have been involved in the high yield business, where he would have shined among these retards like John.

Nero tried to soothe his jealousy by investigating the rules of pecking order. Psychologists Kahneman and Tversky showed that most people prefer to make $70,000 when others around them are making $60,000 to making $80,000 when others around them are making $90,000. Economics, shmeconomics, it is all pecking order, he thought. No such analysis could prevent him from assessing his condition in an absolute rather than a relative way. Nero felt that, for all his intellectual training, he was just another one of those who would prefer to make less money provided others made even less.

Nero thought that there was at least one piece of evidence to support the idea of John being merely lucky –in other words Nero, after all, might not need to move away from his neighbor’s starter palazzo. There was hope that John would meet his undoing. For John seemed unaware of one large hidden risk he was taking, the risk of blowup, a risk he could not see because he had too short an experience of the market (but also because he was not thoughtful enough to study history). How could John, with his coarse mind, otherwise be making so much money? All this business of junk bonds depends on some knowledge of the "odds", a calculation of the probability of these rare events. What do these fools know about odds? These traders use "quantitative tools" that give them the odds –and Nero disagreed with the methods used. This high yield market resembles a nap on a railway track. One afternoon, the surprise train would run you over. You make money every month for a long time, then lose a multiple of your cumulative performance in a few hours. He has seen it with option sellers in 1987, 1989, 1992, and 1998. One day they are taken off the exchange floors, accompanied by oversized security men, and nobody ever sees them again. The big house is simply a loan; John might end up as a luxury car salesman somewhere in New Jersey, selling cars to the new newly rich who no doubt would feel comfortable in his presence. Nero cannot not blow up. His less oversized abode, with its 4,000 books, is his own. No market event can take it away from him. Every one of his losses is limited. His trader’s dignity will never, never, be threatened.

John, for his part, thinks of Nero as a loser, and a snobbish overeducated loser at that. Nero is involved in a mature business. He believes that he is way over the hill. These "prop" traders are in an efficient and dying business. They think they are smarter than everybody else, but they are passé.

Now the question: who is the better trader, Nero or John?

The Red Hot Summer

The answer was provided during September 1998. Nero felt vindicated. One morning while leaving to go to work he saw John in his front yard unusually smoking a cigarette. He was not wearing a business suit. He looked humble; his customary swagger was gone. Nero immediately knew that John had been fired. What he did not suspect was that John also lost almost everything he had. We will see more details of John's losses in chapter x.

Nero felt ashamed of his feelings of schadenfreude, the joy humans can experience upon their rivals misfortune. But he could not repress it. Aside from it being unchivalrous, it was said to bring bad luck (Nero is weakly superstitious). But in this case, Nero's merriment did not come from the fact that John went back to his place in life, so much as it was from the fact that Nero's methods, beliefs, and track record have suddenly gained in credibility. Nero would be able to raise public money on his track record precisely because such a thing could not possibly happen to him. Part of Nero's elation also came from the fact that he felt proud of sticking to his strategy for so long, in spite of the pressure to be the alpha-male. It was also because he felt that he would no longer question his trading style upon the sight of retards getting rich because they misunderstand the structure of randomness and market cycles.

Serotonin and Randomness

Can we judge the success of people by their raw performance and their personal wealth? Sometimes – but not always. We will see how, at any point in time, a large section of businessmen with outstanding track records will be no better than randomly thrown darts. More curiously, and owing to a peculiar bias, cases will abound when the dumbest and less skilled businessmen will be by far the richest. However, they will fail to make an allowance for the role of luck in their performance.

Lucky idiots do not look like lucky idiots –by definition, they do not know that they belong to such category. They will act as if they deserved the money. Their strings of successes will inject them with so much serotonin (or some similar substance) that they will even fool themselves about their ability to outperform markets. One can notice it at their posture: a profitable trader will walk upright, dominant style --and will tend to walk more than a losing trader. Scientists found out that serotonin, a neurotransmitter, seems to command a large share in our human behavior. It sets a positive feedback, the virtuous circle, but, owing to an external kick from randomness, can start a reverse motion and cause a vicious circle. It has been shown that Monkeys injected in serotonin will rise in the pecking order, which in turn causes an increase of the serotonin level in their blood —until the virtuous cycle breaks and starts a vicious one. Likewise, an increase in personal performance (regardless of whether it is caused deterministically or by the agency of lady Fortuna) induces a rise of serotonin in the subject, itself causing an increase of what is commonly called leadership ability. One is "on the roll". Some imperceptible changes in deportment, like an ability to express oneself with serenity and confidence, makes the subject look credible –as if he truly deserved the shekels. Randomness will be ruled out as a possible factor in the performance.

People have often the bad taste of asking me in a social setting if my day in trading was profitable. My father usually stops them by saying "Never ask a man if he is from Sparta: if he were, he would have let you know such an important fact–and if he were not, you could hurt his feelings". Likewise, never ask trader if he is profitable: you can easily see it at his gesture and gait. People in the profession can easily tell if traders are making or losing money: head traders are quick at identifying an employee who is faring poorly. Their face will seldom reveal much, as people consciously attempt to gain control of their facial expressions. But the way they walk, the way they hold the telephone, and the hesitation in their behavior, will not fail to reveal their true disposition. On the morning after John had been fired, he certainly lost much of his serotonin --unless it is another substance that researchers will discover in another decade. It was visible in his expression: could it be mother nature's way to signal to a potential mate one's eligibility?

Your Dentist is Rich, Very Rich

We close this chapter with a hint on the next discussion of resistance to randomness. Recall that Nero would be considered prosperous but not "very rich" by his day's standards. However, according top some strange accounting measure we will see in the next chapter, he would be extremely rich on the average of lives he could have led --he took so little risk in his trading career that there could have been very few disastrous outcomes. The fact that he did not experience John's success was the reason he did not suffer his downfall. He would be therefore wealthy according to this unusual (and probabilistic) method of accounting for wealth. Recall that Nero protected himself from the rare event. Had Nero had to relive his professional life a few million times, very few sample paths would be marred by bad luck --but, owing to his conservatism, very few as well would be affected by extreme good luck. That is, his life in stability would be similar to that of an ecclesiastic clock repairman. Naturally, we are only discussing his professional life, excluding his private one.

Arguably, on average, a dentist is considerably richer than the rock musician who is driven in a pink Bentley, the speculator who bids up the price of impressionist paintings, or the entrepreneur who collects private jets. For one cannot consider a profession without taking into account the average of the people who enter it, not the sample of those who have succeeded in it. We will examine the point later from the vantage point of the survivorship bias, but here, in Part I, we will look at it with respect to resistance to randomness.

Consider two neighbors, John Doe A, a janitor who won the New Jersey lottery and moved to a wealthy neighborhood, compared to John Doe B his next door neighbor of more modest condition who has been drilling teeth 8 hours a day over the past 35 years. Clearly one can say that, thanks to the dullness of his career, had John Doe B had to relive his life a few thousand times since graduation from dental school, the range of possible outcomes would be rather narrow (assuming he is properly insured). At the best, he would end up drilling the rich teeth of the New York Park avenue residents, while the worst would show him drilling those of some semi-deserted town full of trailers in the Catskills. Furthermore, assuming he graduated from a very prestigious teeth-drilling school, the range of outcomes would be even more compressed. As to John Doe A, if he had to relive his life a million times, almost all of them would see him performing janitorial activities (and spending endless dollars for fruitless lottery tickets), and one in a million would see him winning the New Jersey lottery.

The idea of taking into account both the observed and unobserved possible outcomes sounds like a lunacy. For most people, probability is about what may happen in the future, not events in the observed past; an event that has already taken place has 100% probability, i.e., certainty. I have discussed the point with many people who platitudinously accuse me of confusing myth and reality. Myths, particularly well aged ones, we saw with Solon's warning, can be far more potent (and provide us with more experience) than plain reality.

A Bizarre Accounting Method

Alternative History

I start with the platitude that one cannot judge a performance in any given field (war, politics, medicine, investments) by the results, but by the costs of the alternative (i.e. if history played out in a different way). Such substitute course of events are called alternative histories. Clearly, the quality of a decision cannot be solely judged based on its outcome, but such a point seems to be only voiced by people who fail (those who succeed attribute their success to the quality of their decision). Such opinion is what politicians on their way out of office keep telling those members of the press who still listen to them-- eliciting the customary commiserating "yes, we know" that makes the sting even worse. And like many platitudes, this one, while being too obvious, is not easy to carry out in practice.

The Russian Roulette

One can illustrate the strange concept of alternative histories as follows. Imagine an eccentric (and bored) tycoon offering you $10 Million to play Russian roulette, i.e. to put a revolver with a barrel containing one single bullet out of six to your head and pull the trigger. Each realization would count as one history, for a total of six possible histories of equal probabilities. Five out of these six histories would lead to enrichment; one would lead to a statistic, that is, an obituary with an embarrassing (but certainly original) cause of death. The problem is that only one of the histories is observable; and the winner of $10 Million would elicit the admiration and praise of some fatuous journalist (the very same ones who unconditionally admire the Forbes 500 billionaires and trash those who refrain from taking some market risks). Like almost every executive I have encountered during a 15 year career on Wall Street (and such executive's role is to be a judge of results delivered in a random manner), the public observes the external signs of wealth without even having a glimpse at the source (we call such source the generator). Consider the possibility that the roulette winner would be used as a role model by his family, friends, and neighbors.

While the remaining five histories are not observable, the wise and thoughtful person could easily make a guess as to their attributes. It requires some thoughtfulness and personal courage. In addition, in time, if the roulette-betting fool keeps playing the game, the bad histories will tend to catch up with him. Thus, if a 25 year old played Russian roulette, say, once a year, there would be very slim possibility of his surviving his 50th birthday --but, If there are enough players, say thousands of 25 year old players, we can expect to see a handful of (extremely rich) survivors (and a very large cemetery). Here I have to admit that the example of the Russian roulette is more than intellectual to me: I have lost a comrade to Russian Roulette, during the Lebanese war, when we were in our teens. Furthermore, my interests in literature were confirmed when I read the account by the novelist Graham Greene of his own experience with Russian roulette: it bore a stronger effect on me than the actual events I had recently witnessed. Greene claimed that he once tried to soothe the dullness of his childhood by pulling the trigger on a revolver –making me shiver that I had at least a one in sixth probability of having been without his novels.

The reader can see our views on alternative accounting: $10 million earned through Russian roulette do not have the same value as $10 million earned through the diligent and artful practice of dentistry. They are the same, can buy the same goods, except that one's dependence on randomness is greater than the other. To an accountant, though, they would be identical. To your next door neighbor too. Yet, deep down, I cannot help considering them qualitatively as different. The notion of such alternative accounting has interesting intellectual extensions and lends itself to mathematical formulation, as we will see next chapter with our introduction of the Monte Carlo engine. Note that such use of mathematics is only illustrative, aiming at getting the intuition of the point, and should not be interpreted as an engineering issue. In other words one need not to actually compute the alternative histories so much as assess their attributes. Mathematics is not just a "numbers game": it is a way of thinking. We will see that probability is a qualitative subject.

The Vicious Roulette

Reality is far more vicious than a Russian Roulette.

First, it delivers the fatal bullet rather infrequently, like a roulette that would have hundreds, even thousand of holes instead of six. After a few dozen tries, one forgets about the existence of a bullet, under a numbing false sense of security. The point is dubbed in this book the the black swan problem, which we belabor in Chapter X, as it is linked to the problem of induction, a problem that kept a few philosophers of science awake at night. It is also related to a problem called denigration of history as gamblers, investors, and decision makers feel that the sort of things that happen to others would not necessarily happen to them.

Second, unlike a well defined precise game like Russian roulette, where the risks are visible to anyone capable of multiplying and dividing by six, one does not observe the barrel of reality. Very rarely is the generator visible to the naked eye. One is thus capable of unwittingly playing Russian roulette --and call it by some alternative "low risk" name. We see the wealth being generated, never the processor, a matter that makes people lose sight of their risks.

Smooth Peer Relations

The degree of resistance to randomness in one's life's is an abstract idea, part of its logic counterintuitive, and, to confuse matters, its manifestations non-observable. But I have been increasingly devoted to it --for a collection of personal reasons I will leave for later. Clearly my way of judging matters is probabilistic in nature; it relies on the notion of what could have probably happened, and requires a certain mental attitude with respect to one's observations. I do not recommend engaging an accountant in a discussion about such probabilistic considerations. For an accountant a number is a number. If he were interested in probability he would have gotten involved in more introspective professions --and would be inclined to make a costly mistake on your tax return.

While we do not see the roulette barrel of reality, some people give it a try; it takes a special mindset to do so. Having seen hundreds of people enter and exit my profession (characterized by extreme dependence on randomness), I have to say that those who have had a modicum of scientific training tend to go the extra mile. For many, such thinking is second nature. This might not necessarily come from their scientific training per se (beware of causality), but possibly from the fact that people who have decided at some point of their lives to devote themselves to scientific research tend to have an ingrained intellectual curiosity and a natural tendency for such introspection. Particularly thoughtful are those who had to abandon scientific studies because of their inability to keep focused on a narrowly defined problem. Without excessive intellectual curiosity it is almost impossible to complete a Ph.D. thesis these days, but without a desire to narrowly specialize it is impossible to make a scientific career. (There is a distinction, however, between the mind of a pure mathematician thriving on abstraction and that of a scientist consumed by curiosity). However, some people's concern for randomness can be excessive; I have even seen people trained in some fields, like say, quantum mechanics, push the idea to the other extreme, only seeing alternative histories and ignoring the one that actually took place.

I thus view people distributed across two polar categories: on one extreme, those who never accept the notion of randomness; on the other, those who are tortured by it. When I started on Wall Street in the 80s, trading rooms were populated with people with a "business orientation", that is generally devoid of any introspection, flat as a pancake, and likely to be fooled by randomness. Their failure rate was extremely high, particularly when financial instruments gained in complexity. Somehow tricky products, like exotic options, were introduced and carried counterintuitive payoffs that were too difficult for someone of such culture to handle. They dropped like flies; I do not think that many of the 100s of MBAs of my generation I met on Wall Street in the 80s still engage in such form of professional and disciplined risk taking.

Cheap Labor on Aeroflot

The 90s witnessed the arrival of people of richer and more interesting background, which made the trading rooms far more entertaining to me. Many scientists, some of them extremely successful in their field, arrived with a desire to make a buck. They, in turn, hired people who resembled them. While most of these people were not Ph.D.s (indeed the Ph.D. is still a minority), the culture and values suddenly changed, becoming more tolerant of intellectual depth. It caused in increase in the already high demand for scientists on Wall Street, owing to the rapid development of financial instruments. The dominant previous specialty was physics, but one could find all manner of quantitative backgrounds among them. Russian, French, Chinese, and Indian accents (by order) began dominating in both New York and London. It was said that every plane from Moscow had at least its back row full of Russian mathematical physicists en route to Wall Street (they lacked the street smarts to get good seats). One could hire very cheap labor by going to JFK airport with a (mandatory) translator, randomly interviewing those that fit the stereotype. Indeed by the late 90s one could get someone trained by a world class scientist for almost half the price of an MBA. As they say, marketing is everything; these guys do not know how to sell themselves.

I had a strong bias in favor of Russian scientists: many can be put to active use as chess coaches (I also got a piano teacher out of the process). In addition, they are extremely helpful in the interview process. When MBAs apply to trading positions, they frequently boast "advanced" chess skills on their resume. I recall the MBA career counselor at Wharton recommending our advertising chess skills "because it sounds intelligent and strategic". MBAs, typically, can interpret their superficial knowledge of the rules of the game into "expertise". We used to verify the accuracy of claims of chess expertise (and the character of the applicant) by pulling a chess set out of a drawer and telling the student, now turning pale: "Yuri will have a word with you".

The failure rate of these scientists, though, was better, but only slightly so than that of MBAs; but it came from another reason, linked to their being on average (but only on average) devoid of the smallest bit of practical intelligence. Some successful scientists had the judgment of a door knob --but by no means all of them. Many people were capable of the most complex calculations with utmost rigor when it came to equations, but be totally incapable to solve a problem with the smallest connection to reality: it is as if they understood the spirit but not the letter of the math. I am convinced that X., a likable Russian man of my acquaintances, had two brains: one for math and another, considerably inferior one, for everything else (which included solving problems related to the mathematics of finance). But on occasion a fast-thinking scientific-minded person with street smarts would emerge. Whatever the benefits of such population shift, it improved our chess skills and provided us with quality conversation during lunchtime --it extended the lunch hour considerably. Consider that I had in the 80s to chat with colleagues who had an MBA or tax accounting background and were capable of the heroic feast of discussing FASB standards. I have to say that their interests were not too contagious. The interesting thing about these physicists does not lie in their ability to discuss fluid dynamics; it is that they were naturally interested in a variety of intellectual subjects and provide a pleasant conversation.

Solon Visits Regine's Night Club

As the reader may already suspect, my opinions about randomness have not earned me the smoothest of relations with some of my peers during a 15 year Wall Street career (many of whom the reader can see indirectly --but only indirectly-- portrayed in these chapters). But where I had uneven relations was with some of those who had the misfortune of being my bosses. For I had two bosses in my life of contrasting characteristics in about every trait.

The first, K., was the epitome of the suburban family man. He would be of the type to coach soccer on Saturday morning, and invite his brother in law for a Sunday afternoon barbecue. He gave the appearance of someone I would trust with my savings -- indeed he rose quite rapidly in the institution in spite of his lack of technical competence in financial derivatives (his firm’s claim to fame). But he was too much a no-nonsense person to make out my logic. He once blamed me for not being impressed with the successes of some of his traders who did well during the bull market for European bonds of 1993, whom I openly considered nothing better than random gunslingers. I tried presenting him with the notion of survivorship bias (Part II of this book) in vain. His traders have all exited the business since then "to pursue other interests" (including him). But he gave the appearance of being a calm, measured man, who spoke his mind and knew how to put the other person at ease during a conversation. He was articulate, extremely presentable thanks to his athletic looks, well measured in his speech, and was endowed with the extremely rare quality of being an excellent listener. His personal charm allowed him to win the confidence of the chairman--but I could not conceal my disrespect, particularly as he could not make out the nature of my conversation. In spite of his conservative looks he was a perfect time bomb, ticking away.

The second, J-P, in contrast, was a moody Frenchman with an explosive temper and a hyper-aggressive personality. Except for those he truly liked (not that many), he was expert at making his subordinates uncomfortable, putting them in a state of constant anxiety. He greatly contributed to my formation as a risk-taker; he is one of the very rare people who have the guts to only care about the generator, entirely oblivious of the results. He presented the wisdom of Solon, but, while one would expect someone with such personal wisdom and such understanding of randomness to lead a dull life, he lived a colorful one. In contrast with K. who wore conservative dark suits and white shirts (his only indulgence was in the $100 equestrian Hermes ties), J-P dressed like a peacock: blue shirts, plaid sports coats stuffed with gaudy silk pocket squares. No family man, he rarely came to work before noon --though I can safely say that he carried his work with him to the most unlikely places. He frequently called me from Regine, an upscale night-club in New York, waking me up at three in the morning to discuss some small (and irrelevant) details of my risk exposure. In spite of his slight corpulence, women seemed to find him irresistible; he frequently disappeared in midday and was unreachable for hours. Once, recently, he invited me to discuss an urgent business issue with him. Characteristically, I found him mid-afternoon in a strange "club" in Paris that carried no nameplate and where he sat with documents strewn across the table from him. Sipping champagne, he was simultaneously caressed by two scantily dressed young ladies. Strangely, he involved them in the conversation as if they were part of the meeting. He even had one of the ladies pick up his constantly ringing mobile phone as he did not want our conversation to be interrupted.

I am still surprised at this flamboyant man's obsession with risks, which he constantly played in his head --he literally thought of everything that could possibly happen. He forced me to make an alternative plan should a plane crash into the office building –and fumed at my answer that the financial condition of his department would be of small interest to me in such circumstances. He had a horrible reputation as a philanderer, a temperamental boss capable of firing someone at a whim, yet he listened to me and understood every word I had to say, encouraging me to go the extra mile in my study of randomness. He taught me to look for the invisible risks of blowup in any portfolio. Not coincidentally, he has an immense respect for science and an almost fawning deference for scientists; a decade or so after we worked together he showed up unexpectedly during the defense of my doctoral thesis, smiling from the back of the room. While K. knew how to climb the ladder of an institution, reaching the level of [censored] before being forced out, J-P did not have such a happy career, a matter that taught me to beware of mature financial institutions.

It can be disturbing for many self-styled "bottom line" oriented people to be questioned about the histories that did not take place rather than the ones that actually happened. Clearly, to a no-nonsense person of the "successful in business" variety, my language (and, I have to reckon, some traits of my personality) appear strange and incomprehensible. To my amusement, the argument appeared offensive to many. The contrast between K. and J-P is not a mere coincidence. Beware the spendthrift "businesswise" person: the cemetery of markets is disproportionately well stocked with the self-styled "bottom line" people. In contrast with their customary Masters of the Universe demeanor, they suddenly look pale, sallow, humble and serotonin-deprived on the way to the personnel office for the customary discussion of the severance agreement.

K. was not an atypical manager. I have another two examples to proffer. S., a man of personal charisma and remarkable integrity had the bad luck to be (very briefly) my head trader. He had become powerful as the result of a protracted, decade long, rally, in emerging market securities. Like K., he knew how to conduct himself in public, with his modicum of business charisma. He genuinely liked me, but acted patronizingly on occasion. He told me that he found me intelligent, hard working, but, not understanding my arguments, informed me that "there was a little too much confusion in my mind". He offered to help me get rid of it. He too is out of the business, the casualty of a rapid blowup.

Finally, I will summarize the obscurantism that prevailed in the Wall Street of the dark ages by a remark one A. M. threw at me in 1993: "You write books. I despise people who write books" (I made the mistake of showing him the draft of what became my first publication, Dynamic Hedging). He is the only fool-of-randomness who rose in life without having a pleasant personality (although he could produce some personal charm and urbanity when needed, that is, in the presence of superiors). M. had been criticizing my method of trading which consists in playing the rare event, and refused to discuss it with me. We will come back to him later in the book.

George Will is no Solon

Realism can be punishing. Probabilistic skepticism is worse. It is difficult to go about life wearing probabilistic glasses, as one starts seeing fools of randomness all around, in a variety of situations --obdurate in their perceptional illusion. To start, it is impossible to read a historian's analysis without questioning the inferences: We know that Hannibal and Hitler were mad in their pursuit as Rome is not Phoenician-speaking and Times Square in New York currently exhibits no swastikas. How about all these generals who were equally foolish but end up winning the war and consequently the esteem of the historical chronicler? It is hard to think of Alexander the Great or Julius Caesar in that light. Again I am not contesting that a general won the war, but the claims concerning the quality of his strategy.

Listening to the media can cause me on occasion to jump at my seat, mostly because I am not used to it. One illustration of a dangerous refusal to consider alternative histories is provided by the interview that media person George Will, a "commentator" of the commenting variety gave to Professor Robert Shiller, a man known to the public for his best-selling book Irrational Exuberance, but known to the connoisseur for his remarkable insights about the structure of market randomness and volatility (expressed in the precision of mathematics).

The interview is illustrative of the destructive aspect of the media, in catering to our heavily warped common sense and biases. I was told that George Will was very famous and extremely respected (that is for a journalist). He might even be someone of utmost intellectual integrity; his profession, however, is merely to sound smart and intelligent to the hordes. Shiller, on the other hand, understands the ins and outs of randomness, is trained to deal with rigorous argumentation, but does not sound smart in public because his subject matter is highly counterintuitive --he doesn't have to. Shiller had been pronouncing the stock market to be overpriced for a long time. George Will indicated to Shiller that had people listened to him in the past they would have lost money, as the market has more than more than doubled since he started pronouncing it overvalued. To such journalistic and well sounding (but senseless) argument, Shiller was unable to respond except to explain that the fact that he was wrong in one single market call should not carry undue significance. Shiller apparently had no claims for being a prophet or one of the entertainers. Yogi Berra would have had a better time with his confident comment on the fat lady not having sung yet.

I could not understand what Shiller, untrained to compress his ideas into vapid sound-bites, was doing on such a TV show. Clearly, it is foolish to think than an irrational market cannot become even more irrational; Shiller's views on the rationality of the market is not invalidated by the argument that he was wrong in the past. Here I could not help seeing in the person of George Will the representative of so many nightmares in my career; my attempting to prevent someone from playing Russian Roulette for $10 Million and seeing journalist George Will humiliating me in public by saying that had the person listened to me it would have cost him $10 Million. In addition, Will's comment was not an off-the-cuff remark; he wrote an article on the matter discussing Shiller's bad "prophecy". Such tendency to make and unmake prophets based on the fate of the roulette wheel, as we will see in Chapter x, is symptomatic of our genetic inability to cope with the complex structure of randomness prevailing in the modern world. Mixing forecast and prophecy is symptomatic of randomness foolishness.

Humiliated in Debates

Clearly, this idea of alternative history does not make intuitive sense, which is where the fun starts. For starters, we are not wired in a way to understand probability, a point that we will examine backward and forward in this book, at the risk of boring the reader with it. We will just say at this point that researchers of the brain believe that mathematical truths make little sense to our mind, particularly when it comes to the examination of random outcomes. Most results in probability are entirely counterintuitive; we will see plenty of them. Then why argue with a mere journalist whose paycheck comes from playing on the conventional wisdom of the hordes? I recall that every time I have been humiliated in a public discussion by someone (of the George Will variety) who seemed to present more palatable arguments than mine, I turned out to be right. I do not dispute that arguments should be simplified to their maximum potential; but, like S., people often confuse complex ideas that cannot be simplified into a media-friendly statement as symptomatic of a confused mind. MBAs learn the concept of clarity and simplicity, the five-minute manager take on things. The concept may apply to the business plan for a fertilizer plant, but not to highly probabilistic arguments --which is the reason I have anecdotal evidence in my business that MBAs tend to blow up in financial markets, as they are trained to simplify matters a couple of steps beyond their requirement (I beg the MBA reader not to take offense: I am myself am the unhappy holder of such blinding degree).

Beware the confusion between quality and intelligibility. Part of conventional wisdom favors things that can be explained rather instantly and "in a nutshell" --in many circles it is considered law. Having attended a French elementary school, a Lycée Primaire, I was trained to rehash the piece

Ce qui se concoit bien s'énonce clairement

Et les mots pour le dire viennent aisément

Translation: What is easy to conceive is clear to express /Words to say it would come effortlessly. The reader can image my disapointment at realizing, while growing up as a practitioner of randomness, that most poetic sounding popular adages are plain wrong. I need to make a huge effort not to be swayed by well sounding remarks. I remind myself of the following:

What sounds great in a conversation or a meeting, or, particularly in the media, is suspicious

All the smart things that have been proven by science appeared like lunacies at the time they were first discovered. Try to explain to a London Times journalist in 1905 that time slows down when one travels. Or to someone with no exposure to physics that there are places in our universe where time does not exist. Try to explain to K. that, although his star trader had made him a lot of money, that I have enough arguments to convince him that he is a nothing beyond a pure and dangerous idiot. Try to explain to A.M. the difference between noise and performance.

Wall Street Risk Managers

Wall Street firms have recently created the strange position of a risk manager, someone who is supposed to monitor the institution and verify that it is not in the business of playing Russian roulette. Clearly, having being burned a few times, the incentive is there to have someone take a look at the generator, the roulette that produces the profits. Although it is more fun to trade, many extremely smart people among my friends (including J-P) felt attracted by such position. Many of the people in my surrounding work in such area. It is an important and attractive fact that the average risk manager earns more than the average trader (particularly when we take into account the number of traders thrown out of the business). But their job feel strange, for the following reason. As we said, the generator of reality is not observable. They are limited in their power to stop profitable traders from taking risks, given that they would, ex post be accused by the George Wills around of costing the shareholder some precious opportunity shekels. On the other hand, the occurrence of a blowup would cause them to be responsible for it. What to do in such circumstances?

Their focus becomes to play politics, cover themselves by issuing vaguely phrased internal memoranda that warn against risk-taking activities yet stops short from completely condemning it, lest they lose their job. Like a doctor torn between the two types of errors: the false positive (telling the patient he has cancer when in fact he does not) and the false negative( telling the patient he is healthy when in fact he has cancer), they need to balance their existence with the fact that they inherently need some margin of error in their business. For my part, I resolved the problem long ago by being both the risk manager and the boss at my current operation.

No More A.

I no longer have trading managers, as, being self-employed, I am currently experiencing the lightness of semi-perfect boss-lessness. Accordingly, my current refuge from debates is in saying "please, call me an intellectual snob, someone following an incomprehensible logic, a complicated man, an arrogant fart, but I will not engage you in a discussion". The costs of being unfairly called an intellectual snob are considerably smaller than the loss of dignity from a mediatized conversation with George Will or A. M. Since I started my own hedge fund management operation, my professional world has been populated with people like J-P who are committed to go the extra mile to understand randomness. I have been able to erect a wall around me and my business; if I do not accept any investor's money it is not without a reason, I simply do not want to have to risk twisting my tongue talking to a fool of randomness about risks and probability. My pool of capital may not be as large as its potential, but I have time to write this book. My life now is a far cry from the epoch when I had bitter arguments with A. --gone are the days when I make attempts at convincing others of the notion of alternative possible histories. The designation intellectual snob never bothered the classical writers I frequent: Horace proclaimed his contempt for the crowds with Odi profanum vulgum et arceo (Í despise the vulgar crowd and insulate myself from it). Traders calls that a contrarian. I do not proclaim my contempt for the crowd (or, if I did, it would be concealed in some politically correct terms), but, certainly, I would like to avoid having to express my admiration.

Unfortunately, the world is not just populated with babbling but ultimately inconsequential journalists with no money to invest. Someone in business who does not want to be a total fool of randomness would be penalized, not just by George Will, but by the more consequential investors and employers, for focusing on the non-observable histories, that is events that could have taken place, but clearly did not. While such obsessive conservatism will perhaps allow an investor to outlive many other ones, it can cause him some occasional difficulties, as we will see, in his encounters with people of more elevated, but more fragile, status. They will be unrelenting in demanding comparative performance. "How did you fare in comparison with Jack Welsh or Jeff Bezos?". Or, a la George Will, "By investing with you I missed out on the internet rally; I underperformed the market by 20%; you are costing me money". Neighbors will be flashing a new convertible Mercedes obtained through Russian roulette type strategies. Traders and investors are often blamed for not doing as well as others in their category (without reference to the effect of other possible outcomes). For instance, New York University recently blamed one of its skeptical and conservative trustees for making them miss on the great bull market in their endowment fund. They found that such policy cost them billions. Clearly, it is hard to argue that the other trader played Russian roulette and that he is an idiot when the boss flashes the profit and loss reports of those currently in a state of temporary prominence.

Randomness and History in Monte Carlo

The stereotype of a pure mathematician presents an anemic man with a shaggy beard and grimy and uncut fingernails silently laboring on a Spartan but disorganized desk. With thin shoulders and a pot belly, he sits in a grubby office, totally absorbed in his work, oblivious to the grunginess of his surroundings. He grew up in a communist regime and speaks English with an astringent and throaty Eastern European accent. When he eats, crumbs of food accumulate in his beard. With time he becomes more and more absorbed in his subject matter of pure theorems, reaching levels of ever increasing abstraction. The American public was recently exposed to one of these characters with the unabomber, the bearded and recluse mathematician who lived in a hut and took to murdering people who promoted modern technology. No journalist was capable of even coming close to describing the subject matter of his thesis, Complex Boundaries, as it has no intelligible equivalent --a complex number being an entirely abstract and imaginary number, the square root of -1, an object that has no analog outside of the world of mathematics.

The name Monte Carlo conjures up the image of a suntanned urbane man of the Eurotrash variety entering a casino under a whiff of the Mediterranean breeze. He is an apt skier and tennis player, but also can hold his own in chess and bridge. He drives a gray sports car, dresses in a well ironed Italian handmade suit, and speaks carefully and smoothly about mundane, but real, matters, those a journalist can easily describe to the public. Inside the casino he astutely counts the cards, mastering the odds, and bets in a studied manner, his mind producing precise calculations of his optimal betting size. He could be James Bond's smarter lost brother.

Now 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 intuitions without the excessive abstraction. For indeed this branch of mathematics is of immense practical use -- it does not present the same dryness commonly associated with mathematics. I became addicted to it the minute I became a trader. It shaped my thinking in most matters related to randomness. Most of the examples used in the book are created with my Monte Carlo generator. It is far more a way of thinking than a computational method.

The Tools

The notion of alternative histories discussed in the last chapter can be extended considerably further and subjected to all manner of technical refinement. This brings us to the tools used in my profession to toy with uncertainty. I will outline them next.

Concepts

Sample Path: The invisible histories have a scientific name, alternative sample paths, a name borrowed from the field of mathematics of probability called stochastic processes. The notion of path, as opposed to outcome, indicates that it is not a mere MBA-style scenario analysis, but the examination of a sequence of scenarii along the course of time. We are not just concerned at where a bird can end up tomorrow night, but rather at all the various places it can possibly visit during the time interval. We are not concerned with what the investor's worth would be in, say, a year, but rather of the heart wrenching rides he may experience during that period. The word sample stresses that one sees only one realization among a collection of possible ones.

INSERT GRAPH HERE

Random Run: A random run, also called a random sample path is another mathematical name for such succession of virtual historical events, starting at a given date and ending at another. However the word random should not be mistaken for equiprobable (i.e. having the same probability). Some outcomes will gave a higher probability than others.

Stochastic Processes: refers to events unfolding with the course of time. Stochastic is a fancy Greek name for random. This branch of probability concerns itself with the study of the evolution of successive random events --one could call it the mathematics of history. The key about a process is that it has time in it.

Monte Carlo Generator: Imagine that you can replicate a perfect roulette in your attic without having recourse to a carpenter. Computer programs can be written to simulate about anything. They are even better (and cheaper) than the roulette built by your carpenter, as the physical roulette may be inclined to favor a number more than others owing to a possible slant in its built, or the floor of your attic. These are called the biases.

Monte Carlo simulations are closer to a toy than anything I have seen in my adult life. One can generate thousands, perhaps millions of random sample paths, and look at the prevalent characteristics of some of their features. The assistance of the computer is instrumental in such studies. The glamorous reference to Monte Carlo indicates the metaphor of simulating the random events in the manner of a virtual casino. One sets conditions believed to resemble the ones that prevail in reality, and launches a collection of simulations around possible events. With no mathematical literacy we can launch a Monte Carlo simulation of an 18 year old Christian Lebanese playing successively Russian roulette for a given sum, and see how many of these attempts result in enrichment, or how long it takes on average before he hits the obituary. We can change the barrel to contain 500 holes, a matter that would decrease the probability of death, and see the results.

Monte Carlo simulation methods were pioneered in martial physics in the Los Alamos laboratory during the A bomb preparation. They became popular in financial mathematics in the eighties, particularly in the theories of the random walk of asset prices. Clearly, we have to say that the example of the roulette is too simple as to be examined without the aid of such apparatus, but many problems, particularly those resembling real life situations, require the potency of a Monte Carlo simulator.

Monte Carlo Mathematics

It is a fact that that "true" mathematicians do not like Monte Carlo methods. They consider that they rob us of the finesse and elegance of mathematics. They call it "brute force". For we can replace a large portion of mathematical knowledge with a Monte Carlo simulator (and other computational tricks). For instance, someone with no formal knowledge of geometry can compute the mysterious, almost mystical Pi. How? By drawing a circle inside of a square, and "shooting" random bullets into the picture (as in an arcade), specifying equal probabilities of hitting any point on the map (something called a uniform distribution). The ratio of bullets inside the circle divided by those inside and outside the circle will deliver a multiple of the Mystical Pi, with possibly infinite precision. Clearly, this is not an efficient use of a computer as Pi can be computed analytically, that is, in a mathematical form, but the method can give some users more intuition about the subject matter than lines of equations. Some people' brains and intuitions are oriented in such a way that they are more capable of getting a point in such a manner (I count myself one of those). The computer might not be natural to our human brain; so is mathematics.

I am not a "native" mathematician, that is someone who does not speak mathematics as a native language, but someone who speaks it with a trace of a foreign accent. I am not interested in mathematical properties per se, only in the application, while a mathematician would be interested in improving mathematics (via theorems and proofs). I proved incapable to concentrate on deciphering a single equation unless I was motivated by a real problem (with a modicum of greed); thus most of what I know comes from derivatives trading --options pushed me to study the math of probability. Many compulsive gamblers, who otherwise would be of middling intelligence, acquire remarkable card counting skills thanks to their passionate greed.

Another analogy would be with grammar: mathematics is often tedious and insightless grammar. There are those who are interested in grammar for grammar's sake, and those interested in avoiding solecisms while writing documents. We are called "quants" -- like physicists, we have more interest in the employment of the mathematical tool than in the tool itself. Mathematicians are born, never made. Physicists and quants too. I do not care about the "elegance" and "quality" of the mathematics I use so long as I can get the point right. I have recourse to Monte Carlo machines whenever I can. they can get the work done. They are also far more pedagogical, and I will use them in this book for the examples.

Indeed, probability is an introspective field of inquiry, as it affects more than one science, particularly the mother of all sciences: that of knowledge. It is impossible to assess the quality the knowledge we are gathering without allowing a share of randomness in the manner it is obtained and cleaning the argument from the chance coincidence that could have seeped in its construction. In science, probability and information are treated in exactly the same manner. Literally every great thinker has dabbled with it, most of them obsessively. The two greatest minds to me, Einstein and Keynes, both started their intellectual journeys with it. Einstein wrote a major paper in 1905, in which he was almost the first to examine in probabilistic terms the succession of random events, namely the evolution of photo-particles in space. His Brownian paper is the backbone of the random walk theories used in financial modeling. As to Keynes, to the literate person he is not the political economist that tweed-clad leftists love to quote, but the author of the magisterial, introspective, and potent Treatise on Probability. For before his venturing into the murky field of political economy, Keynes was a probabilist. He also had other interesting attributes (he blew up trading).

The reader can guess that the next step from such probabilistic introspection is to get drawn into philosophy, particularly the branch of philosophy that concerns itself with knowledge, called epistemology or methodology, or philosophy of science, popularized by such persons as Karl Popper and George Soros. We will not get into the topic until later in the book.

Fun in my Attic

Making History

In the early 90s, like many of my friends in quantitative finance, I became addicted to the various Monte Carlo engines, which I taught myself to build, thrilled to feel that I was generating History, a Demiurgus. It can be electrifying to generate virtual histories and watch the dispersion between the various results. Such dispersion is indicative of the degree of resistance to randomness. This is where I am convinced that I have been extremely lucky in my choice of career: one of the attractive aspects of my profession as a quantitative option trader is that I have close to 95% of my day free to think, read, and research (or "reflect" in the gym or on ski slopes). I also had the privilege of frequently "working" from my well-equipped attic.

The dividend of the computer revolution to us did not come in the flooding of self-perpetuating e-mail messages and access to chat rooms; it was in the sudden availability of fast processors capable of generating a million sample paths per minute. Recall that I never considered myself better than an unenthusiastic equation solver and was rarely capable of the prowess in the matter --being better at setting up equations than solving them. Suddenly, my engine allowed me to solve with minimal effort the most intractable of equations. Few solutions became out of reach.

Zorglubs Crowding the Attic

My Monte Carlo engine took me on a few interesting adventures. While my colleagues were immersed in news stories, central bank announcements, earning reports, economic forecasts, sports results and, not least, office politics, I started toying with it in bordering fields to my home base of financial probability. A natural field of expansion for the amateur is evolutionary biology --the universality of its message and its application to markets are appealing. I started simulating populations of fast mutating animals called Zorglubs under climatic changes and witnessing the most unexpected of conclusions --some of the results are recycled in chapter x. My aim, as a pure amateur fleeing the boredom of business life, was merely to develop intuitions for these events --the sort of intuitions that amateurs build away from the overly detailed sophistication of the professional researcher. I also toyed with molecular biology, generating randomly occurring cancer cells and witnessing some surprising aspects to their evolution. Naturally the analogue to fabricating populations of Zorglubs was to simulate population of "idiotic bull", "impetuous bear" and "cautious" traders under different market regimes, say booms and busts, and examine their short term and long term survival. Under such a structure, "idiotic bull" traders who get rich from the rally would use the proceeds to buy more assets, driving prices higher, until their ultimate shellacking. Bearish traders, though, rarely made it in the boom to get to the bust. My models showed almost nobody to really ultimately make money; bears dropped out like flies in the rally and bulls got ultimately slaughtered, as paper profits vanished as the music stopped. But there was one exception: some of those who traded options (I called them option buyers) had remarkable staying power and I wanted to be one of those. How? Because they could buy the insurance against blowup; they could get anxiety-free sleep at night, thanks to the knowledge that if their careers were threatened, it would not be owing to the outcome of a single day.

If the tone of this book seems seeped in the culture of Darwinism and evolutionary thinking, it does not come from any remotely formal training in the natural sciences, but from my getting an evolutionary way of thinking from my Monte Carlo simulators.

I have to reckon that I outgrew the desire to generate random runs every time I want to explore an idea --but by dint of playing with a Monte Carlo engine for years I can no longer visualize a realized outcome without reference to the non-realized ones. I call that "summing under histories", borrowing the expression from the colorful physicist Richard Feynman who applied such methods to examine the dynamics of particles.

Denigration of History

One more word on history seen from a Monte Carlo perspective. The wisdom of such classical stories as Solon prods me to spend even more time in the frequentation of the classical historians, even if the stories, like Solon's warning, have been embellished by the patina of time. However, this goes against the grain: learning from history does not come naturally to us humans, a fact that is so visible in the endless repetitions of identically configured booms and busts in modern markets. By history I refer to the anecdotes, not the historical theorizing, the grand scale historicism that aims to interpret events with theories based on uncovering some laws in the evolution of history (the sort of Hegelianism and pseudo-scientific historicism leading to such calls as the end of history ---a lot more on these in our discussion of the survivorship biases and Karl Popper). It is merely at the level of my desired intellectual sensibility, affecting the way I would wish to think by reference to past events, by being able to better steal the ideas of others and leverage them, correct the intellectual defect that seems to block my ability to learn from others. It is the intellectual respect of the elders that I would like to develop, reinforcing the awe I instinctually feel for people with gray hair, but that has eroded in my life as a trader where age and success are somewhat divorced. Indeed I have two ways of learning from history: from the past by reading the elders, and from the future thanks to my Monte Carlo toy.

The Stove is Hot

It is not natural for us to learn from history. We have enough clues to believe that our genetic endowment as Homo erectus does not favor transfers of experience. It is a platitude that children only learn from their own mistakes; they will only cease to touch a burning stove when they are themselves burned; no possible warning by others can lead to developing the smallest form of cautiousness. Adults, too, suffer from such a condition. The point has been examined by behavioral economics pioneers Daniel Kahneman and Amos Tversky when it comes to the choices people make in selecting risky medical treatments --I myself have seen it in my being extremely lax in the area of detection and prevention (i.e., I refuse to derive my risks from the probabilities computed on others, feeling that I am somewhat special) yet extremely aggressive in the treatment of medical conditions (I overreact when I am burned), which is not coherent with rational behavior under uncertainty. This congenital denigration of the experience of others is not limited to children or to people like myself; it affects business decision makers and investors in a grand scale.

All of my colleagues whom I have known to denigrate history blew up spectacularly --and I have to say that (except for investors partaking of the bull market still prevailing at the time of writing) I have yet to encounter some such person who has not blown up yet. But that is not the interesting point: there are remarkable similarities in their approaches. I have noticed plenty of analogies between those who blew up in the stock market crash of 1987, those who blew up in the Japan meltdown of 1990, those who blew up in the bond market debacle of 1994, those who blew up in Russia in 1998, and those who blew up buying Nasdaq stocks in 2000. They all made claims to the effect that "these times are different" or that "their market was different", and offered seemingly well constructed intellectual arguments (of an economic nature) to justify their claims; they were unable to accept that the experience of others was out there, in the open, freely available to all, with books detailing crashes in every bookstore. Aside from these generalized systemic blowups, I have seen hundreds of option traders forced to leave the business for blowing up in a stupid manner, in spite of warnings by the veterans, similar to a child's touching the stove. This I find to resemble my own personal attitude with respect to the detection and prevention of the variety of ailments I may be subjected to. Every man believes himself to be quite different, a matter that amplifies the "why me?" shock upon a diagnosis.

We can discuss this point from different angles. Experts call one manifestation of such denigration of history historical determinism; in a nutshell we think that we would know when history is made; we believe that people who, say, witnessed the stock market crash of 1929 knew then that they lived an acute historical event, and that, should these events repeat themselves, they would know about such fact. Life for us is made to resemble an adventure movie, as we know ahead of time that something big is about to happen.

My Solon

I have another reason to be obsessed with Solon's warning. I hark back from the very same strip of land in Asia Minor where the story took place. My ancestors did experience bouts of extreme opulence and embarrassing penury in the same generation, with abrupt regressions that people around me who have the memory of steady and linear betterment do not think feasible (at least not at the time of writing). Those around me either have (so far) had few family setbacks (except for the great depression) or, more generally, are not suffused with enough sense of history to reflect backward. For people of my background, Eastern Mediterranean Greek-Orthodox and invaded Eastern Roman citizens, it was as if our soul has been wired with the remembrance of that sad April day circa 500 years ago when Constantinople, under the invading Turks, fell out of history, leaving us the lost subjects of a dead empire, very prosperous minorities in an Islamic world --but with an extremely fragile wealth. Moreover, I vividly remember the image of my own dignified grandfather, former deputy prime minister and son of deputy prime minister (whom I never saw without a suit), residing in a nondescript apartment in Glifada, near Athens, his estate having been blown up during the Lebanese civil war. Incidentally, having experienced the ravages of war, I find undignified impoverishment far harsher than physical danger (somehow dying in full dignity appears to me far preferable to living a janitorial life, which is one of the reasons I dislike financial risks). I am certain that Solon worried more about the loss of his Kingdom than the perils to his life.

Enough of the anecdote; there is an important and non-trivial aspect of historical thinking, perhaps more applicable to the markets than anything else: unlike many "hard" sciences, history cannot lend itself to experimentation. But somehow, overall, history is potent enough to deliver, on time, in the medium to long run, most of the possible scenarii, burying the bad guy. Bad trades catch up with you, it is frequently said in the markets. Mathematicians of probability give that a fancy name: ergodicity, from ergo, sameness. It means, roughly, that (under certain conditions), very long sample paths would end up resembling each other. The properties of a very, very long sample path would be similar to the Monte Carlo properties of an average of shorter ones. The janitor in Chapter x who won the lottery, if he lived 1000 years, cannot be expected to win more lotteries. Those who were unlucky in life in spite of their skills would eventually rise. The lucky idiot might have benefited from some luck in life; over the longer run he would slowly converge to the state of a less-lucky idiot. Each one would revert to his long term properties.

Distilled Thinking on Your PalmPilot

Breaking News

The journalist, my bete noire, entered this book with George Will dealing with random outcomes. In the next step I will show how my Monte Carlo toy taught me to favor distilled thinking. For the difference between noise and information, the topic of this book (noise has more randomness) has an analog: that between journalism and history. To be competent, a journalist should view matters like a historian (and perhaps lose his job).

For an idea, age is beauty. The applicability of Solon's warning to a life in randomness, in contrast with the exact opposite message delivered by the prevailing media-soaked culture, reinforces my instinct to value distilled thought over newer thinking, regardless of its apparent sophistication --another reason to accumulate the hoary volumes by my bedside (I confess that the only news items I currently read is the far more interesting upscale social gossip found in Tatler, Paris Match and Vanity Fair). Aside from the decorum of ancient thought as opposed to the coarseness of fresh ink, I spent some time phrasing the idea in the mathematics of evolutionary arguments and conditional probability. For an idea to have survived so long across so many cycles is indicative of its relative fitness. Noise, at least some noise, was filtered out. Mathematically, progress means that some new information is better than the past ones, not that the average of new information will supplant the past ones, which means that it is optimal for someone, when in doubt, to systematically reject the new idea, information, or method. Clearly and shockingly, always.

We will return to the value of the highly frequent news with a more technical discussion of signal filtering and observation frequency. I will say here that such respect for the time honored provides arguments to rule out any commerce with the babbling modern journalist, and implies a minimal exposure to the media as a guiding principle for someone involved in decision-making under uncertainty. If there is anything better than noise in the mass of "urgent" news pounding us, it would be like a needle in a haystack.

On the rare occasion when I boarded the 6:42 train to New York I observed with amazement the hoards of depressed business commuters (they seem to would have preferred to be elsewhere) studiously buried into the Wall Street Journal, apprised of the minutia of companies that, at the time of writing, are probably out of business. But while early on in my career such focus on noise would have offended me intellectually, as I would have deemed much information too statistically insignificant for the derivation of any meaningful conclusion, I currently look at it with delight, happy to see such a mass-scale of idiotic decision-making, prone to overreaction in their post-perusal investment orders --in other words I currently see in the fact that people read such material an insurance for my continuing in the business of option trading.

Shiller Redux

Most of the thinking about the negative value of information on society in general was sparked by one Robert Shiller. Not just in financial markets; but overall this may be the first mathematically formulated introspection on the manner society in general handles information. Interestingly, and by some strange coincidence, it is that very same Shiller that was trounced by George Will only one chapter ago. Shiller made his mark with his 1981 paper on the volatility of markets, where he determined that, if a stock price is the estimated value of "something" (say the discounted cash flows from a corporation), then market prices are way too volatile in relation to tangible manifestations of that "something" (he used dividends as proxy). Something about "rational expectation" did not work (from the inherent properties of an expectation operator). He then pronounced markets as not efficient. This set off calls by the religious orders of high finance for destroying the infidel who committed such apostasy. The principal criticism came from Robert C. Merton. The attacks were purely on methodological grounds (Shiller's analysis was extremely rough; for instance, his using dividends was rather weak). Now the same Robert C. Merton later was going about introducing himself as the "founding partner" of a hedge fund that aimed at taking advantage of market inefficiencies. Setting aside the fact that Merton's hedge fund blew up rather spectacularly from the black swan problem (with characteristic denial), such implied statement on the efficiency of markets should rather diminish the value of the leading criticism of Shiller's paper. It is as if the Pope converted to Islam.

But things are not getting any better these days. At the time of writing, news providers are offering all manner of updates, "breaking news" that can be delivered electronically to you in a wireless manner. The ratio of un-distilled information to that of the distilled is rising, saturating markets. The elder's messages need not to be delivered to you as imminent news.

This does not mean that all journalists are mere fooled by randomness noise providers: there are hordes of thoughtful journalists in the business (I would suggest London's Anatole Kaletsky and New York's Jim Grant and Alan Abelson as the underrated representatives of such class); it is just that prominent media journalism is a thoughtless process of providing the noise that can capture people's attention and there exists no mechanism of separating the two. Like A. D., the lawyer in Chapter x who does not care about the truth, but about arguments that can sway a jury whose intellectual defects he knows intimately, journalism goes to what can capture our attention, with adequate sound-bites. Again my scholarly friends would wonder why I am getting emotional saying obvious things about the journalist; the problem with my profession is that we depend on them for what information we need to obtain.

Gerontocracy

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 younger whenever possible. I toyed with Monte Carlo simulations of heterogeneous populations of traders under a variety of regimes (closely resembling historical ones), and found a significant advantage in selecting aged traders, using, as a selection criterion their cumulative years of experience rather than their absolute success (conditional on their having survived without blowing up). "Survival of the fittest", a term so hackneyed in the investment media, does not seem to be properly understood: under regime switching, as we will see in Chapter x, it will be unclear who is actually the fittest, and those who will survive are not necessarily those who appear to be the fittest. Curiously, it will be the oldest, simply because older people have been exposed longer to the rare event and can be, convincingly, more resistant to it. I was amused to discover a similar evolutionary argument in mate selection that considers that women prefer (on balance) to mate with healthy older men over healthy younger ones, everything else being equal, as the former provide some evidence of better genes. Gray hair signals an enhanced ability to survive --conditional on having reached the gray hair stage, he is likely to be more resistant to the vagaries of life. Curiously, life insurers in renaissance Italy seem to have reached the same conclusion, by charging the same insurance for a man in his 20s as they did for a man in his 50s, a sign that, curiously, they had the same life expectation: once a man crossed the 40 year mark, he has shown that very few ailments could harm him.

Monte Carlo, Nonsense, and the Scientific Intellectual

Our Monte Carlo engine can take us into a more literary territory. Increasingly, a distinction is being made between the scientific intellectual and the literary intellectual --culminating with what is called the "science wars". The distinction originated in Vienna in the 1930s, with a collection of physicists who decided that the large gains in science were starting to become significant enough to make claims on the field known to belong to the humanities. They wanted to strip thinking from rhetoric (except in literature and poetry where it properly belonged). Such circle was at the origin of the development of the ideas of Wittgenstein, Popper, Carnap, and flocks of others. Whatever merit have their original ideas, the impact on both philosophy and the practice of science was significant. Some of their impact of the non-philosophical intellectual life is starting to develop, albeit considerably more slowly.

One conceivable way to make the separation between a scientific intellectual and a literary intellectual is by considering that a scientific intellectual can usually recognize the writing of another but that the literary intellectual would not be able to tell the difference. This is even more apparent when the literary intellectual starts using scientific buzzwords, like "uncertainty principle" or "Godel's theorem" or "parallel universe" "relativity" either out of context or, as often, in exact opposition to the scientific meaning. I suggest reading the hilarious Fashionable Nonsense by Alan Sokal for an illustration of such practice (I was laughing so loud and so frequently reading it on a plane that other passengers kept whispering things about me). By dumping the kitchen sink of scientific references in a paper, one can make another literary intellectual believe that your material has the stamp of science. Clearly, to a scientist, science lies in the rigor of the inference, not in references to such grandiose concepts as general relativity. Such rigor can be spelled out in plain English. What struck me while reading Dawkins' Selfish Gene is that, although the text does not exhibit a single equation, it seems as if it were translated from the language of mathematics.

Reverse Turing Test

But there is another, far more entertaining way to make the distinction. You can often replicate something that can be mistaken for a literary discourse with a Monte Carlo generator; but it is not possible to randomly construct a scientific one. Rhetoric can be constructed randomly, not genuine scientific knowledge. This is the application of Turing's Test of artificial intelligence, except in reverse. Brilliant British Mathematician, eccentric, and computer pioneer Alan Turing came up with the following test: a computer can be said to be intelligent if he could (on average) fool a human into mistaking him for another human. The converse should be true: a human can be said to be un-intelligent if we can replicate his speech by a computer, whom we know is un-intelligent, and fool a human into believing that it was written by a human. Can one produce a piece of work that can be largely mistaken for Derida entirely randomly?

The answer seems to be yes. Aside from the hoax by Alan Sokal (the same of the hilarious book a few lines ago) who managed to produce nonsense and get it published by some prominent journal, there are Monte Carlo generators designed to structure such texts and write entire papers. Fed with "postmodernist" texts, they can randomize phrases under a method called recursive grammar, and produce grammatically sound but entirely meaningless sentences that sound like Jacques Derida, Camille Paglia, and such a crowd. Owing to the fuzziness of his thought, the literary intellectual can be fooled by randomness.

I refer to the Monach University program in Australia featuring the Dada Engine built by Andrew C. Bulha. I toyed with the engine and generated a few papers containing the following sentences:

However, the main theme of the works of Rushdie is not theory, as the dialectic paradigm of reality suggests, but pretheory. The premise of the neosemanticist paradigm of discourse implies that sexual identity, ironically, has significance.

If the neosemanticist paradigm of discourse holds, we have to choose between realism and posttextual discourse.

In a sense, Lacan's critique of semantic appropriation implies that the law is capable of significance, given that the premise of cultural narrative is invalid.

Many narratives concerning the role of the writer as observer may be revealed. It could be said that if cultural narrative holds, we have to choose between the dialectic paradigm of narrative and neoconceptual Marxism. Sartre's analysis of cultural narrative holds that society, paradoxically, has objective value.

It could be said that the premise of subtextual structuralist theory holds that reality is created by the masses, given that narrativity is interchangeable with culture. If dialectic nationalism holds, the works of Joyce are postmodern.

Thus, the premise of the neodialectic paradigm of expression implies that consciousness may be used to reinforce hierarchy, but only if reality is distinct from consciousness; if that is not the case, we can assume that language has intrinsic meaning.

Some business speeches belong to that category in their own right, except that they are less elegant and draw on a different type of vocabulary than the literary ones. We can randomly construct a CEO speech to insure whether what he is saying has value, or if it is merely dressed-up nonsense from someone who was lucky to be put there. How? You select randomly five phrases below, then connect them by adding the minimum required to construct a grammatically sound speech.

We look after our customer's interests/ the road ahead/ our assets are our people/ creation of shareholder value/ our vision/ our expertise lies in/ we provide interactive solutions/ we position ourselves in this market/ how to serve our customers better/ short term pain for long term gain/ we will be rewarded in the long run/ we play from our strength and improve our weaknesses/ courage and determination will prevail/ we are committed to innovation and technology/ a happy employee is a productive employee/

If that resembles too much the speech you just heard from the CEO of your company, then I suggest looking for a new job.

The Father of All Pseudothinkers

It is hard to resist closing this section without a comment on the father of all pseudothinkers: Hegel. Hegel writes a jargon that is so meaningless outside of a chic Left Bank Parisian café or the humanities department of some university extremely well insulated from the real world. I suggest this passage from the German "philosopher" (this passage was detected, translated & reviled by Karl Popper):

Sound is the change in the specific condition of segregation of the material parts, and in the negation of this condition;-merely an abstract or an ideal ideality, as it were, of that specification. But this change, accordingly, is itself immediately the negation of the material specific subsistence; which is, therefore, real ideality of specific gravity and cohesion, i.e. -heat. The heating up of sounding bodies, just as of beaten and or rubbed ones, is the appearance of heat, originating conceptually together with sound

Even a Monte Carlo engine cannot sound as random as the great philosophical master thinker (it would take plenty of sample runs to get the mixture of heat and sound). Now consider that Hegelian thinking is generally linked to a "scientific" approach to history; it has produced such products as Marxist regimes and even a branch called "neo-Hegelian" thinking.

Monte Carlo Poetry

There are instances where I like to be fooled by randomness. My allergy to nonsense and verbiage dissipates when it comes to art and poetry. On the one hand I try to define myself and behave officially as a no-nonsense hyper-realist ferreting out the role of chance; on the other I have no qualms indulging in all manner of personal superstitions. Where do I draw the line? The answer is esthetics. Some esthetic forms appeal to something genetic in us, whether or not they originate in random associations or plain hallucination. Something in our human genes is deeply moved by the fuzziness and ambiguity of language; then why fight it?

The poetry and language-lover in me has been initially depressed by the account of the Exquisite Cadavers poetic exercise where interesting and poetic sentences are randomly constructed, that, by throwing enough words together, some unusual and magical-sounding metaphor is bound to emerge according to the laws of combinatorics. Yet one cannot deny that some of these poems are of ravishing beauty. Who cares about their origin if they manage to please our esthetic senses?

The story of the Exquisite Cadavers is as follows. In the aftermath of the great war, a collection of surrealists poets, which included André Breton, their pope, Paul Eluard, and others got together in cafés and tried the following exercise (modern literary critics attribute the exercise to the depressed mood after the war and the need to escape reality). On a folded piece of paper, in turn, each one of them would write a predetermined part of a sentence, not knowing the other's choice. The first would pick an adjective, the second a noun, the third a verb, the fourth an adjective, and the fifth a noun. The first publicized exercise of such random (and collective) arrangement produced the following poetic sentence:

The exquisite cadavers shall drink the new wine.

(Les cadavres exquis boiront le vin nouveau). Impressive? It sounds even more poetic in the native French. Quite impressive poetry was produced in such a manner, sometimes with the aid of a computer. But poetry has never been truly taken seriously outside of the beauty of its associat ions, whether they have been produced by the random ranting of one, or more, disorganized brains, or the more elaborate constructions by a conscious creator.

Now regardless of whether the poetry was obtained by a Monte Carlo engine, or sung by a blind man in Asia Minor, language is potent in bringing pleasure and solace. A Turing-style test by translation would rob it of a varying degree of its potency, sometimes excessively: nothing can be more bland than translated poetry. A convincing argument of the role of language is the existence of surviving holy languages, uncorrupted by the no-nonsense tests of daily use. Semitic religions, that is Judaism, Islam, and original Christianity understood the point: keep a language away from the rationalization of daily use and avoid the corruption of the vernacular. Four decades ago, the Catholic church translated the services and liturgies from Latin to the local vernaculars; it can be argued that this did caused a drop in religious beliefs. Suddenly religion subjected itself to being judged by intellectual and scientific, without the esthetic, standards. The Greek Orthodox church made the lucky mistake, upon having to translate some of its payers from Church-Greek into the Semitic-based vernacular spoken by the Grecosyrians of the Antioch region (Southern Turkey and Northern Syria), of choosing classical Arabic, an entirely dead language. My folks are thus lucky to pray in a mixture of dead Koiné (church Greek) and no less dead Koranic Arabic.

What does this point have to do with a book on randomness? Our genes are péché mignon. Even the economists, who usually find abstruse ways to completely escape reality, are starting to understand that what makes us tick is not necessarily the calculating accountant in us. We do not need to be rational and scientific when it comes to the details of our daily life --only in those that can harm us. Modern life seems to invite us to do the exact opposite: become extremely realistic and intellectual when it comes to such matters as religion and personal behavior, yet as irrational as possible when it comes to markets and matters ruled by randomness. I have encountered colleagues, "rational" no-nonsense people, who do not understand why I cherish the poetry of Baudelaire or obscure writers. Yet they get sucked into listening to the "analyses" of such a person as George Will, or into buying the stock of a company they know absolutely nothing about, based on tips by neighbors who drive expensive cars. The Vienna circle, in their dumping on Hegel-style philosophy, explained that, from a scientific standpoint, it was plain garbage, and, from an artistic point of view, it was inferior to music. I have to say that I find Baudelaire far more pleasant to frequent than CNN newscasters or George Will.

There is a Yiddish saying: If I am going to be forced to eat pork, it better be of the best kind. If I am going to be fooled by randomness; it better be of the beautiful (and harmless) kind. The point will be part III of the book Wax in my Ears.

Survival of the Least Fit

Rodrigo the Emerging Markets Wizard

I used to meet Rodrigo at a variety of New York parties, where he would show up impeccably dressed, though a bit shy with the ladies. I used to pounce on him and try to pick his brains about emerging market bonds, not necessarily because he respected his opinion, so much as to get an idea about his complacency about the bull market in emerging markets. Rodrigo supposedly comes from a patrician Latin American family that was heavily impoverished by the economic troubles of the 80s, but, again, I have rarely run into anyone from a ravaged country whose family did not at some juncture own an entire province or, say, supply the Russian Czar with sets of dominoes. After brilliant undergraduate studies, he went to Harvard to pursue a Ph.D. in economics, as it was the sort of things Latin American patricians had gotten into the habit of doing at the time(with a view of saving their economies from the evils of non-Ph.D. hands). He was a good student but could not find a decent thesis topic for his dissertation. Nor did he gain the respect of his thesis advisor, who found him unimaginative. Rodrigo settled for a Master’s degree and a Wall Street career. Universities have a special way of getting rid of their unsuccessful Ph.D. students: they give them an intermediate Master’s degree.

Rodrigo was hired in the nascent emerging market desk of a New York bank in 1992. He had the right ingredients for success: he knew where to find on the map the countries that issued "Brady bonds", dollar denominated debt instruments issued by Less Developed Countries. He knew what Gross Domestic Product meant. He looked serious, brainy and well spoken, in spite of his heavy Spanish accent. He was the kind of person banks felt comfortable putting in front of their customers. What a contrast with the other traders who lacked polish!

Rodrigo got there right in time to see thing happening in that market. The desk specialized in the U.S. dollar denominated debt of third world countries. When he joined the bank, the market was small and traders were located in undesirable parts of trading floors. But rapidly the activity became a large, and growing, part of the bank’s revenues.

Rodrigo was quite generic among this community of emerging market traders; they are a collection of cosmopolitan patricians from across the emerging market world that remind me of the international coffee hour at his business school. I found it odd that rarely does a person specialize in the market of his or her birthplace: Mexicans based in London trade Russian securities, Iranians and Greeks specialize in Brazilian bonds, and Argentines trade Turkish securities. Unlike my experience with real traders, they are generally urbane, dressed well, collected art, but are non-intellectual. They seem too conformists to be true traders. They are mostly between 30 and 40, owing to the youth of their market. You can expect many of them to hold season tickets to the Metropolitan Opera. True traders, I believed, dress sloppily, are often ugly and exhibit the intellectual curiosity of someone who would be more interested in the information-revealing contents of the garbage can than the Cézanne painting on the wall.

Rodrigo thrived as a trader-economist. He had a large network of friends in the various Latin American countries and knew exactly what took place there. He bought bonds that he found attractive, either because they paid him a good rate of interest, or because he believed that they would become more in demand in the future, therefore appreciating in price. It would be perhaps erroneous to call him a trader. A trader buys and shorts; Rodrigo just bought –and he bought in size. He believed that he was paid a good risk premium to hold these bonds because there was economic value in lending to these countries. Shorting, in his opinion, makes no economic sense. "There is no value in shorting", he frequently said.

Rodrigo was the emerging markets reference within the bank. He could produce the latest economics figures at the drop of a hat. He had frequent lunches with the chairman. In his opinion, trading was economics, little else. It had worked so well for him. He got promotion after promotion, until he became the head trader of the emerging market desk at the institution. Starting in 1995, Rodrigo did exponentially well in his new function, getting an expansion of his capital on a steady basis –so fast that he was incapable of using up the new risk limits.

The Good Years

The reason Rodrigo had good years was not just because he bought emerging market bonds and their value went up over the period. It was mostly because he also bought dips. The year 1997 would have been a bad year had he not added to his position after the dip in October that accompanied the false stock market crash. Overcoming these small reversals of fortune made him feel invincible. He could do no wrong. He believed that the economic intuition he was endowed with allowed him to make good trading decisions. After a market dip he would verify the fundamentals, and, if they remained sound, he would buy more of the security and lighten up as the market recovered.

Figure 2 shows us the index of emerging market bonds between the time Rodrigo started his involvement with emerging markets and his last bonus check in December 1997. One can see that, after the Mexican devaluation of 1995 the market experienced an extended rally. One can also see some occasional dips that turned out to be "excellent buying opportunities".

Figure –2 The Emerging Bond Market Rally.

It was the summer of 1998 that undid Rodrigo. His track record includes just one bad quarter —but bad it was. He had earned close to $80 Million cumulatively in his previous years. He lost $300 Million in just one summer.

Next we go through the course of events. When the market started dipping in June, his friendly sources informed him that the sell-off was merely the result of a "liquidation" by a New Jersey hedge fund run by a former Wharton professor. That fund specialized in mortgage securities and had just received instructions to wind down the overall inventory. The inventory included some Russian bonds, mostly because yield hogs, as these funds are known, engage in the activity of building a "diversified" portfolio of high yielding securities.

Averaging Down

When the market started falling, he accumulated more Russian Bonds, at an average of around $52. That was Rodrigo’s trait: average down. The problems, he deemed, had nothing to do with Russia, and it was not some New Jersey fund run by some mad scientist that was going to decide the fate of Russia. "Read my lips: It’s a li-qui-da-tion!" he yelled at those who questioned his buying.

By the end of June, his trading revenues had dropped from up $60 Million to just up $20 Million. That made him angry. But he calculated that should the market rise back to the pre-New Jersey sell-off, then he would be up $100 Million. That was unavoidable, he asserted. These bonds, he said, would never, ever trade below $48. He was risking so little, to possibly make so much.

Then came July. The market dropped a bit more. The benchmark Russian bond was now at $43. His positions were under water, but he increased his stakes. By now he was down $30 Million for the year. His bosses were starting to become nervous but he kept telling them that, after all, Russia would not go under. He repeated the cliché that it was too big to fail. He estimated that bailing them out would cost so little and would benefit the world economy so much that it did not make sense to liquidate his inventory now. "This is the time to buy, not to sell", he said repeatedly. "These bonds are trading very close to their possible default value". In other words, should Russia go into default, and run out of dollars to pay the interest on its debt, these bonds would hardly budge. Where did he get this idea? From discussions with other traders and emerging market economists (or trader-economists hybrids).

Rodrigo put about half his net worth, then $5,000,000, in the Russia Principal Bond. "I will retire on these profits"; he told the stockbroker who executed the trade.

Lines in the Sand

The market kept going through the lines in the sand. By early August, they were trading in the 30s. By the middle of August, they were in the 20s. And he was taking no action. He felt that the price on the screen was quite irrelevant in his business of buying "value".

Signs of battle fatigue were starting to show in his behavior. Rodrigo was getting jumpy and losing some of his composure. He yelled at someone in a meeting: "stop losses are for shmucks! I am not going to buy high and sell low!" During his string of success he had learned to put down and berate traders of the non-emerging market variety. "Had we gotten out in October 1997 after our heavy loss we would not have had those excellent 1997 results", he was also known to repeat. He also told management: "these bonds trade at very depressed levels. Those who can invest now in these markets would realize wonderful returns".

Every morning, Rodrigo spent an hour discussing the situation with market economists around the globe. They all seemed to present a similar story: this selloff is overdone.

Rodrigo’s desk also experienced losses in other emerging markets. He also lost money in the domestic Russian Ruble Bond market. His losses were mounting, but he kept telling his management rumors about very large losses among other banks –larger than his. He felt justified to show that "he fared well relative to the industry". This is a symptom of systemic troubles; it shows that there was an entire community of traders who were conducting the exact same activity. Such statements, that other traders had also gotten into trouble, are self-incriminating. A trader’s mental construction should direct him to precisely do what other traders do not do.

Towards the end of August, the bellwether Russia Principal Bonds were trading below $10. Rodrigo’s net worth was reduced by almost half. He was dismissed. So was his boss, the head of trading. The president of the bank was demoted to a "newly created position". Board members could not understand why the bank had so much exposure to a government that was not paying its own employees –which, disturbingly, included armed soldiers. That was one of the small points that emerging market economists around the globe, from talking to each other so much, forgot to take into account. Veteran trader Marty O’Connell calls that the firehouse effect. He had observed that firemen with much down time who talk to each other for too long come to agree on many things that an outside, impartial observer, would find ludicrous. Psychologists give it a fancier name, but my friend Marty has no training in clinical psychology.

The nerdy types of International Monetary Fund had been taken for a ride by the Russian government who cheated in their account. Let us remember that economists are evaluated on how intelligent they sound, not on a scientific measure of their knowledge of reality. However, the price of the bonds was not fooled. It knew more than the economists, more than the Rodrigos of the emerging market departments.

Louie, a veteran trader with whom we will spend quality time in Chapter X , was there, vindicated. He muttered on the day Rodrigo was fired: "Economics Shmeconomics. It is all market dynamics", as Rodrigo was escorted by a security guard to the door like a captured soldier taken to the arena.

Rodrigo is now out of the market. The possibility that history may prove him right (at some point in the future) has nothing to do with the fact that he is a bad trader. He has all of the traits of a thoughtful gentleman, and would be an ideal son-in-law. But he has most of the attributes of the bad trader. And, at any point in time, the richest traders are often the worst traders. This, we will call the cross sectional problem: at a given time in the market, the most profitable traders are likely to be those that are best fit to the latest cycle. This does not happen too often with dentists or pianists –because of the nature of randomness.

John the High Yield Trader

We met John, Nero’s neighbor, in chapter X. He is 35 and has been on Wall Street as a corporate "high yield" bonds trader for 7 years, since his graduation from Pace Graduate Business School. He rose to head up a team of 10 traders in a record time –thanks to a jump between two similar Wall Street firms that afforded him a generous profit sharing contract. The contract allows him to be paid 20% of his profits, as they stand at the end of each calendar year. In addition, he is allowed to invest his own personal money in his trades –a great privilege.

John is not someone who can be termed as principally intelligent, but he was believed to be endowed with a good measure of business sense. He was said to be "pragmatic" and "professional". He gave the impression that he was born a businessperson, never saying anything remotely unusual or out of place. He remained calm in most circumstances, rarely betraying any form of emotion. Even his occasional cursing (this is Wall Street!) was so much in context that it sounded, well, professional.

John dresses impeccably. This is in part to his monthly trips to London (by Concorde) where his unit had a satellite supervising European high yield activities. He wears a Saville Row tailored dark business suit, dons a Ferragamo tie ($100 at Heathrow airport) –enough to convey the impression that he is the epitome of the successful Wall Street professional. Each time Nero ran into him he came away feeling poorly dressed.

John’s desk engaged principally in an activity called "high yield" trading, which consisted in acquiring "cheap" bonds that yielded, say 10%, while the borrowing rate for his institution was 5.5%. It netted a 4.5% profit –which seemed small except that he could leverage himself and multiply such profit by the leverage factor. He did this in various countries, borrowing at the local rate and investing in "risky" assets. It was easy for him to amass over $3 billion dollars in face value of such trade across a variety of continents. He hedged the interest rate exposure by selling U.S., U.K., French, and other government bond futures, thus limiting his bet to the differential between the two instruments. He felt hedged against those nasty fluctuations in the world’s global interest rates.

The Quant Who Knew Computers and Equations

John was assisted by Henry, a foreign quant whose English was incomprehensible, but who was believed to be at least equally competent in the risk management methods. John knew no math, be he relied on Henry. "His brains and my business sense", he was wont to say. Henry supplied him with risk assessments concerning the overall portfolio. Whenever John felt worried, he would ask Henry for another freshly updated report. Henry was a graduate student in Operations Research when John hired him. His specialty is a field called Computational Finance, which, as it names indicates seems to solely focus on running computer programs overnight. Henry’s income went from $50,000 to $600,000 in 3 years.

Most of the money John made for the institution was not attributable to the interest rate differential between the instruments. The differential had the tendency to narrow. It was getting closer to what John believed was "fair value". John believed that the methods he used to calculate "fair value" were sound. He was backed by an entire department that helped him analyze and determine which bonds were attractive and offered capital appreciation potential. It was normal for him to be earning these large profits over time.

John made steady money for his employers, perhaps even better than steady. Every year the revenues he generated almost doubled as compared to the previous year. During his last year, his income experienced a quantum leap as he saw the capital allocated to his trades swell beyond his wildest expectations. His bonus check was for $10 Million (pretax, which would generate close to a $5 Million total tax bill ). John’s personal net worth reached $1 Million at the age of 32. By the age of 35 it had exceeded $16 Million. Most of it came from the accumulation of bonuses –but a sizeable share came from profits on his personal portfolio. Of the $16 Million about $14 Million he insisted in keeping invested in his business. They allowed him, thanks to the leverage, to keep a portfolio of $50 Million involved in his trades.

It took only a few days for the $14 Million to turn into thin air –and for John to lose his job at the same time. It all happened during the summer of 1998, with the meltdown of high yield bond values. What was more annoying is that all the hedges were in a short position in government securities and U.S. bond futures that went up in value. Markets went into a rapid phase in which nearly everything he had invested in went against him at the same time. His hedges no longer worked out. He was mad at Henry for not having figured out that these events could happen. Perhaps there was a bug in the program.

His reaction to the first losses was, characteristically, to ignore the market. "One would go crazy if one were to listen to the mood swings of the market", he said. What he meant by his statement is that the "noise" was mean reverting, and would likely be offset by "noise" in the opposite direction. That was the translation in plain English of what Henry explained to him. But the "noise" kept adding up in the same direction.

As in a biblical cycle, it took 7 years to make John a hero and just 7 days to make him an idiot. John is now a pariah; he is out of a job and his telephone calls are not returned. Many of his friends were in the same situation. How come?

It took a long time for John to figure out what had happened, owing to the rapidity of the unfolding of the events and his state of shellshock. The dip we saw on Figure 3-5 was not very large. It was just that his leverage was enormous. What was more shocking for him was that all their calculations gave the event a probability of 1 in 1,000,000,000,000,000,000,000,000 years. Henry called that a "ten sigma" event. The fact that Henry doubled the odds did not seem to matter. It made the probability 2 in 1,000,000,000,000,000,000,000,000 years.

When will John recover from the ordeal? Probably never. The reason is not because John lost money. Losing money is something good traders are accustomed to. It is because he blew up: He lost more than he planned to lose. His personal confidence was wiped out.

But there is another reason why John may never recover. The reason is that John was never a trader in the first place. He is one of those people who happened to be there when it all happened.

John calls himself "ruined"; yet his net worth is still close to $1 Million, which could be the envy of more than 99.9% of the inhabitants of our planet. Yet there is a difference between a wealth level reached from above and a wealth reached from below. The road from $16 Million to $1 Million is not as pleasant as the one from 0 to $1 Million. In addition, John is full of shame; he worries about running into old friends on the street.

His employer should perhaps be most unhappy with the overall outcome. John pulled some money out of the episode, the $1 Million he has saved. He should be thankful that the episode did not cost him anything –except the emotional drain. That was not the case for his last employer. John had earned for the employers, New York investment banks, upwards of $250 Million in the course of the seven years. He lost upwards of $600 Million for his last employer in barely a few days.

The Traits They Shared

The reader needs to be warned that not all of the emerging market and high yield traders talk and behave like Rodrigo and John. Only the most successful ones –alas, or perhaps those who were the most successful during the 1992-1998 bull cycle.

At 35, both John and Rodrigo still have the chance to make a career. It would be wise for them to look outside of the financial markets. The odds are that they will not survive the incident. Why? Because by discussing the situation with each one of them one can rapidly see that they share bad trader traits. What is more worrisome is that their bosses and employers shared the same bad trader trait. They, too, are permanently out of the market.

We will see throughout this book what characterizes the trait. Again, there may not be a clear definition for it, but you can recognize it when you see it. No matter what John and Rodrigo do, they will remain fools of randomness.

A Review of Market Fools of Randomness Constants

Most of the traits partake of the same Table 1-1 right column-left column confusion --how they are fooled by randomness. Below is a brief outline of what they are:

A gullibility in their beliefs in some measure, either economic (Rodrigo) or statistical (John). They never considered that the fact that trading on economic variables has worked in the past may have been merely coincidental, or, perhaps even worse, that economic analysis was fit to past events in order to mask the random element in it. Rodrigo entered the market at a time when it worked --but he never tested for periods when markets did the opposite of sound economic analysis. There were periods when economics failed traders, and others when it helped them.

The U.S. dollar was overpriced (i.e. the foreign currencies were undervalued) in the early eighties. Traders who used their economic intuitions and bought foreign currencies were wiped out. But later those who did so got rich (members of the first crop were bust). It is random! Likewise, those who shorted Japanese stocks in the late eighties suffered the same fate –few survived to recoup their losses during the collapse of the nineties. At the time of writing, there is a group of operators called "macro" traders who are dropping like flies, with "legendary" (rather, lucky) investor Julian Robertson closing shop. Our discussion of survivorship bias will enlighten us further, but, clearly, there is nothing less rigorous than their seemingly rigorous use of economic analysis to trade.

A tendency to get married to positions. There is a saying that bad traders divorce their spouse sooner than abandon their positions. Loyalty to ideas is not a good thing for traders, scientists –or anyone.

The tendency to mistake themselves for investors "for the long haul"–mostly when they are losing money. 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 lost money, postponing their decision to sell, as part of their denial.

No precise game plan ahead of time as to what to do in the event of losses. They simply were not aware of such a possibility. Both bought more bonds after the market declined sharply, but not in response to a predetermined plan.

No stop losses. Middlebrow traders do not like selling when it is "even better value". They did not consider that perhaps their method of determining value is wrong, rather than the market having failed to accommodate their measure of value. They may be right, but, perhaps, some allowance for the possibility of their methods being flawed was not made. For all his flaws, we will see that Soros seems to rarely examines an unfavorable outcome without testing his own framework of analysis.

Denial. When the losses occurred there was no clear acceptance of what had happened. The price on the screen lost its reality in favor of some abstract "value". In classic denial mode, the usual "this is only the result of liquidation, distress sales" was proffered. They continuously ignored the message from the market.

How could traders who made every single mistake in the book become so successful? Because of a simple principle concerning randomness. This is one manifestation of the survivorship bias. We tend to think that traders made money because they are good. Perhaps we have turned the causality on its head: We hardly think that because they made money we consider them good -since one can make money in the financial markets totally out of randomness.

Both Rodrigo and John belong to the class of people who benefited from a market cycle. It was not merely because they were long. It was because they had a bent in their style that closely fit the properties of the rallies experienced in their market. They were dip buyers. That happened, in hindsight, to be the trait that was the most desirable between 1992 and the summer of 1998 in the specific markets in which the two men specialized.

Most of those who happened to have that specific trait, over the course of that segment of history, dominated the market. Their score was higher and they replaced people who, perhaps, were better traders.

The Evolutionary Cycle

Figure 3-6 shows the evolutionary cycle in skewed markets, that is, markets subjected to rare events (and present asymmetries in returns). Quiet markets favor rare event traders. Other traders cannot keep up with the returns; they are slowly eliminated from the system, either through attrition or because the capital flows towards those rare event traders and yield hogs. Department managers come from their ranks; they in turn will select traders with biases similar to their own. When the crashes occur these traders are rapidly eliminated –but there are very few traders left who really know how to trade. So the cycle starts again. If we were rational and had a good memory, these rare event traders would not be able to start operating; people’s memory of these events fades in an exponential manner.

Bad traders have a short and medium term survival advantage over good traders. Stock traders with a bullish bias, for instance, do well during rallies. In this chapter, we saw that the succession of sunny and panicky market regimes causes traders whose trading style is in agreement with the cycle to surpass others, and proliferate at the expense of better traders.

Why I chose the Story

I chose this story surrounding the debacle of August 1998, to illustrate one point owing to my familiarity with the situation. However, the applicability is universal. It is my belief that the next meltdown in asset prices, if it occurs, will be similar --as were almost all documented market debacles. One symptom of our ingrained foolishness is the remarkable similarity between the episodes, down to the most minute of the properties.

The following historical analogies can be presented:

1) The bull market in European bonds in 1992-1994. The debacle came extremely quickly. I had the luxury of seeing extremely successful but rather incompetent traders completely exterminated.

2) The bull market 1982-1987, before the crash of 1987. This well documented crash made me, so to speak.

3) The dollar collapse 1985-1992. All traders who fared well during that period because they had the traits of the cycle went subsequently out of business.

4) The episode in financial pathology called tulip bulb craze. It took literally no time to eradicate the years of steady enrichment by tulip speculators. Here I do not recommend the embellished and flawed account by Mackay so prized by investors, but the more factual Tulipomania by the professional historian Mike Dash.

5) The Kuweiti Manach, the local stock market produced the same pattern of rapid, but steady growth in values prior to a complete collapse.

6) The Nikkei bubble of late 1990. Unfortunately I was not yet involved in Japanese stocks, but saw some ripple effects on the currency which I traded then.

7) The current episode in financial pathology. I prefer to defer to the discussion in Shiller (2000). There are no reasons for it not to end like the others, if indeed it is one half as unjustified as Shiller claims. As to my opinion, I will only say that I recently went to the doctor for a sports-injury related surgery. While discussing painkillers I told him, only half-jokingly: "I have been bearish for 10 years, and I am here. We bears do not need painkillers!"

Naïve Evolutionary Theories

One should be either blind or foolish to reject the theories of Darwinian self-selection. However, the simplicity of the concept has drawn segments of amateurs (as well as a few professional scientists) into blindly believing in continuous and infallible Darwinism in all fields, which includes economics. The biologist Jacques Monod bemoaned already a coupled of decades ago that everyone believes himself an expert on evolution (the same can be said about the financial markets); things have gotten worse. These amateurs believe that plants and animals reproduce on a one-way route towards perfection. Translating the idea in social terms, they believe that companies and organizations are, thanks to competition (and the discipline of the quarterly report), irreversibly heading towards betterment. The strongest will survive; the weakest will become extinct. As to investors and traders, they believe that by letting them compete, the best will prosper and the worst will go learn a new craft (like pumping gas or, sometimes, dentistry).

Things are not as simple as that. We will ignore the basic misuse of Darwinian ideas in the fact that organizations do not reproduce like living members of nature –Darwinian ideas are about reproductive fitness, not about survival. The problem comes from, as everything else in this book, from randomness. Zoologists found that once randomness is injected into a system, the results can be quite surprising: what seems to be an evolution may be merely a diversion, and possibly regression. For instance, Steven Jay Gould (admittedly more of a popularizer than a genuine scientist) found ample evidence of what he calls "genetic noise", or "negative mutations", thus causing the wrath of some of his colleagues (he took the idea a little too far). An academic debate ensued, plotting Gould against colleagues like Dawkins who are considerably better at understanding randomness. Negative mutations are traits that survive in spite of being worse, from the reproductive fitness standpoint, than the ones they replaced. However than cannot be expected to last more than a few generations (under what is called temporal aggregation). However, things can get even more surprising when randomness changes in shape, as with regime switches. A regime switch corresponds to situations when all of the attributes of a system change to the point of it becoming unrecognizable to the observer. Darwinian fitness applies to species developing over a very long time, not observed over a short term –time aggregation eliminates much of the effects of randomness: things (I read noise) balance out over the long run, as people say.

Back to the Monte Carlo Engine: The Forest and the Regime Switch

Assume that the creator does not "play dice", and that the world is a small tropical island. Down under, in the tropical forest, the leaves have a blue-green coloration. Lizards compete in the food chain. Those that are closer to the green color of the forest will fare well. They will be invisible to predators. They can lay on a branch and remain unseen. They will survive to produce more offspring.

There are small variations in the make up of the genetic structure of the progeny. They do not all share the same exact color. They will take on different varieties of green: Some will be greener than others. Randomly so. A few will be pale green; others will be dark green. In the middle, some will be a close match to the coloration of the forest. These animals will reproduce more than others. As their reproduction cycle is short, an observer can witness the color of the surviving lizards inching towards the color of the forest. The other animals are less likely to live long enough to produce offspring. Odds are that they will be eaten by one of those swift wild mammals. The red lizards will become extinct as their color contrasts the most with that of the leaves.

Consider that, suddenly, the creator decides to "play dice". He infrequently does so –but he has to. By definition, the creator can change the rules at will. Should the green lizards proliferate exceedingly, they will devour the entire island and perhaps become extinct themselves.

More exactly, he plays with a coin. He flips it: heads and the tropical forest of the small island will take a stark red coloration; tails, the forest will be green. He calls them the red and green regimes.

We run the Monte Carlo engine, flip the figurative coin, and …head. The forest turns red –vivacious red. A carnage results, with the rodents and other mammals pouncing on the green lizards now standing out as an open invitation for a meal. The lizards that are green, and most likely to thrive in the green cycle, will be extinct during the red cycle. Those that are furthest from the green have a chance. Those that are red will repopulate and thrive –except that very few of them are accidentally left.

This parable is not exceedingly schematic. Our planet did experience cycles that shifted the entire composition of the species –to wit the extinct species we know of (among those we will never hear about). These extinct species had to be fit at some point. But the changes in the physical make up of the planet take place slowly, too slowly to dramatically and suddenly alter the reproductive advantage of species. Only rarely do meteors disrupt our ecosystem. Physical randomness represents too small a part in the overall movement of things. This is not the case with randomness in social and economic events.  It is often said that nature does not make jumps; people quote the well sounding latin natura no facit saltus by some 18th century botanist who obviously got it all wrong. (Note that this statement has also been attributed to Leibniz; like many well sounding ‘make sense" type of statements, it turned out to be entirely wrong, as it was denied by quantum mechanics).

Can Evolution Be Fooled By Randomness?

We end the chapter with the following thought. Recall that someone with only casual knowledge about the problems of randomness would believe that an animal is at the maximum fitness for the conditions of his time. This is not what evolution means: on average animals will be fit, but not every single one of them, and not at all times. Just as an animal could have survived because its sample path was lucky, the "best" traders can come from a subset of operators who survived because of over-fitness to a sample path –a sample path that was free of the evolutionary rare event. One vicious attribute is that the longer these animals can go without encountering the rare event, the more vulnerable they will be to it. For to be precise, evolution means fitness to one and only time series, not the average of all the possible environments. Solon seems to have gotten the point; but try to explain the problem to a naïve business Darwinist —or your rich neighbor across the street.

The Black Swan Problem

Bull and Bear Zoology

· · Your Cousin's Pictures of Yellowstone

The general press floods us with concepts like bullish and bearish as these mean to refer to the effect of higher or lower prices in the financial markets. But also we hear people saying "I am bullish on Johnny" or "I am bearish on that guy Nassim in the back who seems incomprehensible to me", to denote the belief in the likelihood of someone's rise in life. I start this chapter with the statement that the notion bullish or bearish are often hollow words with no application in a world of randomness --particularly if such world, like hours, presents asymmetric outcomes.

When I was in the employment of the New York office of a large investment house, I was subjected on occasion to the harrying weekly "discussion meeting", which gathered most professional of the New York trading room. 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 pronouncement 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 opinion on the state of the world. To me the meeting resembled a dinner party where the enthusiastic host insists on showing the guests the videotape of the family trip to Yellowstone National Park or the wedding of his sister-in-law. Everyone had a story, a theory, and insights that they wanted others to share. I have to confess that my optimal strategy (to sooth my boredom and allergy to platitudes) was to speak as much as I could, while avoiding totally to listen to other people's reply 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 (that is forced to attend) the following week.

I was once asked in one of those meetings to express my views on the stock market. I said 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 replied that I never changed my mind, and that I had a lot of faith in my short SP500 position (audience laughing). As a matter of fact I now felt like selling even more. "Are you bullish or are you bearish?" I was asked by the strategist. I replied that I could not understand the words "bullish" or "bearish" outside of their purely zoological consideration. My opinion was that the 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 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 market over the next week had 70% probability to go up and 30% probability to go 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 is he bearish?

Accordingly bullish or bearish are terms used by people who do not engage in practicing uncertainty, like the television commentator, or those who have no experience 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, whom, we will see, are nothing better than entertainers.

This brings us to the difference between expectation and frequency. The best description of my lifelong business in the market is "skewed bets", that is benefit for rare events, events that do not tend to repeat themselves frequently, but, accordingly, present a large payoff when they occur. One such event is the stock market crash of 1987, which made me as a trader and allowed me the luxury of becoming involved in all manner of scholarship.

The Median is not the Message

The writer and scientist Steven Jay Gould (who, for a while, was my role model), was once diagnosed with a deadly form of cancer of the lining of the stomach. The first piece of information he received about his odds was that his the median survival for the ailment is approximately 8 months, an information akin to Isaiah's injunction to King Hezekiah's to put his house in order in preparation for death.

Now a medical diagnosis, particularly one of such severity, can motivate people to do intensive research, particularly those like Gould who felt they needed more time with us to complete a few book projects. Further research by Gould about the matter showed a different story, mainly that the expected survival was considerable higher than 8 months. Median means roughly that 50% of the people die before 8 months and 50% survive longer than 8 months. But those who survive would live considerably longer. The average survival was not the median survival. This prompted Gould, who thus discovered skewness, to write his heartfelt piece The Median is Not the Message. His point is that the concept of median used in medical research does not characterize a probability distribution.

I will simplify Gould's point by introducing the concept of mean, often called expectation, as follows. Assume I engage in a gambling strategy that has 999 chances in 1,000 of making $1 and 1 chance in 1000 of losing $10,000, as in the table below.

Probability

Outcome

Expectation

999/1000

$1

$.999

1/1000

-$10,000

-$10.00

Total

-$9.001

· · My expectation is a loss of close to $9 (obtained by multiplying the probabilities by the corresponding outcomes). The frequency or probability of the loss, in and by itself, is totally irrelevant; it needs to be judged in connection with the magnitude of the outcome. A hint on the problem of induction (to come in a few paragraphs): I cannot interpret much from a past times series if I know that it can be subjected to those infrequent bad and severe hits, yet my sample contains none.

How could people miss such a point? Why do they confuse probability and expectation, that is, probability and probability times the payoff? Mainly because much of people's schooling comes form examples in symmetric environents, like a coin-toss, where such difference does not matter. In fact the so-called "Bell Curve" that seems to have found universal uses in society is entirely symmetric.

INSERT BELL CURVE GRAPH HERE

In addition, in many disciplines, such symmetry does not matter. Unfortunately, the techniques used in finance are often imported from other areas –finance is still a young discipline (it is certainly not yet a "science"). People outside of finance do not have problems eliminating extreme values from their sample. A professor who computes the average of his students’ grades removes the highest and lowest observations, which he would call outliers, and takes the average of the remaining ones. A casual weather forecaster does the same with extreme temperatures –an unusual occurrence might be deemed to skew the overall result (though we will see that this may turn out to be a mistake when it comes to forecasting future properties of the ice cap). So people in finance borrow the technique and ignore infrequent events, not noticing that the effect of a rare event can bankrupt a company. Think of the hedge fund that blew up: if you eliminate that bad quarter in which they lost almost 100% of their capital, considering it an outlier, they would be the best thing that graced connecticut!

But even some well practiced financial 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 man who thrived on rare events). [Endnote on the gamma distribution].

Many scientists in the physical world are also sensitive to such foolishness, misreading statistics. One flagrant example is in the global warming debate. Many scientists failed to notice it as they took the spikes in temperature, the "outliers", out of their sample, under the belief that these were not likely to recur. It may be a good idea to take out the extremes when computing the average temperatures for vacation scheduling. But it does not work when we study the physical properties of the weather. These scientists initially ignored the fact that these spikes, although rare, had the effect of adding to the cumulative melting of the ice cap. Just as in finance, an event that, although rare, carries a large magnitude, cannot just be ignored.

A Primer on Time Series

INSERT TIME SERIES GRAPH HERE

Figure x shows a series of points starting with an initial level W_0 and ending at the period concerned t. It can also be seen as the performance, hypothetical or realized, of your favorite trading strategy, the track record of an investment manager, the price of a foot of average Palazzo real estate in Renaissance Florence, the price series of the Mongolian stock market, or the difference between the U.S. and Mongolian stock markets. It is composed of a given number of sequential observations W_1, W_2, etc., ordered in such a way that the ones to the right comes after the one to the left.

If we were dealing with a deterministic world –that is, a world stripped of randomness (the right-column world in Table 1-1 in the Prologue), and we knew with certainty that it were the case, things would be rather easy. The pattern of the series would reveal considerable and predictive information. You could tell with precision what would happen one day ahead, one year ahead, and perhaps even a decade ahead. We would not even need a statistician: a second rate engineer would do. He does not even need to be armed with a modern degree: someone with 19th century training under Laplace would be able to solve the equations, called differential equations, or, equivalently, equations of motion –since we are studying the dynamics of an entity whose position depends on time.

If we were dealing with a world where randomness were charted, things would be easy as well, given that there is an entire field created for that called Econometrics or Times Series Analysis. You would call a friendly econometrician (my experience of econometricians is that they are usually friendly to market practitioners). He would run the data in his software, and provide you with diagnostics that would tell you if it is worth investing in the trader generating such track record, or if it is worth for you to pursue the given trading strategy. You can even buy the student version of his software for under $999 and run it yourself during the next rainy weekend.

But we are not sure that the world we live in is well charted. We will see that the judgment derived from the analysis of these past attributes may on occasion be relevant. But it may be meaningless; it could on occasion mislead you and take you in the opposite direction. Sometimes market data becomes a simple trap; it shows you the opposite of its nature, simply to get you to invest in the security or mismanage your risks. Currencies that exhibit the largest historical stability, for example, are the most prone to crashes. This was bitterly discovered in the summer of 1997 by investors who chose the safety of the pegged currencies of Malaysia, Indonesia, and Thailand (they were pegged to the U.S. dollar in a manner to exhibit no volatility, except fror a sharp and brutal meltdown). We could be either too lax or too stringent in accepting the past information as a prediction of the future. As a skeptic, I reject a sole times series of the past as an indication of future performance; I need a lot more than data. My major reason is the rare event, but I have plenty of others.

The Rare Event Fallacy

· · The Mother of all Deceptions

The rare event, owing to its dissimulative nature, can take a variety of shapes. It is in Mexico that it was spotted first, where it was called peso problem. Econometricians were puzzled by the behavior of the Mexican economic variables during the eighties. The money supply, interest rates, or some similar measure of small relevance to the story exhibited some moody behavior, thwarting many of their efforts at modeling them. These indicators erratically switched between periods of stability to brief burst of turbulence without so much as a warning.

By generalization, I started to label rare event any behavior where the adage "beware of calm waters" can hold. Popular wisdom often warns of the old neighbor who appears to remain courtly and reserved, the model of an excellent citizen, until you see his picture in the national paper as a killer who went on a rampage. Until then, he was not known to have committed any transgression. There was no way to predict that such pathological behavior could emanate from such a nice person. I associate rare events with any misunderstanding of the risks derived from a narrow interpretation of past times series.

Rare events are always unexpected, otherwise they would not occur. The typical case is as follows. You invest in a fund that enjoys stable returns and no volatility, until one day, you receive a letter starting with "An unforeseen and unexpected event, deemed of rare occurrence…"(emphasis mine). But rare events exist precisely because they are unexpected. They are generally caused by panics, themselves the results of liquidations. If the fund manager or trader expected it, he and his like-minded peers would not have invested in it, and the rare event would not have taken place.

Some financial securities can be best described as following an "up the escalator, down the chute" process. A security (or a strategy) exhibits remarkable stability and produces excellent returns for a long time, then suddenly (and "unexpectedly") crashes. The fund manager or form trader uses "unexpectedly" because, indeed, he did not expect it. But to someone who has read any book on the history of markets, such as Charles Kindleberger’s classic Panics, Manias, and Crashes, these are routine events –with one exception: they tend to happen to people and places where and when they are the least expected.

The rare event is not limited to one security. It can readily affect the performance of a portfolio. For example, many traders engage in the purchase of mortgage securities and hedge them in some manner to offset the risks and eliminate the volatility, hoping to derive some profits in excess of the Treasury bond returns. They use computer programs and draw meaningful assistance from Ph.D.s in applied mathematics, astrophysics, particle physics, electrical engineering, fluid dynamics, or sometimes (though rarely) plain Ph.D.s in Finance. Such portfolio shows stable returns for long periods. Then, suddenly, as by accident (I consider that no accident), the portfolio drops by 40% of its value when you expect, at the worst, a 4% drop. You call the manager to express your anger and he tells you that it was not his fault, but somehow the relationship dramatically changed (literally). He will also point out to you that similar funds also experienced the same problems.

Recall that some economists call the rare event "peso problem". The designation peso problem does not appear to be undeservedly stereotypical. Things have not gotten better since the early eighties with the currency of our southern neighbor. Long periods of stability draw hordes of bank currency traders and hedge fund operators to the calm waters of the Mexican peso; they enjoy owning the currency because of the high interest rate it commands. Then they "unexpectedly" blow up, lose money for investors, lose their jobs and switch careers. Then a new period of stability sets in. New currency traders come in with no memory of the bad event. They are drawn to the Mexican peso, and the story repeats itself.

It is an oddity that most fixed income financial instruments present rare events. In the spring of 1998, I spent two hours explaining to a then-important hedge fund operator the notion of rare events, which I called by its economic name peso problem. I went to great lengths to explain to him that the concept was generalized to every form of investment that was based on a naïve interpretation of the volatility of past times series. The reply was: "You are perfectly right. We do not touch the Mexican peso. We only invest in Russian ruble". He blew up a few months later. Until then, the Russian ruble carried attractive interest rates, which invited yield hogs of all types to get involved. He and other holders of investments denominated in ruble lost close to 97% of their investment during the summer of 1998.

Effect of Rare events

These jumps are hard to measure because they are so infrequent. We can infer the following:

For markets: We can only assume that past risks are only an effective indication of future risks for markets that do not have possible rare events. Which ones? I am inclined to say that markets that are naturally volatile and scary are the least likely to exhibit these deceptions. Volatile stocks and currencies have shown their colors; I feel more comfortable with their risks (because I know them) than with those that appear to have none

For businessmen and investors: We can immediately conclude that track records are only an effective indication for the subset of people who do not play Russian roulette with a 500 hole barrel. One example is traders who operate in liquid markets –and trade a symmetric trading strategy –unlike Ricardo and John. A symmetric trading strategy is one in which the magnitude of the losses is not very different from that of the gains. John’s strategy produces steady small gains and occasional large losses. In fact, fools of randomness can disguise themselves as steady earners, to the point of attracting considerable money before blowing up and making their capital evaporate. Furthermore, so many frauds masquerade as steady earners that I now suspect everyone with the adumbration of stable returns (except those who are market makers and share characteristics with casino owners).

In addition, there is a category of traders who have inverse rare events, for whom the volatility is often a bearer of good news. These traders lose money frequently, but in small amounts, and make money rarely, but in large amounts.

Why don’t statisticians detect rare events?

Statistics to the layman can appear rather complex, but the concept behind what is used today is so simple that my French mathematician friends call deprecatorily "cuisine". It is all based on one simple notion: the more you have information, the more you are confident about the outcome. Now the problem: by how much? Common statistical method is based on the steady augmentation of the confidence level, in nonlinear proportion to the number of observations. That is, for an n times increase in the sample size, we increase our knowledge by the square root of n. Suppose I am drawing from an urn containing red and black balls. My confidence level about the relative proportion of red and black balls, after 20 drawings is not twice the one I have after 10 drawings; it is merely multiplied by the square root of 2 (that is, 1.41).

Where statistics becomes complicated, and fails us, is when we have distributions that are not symmetric, like the urn above. If there is a very small probability of finding a red ball in an urn dominated by black ones, then our knowledge about the absence of red balls will increase very slowly –more slowly than at the expected square root of n rate. On the other hand our knowledge of the presence of red balls will dramatically improve once one of them is found. This asymmetry in knowledge is not trivial; it is central in this book --it is a central philophical problem for such people as Hume and Karl Popper. I can confirm that an investor trader is a bad investor (if he blows up); but I can never rule out that he may be one.

To assess an investorr’s performance, we either need more astute, and less intuitive, techniques, or we may have to limit our assessments to situations where our judgment is independent of the frequency of these events.

A Vicious Child Replaces the Black Balls

But there is even worse news. In some cases, if the incidence of red balls is itself randomly distributed, we will never get to know the composition of the urn. This is called the problem of stationarity. Think of an urn that is hollow at the bottom. As I am sampling from it, and without my being aware of it, some vicious child is adding balls of one color or another. My inference becomes thus insignificant. I may infer that the red balls represent 50% of the urn while the vicious child, hearing me, would swiftly replace all the red balls with black ones. This makes much of our knowledge derived through statistics quite shaky.

The very same effect takes place in the market. We take past history as a single homogeneous sample and believe that we have considerably increased our knowledge of the future from the observation of the sample of the past. What if vicious children were changing the composition of the urn? In other words, what if things have changed?

I have studied and practiced econometrics for half my life (since I was 19), both in the classroom and in the activity of a quantitative derivatives trader. The "science" of econometrics consists of the application of statistics to samples taken at different periods of time, which we called times series. It is based on studying the times series of economic variables, data, and other matters. In the beginning, when I knew close to nothing (that is even less than today), I wondered whether the times series reflecting the activity of people now dead or retired should matter for the predicting the future. Econometricians who knew a lot more than I did about these matters asked no such question; this hinted that it was in all likelihood a stupid one. One prominent econometrician, Hashem Pesaran answered a similar question by recommending to do ‘more and better econometrics’. I am now convinced that, perhaps, if my question were right, most of econometrics would be useless –much of what financial statisticians know would not be worth knowing. For a sum of zeros, even repeated a billion times, remains zero; likewise an accumulation of research and gains in complexity will lead to naught if there is no firm ground behind it.

Studying the European markets of the 1990s will certainly be of great help to a historian; but what kind of inference can we make now that the structure of the institutions and the markets has changed so much?

Stanford economist Mordecai Kurz puts it as follows:

The process of structural change (i.e. non-stationarity) in our society is the central building block of its complexity and the root cause of the diversity of beliefs about it. In such a system, the past is not an entirely satisfactory basis for assessment of risks in the future.

The notion of "financial engineering" deserves an entire chapter and will not be discussed here. Practitioners of these methods measure risks, using the tool of past history as an indication of the future. They call themselves scientists but do not show an inch of critical thinking, or self-doubt, which is the hallmark of science. We will just say that the mere possibility of the distributions not being stationary makes the entire concept seem like a costly (perhaps very costly) mistake. This leads us to a more fundamental question: the problem of induction.

A First Glimpse of the Problem of Induction

· · From Bacon to Hume

Next, we will discuss the same problem viewed from the broader standpoint of the philosophy of scientific knowledge. There is a problem in inference well known as the problem of induction. It is a problem that has been haunting science for a long time, but science has not been as harmed by it as the financial markets. Nowhere is the problem of induction more relevant than in finance –and nowhere has it been as much ignored!

In his Treatise on Human Nature, the Scots philosopher David Hume posed the issue in the following way (as rephrased in the now famous black swan problem by John Stuart Mill): No amount of observations of white swans can allow the inference that all swans are white, but the observation of a single black swan is sufficient to refute that conclusion.

Hume had been irked by the fact that science in his day (the 18th century) had experienced a swing from scholasticism, entirely based on deductive reasoning (no emphasis on the observation of the real world) to, owing to Francis Bacon, an overreaction into naïve and unstructured empiricism. Bacon had argued against the "spinning of cobweb of learning" with little practical results. Science shifted, thanks to Bacon into an emphasis on empirical observation. The problem is that, without a proper method, empirical observations can lead you astray. Hume came to warn us against such knowledge, and to stress the need for some rigor in the gathering and interpretation of knowledge –what is called epistemology (from episteme, learning). Hume is the first modern epistemologist, also called methodologist or philosopher of science.

It is worthy noting that finance has its Francis Bacon in the person of Victor Niederhoffer. Niederhoffer was the very first to stand against the cobweb of learning of the University of Chicago and the efficient market religion of the 60s, when it was at its worst. In contrast with the scholasticism of financial theorists, he looked at data in search of anomalies –and found enough of them to be able to conduct a successful trading career and deliver an insightful book. Since then, an entire industry of "statistical arbitrageurs" flourished, the major and most successful ones being his trainees. His trainees fared well because they added method to their statistical inference.

Sir Karl Popper, Epistemologist Extraordinaire

A major answer to that problem, one to which I blindly subscribe, came from the greatest methodologist of our time, Sir Karl Popper. No man has influenced the way scientists do science more than Sir Karl Popper –in spite of the fact that his fellow philosophers find him quite naïve (to his credit, in my opinion). Sir Karl is the man whose ideas have haunted George Soros since his early adulthood (although I have reasons to believe that Soros, from his writings, did not understand much of Popper). Having read him repeatedly, I come to one conclusion: that he was obsessed with anything that can be closed, like a model, or merely a system of belief. I have read much commentary on Popper, without quite encountering the same interpretation –one has to be a trader to view things in this manner. In addition, it is by reading his detractors that I understood him best. Accordingly Sir Karl will be a major presence in this book; we will discuss his problem of demarcation between science and charlatanism when we will examine financial engineering and the application of modern financial theory to risk management.

Popper’s answer comes in the following way: there are two types of theories: those that are wrong (because they have been falsified, that is, shown to be wrong) and those that are exposed to be falsified. In other words, theories are only innocent because they not been proven guilty. To paraphrase baseball coach Yogi Bera again, past data has a lot of good in it, but it is the bad side that is bad. A theory, say like astrology, that does not present a set of conditions under which it would be wrong would be termed charlatanism --they would be impossible to reject otherwise.

Popper's point does not mean that we should treat theories as if they were plain wrong, merely that we should not put ourselves in a position that could leads to harm if these theories were falsified.

Popper had many problems with statisticians. He refused to blindly accept the notion that knowledge can increase with incremental information –which is the foundation of statistical inference. It may in some instances, but we do not know which ones. Many of the insightful people we will see in this book, such as John Maynard Keynes, reached the same conclusions. Many of Sir Karl’s detractors can be loosely termed Bayesian probabilists; they believe that favorably repeating the same experiment again and again should lead to an increased comfort with the notion that "it works". I came to understand Popper’s positions better once I saw the first rare event ravaging a trading room. Sir Karl feared that some type of knowledge did not increase –but which one we could not ascertain. The reason I feel that he is important for us traders is because to him the matter of knowledge and discovery is not so much in dealing with what we know, as in dealing with what we do not know.

My extreme and obsessive Popperism is carried out as follows. I speculate 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. More on that next.

A Single Black Swan Can Bankrupt You

Recall that in finance, more than any other discipline, we face the problem of dependence on a single unwanted observation: a single black swan can bankrupt you, or worse, bring down the entire financial system. In other disciplines, say, zoology, a single black swan will be a mere oddity of small consequence. It will be called an outlier and merit an entry in some book of records –but it will cause no serious financial penalty to the research institute. In finance, more than the sciences, we cannot merely look at frequencies, we have to consider the outcome, namely, the loss, which can be very negative.

Conclusion: Pascal’s Wager

I can conclude the following:

If I know that there may be rare events in history, then I cannot infer anything about the properties of the data, quality of the trader or the strategy under consideration, solely from past returns.

If I believe that there cannot be rare events, then I can probably start making a judgment on the asset, the trader, or the strategy. I can then call the friendly econometrician for a chat.

Accordingly, we need to accept the asymmetry in knowledge: if a rare event can helo me in my business, then I can accept its quality.

Finally, there are situations in which using statistics and econometrics can be useful. But I do not want my life to depend on it. Like Pascal, I will therefore state the following argument (it seems to have been followed by Karl Popper in the context of scientific knowledge). If the science of statistics can benefit me in anything, I will use it. If it poses a threat, then I will not. Accordingly, I will use statistics and inductive methods to make bets, but I will not use them to manage my risks. Surprisingly, all the surviving traders seem to have done the same. They trade on ideas based on some observation (that includes past history), but they manage their risks with the stop loss. This is exactly the opposite of what many financial institutions seem to do.

Part 2 : Monkeys on a Typewriter

Well Built Typewriters

If one puts an infinite number of monkeys in front of (strongly built) typewriters, and let them clap away (without destroying the machinery), there is a certainty that one of them would come out with an exact version of the Iliad. Upon examination, this may be less interesting a concept than it appears at first: such probability is very low. But let us carry the reasoning one step beyond: Now that we find that hero among monkeys, would any reader invest his life’s savings on a bet that the monkey would write the Odyssey next?

In this story, it is the second step that is interesting. How much can the past performance (here the typing of the Iliad) be relevant in the forecasting of the future one? The same applies to any decision based on past performance, merely relying on the attributes of the past times series. Think about the monkey showing at your door with his impressive past performance. Hey, he (independently) wrote the Iliad.

The major problem with inference in general is that those whose profession is to derive conclusions from data often fall into the trap faster and more confidently than others. The more data we have, the more likely we are to drown in it. For common wisdom among people with a budding knowledge of probability laws is to base their decision-making on the following principle: it is very unlikely for someone to perform considerably well in a consistent fashion without his doing something right. Track records become therefore preeminent. They call on the rule of the likelihood of such a successful run and tell themselves that if someone performed better than the rest in the past then there is a great chance of him performing better than the crowd in future days –and a very great one at that. But, as usual, a small knowledge of probability can lead to worse results than no knowledge at all.

It Depends on the Number of Monkeys

I do not deny that if someone performed better than the crowd in the past, there is a presumption of his ability to do better in the future. But the presumption might be weak, very weak, to the point of being useless in a decision making. Why? Because it all depends on two factors: the randomness content of his profession and the numbers of monkeys in operation.

The initial sample size matters greatly. If there are five monkeys in the game, I would be rather impressed with the Iliad writer, to the point in suspecting him to be a reincarnation of the blind poet. If there are a billion billion billion monkeys I would be less impressed –as a matter of fact I would be surprised if one of them did not get some well known (but unspecified) piece of work, just by luck (perhaps Casanova’s Memoirs of My Life). One monkey would be even expected to provide us with Al Gore’s Earth in the Balance, perhaps stripped of the platitudes.

This problem enters viciously the business world, more than other walks of life, owing to the high dependence on randomness (we have already contrasted business with dentistry). The greater the number of businessmen, the greater the likelihood of one of them performing in a stellar manner just by luck. I have rarely seen anyone count the monkeys. Few count the investors in the market in order to calculate, instead of the probability of success, the conditional probability of successful runs given the number of investors in operation over a given market history.

Vicious Real Life

There are other aspects to the monkeys problem: in real life the other monkeys are not countable, let alone visible. They are hidden away, as one only sees the winners –it is natural for those who failed to vanish completely. Accordingly one sees the survivors, and only the survivors, which imparts such a mistaken perception of the odds. We do not respond to probability, but to society’s assessment of it. As we saw with Nero, even people with training in probability respond unintelligently to social pressure.

Too Many Millionaires Next Door

How To Stop the Sting of Failure

Somewhat Happy

The (extremely fictional) character Marc lives on Park avenue in New York City with his wife Janet and their three children. He makes $500,000 a year, give or take a boom or a recession --he does not believe that the recent spurt in prosperity is here to last and has not mentally adjusted yet to his recent abrupt rise in income. A rotund man in late forties, with spongy features that make him even look ten years older than his age, he leads the seemingly comfortable (but heckled) life of a New York city lawyer. But he is on the quiet side of Manhattan residents. Marc is clearly not the man one would expect to go bar-hopping or attend late night Tribecca and Soho parties. He and his wife have a country house and a rose garden and tend to be concerned, life many people their age, mentality, and condition, with (in the following order) material comfort, health, and status. Weekdays, he does not come home until at least 9:30 P.M. and, at times, he can be found in the office at close to midnight. By the end of the week Marc is so fatigued that he falls asleep during their three hour drive to "the house"; and Marc spends most of Saturday lying in bed recovering and healing.

Marc grew up in a small town in the Midwest, the son of a quiet tax accountant who worked with sharp yellow pencils. His obsession with sharpness was so strong that he carried a portable sharpener in his pocket at all times. Marc exhibited very early signs of intelligence. He did extremely well in high school. He attended Harvard College, then Yale law school. Not bad, one would say. Later his career took him to corporate law, where he started working on large cases for a New York prestigious law firm, with barely enough hours left for him to brush his teeth. This is not too much an exaggeration, for he ate almost all of his dinners in the office accumulating body fat and brownie points towards his partnership. He later became partner within the usual seven years, but not without the usual human costs. His first wife (whom he met in college) left him, as she was tired of an absentee lawyer husband and weary of the deterioration in his conversation that started after he started working --but, ironically, she ended up moving in and later marrying another New York lawyer, probably with a no-less flat conversation, but who made her happier.

Too Much Work

Marc's body became progressively flabbier, and his tailored suits needed periodic visits to the tailor, in spite of his occasional crash diets. After he got over the depression of the abandonment, he started dating Janet, his paralegal, promptly married her. They rapidly engendered three children, a Park Avenue apartment, and a country house somewhere is some quiet but supposedly "charming" upstate New York location.

Janet's immediate surrounding is composed of the other parents of the Manhattan private school attended by their children, and their neighbors at the cooperative apartment building where they live. From a materialistic standpoint, they come at the low end of such set, perhaps even at the exact bottom. They would be the poorest of these circles, as their co-op is inhabited by extremely successful corporate executives, Wall Street traders, and high flying entrepreneurs. Their children's private school harbors the second set of children of corporate raiders, from their trophy wives --perhaps even the third set, if one takes into account the age discrepancy and the model-like features of the other mothers. By comparison, Marc's wife Janet, like him, presents a homely country-home-with-a-rose-garden type of appearance.

You’re a Failure

Marc's strategy of staying in Manhattan may be rational, as his demanding work hours would make it impossible for him to commute. But the costs on his wife Janet appear monstrous. Why? Because of their relative nonsuccess –as geographically defined by their Park Avenue neighborhood. Every month or so, Janet, under the strains and humiliations of being snubbed by some other mother at the school where she picks up the children, or some other lady with larger diamonds by the elevator of the coop where they live in the smallest type of apartments (the G line); every month or so, Janet has her crisis. Why isn't her husband so successful? Isn't he smart and hard working? Didn't he get close to 1600 at the SAT? Why is this Ronald Something whose wife never even nods to Janet, worth hundred of millions when her husband went to Harvard and Yale and has such a high I.Q., and has hardly any substantial savings?

We will not get too involved in the Tchekovian dilemmas in the private lives of Marc and Janet, but their case provides a very common illustration of the emotional effect of survivorship bias. Janet feels that her husband is a failure, by comparison, but she is mis-computing 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 at all, thus making him look as if he were not doing well at all. By living on Park Avenue he does not have exposure to the losers, only seeing the winners.

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.

Someone would rationally say to Janet: "go read this book, Fooled by Randomness by one N. N. Taleb on the deformations of chance in life; it would give you a statistical sense of perspective and would accordingly make you feel better". As an author, I would like to offer panaceas for $24.95, but I would rather say that in my best hopes it may provide an hour or so of solace. Janet may need something more drastic for a relief. I have repeated that becoming more rational, or not feeling emotions of social slights is not part of the human race, at least not with our current DNA code. There is no solace to be found from reasoning --as a trader I have learned something about these unfruitful efforts to reason against the grain. I would advise Janet to move out, and go live in some blue collar neighborhood where they would feel less humiliated by their neighbors and rise in the pecking order beyond their probability of success. They could use the deformation in the opposite direction. If Janet cares about status, then I would even recommend some of these large housing blocks.

Double Survivorship Biases

More Experts

I recently read a bestseller called The Millionaire Next Door, an extremely misleading (but almost enjoyable) book by two "experts", in which the authors try to infer some attributes that are common to rich people. They examined a collection of currently wealthy people and found out that these are less likely to lead lavish lives. They call such people the accumulators: persons ready to postpone consumption in order to amass funds. Most of the appeal of the book comes form the simple but counterintuitive fact that these are less likely to look like very rich people –it clearly costs money to be look and behave rich, not to count the time demands of spending money. Leading the lives of prosperous people is time consuming: shopping for trendy clothes, becoming conversant in Bordeaux wines, getting to know the expensive restaurants: all these activities can put high demands on one’s time and divert the subject from what should be the real preoccupation, namely the accumulation of nominal (and paper) wealth. The moral of the book is that the wealthiest are to be found among those less suspected to be wealthy. On the other hand those who act and look wealthy subject their net worth to such drain that they inflict considerable and irreversible damage to their brokerage account.

I will set aside the point that I see no special heroism in accumulating money, particularly if, in addition, the person is foolish enough to not even try to derive any tangible benefit from the wealth (aside from the pleasure of regularly counting the beans). I have no large desire to sacrifice much of my personal habits and standards in order to become a billionaire like Warren Buffet, but I do not see the point of becoming one if I were to adopt Spartan (nay miserly) habits and live in my starter house. Something about the praise lavished upon him for living in austerity while being so rich escapes me: if austerity is the end, he should become a monk or a social worker –we should remember that becoming rich is a purely selfish act, not a social one. The virtues of capitalism is that society can take advantage of people’s greed rather than their benevolence, but there is no need to, in addition, extol such greed as a moral accomplishment. Becoming rich is not directly a moral achievement, but that is not where the severe flaw in the book lies.

As we said, the heroes of The Millionaire Next Door are the accumulators, people manage who defer spending in order to invest. It is undeniable that such strategy might work; money spent bears no fruit (except for the enjoyment of the spender). But the benefits promised in the book seem grossly overstated. A finer read of their thesis reveals that their sample includes a double dose of survivorship bias. In other words, it has two compounding flaws.

Visibility Winners

The first bias comes from the fact that the rich people selected for their sample are among the lucky monkeys on the typewriter. The authors made no attempt to correct their statistics with the fact that they only saw the winners. They make no mention of the "accumulators" who have accumulated the wrong things (members of my family are experts on that: those who accumulated managed to accumulate currencies about to be devalued and stocks of companies that later went bust). Nowhere do we see the mention of the fact that some people were lucky enough to have invested in the winners; these people no doubt would make their way into the book. There is a way to take care of the bias: lower the wealth of your average millionaire by, say, 50%. It would certainly modify the conclusion.

It’s a Bull Market

As to the second, more serious flaw, I have already mentioned my problem of induction. The story focuses on an unusual episode in history; buying its thesis implies accepting that the current returns in asset values are permanent (the sort of belief that prevailed before the great crash that started in 1929). Remember that asset prices have (at the time of writing) witnessed the greatest bull market in history and that values did compound astronomically during the past two decades. A dollar invested in the average stock would have grown almost twenty-fold since 1982 –and that is the average stock. The sample might include people who invested in above average stocks. Virtually all of the subjects became rich from asset price inflation, in other word from the recent inflation in financial paper and assets that started in 1982. An investor who engaged in the same strategy same during less august days for the market would certainly have a different story to tell. Imagine the book being written in 1982, after the prolonged erosion of the inflation-adjusted value of the stocks, or in 1935, after the loss in interest in the stock market.

Or consider that the United States stock market is not the only investment vehicle. Consider the fate of those who, in place of spending their money buying expensive toys and paying for ski trips, bought Lebanese lira denominated Treasury bills (as my grandfather did), or junk bonds from Michael Melkan (as many of my colleagues in the 80s did). Go back in history and imagine the accumulator buying Russian Imperial bonds bearing the signature of Czar Nicholas II and trying to accumulate further by cashing them from the Soviet government, or Argentine real estate in the 30s (as my great grandfather did).

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 one that we do not see.

A Guru Called Schwagger

The funds management industry is populated with gurus. Clearly, the field has randomness and the guru is going to fall into a trap, particularly if he has no proper training in inference. At the time of writing there is one such guru called Jack Schwagger who developed the habit of writing books on the subject. Along with one of his peers, one Basso, he computed the success of a "Robin Hood" policy of investing with the less performing manager in a given population of managers. This goes against the prevailing wisdom of investing with a winning manager and taking away money from a losing one. They tried to constantly switch to the loser, and take away money from the current manager in the event of his making money. Doing so their paper strategy derived considerably higher returns than if they stuck to the winning manager. Their hypothetical example seemed to them to prove that one should not stay with the better manager, as we would be inclined to do, but rather switch to the worst manager, or at least such seems to be the point they were attempting to convey.

Their analysis presents one severe hitch that any graduate student in financial economics should be able to pinpoint at the first reading. Their sample only had survivors. They simply forgot to take into account the managers who went out of business. Such sample includes managers that were operating during the simulation, and are still operating today. True, their sample included managers who did poorly, but only those managers who did poorly and recovered, without getting out of business. So it would be obvious that investing with those who fared poorly at some point, but recovered (with the benefit of hindsight) would yield a positive return! Had they continued to fare poorly they would be out of business and would not be included in the sample.

How should one conduct the proper simulation? By taking a population of managers in existence, say, five years ago and running the simulation until today. Clearly the attributes of those who leave the population are biased towards failure: few successful people in such a lucrative business would call it quits for making too much money.

[fn: I did not run the simulation myself as I am not discussing their conclusion, merely their methodology]

Next we turn to a more technical presentation of these issues.

It is Easier to Buy and Sell than Fry an Egg –Introduction to Data Mining and the Survivorship Bias

This afternoon I have an appointment with my dentist. I can state with a certain level of comfort that she knows something about teeth, particularly if I enter her office with a toothache and exit from it with some form of relief. It will be difficult for someone who knows literally nothing about teeth to provide me with such a relief, except if she is particularly lucky on that day –or has been very lucky in her life to become a dentist while not knowing anything about teeth. Looking at her diploma on the wall, I determine that the odds that she repeatedly gave correct answers to the exam questions, and performed satisfactorily on a few thousand cavities before her graduation –out of plain randomness— are remarkably small.

Later, in the evening, I am going to Carnegie hall. I can say little about the pianist; I even forgot his unfamiliar foreign sounding name. All I know is that he studied in some Muscovite conservatory. But I can expect to get some music out of the piano. It will be rare to have someone who performed brilliantly enough in the past to get to Carnegie Hill and now turn out to have benefited from luck alone. The expectation of having a fraud who will bang on the piano producing cacophonous is indeed low enough for me to rule it out completely.

I was in London last Saturday. Saturdays in London are magical: bustling but without the mechanical industry of a weekday or the sad resignation of a Sunday. Without a wristwatch or a plan I found myself in front of my favorite carvings by Canova at the Victoria & Albert Museum. My professional bent immediately made me question whether randomness played a large role in the carving of these marble statues. The bodies were realistic reproductions of human figures, except that they were more harmonious and more finely balanced than anything I have seen mother nature produce on its own. Could such finesse be a product of luck?

I can practically make the same statement about anyone operating in the physical world, or in a business in which the degree of randomness is low. But there is a problem in anything related to business world. That problem we will call the monkeys on a typewriter bias. And that problem exists because of randomness.

It is an unfortunate fact that tomorrow I have an appointment with a fund manager seeking my help, and that of my friends, in finding investors. He has what he claims a good track record. All I can infer is that he has learned to buy and sell. And it is harder to fry an egg than buy and sell. Well…the fact that he made money in the past may have some relevance, but not terribly so. This is not to say that this is always the case: there are some instances in which one can trust a track record. But, alas, there are not too many of these.

In this chapter, I discuss some well-known counterintuitive properties of performance records and historical time series. The concept presented here is well known for some of its variations under the name survivorship bias, data mining, data snooping, overfitting etc., basically situations where the performance is exaggerated by the observer owing to a misperception of the importance of randomness. Clearly this concept has rather unsettling implications. It extends to more general situations where randomness may play a share, such as the choice of a medical treatment or the interpretation of coincidental events.

When I am tempted to suggest a possible future contribution of financial research to science in general, I adduce the analysis of data mining and the study of survivorship biases. These have been refined in finance but can extend to all areas of scientific investigation. Why is finance so rife a field? Because it is one of the rare areas of investigation where we have plenty of information (in the form of abundant price series), but no ability to conduct experiments as in, say, physics. This dependence on past data brings about its salient defects.

Fooled by Statistics

George Soros Has High Standards

I have often been faced with questions of the sort: "Who do you think you are to be able to tell me that I might have been plain lucky in my life?" Well, nobody really believes that he or she were lucky. My approach is that, with our Monte Carlo engine, we can manufacture purely random situations. We can do the exact opposite of conventional methods; in place of analyzing existing real people hunting for attributes we can create artificial ones with precisely known attributes. Thus we can manufacture situations that depends on pure, unadulterated luck, without the shadow of skills or whatever we have called non-luck in Table 1. In other words we can man-make pure nobodies to laugh at; they will be by design stripped of any shadow of ability.

The first such exercise is a finessing of the old popular saying that even a broken clock is right twice a day. We will take it a bit further to show that statistics is a knife that cuts on both sides. Let us use the Monte Carlo generator introduced earlier and construct a population of 10,000 fictional investment managers (the generator is not terribly necessary since we can use a coin, or even do plain algebra, but it is considerably more illustrative –and fun). Assume that they each have a perfectly fair game: each one has a 50% probability of making $10,000 at the end of the year, and a 50% probability of losing $10,000. Let us introduce an additional restriction: once a manager has a single bad year, he is thrown out of the sample, good bye and have a nice life. Thus we will operate like George Soros who was said to tell his managers gathered in a room: "half of you guys will be out by next year" (with an Eastern European accent). Like Soros, we have extremely high standards: we are only looking for managers with an unblemished record. We have no patience for low performers.

The Monte Carlo generator will toss a coin: head and the manager will make $10,000 over the year; tail and he will lose $10,000. We run it for the first year. At the end of the year, we expect 5000 managers to be up $10,000 each, and 5,000 to be down $10,000. Now we run the game a second year. Again, we can expect 2,500 managers to be up 2 years in a row. Another year: 1,250. A fourth one: 625. A fifth: 313. We have now, simply in a fair game, 313 managers who made money for 5 years in a row. Out of pure luck.

INSERT FIGURE HERE

Nobody Has to be Competent

Let’s push the argument further to make it more interesting. We create a cohort that is composed exclusively of incompetent managers. We will define an incompetent manager as someone who has a negative expected return, the equivalent of the odds being stacked against him. We instruct the Monte Carlo Generator now to draw from an urn. The urn has 100 balls, 45 black and 55 red. By drawing with replacement, the ratio of red to black balls will remain the same. If we draw a black ball, the manager will earn $10,000. If we draw a red ball, he will lose $10,000. The manager is thus expected to earn $10,000 with 45% probability, and lose $10,000 with 55%. On average the manager will lose $1,000 each round on average –but only on average.

At the end of the first year, we still expect to have 4500 manager turning a profit (45% of them), The second, 45% of that number, 2025. The third, 911; the fourth, 410; the fifth, 184.

Let us give the surviving managers names and dress them in business suits. True, they represent less than 2% of the original cohort. But they will get attention. Nobody will mention the other 98%. What can we conclude?

The first counterintuitive point is that a population entirely composed of bad managers will produce a small amount of great track records. As a matter of fact, assuming the manager shows up unsolicited at your door, it will be practically impossible to figure out whether he is good or bad. The graph in Figure 1 would not markedly change, even if the population were composed entirely of managers who are expected in the long run to lose money. Why? Because owing to volatility, some of them will make money. We can see here that volatility actually helps bad investment decisions.

The second counterintuitive point is that the expectation of the maximum of track records, with which we are concerned, depends more on the size of the initial sample, than on the individual odds per manager. In other words the number of managers with great track records I will find in a given market depends far more on the number of people who started in the investment business (in place of going to dental school), rather than on their ability to produce profits. It also depends on the volatility. Why do I use the notion of expectation of the maximum? Because I am not concerned at all with the average track record. I will only get to see the best of the managers, not all of the managers. This means that we will see more "excellent managers" in 2002 than in 1998, provided the cohort of beginners was greater in 1997 than it was in 1993 –I can safely say that it was.

Ergodicity

To get more technical, I have to say that people believe that they can figure out the properties of the distribution from the sample they are witnessing. When it comes to matters that depends on the maximum, it is altogether another distribution that is being inferred, that of the best performers. We call the average of such distribution the survivorship bias – here the fact that about 3% of the initial cohort will make money 5 years in a row.

In addition, this example illustrates the properties of ergodicity, namely, that time will eliminate the annoying effects of randomness. Looking forward, in spite of the fact that these managers were profitable in the past five years, we expect them to break-even in any future time period. They will fare no better than those of the initial cohort who failed earlier in the exercise.

Fooled Even More by Statistics

A few years ago, when I told A. M. of Chapter x that track records were less relevant that he thought, he found the remark so offensive that he violently flung his cigarette lighter in my direction. His ego was pumped up as he was heading up a department of "great traders" who were then making a fortune in the markets. They subsequently blew up during the harsh New York winter of 1994 (it was the bond market crash that followed the surprise interest rate hike by Alan Greenspan). I later tried to explain it to many people in the business, but to no avail. People are way too impressed by "great performers" to make such introspective effort.

Recall that the survivorship bias depends on the size of the initial population. The information that a manager made money in the past, just by itself, is accordingly, neither meaningful nor relevant. We need to know the size of the population from which he came. In other words, without knowing how many managers out there have tried and failed, we will not be able to assess the validity of the track record. If the initial population includes 10 managers, then I would give the performer half my savings without a blink. If the initial population is composed of 10,000 managers, I would ignore the results. The latter situation is generally the case: these days so many people have been drawn to the financial markets. Many college graduates are trading as a first career, failing, then going to dental school.

If, as in a fairy tale, these fictional managers materialized into real human beings, one of these could be the person I am meeting tomorrow at 11:45 a.m. Why did I select 11:45 a.m.? Because I will question him about his trading style. I need to know how he trades. I will then be able to claim that I have to rush to a lunch appointment if the manager puts too much emphasis on his track record.

The Mysterious Letter

You get an anonymous letter on January 2nd informing you that the market will go up during the month. It proves to be true, but you disregard it owing to the well known January effect (stocks have gone up historically during January). Then you receive another one on Feb 1st telling you that the market will go down. Again, it proves to be true. Then you get another letter on March 1st –same story. By July you are intrigued by the prescience of the anonymous person until you are asked to invest in a special offshore fund. You pour all your savings into it. Two months later, your money is gone.

You go spill your tears on your neighbor's shoulder and he tells you that he remembers that he received two such mysterious letters. But the mailings stopped at the second letter. He recalls that the first one was correct in its prediction, the other incorrect.

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, 5000 names. The next month he does the same with the remaining 2500 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.

An Interrupted Tennis Game

It is not uncommon to turn on the TV set during a tennis game and 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 door bell, the chance of the soliciting party being a spurious survivor is closer to 100%.

The Birthday Paradox

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 a person randomly, there is one in 365.25 chance of your sharing her 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.

It’s a Small World!

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.

Now 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 and the length of women’s skirts. And just like the birthday coincidences, it will amaze people.

Data Mining, Statistics, and Charlatanism

What is your probability of winning twice the New Jersey lottery? 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, Harvard’s 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. An interesting extension of data mining into biblical exegesis is provided in The Bible Code by Michael Drosnin.. Drosnin, a former journalist (seemingly innocent of any training in statistics), aided by the works of a "mathematician", helped "predict" 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 that the book sold well.

The Best Book I have Ever Read!

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 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. Frequently jackets contain praise by someone, famous or not, or excerpts from a book review. A 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 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 unfavorable book review and selecting words in it that appear to praise the book. One such dishonesty came from one Paul Wilmott, who managed to announce that I gave him his "first bad review", yet used excerpts from it as praise on the book jacket.

The first time I was fooled by this bias was upon buying, when I was 16, Manhattan Transfer, a book by John Dos Passos, the American writer, based on a praise on the jacket by the French pseudo-philosopher Jean-Paul Sartre, who claimed something to the effect that Dos Passos was the greatest writer of our time (I did not know then that Sartre was a fraud). 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 having received the Nobel Prize in literature, Dos Passos has reverted back to obscurity).

Recently some friends were fooled into buying a book Against the Gods by one Peter Bernstein based on a remark by one John Rothchild comparing it to Russel’s History of Western Philosophy. I was unaware of the fact that neither was John Rothchild an expert in the subject matter, not was it unusual to find someone somewhere making a claim

The Backtester

A programmer helped me build a backtester. It is a software program connected to a database of historical prices; it allows me to check the hypothetical past performance of any trading rule of average complexity. I can just apply a mechanical trading rule, like buy NASDAQ stocks if they close more than 1.83% above their average of their previous week, and immediately get an idea of its past performance. The screen will flash my hypothetical track record associated with the trading rule. If I do not like the results, I can change the percentage, to say, 1.2%. I can also make the rule more complex. I will keep trying until I find something that works well.

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 will 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 Oulan Bator, Mongolia.

To get technical, there are even worse extensions. An outstanding recent paper by Ryan, Timmerman and White goes further and consider 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 thousand of parametrizations of 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.

Clearly we cannot separate the problem of manager survivorship from that of the survivorship of the trading rule. This makes the problem very ubiquitous.

I have to decry some excesses in back-testing I have closely witnessed in my private career. There is a product called Omega TradeStation ™ that is currently on the market, in use by tens of thousand of users. Beset with insomnia, the computerized day-traders become night-testers plowing the data for some of its properties. By dint of throwing their monkeys on typewriters, without specifying what book they want their monkey to write, they will hit upon hypothetical gold somewhere. Many of them blindly believe in it.

One of my colleagues, a man with prestigious degrees, grew to believe in such virtual world to the point of losing all sense of reality. Whether the modicum of common sense left in him might have had rapidly vanished under the mounds of simulations, or whether he might have had none to engage in such pursuit, I cannot tell. I learned by closely watching him that what natural skepticism we may have vanishes under the weight of data –for he was extremely skeptical, but in the wrong area.

A More Unsettling Extension

Historically, medicine has operated by trial and error –in other words, statistically. We know by now that there can be entirely fortuitous connections between symptoms and treatment, and that some medications succeed in medical trials for mere random reasons. I cannot claim expertise in medicine, but have been a steady reader of a segment of the cancer literature over the past half decade, long enough to be concerned with the standards, as we will see in the next chapter. Medical researchers are rarely statisticians; statisticians are rarely medical researchers. Many medical researchers are not even remotely aware of this bias. True, this bias may play a small role, but it is certainly present. One recent medical study links cigarette smoking to a reduction in breast cancer, thus conflicting with all previous studies. Logic would indicate that the result may be suspicious, the result of mere coincidence.

The Earnings Season: Fooled by the Results

Wall Street analysts, in general, are trained to find the accounting tricks that companies use to hide their earnings. They tend to beat the companies at that game. But they are not trained yet to deal with randomness. When a company shows an increase in earnings once, it draws no immediate attention. Twice, and the name starts showing up on computer screens. Three times, and the company will merit some buy recommendation.

Just as with the track record problem, consider a cohort of 10000 companies that are assumed on average to barely return the risk-free rate. They engage in all form of volatile businesses. At the end of the first year, we will have 5000 "star" companies showing an increase in profits (assuming no inflation), and 5000 "dogs". After 3 years, we will have 1250 "stars". The stock review committee at the investment house will give your broker their name as a "strong buy". He will leave a voice-message that he has a hot recommendation that necessitates immediate action. You will be e-mailed a long list of names. You will buy one or two of them. Meanwhile the manager in charge of your 401K retirement plan will be acquiring the entire list.

We can apply the reasoning to the selection of investment categories –as if they were the managers in the example above. Assume you are standing in 1900 with hundreds of investments to look at. There are the stock markets of Argentina, Imperial Russia, The United Kingdom, Unified Germany, and plenty of others to consider. A rational person would have bought not just the emerging country of the United States, but those of Russia and Argentina as well. The rest of the story is well known: while many of the stock markets like those of the United Kingdom and the United States fared extremely well, the investor in Imperial Russia would have no better than medium-quality wallpaper in his hands. The countries that fared well are not a large segment of the initial cohort: randomness would be expected to allow a few investment classes to fare extremely well. I wonder if those "experts" who make foolish (and self serving) statements like "markets will always go up in any 20-year period" are aware of this problem.

Cancer Cures

When I return home from an Asian or European trip, my jet lag often causes me to rise at a very early hour. Occasionally (though rarely) I switch on the TV set searching for market information. What strikes me in these morning explorations is the abundance of claims by the alternative medicine vendors of cures by some of their products. These no doubt are caused by the lower rates at that time. To prove their claim, they present the convincing testimonial of someone who was cured thanks to their methods. For instance I saw a former throat cancer patient explaining how he was saved by a combination of vitamins –in all likelihood he was sincere (although of course compensated for his account, perhaps with a lifetime supply of such medicine).

In spite of our advances, people still believe in the existence of links between disease and cure based on such information, and there is no scientific evidence that can convince them more potently than a sincere and emotional testimonial. Such testimonial does not always come from the regular guy: Statements by Nobel prize winners (in the wrong discipline) could easily do. Linus Pauling, a Nobel Prize winner in Chemistry, was said to believe in Vitamin C’s medicinal properties, himself ingesting massive daily doses. With his bully pulpit, he contributed to the common belief in Vitamin C’s curative properties. Many medical studies, unable to replicate Pauling’s claims, fell on deaf ears as it was difficult to undo the testimonial by a "Nobel Prize winner", even if he was not qualified in to discuss matters related to medicine.

Many of these claims have been harmless outside of the financial profits for these charlatans –but many cancer patients have replaced the more scientifically proven therapies in favor of these methods and died as a result of their neglecting more orthodox cures. The reader might wonder about my claims that the user of these products could be sincere, without it meaning that he was cured by the illusory treatment. The reason is something called "spontaneous remission", in which a very small minority of cancer patients, for reasons that remain entirely speculative, wipe out cancer cells and recover "miraculously". Some switch causes the patient's immune system to eradicate all cancer cells from the body. These people would have been equally cured by drinking a glass of Vermont spring water or chewing on dried beef as they were by taking these beautifully wrapped pills. Finally, these spontaneous remissions might not be so spontaneous; they might, at the bottom, have a cause that we are not yet sophisticated enough to detect.

The late astronomer Karl Sagan, a devoted promoter of scientific thinking and an obsessive enemy of non-science, examined the cures from cancer that result from a visit to Lourdes in France where people were healed by simple contact with the holy waters, and found out the interesting fact that, of the total cancer patients who visited the place, the cure rate was, if anything, lower than the statistical one for spontaneous remissions. It was lower than the average for those who did not go to Lourdes. Should a statistician infer here that cancer patients’ odds of surviving deteriorates after a visit to Lourdes?

Professor Pearson Goes to Monte Carlo (Literally): Randomness Does Not Look Random!

At the beginning of the 20th century, as we were starting to develop techniques to deal with the notion of random outcomes, several methods were designed to detect anomalies. Professor Karl Pearson (of the Neyman-Pearson fame) devised the first test of non-randomness (it was in reality a test of deviation from normality, which, for all intents and purposes, was the same thing). He examined millions of runs of what was called a Monte Carlo (the old name for a roulette) during the month of July 1992. He discovered that the odds were at least one billion to one that the roulette runs were not purely random. Professor Pearson was greatly surprised at the discovery. But this result in itself tells us nothing: we know that there is no such thing as a pure random draw, for the outcome of the draw depends on the quality of the equipment: with enough minutiae one would be able to uncover the non-randomness somewhere. Philosophers of statistics call this the reference case problem, to explain that there is no true attainable randomness in practice, only in theory. Besides, a manager would question whether such non-randomness can lead to any meaningful profitable rules. If I need to gamble $1 on 10,000 runs and expect to make $1 for my efforts, then I would do much better in the employment of a janitorial agency.

But the result bears another suspicious element. Of more practical relevance there is the following severe problem about non-randomness. Even the fathers of statistical science forgot the fact that a random series of runs need not exhibit any 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 –that is if one looks hard enough. Professor Pearson was among the first scholars who were interested in creating artificial random data generators, tables one could use as inputs for various scientific and engineering simulations (the precursors of our Monte Carlo simulator). The problem is that they did not want these tables to exhibit any form of regularity. Yet real randomness does not look random!

I would further illustrate the point with the study of a phenomena well known as cancer clusters. Consider an artificial map composed of a square with 16 random darts hitting it with equal probability of being at any place in the map. If we divide the map in 16 smaller squares, it is expected that each square will contain one dart on average –but only on average. But there is a very small probability of having a given map with exactly 16 darts in 16 different squares. The average map will have more than one dart in a few squares, and no dart at all in many squares. Some newspaper will declare that one of the areas has radiation that caused cancer, prompting lawyers to start soliciting the patients.

Conclusion

This chapter described situations where, even if we lived in well-charted randomness, evaluating the performance of an investment strategy, a manager, a company, or a medical study can be laden with misperceptions. To completely reject the validity of historical data would be extreme. The wise approach would be to keep the following platitude in the back of one’s mind: a historical record is merely one minor representation of a phenomenon and does not necessarily present evidence. Like many platitudes, this may de difficult to bear in mind when someone with an impressive title pounds you with definitive statistics. I no longer take part of market debates and discussions with other practitioners –for I have often been embarrassed in debates by someone quoting history in a confident and definitive way. The more my skepticism made me look foolish, the more I turned out to be right.

At the cost of presenting another platitude, and being branded with "naïve falsificationism", I will present another manifestation of my obsessive Popperism. The method I strive to apply is to conditionally accept a statistical test while making every single possible allowance for it being wrong. As I am writing these lines, I am using, as an appendage to my trading, a statistical machinery. I believe that it is sophisticated and purged of data mining biases –I only test for relationships that I believe to make sense. To make sure that I do not take it very seriously, I christened the system Karl II. Karl-the-first was destroyed as I lost faith in it.

Randomness and Our Brain: We Are Probability Blind

Paris or the Bahamas?

You have two options for your next brief vacation in March. The first is to fly to Paris; the second is to go to the Caribbean. You expressed indifference between the two options; your spouse will tip the decision one way or another. Two distinct and separate images come to you when you think of the possibilities. In the first one, you see yourself standing at the Musée d’Orsay in front of some Pissaro painting depicting a cloudy sky—the gray Parisian wintry sky. You are carrying an umbrella under your arm. In the second image, you are lying on a towel with a stack of books by your favorite authors next to you (Tom Clancy and Amianus Marcellinus), and an obsequious waiter serving you a banana daiquiri.

You know that the two states are mutually exclusive (you can only be in one place at one time), but exhaustive (there is a 100% probability that you will be in one of them). They are equiprobable, with, in your opinion, 50% probability assigned to each.

You derive a great measure of pleasure thinking about your vacation; it motivates you and makes your daily commute more bearable. But the adequate way to visualize yourself, according to rational behavior under uncertainty, is 50% in one of the vacation spots and 50% in the other –what is mathematically called a linear combination of the two states. Can your brain handle that? How desirable would it be to have your feet in the Caribbean waters and your head exposed to the Parisian rain? Our brain can properly handle one and only one state at once –unless you have personality troubles of a deeply pathological nature.

Now try to imagine an 85%/15% combination. Any luck?

Consider a bet you make with a colleague for the amount of $1,000, which, in your opinion, is exactly fair. Tomorrow night you will have zero or $2,000 in your pocket, each with a 50% probability. The fair value of a bet is the linear combination of the states, here called the mathematical expectation, i.e., the probabilities of each payoff multiplied by the dollar values at stake. Can you imagine (not compute) the value being $1000? We can conjure up one and only one state at a given time. Left to our own devices, we are likely to bet in an irrational way, as one of the states would dominate the picture.

Physicists bickered with each other after someone first represented a particle as being in two physical locations at the same time (it was a wave until the act of observation caused it to have the appearance of a particle), with for probability the square of a complex function that has no possible physical representation. They called it, in turn, nonsense and magic, just as you would have reacted if you were told you that you would be ½ in Paris and ½ in the Caribbean on March 4.

For reasons we just saw, the laws of probability are said to be counterintuitive by the researchers in the cognitive and behavioral sciences. We are probability blind, these scientists say. This chapter will rapidly illustrate some manifestations of such blindness, particularly with the financial markets, with a cursory exposition of the research in that area.

From Psychology to Neurobiology

The idea of probability blindness gave rise to an entire discipline dedicated to the study of the effect these biases carry on our behavior. It is filling out library shelves and causing the creation of numerous investment funds dedicated to the sister idea that people do not behave in a rational way in the markets. Some funds have been built around the idea that people overreact to news, while others have been devoted to the notion that, to the contrary, people underreact (I was told early in my career that the more diversity the better for the market). These beliefs give rise to two categories of trading strategies. On one side we find the contrarians who subscribe to the following rationale: Hey, since people systematically overreact, let us take the other side, sell the winners and buy the losers. On the other side stand the momentum players who do the exact opposite: Since markets do not adjust fast enough, let us buy the winners and sell the losers. Because of randomness, both categories will show periodic victories, which cannot prove directly that either theory is right or wrong.

Even psychiatrists and clinical psychologists are joining the fray by becoming "experts" –after all they know more about the human mind that those financial economists with their unrealistic, unscientific equations. A yearly conference in Boston gathers medical doctors and psychology researchers musing over market strategies.

The idea may seem simple, perhaps even boring, until we encounter professionals whom we expect would deal with the matter with maximal expertise fall right into the trap like the man on the street.

Our Natural Habitat

I will not delve too deep into amateur evolutionary theory to probe at the reasons (besides, in spite of having spent some time in libraries I feel that I am truly an amateur in the subject matter). Clearly, the environment for which we have built our genetic endowment is not the one that prevails today. I have not told too many of my colleagues that their decision-making contains some lingering habits of cavemen –but when markets experience an abrupt move, I experience the same rush of adrenaline as if a leopard was seen prowling near my trading desk. Some of my colleagues who break telephone handles upon losing money might be even closer in their psychological makeup to our common origin.

But the real problem is that our natural habitat does not include much information. By natural habitat, I mean the environment in which we did reproduce the most, the one in which we had the highest number of generations. The consensus is that we have been around as a separate species for 130,000 years, most of which were spent in the African Savannah. But we do not have to go back that far back in history to get the point. Think of your life conditions in an early urban settlement, in Middle-Town, Fertile Crescent, only about 3,000 years ago –surely modern times from a genetic standpoint. Information is limited by the physical means of its transmission: one cannot travel fast, hence information will come from faraway places in concise batches. Traveling is a nuisance fraught with all manner of physical danger; you will settle within a narrow radius of where you were born unless famine or some invading uncivilized tribe dislodges you and your relatives from your happy settlement. The number of persons you would get to know in a lifetime will be small. Should a crime be committed, it will be easy to gauge the evidence of guilt within the small number of possible suspects. If you are unjustly convicted of a crime, you will argue in simple terms, propounding simple evidence like "I was not there as I was praying in the temple of Baal and was seen at dusk by the high priest" and add that Obedshemesh son of Sahar was more likely to be guilty because he had more at stake from the crime. Your life would be simple, hence your space of probabilities will be narrow.

An efficient computation of the odds was never necessary until very recently. This explains why we had to wait until the emergence of the gambling literature to see the growth of the mathematics of probability. Popular belief holds that the religious backdrop of the first and second millennium blocked the growth of tools that hint at absence of determinism, and caused the delays in probability research. The idea is extremely dubious: we simply did not compute probabilities because we did not dare to, rather because we did not have to.

[Note here that the best-selling Against the Gods written by modern finance apologist Peter Berstein attributes the Arab's non-discovery of probability to fatalism, as he has not heard of Al-Gazali and the golden age of skepticists. Note that Berstein is neither a historian, nor a trader, nor a philosopher, nor a probability specialist, which may explain his unfettered promotion of naïve risk measurement.]

That Great Legal Profession

The O.J. Simpson trial provides an example on how our modern society is ruled by probability (because of the explosion in information), while important decisions are made without the smallest regard for its basic laws. We are capable of sending a spacecraft to Mars, but we are incapable of having criminal trials managed by the basic laws of probability —yet evidence is clearly a probabilistic notion. I remember buying a book on probability at Borders Books only a short walking distance from the Santa Monica courthouse where the "trial of the century" was taking place –another book that crystallized the highly sophisticated quantitative knowledge in the field. How could such a leap in knowledge elude lawyers and jurors only half a mile away?

People who are as close to being criminal as probability laws can allow us to infer (that is with a confidence that exceeds the shadow of a doubt) are walking free because of our misunderstanding of basic concepts of the odds. You could be convicted for a crime you never committed owing to a poor reading of probability –for we still cannot have a court of law properly compute the joint probability of events (that is the probability of two events taking place at the same time). When I saw one of the lawyers arguing that there were at least 4 people in Los Angeles capable of carrying O.J. Simpson’s DNA characteristics (thus ignoring the joint set of events), I switched off my television set in disgust. I was under the impression until then that sophistry had been eliminated from legal cases thanks to the high standards of republican Rome. Worse, I cannot believe that Harvard University can have on its staff someone like X who used the argument that only 10% of men who brutalize their wives go on to murder them, which is an unconditional probability (whether the statement was made out of a warped notion of advocacy, pure malice, or ignorance is irrelevant). Aren't universities devoted to the Truth? The proper way to look at it is to see the percentage of murder cases where women were killed by their husband and had previously been battered by him (that is, 50%) –for we are dealing with what is called conditional probabilities: the probability that O.J. killed his wife conditional on her having been killed, rather than the unconditional probability of killing his wife. How can we expect some regular person to understand financial randomness when a Harvard professor who deals and teaches the concept of probabilistic evidence can make such an erroneous statement?

More particularly, where jurors (and lawyers) tend to make mistakes, along with the rest of us, is in the notion of joint probability. They do not realize that evidence compounds. The probability of my being diagnosed with respiratory track cancer and being run over by a pink Cadillac in the same year, assuming each one of them is 1/100,000, becomes 1/10,000,000,000 –by multiplying the two (obviously independent) events. But I do not have to go that far; I can surprise people by saying that the probability of the joint event is lower than either. That is not what our intuition reveals. When we submit rational and educated people to tests where they need to produce the probability of a young woman with a liberal arts education being a bank teller or a feminist bank teller, they assign on average a higher probability to her being a feminist bank teller than to that of her being a bank teller.

We said that mere judgment would probably suffice in a primitive society. It is easy for a society to live without mathematics –or traders to trade without quantitative methods –when the space of possible outcomes is one-dimensional. One-dimensional means that we are looking at one sole variable, not a collection of separate events. The price of one security is one dimensional, whereas the collection of the prices of several securities is multidimensional and requires mathematical modelling –we cannot easily see the collection of possible outcomes of the portfolio with a naked eye, and cannot even represent it on a graph as our physical world has been limited to visual representation in three dimensions only. We will argue later why we run the risk of having bad models (admittedly we have) or making the error of condoning ignorance –swinging between the Carybde of the lawyer who knows no math to the Sylla of the mathematician who misuses his math because he does not have the judgment to select the right model. In other words, we will have to swing between the mistake of listening to the glib nonsense of the O.J. Simpson lawyer and that of applying the flawed theories of Markowitz (i.e., modern portfolio theory). The beauty of science is that it makes an allowance for both error types. Luckily, there is a middle road.

Kahneman and Tversky

Who are the most influential economists of the century, in terms of quotes, their followings, and their influence over the profession? Not Keynes, not Marshall, and certainly not Milton Friedman. They are Daniel Kahneman and Amos Tversky, psychology researchers whose specialty was to uncover areas where human beings are not endowed with rational thinking and optimal economic behavior.

The pair taught us a lot about the way we perceive and handle uncertainty. Their research, conducted on a population of students in the early seventies, showed that we do not correctly understand contingencies (their sample also contained some professors, presumably of the caliber of [ censored ] ). Furthermore, in the rare cases when we understand probability, we do not seem to consider it in our behavior. Before we look at a few examples of the biases they uncovered, a mention needs to be made of some of the conflicts their contributions generated.

Since the Kahneman and Tversky results, an entire discipline called behavioral finance and economics has flourished. It is in open contradiction with the orthodox so-called neoclassical taught in business schools under the normative names of efficient markets, rational expectations, and other such concepts. It is worth stopping, at this juncture, and discussing the distinction between normative and positive sciences. A normative science (clearly a self-contradictory concept) offers prescriptive teachings; it studies how things should be. Some economists, for example, (those of the efficient market religion) believe that humans are rational and act rationally because it is the best thing for them to do (it is mathematically "optimal"). The opposite is a positive science, which is based on how people actually are observed to behave. In spite of economists' envy of physicists, physics is an inherently positive science while economics, particularly microeconomics and financial economics, is predominantly a normative one.

Neurobiology

The soft sciences of psychology and economics have cheated us on occasion in the past. How? Economics has produced the laughable ideas of Merton Miller and James Tobin, ideas that evaporate once one changes the assumptions a little bit. It seems difficult for us to take sides with bickering economists trading often-incomprehensible arguments (even to economists). Biology and medicine, on the other hand, rank higher in scientific firmness; like true sciences, they can explain things. They are both positive and their theories are better theories, that is, more easily testable. The good news is that neurologists are now starting to confirm these results, with what is called environment mapping in the brain, by taking a patient whose brain is damaged in one single spot (say, by a tumor or an injury deemed to be local) and defining the function performed topically. The Kahneman and Tversky results thus found a terra firma with the leaps in our knowledge obtained through behavioral genetics and, further, plain medicine. Some of the physiology of our brain makes us perceive things and behave in a given manner. We are, whether we like it or not, prisoners to our biology.

Furthermore, researchers in evolutionary psychology confirm somewhat the reasons for our biases. We have not had an incentive to develop an ability to understand probability because we did not have to do so –but the more profound reason is that we are not fit to understand things, merely to survive. To survive, we need to overstate some probabilities, such as those that can affect our survival.

The story is being thus corroborated by the various disciplines: the magnitude of the perceptional distortions makes us less than rational, in the sense that rational means both having coherent beliefs (i. e., free of logical contradictions) and acting in a manner compatible with these beliefs.

Examples of Biases in Understanding Probability

I found in the behavioral literature at least 40 damning examples of such acute biases. Below is the account of a well known test, and an embarrassing one for the medical profession. The following quiz was given to medical doctors.

A test of a disease presents a rate of 5% false positives. The disease strikes 1/1000 of the population. A patient’s test is positive. What is the probability of the patient being stricken with the disease?

Most doctors answered 95%, simply taking into account the fact that the test has a 95% accuracy rate. The answer is the joint probability that both the patient is sick and the test shows it: close to 2%. Less than one in five professionals got it right. The medical doctors’ answer is scary: 47 times higher than the true probability.

To understand the correct answer, consider that out of 1000 patients who are administered the test, 1 will be expected to be afflicted with the disease. Out of a population of the remaining 999 healthy patients, almost 50 will show a disease. Finally, the correct answer should be that the probability of being afflicted with the disease for someone who presented a positive test is the following ratio:

here 1 in 51.

Think of the number of times you will be given a medication that carries damaging side effects for a given disease you were told you had, when you may only have 2% probability of being afflicted with it! [example borrowed from Bennet 1998]

We Are Option Blind

As an option trader I noticed that people tend to undervalue options as they are usually unable to correctly mentally value instruments that deliver an uncertain payoff, even when they are fully conscious of the mathematics. Even regulators reinforce such ignorance by explaining to people that options are a decaying or wasting asset. Options that are out of the money are deemed to decay, that is to lose their premium between two dates.

I will clarify next with a simplified (but sufficient) explanation of what an option means. Say a stock trades at $100 and that someone gives me the right to buy it at $110 one month ahead of today. This is dubbed a call option. It only makes sense for me to exercise it, that is to ask the seller of the option to deliver me the stock at $110 if it trades at a higher price than that. 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.

Consider that I buy the option for $1. What do I expect the value of the option to be one month from now? Most people think 0. That is not true. The option has a high probability, say 90% of being worth 0 at expiration, but perhaps 10% probability to be worth an average of $10. Thus selling it is not free money. Buying it is not a wasting asset. Even professionals can be fooled. How? They confuse between the expected value and the most likely scenario (here the expected value is $1 and the most likely scenario is for the option to be worth 0). They mentally overweight the state that is the most likely, namely, the one that the market does not move at all. The option is simply the weighted average of the possible states the asset can take.

There is also a different type of satisfaction provided by the option seller. It is the steady return and the steady feeling of reward –what psychologists call flow. It is very pleasant to go to work in the morning with the expectation of being up some small money. It requires some strength of character to accept the expectation of bleeding a little, losing pennies on a steady basis even if the strategy is bound to be profitable over longer periods. I noticed that very few option traders can maintain what I call a "long volatility" position, namely a position that is most likely to 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 to 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 10% of the time).

We divide the community of option traders in two categories: premium sellers and premium buyers. Premium sellers sell options, and generally make steady money. Premium buyers do the reverse. Option sellers, it is said, eat like chickens and go to the bathroom like elephants. Alas, most option traders I encountered in my career are premium sellers –when they blow up it is generally other people's money.

How could professionals seemingly aware of the (simple) mathematics be put in such a position? The reason is that our understanding of math can remain quite superficial: medicine is getting to believe that our actions are not quite guided by the parts of our brain that dictate rationality (see Antonio Damasio's Descartes' Error or Ledoux's Emotional Brain). For the same reason, people who are otherwise rational engage in smoking or in fights that get them no immediate benefits, likewise people sell options even when they know that it is not a good thing to do.

But things can get worse. There is a category of people, generally academics, who, instead of fitting their actions to their brains, instead fit their brain to their actions. These go back and cheat with the statistics to justify their actions. They will fool themselves with statistical arguments to justify their option selling.

Statisticians and Other Fools

One would think that, owing to their sophistication, statisticians can gain additional insight into financial matters. The answer, as we will see in Chapter x, is that the first effect statistics have on someone is to decrease the quality of his knowledge and increase his misconceptions. We are routinely fooled by traders and investment managers who supply us with the most convincing statistics on their past activities. One needs to be a highly ranked statistician not to fall into a trap. I laugh vigorously while reading reports by investment consultants. Hopefully, the reader, sharing some of my disbelief, will also have a laugh watching some fund manager boasting about his performance during a lunchtime interview on CNBC in front of thousands of investors watching him while working out at the Health Club.

The main way statisticians are fooled is by what is called data mining. As we will see, statisticians develop techniques in uncovering relationships that have a great degree of significance. However, these techniques can be directed at the wrong aim. They are often used to uncover chance and coincidental relationships that, when relied upon, lead to nasty surprises.

Probabilities and the Media

It is an unfortunate fact that many journalists receive their training in methods for expressing themselves rather than in plumbing the depth of things –the selection process favors the most communicative, not the most knowledgeable one. My medical doctor friends claim that many medical journalists do not understand anything about medicine and biology, often making mistakes of a very basic nature. I cannot confirm such statements, being myself a mere amateur (though voracious reader) in medical research; but I noticed that they often misunderstand the probabilities used in medical research announcements. The most common one concerns the interpretation of evidence. They most commonly get mixed up between absence of evidence and evidence of absence. How? Say I test some chemotherapy, say Fluorouracil for upper respiratory track cancer and find that it is better than a placebo, but only marginally so; that (in addition to other modalities) it improves survival from 21 per 100 to 24 per 100. Given my sample size, I may not be confident that the additional 3 percent survival points comes from the medicine; it could be merely attributable to randomness. So I would write a paper outlining my results and saying that there is no evidence of improved survival (as yet) from such medicine, and that further research would be needed. A medical journalist would pick it up and claim that one Professor Taleb from Larchmont, N.Y. (winters), and Amyoun, Lebanon (summers), found evidence that Fluorouracil does not help, which is entirely opposite to my intentions. Some naïve doctor in Smalltown, even more uncomfortable with probabilities than the most untrained journalist, would pick it up and build the mental block against the medication, even when some researcher finally finds fresh evidence that such medicine confers a clear survival advantage.

CNBC at Lunch Time

The advent of the financial television channel CNBC presented plenty of benefits to the financial community; but it allowed a collection of extrovert practitioners long on theories to voice them in a few minutes of television time. There one often sees respectable people making ludicrous (but smart sounding) statements about some properties of the stock market. Among these are statements that blatantly violate the laws of probability. During the summer of 1998 I heard several times such statement as "the real market is only 10% off the highs while the average stock is close to 40% off its highs", which is intended to be indicative of deep troubles or anomalies –some harbinger of bear markets.

There is no incompatibility between the fact that the average stock is down 40% from the highs while the average of all stocks is down 10% from its own highs. One has to consider that the stocks did not all reach their highs at the same time. Given that stocks are not 100% correlated, stock A might reach its maximum in January, stock B might reach its maximum in April, but the average of the two stocks A and B might reach its maximum sometimes in February. Furthermore, in the event of negatively correlated stocks, if stock A is at its maximum when stock B is at its minimum, then they could be both down 40% from their maximum when the stock market is at its highs! By a law of probability called distribution of the maximum of random variables, the maximum of an average is necessarily less volatile than the average maximum.

You Should be Dead by Now

This brings to mind another common violation of probability by prime time T. V. journalists, who may be selected for their looks, charisma and their presentation skills, but certainly not for their incisive minds. For instance, a fallacy that I saw commonly made by a prominent TV financial "expert" is as follows: "The average American is expected to live 73 years. Therefore it you are 68 you can expect to live 5 more years, and should plan accordingly". She went into precise prescriptions of how the person should invest for a 5 more years horizon. Now what if you are 80? Is your life expectancy going to be minus 7 years? What these journalists confuse is the unconditional and conditional life expectancy. At birth, your unconditional life expectancy may be 73 years. But as you advance in age and do not die, your life expectancy increases along with your life. Why? Because the other people dying have taken your spot in the statistics, for expectation means average. So if you are 73 and are in good health, you may still have, say, 9 years in expectation. But the expectation would change, and, at 82, you will have another 5 years, provided, of course you are still alive. Even someone 100 years old still has a positive conditional life expectation. Such a statement, when one thinks about it, is not too different from the one that says: our operation has a mortality rate of 1%. So far we have operated on 99 patients with great success; you are our 100th, hence you have 100% probability of dying on the table.

But TV financial planners may confuse a few people. This is quite harmless. What is far more worrying is the supply of information by non-professionals to professionals; it is to the journalists that we turn next.

The QuoteMachine Explanations

I have, on my desk, a machine called a QuoteMachine , which acts as a safe e-mail service, a news service, a historical data retrieving tool, a charting system, an invaluable analytical aid and, not least, a screen where I can see the price of securities and currencies. I have gotten so addicted to it that I cannot operate without it as I would otherwise feel cut-off from the rest of the world. Somehow, traders who do not have a QuoteMachine address do not exist for us. But there is one aspect of QuoteMachine I would dispense with: the journalist's commentary. Why? Because they explain things too much and perpetuate the right-column, left-column confusion in a serious manner. We will see how next. QuoteMachine is not the sole perpetrator; it is just that I have not been exposed to newspapers' business sections over the past decade, preferring to read real prose instead.

As I am writing these lines I see the following headlines on my QuoteMachine:

à Dow is up 1.03 on lower interest rates.

à Dollar down .12 yen on higher Japanese surplus.

and so on for pages. If I translate it well, the journalist claims to provide an explanation for something that amounts to perfect noise. A move of 1.03 with the Dow at 11,000 constitutes less than a .01% move. Such move does not warrant an explanation. There is nothing there that an honest person can try to explain; there are no reasons to adduce. But like apprentice professors of comparative literature, journalists being paid to provide explanations will gladly and readily provide them.

Now how did I decide that it was perfect noise? The explanation can be made simple if we take a simple analogy. If you engage in a mountain bicycle race with a friend across Siberia and, a month later beat him by one single second, you clearly cannot quite boast that you are faster than him. You might have been helped by something, or it can be just plain randomness, nothing else. But that second is not in itself significant enough for someone to draw conclusions. I would not write in my diary: cyclist A is better than cyclist B because he is fed with spinach whereas cyclist B has a diet of tofu. The reason I am making this inference is because he beat him by 1.3 seconds in a 3000 mile race. Now, if the difference is 1 week, then I could start analyzing whether tofu is the reason, or if there can be other factors.

Another analogy: day Hospital A delivered (owing to the small sample) 52% of boys and Hospital B delivered the same year only 48%, would you try to give the explanation that you had a boy because it was delivered in hospital A?

There is another problem with someone trying to interpret an event, and trying to link it to a single cause when there can be more than one factor affecting it. This is called multivariate analysis. It is very difficult to isolate a single cause when there are plenty around. For instance, if the stock market can react to U.S. domestic interest rates, the dollar against the yen, the dollar against the European currencies, the European stock markets, the United States balance of payments, United States inflation, and another dozen prime factors, then the journalists needs to look at all of these factors, look at their historical effect both in isolation and jointly, look at the stability of such influence, then, after consulting the statistic isolate the factor. Finally, a proper confidence level needs to be given to the factor; if it is less that 90% the story would be dead.

I have a trick to know if something real in the world is taking place. I have set up two QuoteMachine screens to display the price and percentage change of all relevant prices in the world: currencies, stocks, interest rates, and commodities. By dint of looking at the same setup for years, as I keep the currencies in the upper left corner and the various stock markets on the right, I managed to be able to know if something serious is going on. The trick is to only look at the percentage changes. Unless something moves by more than its usual daily percentage move, 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 4 times. The headline of the Dow moving by 1.3 points on my screen today has less than one millionth of the significance of the serious 7% drop of October 1997.

People might tell me: why do I want everybody to learn some statistics? The answer is that too many people read journalists' explanations. Perhaps, at the end, we have too much unfiltered information. Finally I would prefer that someone who makes probabilistic statements would know something about statistics.

Filtering Methods

Engineers use methods to clean up the noise from the signal in the data. Did it ever occur to you while talking to your cousin in Australia or the South Pole that the static on the telephone line could be distinguished from the voice of your correspondent? The method is to consider that when a change in amplitude is small, it is more likely to result from noise –with its likelihood of being a signal increasing exponentially as its magnitude increases. The method is called a smoothing kernel which was applied in Figure 1 and Figure 2. But our auditory system is incapable of performing such function by itself. Likewise our brain cannot see the difference between a significant price change and mere noise, particularly when it is pounded with unsmoothed journalistic noise.

Insert Figure -1 Unfiltered Data Containing Signal and Noise

Insert Figure -2 Same Data With Its Noise Removed

We Do Not Understand Confidence Levels

Professionals, even those involved with options (that is like myself), forget the following reality. It is not so much whether one is bullish or bearish that matters so much as the degree of confidence with the opinion. Consider that you are going on a trip one fall morning and need to formulate an idea about the weather prior to packing your luggage. If you expect the weather to be 60 degrees, plus or minus 10 degrees (say in Arizona), then you would take no snow clothes and no portable electric fan. Now what if you were going to Chicago, where you are told that the weather, while being 60 degrees, will nevertheless vary by about 30 degrees? You would have to pack winter and summer clothes. Here the expectation of the weather where carries little importance concerning the choice of clothing; it is the variance that matters. Your decision to pack is markedly different now that you are told that the variability would be around 30 degrees. Now let us push the point further: what if you were going to a planet where the expectation is also going to be around 60 degrees, but plus or minus 500 degrees?

We can see that my activity in the market depends far less on where I think the market is going so much as it does on the degree of error I allow around such a confidence level.

An Account of my Own Biases

The Greek philosopher Pyrrho, who advocated a life of equanimity and indifference, was criticized for failing to keep his composure during a critical circumstance. His answer was that he found it difficult to rid himself of his humanity. If Pyrrho cannot stop being human, I do not see why the rest of us should resemble the rational man who acts perfectly under uncertainty as propounded by economic theory. To give a convincing example of biases in our reaction to randomness, I adduce my own personal behavior. I discovered that much of the rationally obtained results using my computations of the various probabilities do not register deeply enough to impact my own conduct. In other words, I acted like the doctor who knew of the 2% probability of the disease, but somehow unwittingly treated the patient as if the ailment had a 95% probability of being there. My brain and my instinct were not acting in concert.

The details are as follows. As a rational trader (all traders boast so) I believe as I outlined above that there is a difference between noise and signal, and that noise needs to be ignored while a signal needs be taken seriously. I use elementary (but robust) methods that allow me to calculate the expected noise and signal composition of any fluctuation in my trading performance (both in my personal account and in the one I trade for my employer). For example, after registering a profit of $100,000 on a given strategy, I may assign a 2% probability to the hypothesis of the strategy being profitable and 98% probability to the hypothesis that the performance may be the result of mere noise. A gain of $1,000,000, on the other hand, certifies that the strategy is a profitable one, with a 99% probability. A rational person would act accordingly in the selection of strategies, and set his emotions in accordance with his results. Yet I have experienced leaps of joy over results that I knew were mere noise, and bouts of unhappiness over results that did not carry the slightest degree of statistical significance.

Since my heart does not seem to agree with my brain, I need to take serious action to avoid making irrational trading decisions, namely, by denying myself access to my performance report unless it hits a predetermined threshold. This is no different from the divorce between my brain and my appetite when it comes to the consumption of chocolate: I generally deal with it by ascertaining that there are no chocolate boxes under my trading desk. Moreover, I consider myself lucky for not having a cigarette addiction. For the best way to understand how we could be rational in our perception of the risks and probabilities and, at the same time, be foolish while acting on them, would be to have a conversation with a cigarette smoker. For few cigarette smokers remain unaware of the fact that lung cancer strikes one in three of their population. If you remain unconvinced, take a look at the huddling smoking crowd outside the gate of the Memorial-Sloan Kettering Cancer Center in New York city's upper East side. You will see dozens of cancer nurses (and, perhaps, doctors) standing outside the entrance with a cigarette in hand --as terminal and often hopeless patients are wheeled-in for their treatments.

Part 3: Wax in my Ears

Odysseus, the Homerian hero, had the reputation of using guile to overcome stronger opponents. I find the most spectacular use of such guile was against no other opponent than himself.

In book 12 of the Odyssey, the hero encounter the sirens, on an island not far from the rocks of Caribde and Scylla. Their song are known to charm the sailors into madness, causing them to irresistibly cast themselves into the sea off the sirens’ coast, and perish. The indescribable beauty of the sirens’ songs is contrasted with the moldering corpses of sailors that stray the area around them. Odysseus, forewarned by Circe, contrives the following ruse. He fills the ears of all his men with wax, to the point of total deafness, and has himself tied to the mast. The sailors are under strict instructions not to release him. As they approach the sirens’ island, the sea is calm and over the water comes the sound of a music so ravishing that Odysseus struggles to get loose, expending an inordinate amount of energy to unrestrain himself. His men tie him even further, until they are safely past the poisoned sounds.

The first lesson I took from the story is not to even attempt to be Odysseus. He is a mythological character and I am not. He can be tied to the mast; I merely can reach the rank of a sailor who needs to have his ears filled with wax.

I am Not so Intelligent

The epiphany I had in my career in randomness came when I understood that I was not intelligent enough, nor strong enough, to even try to fight my emotions (besides I did believe that I needed 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 not very smart. Period. Just like every single character in this book whom I ridiculed. Not only that, but I may be even worse than them because there may be a negative correlation between beliefs and behavior. The difference with those I ridicule is that I try to be aware of it.

No matter how long I can 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. I experience leaps of joy upon seeing a profitable day, even if it is not statistically significant. Likewise I experience sadness after a "bad" day, without the ability to reason myself to put things back into perspective. As a matter of fact I no longer try to "put things back into perspective", as my attempts to impose a structure of reason over my emotions have proved futile, entirely futile, hopelessly futile.

Such unintelligent behavior does not just cover probability and randomness. I do not think I am reasonable enough to avoid getting angry when a discourteous driver blows his horn at me for being one nanosecond late after a green light. I am fully aware that such anger is self-destructive and offers no benefit, that if I were to develop anger for every idiot around me doing something of the sort, I would be long dead. These small daily emotions are not rational. But we need them to function properly. We are designed to respond to hostility with hostility. I have enough enemies to have some spice in my life, but I sometimes wish I had a few more. Life would be unbearably bland if we had no enemies on whom to waste efforts and energy.

The good news is that there are tricks. One such trick is to avoid eye contact (through the rear-view mirror) with other persons in such encounters as traffic situations. I try to imagine that the other person is a Martian, rather than a human being. It works sometimes –but it works best when the person presents the appearance of being from a different species. I am an avid road cyclist. Recently, as I was, along with other cyclists, slowing down traffic in a rural area, a small woman in a giant sports utility vehicle opened her window and heaped curses at us. Not only did it not upset me but I did not even interrupt my thoughts to pay attention. When I am on my bicycle people in large trucks become a variety of dangerous animals, capable of threatening me but incapable of making me angry.

I have, like anyone with strong opinions, a collection of critics among finance academics and economists, annoyed by my attacks on their misuse of probability and unhappy of my branding them as pseudoscientists. I am incapable to tame my emotions when reading their comments. The best I can do is just not read them. Wax in my ears.

The Odyssean Mute Command

Recall that the accomplishment from which I derive the most pride is my weaning myself from television and the news media. I am currently so weaned that it actually costs me more energy to watch television than to perform any other activity, like, say, writing this book. But this did not come without tricks. Without tricks I would not escape the toxicity of the information age. In my office I currently have the television set turned on all day with the financial news channel CNBC staging commentator after commentator and CEO after CEO murdering rigor all day long. What is the trick? I have the volume turned completely off. Why? Because when the television set is silent, the babbling person looks ridiculous, exactly the opposite effect as when the sound is on. One sees a person with moving lips and contortions in their facial muscles, taking themselves seriously –but no sound comes out. We are visually intimidated but not auditorily, which causes a dissonance. The speaker’s face expresses some excitement, but since no sound comes out, the exact opposite is conveyed. This is the sort of contrast the philosopher Henri Bergson had in mind in his Treatise on Laughter, with his famous description of the gap between the seriousness of a gentleman about to walk on a banana peal and the comical aspect of the situation. Television pundits lose their intimidating effect; they even look ridiculous. They seem to be excited about nothing. Suddenly pundits become clowns, which is a reason the writer Graham Greene refused to go on television.

I had this idea of stripping people from language while, on a foreign trip, I listened to a speech in Cantonese, a language I do not understand, without the benefit of translation. Since I had no possible clue about his subject, the orator lost a large share of his dignity. The idea came to me that perhaps I could use a genetic bias, here, prejudice, to offset another genetic bias, our predisposition to take information seriously. It seems to work.

This section, the conclusion of this book, discusses both the incidence of gamblers ticks and my personal efforts and failures in averting being a fool of randomness –for I have personally failed.

Table of Contents

Part 2 : Monkeys on a Typewriter