Fooled by Randomness (8 page)

A Different Kind of Earthquake

Try the following experiment. Go to the airport and ask travelers en route to some remote destination how much they would pay for an insurance policy paying, say, a million tugrits (the currency of Mongolia) if they died during the trip (for any reason).Then ask another collection of travelers how much they would pay for insurance that pays the same in the event of death from a terrorist act (and only a terrorist act). Guess which one would command a higher price? Odds are that people would rather pay for the second policy (although the former includes death from terrorism). The psychologists Daniel Kahneman and Amos Tversky figured this out several decades ago. The irony is that one of the sampled populations did not include people on the street, but professional predictors attending some society of forecasters’ annual meeting. In a now famous experiment they found that the majority of people, whether predictors or nonpredictors, will judge a deadly flood (causing thousands of deaths) caused by a California earthquake to be more likely than a fatal flood (causing thousands of deaths) occurring somewhere in North America (which happens to include California). As a derivatives trader I noticed that people do not like to insure against something abstract; the risk that merits their attention is always something vivid.

This brings us to a more dangerous dimension of journalism. We just saw how the scientifically hideous George Will and his colleagues can twist arguments to sound right without being right. But there is a more general impact by information providers in biasing the representation of the world one gets from the delivered information. It is a fact that our brain tends to go for superficial clues when it comes to risk and probability, these clues being largely determined by what emotions they elicit or the ease with which they come to mind. In addition to such problems with the perception of risk, it is also a scientific fact, and a shocking one, that both risk detection and risk avoidance are not mediated in the “thinking” part of the brain but largely in the emotional one (the “risk as feelings” theory). The consequences are not trivial: It means that rational thinking has little, very little, to do with risk avoidance. Much of what rational thinking seems to do is rationalize one’s actions by fitting some logic to them.

In that sense the description coming from journalism is certainly not just an unrealistic representation of the world but rather the one that can fool you the most by grabbing your attention via your emotional apparatus—the
cheapest to deliver
sensation. Take the mad cow “threat” for example: Over a decade of hype, it only killed people (in the highest estimates) in the hundreds as compared to car accidents (several hundred thousands!)—except that the journalistic description of the latter would not be commercially fruitful. (Note that the risk of dying from food poisoning or in a car accident on the way to a restaurant is greater than dying from mad cow disease.) This sensationalism can divert empathy toward wrong causes: cancer and malnutrition being the ones that suffer the most from the lack of such attention. Malnutrition in Africa and Southeast Asia no longer causes the emotional impact—so it literally dropped out of the picture. In that sense the mental probabilistic map in one’s mind is so geared toward the sensational that one would realize informational gains by dispensing with the news. Another example concerns the volatility of markets. In people’s minds lower prices are far more “volatile” than sharply higher moves. In addition, volatility seems to be determined not by the actual moves but by the tone of the media. The market movements in the eighteen months after September 11, 2001, were far smaller than the ones that we faced in the eighteen months prior—but somehow in the mind of investors they were very volatile. The discussions in the media of the “terrorist threats” magnified the effect of these market moves in people’s heads. This is one of the many reasons that journalism may be the greatest plague we face today—as the world becomes more and more complicated and our minds are trained for more and more simplification.

Proverbs Galore

Beware the confusion between correctness 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 Boileau’s adage:

What is easy to conceive is clear to express / Words to say it would come effortlessly.

The reader can imagine my disappointment at realizing, while growing up as a practitioner of randomness, that most poetic sounding adages are plain wrong. Borrowed wisdom can be vicious. I need to make a huge effort not to be swayed by well-sounding remarks. I remind myself of Einstein’s remark that common sense is nothing but a collection of misconceptions acquired by age eighteen. Furthermore,
What sounds intelligent in a conversation or a meeting, or, particularly, in the media, is suspicious.

Any reading of the history of science would show that almost 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
Times
(of London) journalist in 1905 that time slows down when one travels (even the Nobel committee never granted Einstein the prize on account of his insight on special relativity). Or to someone with no exposure to physics that there are places in our universe where time does not exist. Try to explain to Kenny that, although his star trader “proved” to be extremely successful, I have enough arguments to convince him that he is a dangerous idiot.

Risk Managers

Corporations and financial institutions have recently created the strange position of risk manager, someone who is supposed to monitor the institution and verify that it is not too deeply involved in the business of playing Russian roulette. Clearly, having been burned a few times, the incentive is there to have someone take a look at the generator, the roulette that produces the profits and losses. Although it is more fun to trade, many extremely smart people among my friends (including Jean-Patrice) felt attracted by such positions. 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: While a ten-year survival rate for a trader is in the single digits, that of a risk manager is close to 100%). “Traders come and go; risk managers are here to stay.” I keep thinking of taking such a position both on economic grounds (as it is probabilistically more profitable) and because the job offers more intellectual content than the one consisting in just buying and selling, and allows one to integrate research and execution. Finally, a risk manager’s blood has smaller quantities of the harmful kind of stress hormones. But something has held me back, aside from the irrationality of wanting the pains and entertainment from the emotions of speculation. The risk managers’ job feels strange: 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 stop short of 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.

Epiphenomena

From the standpoint of an institution, the existence of a risk manager has less to do with actual risk reduction than it has to do with the
impression
of risk reduction. Philosophers since Hume and modern psychologists have been studying the concept of epiphenomenalism, or when one has the illusion of cause-and-effect. Does the compass move the boat? By “watching” your risks, are you effectively reducing them or are you giving yourself the feeling that you are doing your duty? Are you like a chief executive officer or just an observing press officer? Is such illusion of control harmful?

I conclude the chapter with a presentation of the central paradox of my career in financial randomness. By definition, I go against the grain, so it should come as no surprise that my style and methods are neither popular nor easy to understand. But I have a dilemma: On the one hand, I work with others in the real world, and the real world is not just populated with babbling but ultimately inconsequential journalists. So my wish is for people in general to remain fools of randomness (so I can trade against them), yet for there to remain a minority intelligent enough to value my methods and hire my services. In other words, I need people to remain fools of randomness, but not all of them. I was fortunate to meet Donald Sussman, who corresponds to such an ideal partner; he helped me in the second stage of my career by freeing me from the ills of employment. My greatest risk is to become successful, as it would mean that my business is about to disappear; strange business, ours.

Three

•

A MATHEMATICAL MEDITATION ON HISTORY

Europlayboy Mathematics

T
he 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 that includes the square root of minus one, 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 Europlayboy 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 in compact sentences. 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 this book were created with my Monte Carlo generator, which I introduce in this chapter. Yet it is far more a way of thinking than a computational method. Mathematics is principally a tool to meditate, rather than to compute.

The Tools

The notion of alternative histories discussed in the last chapter can be extended considerably 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. Monte Carlo methods, in brief, consist of creating artificial history using the following concepts.

First, consider the 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 scenarios along the course of time. We are not just concerned with where a bird can end up tomorrow night, but rather with 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. Now, a sample path can be either deterministic or random, which brings the next distinction.

A
random sample path,
also called a random run, is the mathematical name for such a succession of virtual historical events, starting at a given date and ending at another, except that they are subjected to some varying level of uncertainty. However, the word
random
should not be mistaken for equiprobable (i.e., having the same probability). Some outcomes will give a higher probability than others. An example of a random sample path can be the body temperature of your explorer cousin during his latest bout with typhoid fever, measured hourly from the beginning to the end of his episode. It can also be a simulation of the price of your favorite technology stock, measured daily at the close of the market, over, say, one year. Starting at $100, in one scenario it can end up at $20 having seen a high of $220; in another it can end up at $145 having seen a low of $10. Another example is the evolution of your wealth during an evening at a casino. You start with $1,000 in your pocket, and measure it every fifteen minutes. In one sample path you have $2,200 at midnight; in another you barely have $20 left for a cab fare.

Stochastic processes refer to the dynamics of 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.

What is a Monte Carlo generator? Imagine that you can replicate a perfect roulette wheel in your attic without having recourse to a carpenter. Computer programs can be written to simulate just about anything. They are even better (and cheaper) than the roulette wheel built by your carpenter, as this physical version may be inclined to favor one number more than others owing to a possible slant in its build 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 eighteen-year-old Christian Lebanese successively playing 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 1980s, particularly in the theories of the random walk of asset prices. Clearly, we have to say that the example of Russian roulette does not need 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 “true” mathematicians do not like Monte Carlo methods. They believe 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’s 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; neither is mathematics.

I am not a “native” mathematician, that is, I am someone who does not speak mathematics as a native language, but someone who speaks it with a trace of a foreign accent. For 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 of concentrating 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. Those of us in the second category 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 of 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 into 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 suspended particles in a stationary liquid. His article on the theory of the Brownian movement can be used as the backbone of the random walk approach used in financial modeling. As for 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 his account after experiencing excessive opulence—people’s understanding of probability does not translate into their behavior).

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. We will not get into the topic until later in the book.

FUN IN MY ATTIC

Making History

In the early 1990s, 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, on ski slopes, or, more effectively, on a park bench). 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 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, earnings reports, economic forecasts, sports results, and, not least, office politics, I started toying with it in fields bordering 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 5
. 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 of their evolution. Naturally the analog to fabricating populations of Zorglubs was to simulate a population of “idiotic bull,” “impetuous bear,” and “cautious” traders under different market regimes, say booms and busts, and to 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 that ultimately almost nobody really survived; bears dropped out like flies in the rally and bulls ended up being slaughtered, as paper profits vanished when 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.