Fooled by Randomness (6 page)

YOUR DENTIST IS RICH, VERY RICH

We close this chapter with a hint on the next discussion of resistance to randomness. Recall that Nero can be considered prosperous but not “very rich” by his day’s standards. However, according to some strange accounting measure we will see in the next chapter, he is extremely rich
on the average of lives
he could have led—he takes 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 protects 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 discussing only his professional life, excluding his (sometimes volatile) private one.

Arguably,
in expectation,
a dentist is considerably richer than the rock musician who is driven in a pink Rolls Royce, 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 eight hours a day over the past thirty-five years. Clearly one can say that, thanks to the dullness of his career, if John Doe B had to relive his life a few thousand times since graduation from dental school, the range of possible out-comes 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 semideserted town full of trailers in the Catskills. Furthermore, assuming he graduated from a very prestigious teeth-drilling school, the range of out-comes 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 on 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 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, as we saw with Solon’s warning, can be far more potent (and provide us with more experience) than plain reality.

Two

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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 courses 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 voiced only by people who fail (those who succeed attribute their success to the quality of their decision). Such opinion—“that I followed the best course”—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.

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 containing one bullet in the six available chambers 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 observed in reality; 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). Like almost every executive I have encountered during an eighteen-year career on Wall Street (the role of such executives in my view being no more than 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 Russian 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 twenty-five-year-old played Russian roulette, say, once a year, there would be a very slim possibility of his surviving until his fiftieth birthday—but, if there are enough players, say thousands of twenty-five-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 Russian roulette is more than intellectual to me. I lost a comrade to this “game” during the Lebanese war, when we were in our teens. But there is more. I discovered that I had more than a shallow interest in literature thanks to the effect of Graham Greene’s account of his flirt with such a game; 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 at the thought that I had at least a one in six probability of having been without his novels.

The reader can see my unusual notion of alternative accounting: $10 million earned through Russian roulette does 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 but consider them as qualitatively different. The notion of such alternative accounting has interesting intellectual extensions and lends itself to mathematical formulation, as we will see in the 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 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.

Possible Worlds

Note that these ideas of alternative histories have been covered by separate disciplines in intellectual history, worth presenting quickly because they all seem to converge on the same concept of risk and uncertainty (certainty is something that is likely to take place across the highest number of different alternative histories; uncertainty concerns events that should take place in the lowest number of them).

In philosophy, there has been considerable work on the subject starting with Leibniz’ idea of possible worlds. For Leibniz, God’s mind included an infinity of possible worlds, of which he selected just one. These nonselected worlds are worlds of possibilities, and the one in which I am breathing and writing these lines is just one of them that happened to have been executed. Philosophers also have a branch of logic that specializes in the matter: whether some property holds
across all possible worlds
or if it holds across a single world—with ramifications into the philosophy of language called
possible worlds semantics
with such authors as Saul Kripke.

In physics, there is the many-world interpretation in quantum mechanics (associated with the works of Hugh Everett in 1957) which considers that the universe branches out treelike at each juncture; what we are living now is only one of these many worlds. Taken at a more extreme level, whenever numerous viable possibilities exist, the world splits into many worlds, one world for each different possibility—causing the proliferation of parallel universes. I am an essayist-trader in one of the parallel universes, plain dust in another.

Finally, in economics: Economists studied (perhaps unwittingly) some of the Leibnizian ideas with the possible “states of nature” pioneered by Kenneth Arrow and Gerard Debreu. This analytical approach to the study of economic uncertainty is called the “state space” method—it happens to be the cornerstone of neoclassical economic theory and mathematical finance. A simplified version is called “scenario analysis,” the series of “what-ifs” used in, say, the forecasting of sales for a fertilizer plant under different world conditions and demands for the (smelly) product.

An Even More Vicious Roulette

Reality is far more vicious than Russian roulette. First, it delivers the fatal bullet rather infrequently, like a revolver that would have hundreds, even thousands, of chambers 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
black swan problem,
which we cover in
Chapter 7
, as it is linked to the problem of induction, a problem that has kept a few thinkers awake at night. It is also related to a problem called
denigration of history,
as gamblers, investors, and decision-makers feel that the sorts 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 calling 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, and never consider the losers. The game seems terribly easy and we play along carelessly. Even scientists with all their sophistication in calculating probabilities cannot deliver any meaningful answer about the odds, since knowledge of these depends on our witnessing the barrel of reality—of which we generally know nothing.

Finally, there is an ingratitude factor in warning people about something abstract (by definition anything that did not happen is abstract). Say you engage in a business of protecting investors from rare events by constructing packages that shield them from their sting (something I have done on occasion). Say that nothing happens during the period. Some investors will complain about your spending their money; some will even try to make you feel sorry: “You wasted my money on insurance last year; the factory did not burn, it was a stupid expense. You should only insure for events that happen.” One investor came to see me fully expecting me to be apologetic (it did not work). But the world is not that homogeneous: There are some (though very few) who will call you to express their gratitude and thank you for having protected them from the events that did not take place.

SMOOTH PEER RELATIONS

The degree of resistance to randomness in one’s life is an abstract idea, part of its logic counterintuitive, and, to confuse matters, its realizations nonobservable. 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 in 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 (or, in Nero’s case, the minute arcane details and petty arguments). 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. A mathematician is absorbed in what goes into his head while a scientist searches into what is outside of himself.) 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 (in the many-world interpretation) and ignoring the one that actually took place.

Some traders can be unexpectedly introspective about randomness. Not long ago I had dinner at the bar of a Tribeca restaurant with Lauren Rose, a trader who was reading an early draft of this book. We flipped a coin to see who was going to pay for the meal. I lost and paid. He was about to thank me when he abruptly stopped and said that he paid for half of it
probabilistically.

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 1980s, 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 hundreds of MBAs of my generation I met on Wall Street in the 1980s still engage in such forms of professional and disciplined risk taking.

Salvation via Aeroflot

The 1990s witnessed the arrival of people of richer and more interesting backgrounds, which made the trading rooms far more entertaining. I was saved from the conversation of MBAs. 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 an increase in the already high demand for scientists on Wall Street, owing to the rapid development of financial instruments. The dominant 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 who fit the stereotype. Indeed, by the late 1990s 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.