"Where Are You Getting Your Probabilities?"

June 11, 2008

Book Review
James Case

The Black Swan: The Impact of the Highly Improbable. By Nassim Nicholas Taleb, Random House, New York, 2007, 400 pages, $26.95.

Nassim Nicholas Taleb was born in 1960, in the ancient town of Amioun, in the northern part of Lebanon. His politically prominent Greek Orthodox family once owned significant tracts of land in the area. He saw the country transformed---as he puts it---from "paradise to Hell in six months," following the outbreak of the Lebanese war in 1975. He also saw his grandfather, a former deputy prime minister, obliged to live out his days in a dowdy Athens apartment. The main lesson Taleb draws from the turmoil of his youth is that luck is more important for worldly success---relative to individual words and deeds---than the successful care to admit. Indeed, that very conviction became the thesis of his first non-technical book---Fooled by Randomness---published in English in 2001 and subsequently translated into 19 other languages.

Taleb, whose first language is French, boasts literary fluency in English and classical Arabic, conversational fluency in Italian and Spanish, and sufficient command of Greek, Latin, Aramaic, biblical Hebrew, and the Canaanite script to read ancient texts. He holds an MBA from the Wharton School at the University of Pennsylvania, and a PhD in financial mathematics from Université Paris–IX (Dauphine). After an 18-year career as a Wall Street trader, he has achieved whatever degree of financial in-dependence he deems necessary for pursuing a second career as an essayist, public intellectual, and "philosopher of chance."
Taleb has a habit of bestowing polysyllabic names on the simplest of concepts.

The "Ludic fallacy" is the trap awaiting those who take too seriously their estimates of the probabilities needed to compute risk, especially when those estimates are derived from an assumed Gaussian distribution. The "empty-suit problem" (or "expert problem") is that many so-called experts are no more knowledgeable than the rest of the population in their alleged fields of expertise, yet (despite track records documenting their cluelessness) continue to be accepted as experts. Clinical psychologists, academic economists, risk managers, CEOs, political and military analysts are among those he identifies as empty suits. Also in that category are "Locke's madmen"---people who predicate impeccable logic on demonstrably faulty premises: Economists (and Nobel laureates all) Paul Samuelson, Robert Merton, and Gerard Debreu are among the guiltiest, in Taleb's far from humble opinion, because their "phony models of uncertainty" expose the rest of us to undue risk from black swans.

The inclusion of Debreu on the foregoing list suggests, at least to this reviewer, that Taleb underestimates the distance between financial and mainstream economics. Although some economists have become prominent in both branches of the field, Debreu never did; his work never wandered far from the mainstream. Milton Friedman (another Nobel prize winner) apparently went to his grave denying that finance even was a branch of economics.

The black swan of the book's title arises from David Hume's discussion of inductive logic and the fragility of knowledge gained from experience. Modern philosophers credit Hume for the observation that a single non-conforming instance can invalidate any empirical generalization. Hume famously illustrated his point by recalling that (during his own lifetime) the notion that all swans are white had been discredited by the discovery of black swans in Australia. Taleb uses Hume's black swan as a prototype for the unpredictable events---such as the 1975 outbreak of the Lebanese war, in what had long seemed the most peaceful and tolerant of nations---that largely govern the course of history. His first example is the experience of the Mirage Hotel and Casino in Las Vegas.

Taleb relates the incidents leading to the four largest losses incurred or narrowly averted by the hotel and casino: (i) a tiger attacked Roy, of Siegfried and Roy, the firm's signature tourist attraction; (ii) a contractor injured during repairs to the casino took umbrage at what he considered an inadequate settlement offer, and attempted to destroy the facility by detonating explosives attached to the pillars in the basement; (iii) an accounting executive was found to have accumulated certain meticulously completed tax forms in a box under his desk for several years in lieu of filing them with the IRS, thereby exposing the firm to a multitude of fines and back taxes; and (iv) the casino owner was caught dipping into company funds---a violation of Nevada gambling laws--in his haste to ransom his kidnapped daughter.

The hundreds of thousands of dollars spent on gambling theory and model building did nothing to prepare the firm for such catastrophes, each far more costly than any undetected card-counting team from MIT or cheating dealer could have been. Mirage had actually looked into insurance against an attack on a member of the audience by one of Roy's tigers, without entertaining the possibility of an attack on Roy---who had raised the errant creature from a cub, even allowing it to share his bedroom on occasion. How was anyone to imagine such possibilities, Taleb asks, much less estimate the likelihood of their occurrence?

Despite his disdain for the economics profession, Taleb credits University of Chicago economist Frank Knight (1885–1972) with publicizing the distinction between risk, in which there is a credible way of attaching probabilities to the potential effects of a given cause, and uncertainty, in which there is no credible way of doing so. Taleb considers it inexcusable that the two subjects are carelessly intermingled in the classroom, typically with reference to games of chance, in which the relevant probabilities are either obvious or easily calculated. In real life, he argues, the unknowability of key probabilities adds a second (and often dominant) layer of risk.

Because he formulated his ideas while working in finance, Taleb tends to present them in financial terms and to illustrate his points with financial examples. In fact, in their current abstract form, his ideas are much more widely applicable. He points to one of his favorite gadfly questions---which he claims to ask whenever he catches economists and financial engineers pontificating about risk: "Where are you getting your probabilities?" Far too often, he maintains, the answer involves Gaussian normal distributions.

Taleb is well aware that Eugene Fama, who began to study financial markets in the 1960s, soon noted that stock price increments in excess of five standard deviations occur every three or four years, whereas Gaussian normal increments of that magnitude would be observed but once in seven thousand years. As a result, histograms of stock price movements invariably exhibit fat tails, in the sense that extremely large (positive or negative) increments are far more frequent than (Gaussian) normality can account for. These extremely large stock price increments are the black swans of Wall Street, and Taleb has devised an investment strategy to exploit their existence.

In essence, Taleb's strategy consists of buying extraordinarily large numbers of dirt-cheap options. They are cheap because they pay off only on some highly unlikely event; the vast majority expire unexercised. Visiting Taleb a few years ago, the writer Malcolm Gladwell* found that the firm had earned back only 85% of its same-day expenditures on the previous day, 48% the day before, 65% the day before that. . . . On a typical day, the firm loses money. Only on the rare good days does it earn a profit. But when a black swan lands, the profits can be spectacular.

As Gladwell observed, it takes intestinal fortitude to execute such a strategy. Most investors want their 401(k)s, mutual funds, and even hedge fund accounts to appreciate at a relatively steady pace. They sleep poorly when their net worth waxes and wanes abruptly, even though the long-term trend is positive. Only extreme confidence in the inevitability of black swans in financial markets can justify such an investment strategy. In part by surrounding himself with colleagues who shared his confidence, Taleb was able to stick to his guns long enough to reap the rewards of knowing that highly improbable events are underbet on Wall Street.

It would be a mistake to dismiss Taleb as a tiresome blowhard, however verbose his writing style may seem. Buried within his thoughts on probability, risk, and uncertainty is a coherent story about important and frequently overlooked features of the modern world. Readers prepared to separate Taleb's thought-provoking wheat from his often verbose chaff will find the effort rewarding.

* The New Yorker, April 22 and 29, 2002.

James Case writes from Baltimore, Maryland.

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