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 experi
encing 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.
If the tone of this book seems steeped in the culture of Darwinism and evolutionary thinking, it does not come from any remotely formal training in the natural sciences, but from the evolutionary way of thinking taught by my Monte Carlo simulators.
I 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 nonrealized 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 subatomic particles.
Using my Monte Carlo to make and remake history reminded me of the experimental novels (the so-called new novels) by such writers as Alain Robbe-Grillet, popular in the 1960s and 1970s. There the same chapter would be written and revised, the writer each time changing the plot like a new sample path. Somehow the author was freed from the past situation he helped create and allowed himself the indulgence to change the plot retroactively.
Denigration of History
One more word on history seen from a Monte Carlo perspective. The wisdom of such classical stories as Solon’s prods me to spend even more time in the company of the classical historians, even if the stories, like Solon’s warning, have benefited from 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 pseudoscientific historicism leading to such calls as the end of history (it is pseudoscientific because it draws theories from past events without allowing for the fact that such combinations of events might have arisen from randomness; there is no way to verify the claims in a controlled experiment). For me, history is of use merely at the level of my desired 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 mental defect that seems to block my ability to learn from others. It is the respect of the elders that I would like to develop, reinforcing the awe I instinctively 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
As I mentioned above, it is not natural for us to learn from history. We have enough clues to believe that our human endowment does not favor transfers of experience in a cultural way but through selection of those who bear some favorable traits. It is a platitude that children learn only from their own mistakes; they will cease to touch a burning stove only 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. This point has been examined by behavioral economics pioneers Daniel Kahneman and Amos Tversky with regard 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 on a grand scale.
If you think that merely reading history books would help you learn “from other’s mistakes,” consider the following nineteenth-century experiment. In a well-known psychology case the Swiss doctor Claparède had an amnesic patient completely crippled with her ailment. Her condition was so bad that he would have to reintroduce himself to her at a frequency of once per fifteen minutes for her to remember who he was. One day he secreted a pin in his hand before shaking hers. The next day she quickly withdrew her hand as he tried to greet her, but still did not recognize him. Since then plenty of discussions of amnesic patients show some form of learning on the part of people witho
ut their being aware of it and without it being stored in conscious memory. The scientific name of the distinction between the two memories, the conscious and the nonconscious, is declarative and nondeclarative. Much of the risk avoidance that comes from experiences is part of the second. The only way I developed a respect for history is by making myself aware of the fact that I was not programmed to learn from it in a textbook format.
Actually, things can be worse than that: In some respects we do not learn from our own history. Several branches of research have been examining our inability to learn from our own reactions to past events: For example, people fail to learn that their emotional reactions to past experiences (positive or negative) were short-lived—yet they continuously retain the bias of thinking that the purchase of an object will bring long-lasting, possibly permanent, happiness or that a setback will cause severe and prolonged distress (when in the past similar setbacks did not affect them for very long and the joy of the purchase was short-lived).
All of my colleagues who I have known to denigrate history blew up spectacularly—and I have yet to encounter some such person who has not blown up. But the truly interesting point lies in the remarkable similarities in their approaches. The blowup, I will repeat, is different from merely incurring a monetary loss; it is losing money when one does not believe that such fact is possible at all. There is nothing wrong with a risk taker taking a hit provided one declares that one is a risk taker rather than that the risk being taken is small or nonexistent. Characteristically, blown-up traders think that they knew enough about the world to reject the possibility of the adverse event taking place: There was no courage in their taking such risks, just ignorance. 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 débâcle of 1994, those who blew up in Russia in 1998, and those who blew up shorting Nasdaq stocks. 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 after 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.
Fooled by Randomness Page 8
