The result is an informative and, for the most part, richly entertaining guide to investment in the stock market, starting with the question Mr. Paulos used to think he knew the answer to: Do any strategies for playing the market outperform broad-gauge stock-index funds? If, as Mr. Paulos suspects, the answer is a resounding no, then why do so many of us spend so much time and energy playing the market?
Mr. Paulos tackles this second question first, for he recognizes that in his own case he was following no particular investment strategy, but instead had, in an entirely unanalytic fashion, simply gotten carried away. Listing the common mistakes which overenthusiastic investors make, he ruefully acknowledges that he made most of them himself. He was a victim of hype to begin with, listening to analysts like Jack Grubman, who were rating WorldCom shares a strong buy, and convincing himself of the high-tech sector’s rosy prospects. Then, after his initial purchase of shares, Mr. Paulos fell prey to confirmation bias, relentlessly searching for good news about the company and ignoring bad news and warning signs. He succumbed to the anchoring effect, moreover, in which people remain irrationally attached to the first number they encounter in a transaction—having bought shares at $47, Mr. Paulos saw this as a minimum "natural" level to which WorldCom shares would have to return. Worse, as the price of the stock declined, Mr. Paulos bought more shares, reasoning (if it can be called reasoning) that since the share price would return to the $40 range, the stock was an absolute bargain at one-tenth that price. Finally, to add insult to fiscal injury, he was so eager to buy more shares of WorldCom stock that he bought them on margin. He suffered accordingly as the share price dropped further still.
Having analyzed his own irrational behavior, Mr. Paulos moves to a survey of stock-market strategies, since, not unnaturally, he wonders whether there would have been more intelligent ways in which to place his money in the market. As his book’s scope broadens, the mathematician replaces the bruised investor, and his sense of mea culpa is replaced by a penetrating skepticism about others who claim to know better. He’s especially scathing about the myriad technical strategies on offer to investors. The more complicated the technical analysis, the greater Mr. Paulos’ wariness, since, as he notes, the continuous augmentation of theories—such as Elliott’s wave theory, which argues that stock cycles are based on Fibonacci number patterns—can grow so complicated as to make the theory incapable of falsification: No one knows whether it works, and no one can prove that it doesn’t. Mr. Paulos’ dismissive answer to the core question, Do people make money this way?, is that, of course, some people do: "People make money using all sorts of strategies, including some involving tea leaves and sunspots."
He is no more encouraging about the efficacy of so-called fundamental analysis—the "value" investors most famously personified by the legendary Warren Buffett. Although he finds the evidence in favor of fundamentals analysis more compelling than the evidence for technical analysis, Mr. Paulos is still keen to deflate the wilder claims made on its behalf. He shows, for example, that mutual funds consistently mislead customers by stressing their average rather than median return. The contrarian approach of most value investors (We don’t follow the herd) tends to lead only to short-term gains because of the inevitable regression to the mean. And uncritical reliance on statistics such as P/E, P/B, P/D or PEG ratios is foolhardy in an era of dodgy accounting practices. Even the legendary Mr. Buffett is taken down a peg: Mr. Paulos argues that Mr. Buffett’s reputation is so considerable that his predictions are inevitably self-fulfilling, made good by the mimetic reactions of his many followers. Again, Mr. Paulos is contemptuous of pseudo-science, arguing that the superficially dispassionate ethos of fundamentals "does not make them immune to emotional and cognitive distortion. The tango of exuberance and despair can and does affect estimates of stock’s fundamental value."
Throughout this wide-ranging survey, the writing is spirited, funny and clear. Mr. Paulos is continually imaginative in finding apt metaphors and anecdotes for the mechanics he dissects—citing the famous jinx associated with appearing on a Sports Illustrated cover as an example of regression to the mean, he argues that the jinx would work the other way round if struggling rather than successful athletes were featured.
The liveliest parts of his book are the most fanciful—the extended comparison of stock-market strategies to the modern infatuation with diets, for example—and the text is enlivened throughout by his good humor. Here, for example, he describes people who criticize technical analysis but remain in thrall to it: "They bring to mind the old joke about the man who complains to his doctor that his wife has for several years believed she’s a chicken. He would have sought help sooner, he says—‘but we needed the eggs.’"
As he moves into the more complicated realms of chaos theory and volatility analysis, Mr. Paulos may lose some readers who would rather confine their investment strategy to feelgood factors. The mathematics involved does grow more complex, though none of it will prove too difficult for any reader who can remember what a standard deviation is. Yet at certain points, you can’t help but feel that Mr. Paulos is working too hard to analyze an activity which, as he acknowledges himself, is irreducibly "based on hope, dreams, vision, and a certain monetarily tinted yet genuine romanticism." For all his explanations of golden ratios, betas and the Efficient Market Hypothesis, John Allen Paulos is himself pretty clearly a romantic manqué: However embarrassed by the rashness of his dabbling, he remains fascinated by the market. And though by the end of A Mathematician Plays the Stock Market, the author has found no strategy certain to outperform the dull plod of a broad-gauge stock-index fund, the odds are that, given another dose of mad money, he’d jump in all over again.
Andrew Rosenheim, an American writer living in England, has reviewed for the Times Literary Supplement, The Guardian and The Independent.