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New math

John Allen Paulos was your basic bull market knucklehead.

In early 2000 Paulos plowed his money into the still­high-flying stock of telecommunications giant WorldCom and then doubled down on margin over the next 18 months as the stock dialed back from $47 to $5. Before he lost his dignity along with his shirt, Paulos became a denizen of online WorldCom chat rooms, lured friends and family into investing in the doomed stock and eventually even e-mailed WorldCom CEO Bernard Ebbers, offering to help write more persuasive press releases. Finally, months before the stock completely collapsed, Paulos sold at a big loss.

What makes Paulos's foolishness worth pondering is the fact that he is a world-famous smart guy. A professor of mathematics at Temple University in Philadelphia, Paulos has written a number of celebrated books, including the bestseller Innumeracy, about the consequences of widespread mathematical illiteracy in America.

In A Mathematician Plays the Stock Market, Paulos provides an entertaining and instructive account of his plunge into maniacal investing. Professors, of course, are as susceptible to greed as anyone, and Paulos offers no explanation for his behavior beyond the fact that he was just another small investor caught up in the "transient delirium" of the bull market. But unlike the average day trader, this professor uses his own painful investing experience to analyze the ways in which statistical principles and human behavior intersect -- and often collide -- in the financial markets.

Paulos is writing for a mass-market audience, and many of the topics covered in the book, from the academic debate over stock market efficiency to the popular paradoxes of behavioral finance, will be familiar to investment professionals.

Still, many pros will appreciate how the author deftly skewers the popular field of technical analysis. Since the stock market imploded in 2001, the practice of predicting stock moves based on the eyeballing of historical charts appears to be enjoying a surge in popularity. The Internet analysts who once filled financial television shows have been replaced by chartists who claim to be able to forecast every move of the market based on "head and shoulders" patterns or "Elliott waves."

As a mathematician, Paulos believes that stock movements could, in theory, be predicted by analyzing historical charts. In fact, as he notes, some very serious quantitative economists, including Andrew Lo of the Massachusetts Institute of Technology and Craig MacKinlay of the Wharton School of the University of Pennsylvania, have recently documented evidence of a slight positive correlation in short-term stock market returns, suggesting that there may be a momentum in the markets that could be exploited by technical analysts. The technical analysis community has jumped on these academic studies as proof of the validity of their approach.

Paulos, however, dismisses the technical analysis that he has reviewed as either flimsy or flawed. "The justification for technical analysis is murky at best," he warns. "To the extent that there is one, it most likely derives from psychology, or perhaps from some as yet unarticulated systemic interactions. 'Unarticulated' is the key word here: The jargon of technical analysis seldom hangs together as a coherent theory."

The author's deconstruction of technical analysis makes a larger point. Although rigorous mathematical analysis is at the heart of sound investing, mathematical mumbo jumbo can also be the ultimate financial snake oil. Equations, algorithms and Greek letters can look impressive even if people don't understand what they mean. In the mid-1990s, for example, the application of "chaos theory" became all the rage, until econometricians pointed out that the mathematics, however lovely, had little to do with finance.

Paulos is back to owning mostly index funds, but he confesses to still wondering whether his WorldCom investment could have been rationalized, after the fact, if just a few things had turned out differently. Hope springs eternal, even for mathematicians, but it does not always compute. 

Hal Lux, director of research at Paloma Partners Management Co., is a Senior Contributing Editor at Institutional