Crunched by the market’s numbers

For those readers who take the term “bestselling author-mathematician� for an oxymoron to rival “jumbo shrimp� or “smart bomb,� here’s news: It’s not a null set.

John Allen Paulos’ many previous titles (perhaps the breakthrough having been “Innumeracy: Mathematical Illiteracy and Its Consequences�) have won both praise from colleagues and the enthusiasm of a broad and growing readership.

Paulos is the real McCoy, and his newest offering, “A Mathematician Plays the Stock Market,� is a double-chocolate nougat of a book -- a rich, densely packed delight. It is also rueful, funny and disarmingly personal.

Back in the halcyon days of 1999, Paulos was blessed with a modest unexpected windfall and invested the sum in a hot, marked-for-growth tech stock called WorldCom. From this fateful point, his story’s trajectory runs as relentlessly downward as that of any tragic Greek protagonist.

The stock’s price slides. At each decision juncture, Paulos opts to purchase yet more at the lower price, “averaging down� his cost base, while awaiting the inevitable rebound. “There was apparently a loose connection between my brain and my fingers, which kept clicking the ‘buy’ button on my Schwab on-line account.�

As the freefall continues, he buys more on margin, having abandoned principle, discipline and rationality, the Apollonian virtues, for a Dionysian orgy of wild infatuation. As the full wrath of the gods unfolds, however, Paulos realizes that his one-way affair has become, although “occasionally exciting ... for the most part anxiety-inducing and pleasureless, not to mention costly.�

How many souls hurtling toward investors’ perdition can manage to keep their eyes as wide-open as did Paulos, the lapsed mathematician? Like a traveler returned from the realm of the shades, he chronicles, describes and meticulously dissects the multitude of conceptual chimeras he encountered along the way (such wonders as Elliott waves and chartism).

Beyond these monsters, however, the rationality-seeking investor faces even more harrowing challenges: those that come from within. Because, as the numbers man can testify, “we’re all subject to other sorts of counterproductive behavior that spring from cognitive blind spots that are analogues, perhaps, of optical illusions.�

Among the blind spots he points out are “the anchoring effect,� “gambler’s fallacy,� “data-mining� and “confirmation bias.� And while the general public may perceive much “bad� investing as stemming from recklessness, one of the most notorious counterproductive behaviors is actually excess risk aversion, studied at length by Amos Tversky and Daniel Kahneman (Nobel in economics, 1997). Not all of these phenomena are easy to grasp; they are by nature counterintuitive. Paulos does as lucid a job of explaining and illustrating the operative principles as any writer I’ve encountered. But then, Andre Agassi makes serving look easy.

It is one thing to unmask monsters; it is another to sift apparently plausible and sober market stratagems for content and durability. The stock-playing advice “literature� since the Keynesian revolution has accumulated a wealth of prescriptions worth at least a look.

Perhaps the most prominent groupings are value investing -- or fundamental analysis -- and ratio analysis. Paulos often finds something to like logically, or at least to entertain. In an engaging aside, he explores “the parallel between diet and investment regimens

The concluding chapters of this astonishingly succinct report push on into fairly rough conceptual territory -- from the arcane world of longs and shorts, puts and calls and derivatives, to the mathematically ascertainable universe of uncertainty, as it plays out in such constructs as expected and future values, variance, standard deviation.

In other words, just about every theoretical thing the practical stock investor should be aware of is named and explained. Call this book “everything I ever wanted to know about multifractal price changes but was afraid to ask.� I could have used it in business school. I can use it now.