Fortune’s Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street
by William Poundstone. Hill and Wang, 2005, 400 Pages, Paperback $15.00. Reviewed by Bob Shackleton.
This little book probably won’t make you a better economist but it may make you a more entertaining one. Bill Poundstone’s Fortune’s Formula, is a good book to recommend to friends who aren’t about to wade through a textbook on information and markets but who are curious about the subject. A solid writer of popular nonfiction who has produced, among other works, a good introduction to game theory, Poundstone has a real knack for conveying the basic insights behind complex technical ideas in clear, intuitive, non-mathematical prose. In Fortune’s Formula, he takes a stab at explaining theoretical issues at the base of information theory and its implications for finance, while placing its development in historical and social context. In the process, he introduces an extraordinary cast of memorable characters that include gangsters like Frank Costello and Longy Zwillman, financiers behind some of the more spectacular Wall Street scandals of the modern era – Ivan Boesky, Long-Term Capital Management, and the like – as well as the main protagonists, theorists Ed Thorp, Claude Shannon, and John Kelly.
Laying a foundation for introducing key concepts in information theory, Poundstone begins with stories of early 20th century mobsters’ use of wire services to control the flow of information for betting on horse races. From there, he segues into the story of Claude Shannon, whose 1937 article, proving that an electronic digital computer could, in principle, compute anything, has been called the most important master’s thesis of all time, and whose formulation of information theory in 1948 provided the formal mathematical basis of the modern computer age. Poundstone then tells the stories of mathematician Ed Thorp, a colleague of Shannon’s at MIT who developed a method of winning at blackjack, and of John Kelly, a Bell Labs physicist who first formally described the relationship between information theory and gambling with the Kelly formula – also known as the geometric mean principle – from which the book takes its name.
From there, Poundstone easily conveys the basic insight that successful investment both in gambling and in financial markets involves the effective marshalling of information as described by Shannon. (In Kelly’s words, gambling and financial investment differ only by a minus sign: favorable bets are called investments; unfavorable bets are called gambling.) According to the views of his protagonists, in either activity, even in the face of great uncertainty investors can use superior information to have an edge over others and to earn higher than average returns.
Poundstone also contrasts the standard academic economic view that financial markets nearly perfectly incorporate all available information, making arbitrage nearly impossible, with the opinions of his protagonists, who generally believe that many markets provide astute, careful observers with a variety of arbitrage opportunities. In effect, the efficient markets hypothesis presumes that arbitrage opportunities are easy enough to find and exploit that arbitrage keeps prices from ever getting out of line for long; in the experience of successful arbitrageurs, however, mispricing occurs often enough and long enough for a sharp eye and quick mind to consistently earn higher than normal returns.
Ed Thorp, for example, was an early successful investor in warrants (the most widely traded early form of stock option), developing an options formula before Black and Scholes, pioneering the use of what is now called ‘delta hedging,’ and running a successful hedge fund for over twenty years. Claude Shannon also amassed a fortune, earning a higher compound return on investments than Warren Buffet over two decades – though his performance resulted from a successful buy-and-hold involving a handful of very successful stocks – and proposing portfolio rebalancing strategies before they entered the economics literature. (Dying young, John Kelly did not become a successful investor, but his observations are widely known in the gambling world as the Kelly criterion or formula.)
A sizeable part of Fortune’s Formula reviews the rather intense controversy that has persisted between financial economists and proponents of the approach embodied in the Kelly formula, though to a non-participant it is somewhat difficult to understand what the fuss was all about: as one observer notes in the book, “life, and everything in it, is based on arbitrage opportunities and their exploitation.” To Poundstone, the controversy boils down to a difference in focus between utility maximization and wealth maximization: an investment criterion that maximizes long-run expected wealth may not maximize utility over an investors’ lifetime, given the possibility of very significant shifts in the market. Poundstone also suggests that academic economists appear to be “at pains to insist that market prices are ‘fair’ prices and no one ‘exploits’ anyone” while in fact, “many of the market’s participants are always trying to take the maximum advantage of people who know less than they do. We are unlikely to get very far in understanding markets by pretending otherwise.”
To some extent, the book lacks an adequate unifying theme: the Kelly criterion is rather tangential to the financial strategies pursued by Thorp, who exploited market inefficiencies, or Shannon, who pursued a buy-and-hold strategy based on his opinions about long-term technological trends. Nevertheless, for a layperson – or even an expert – interested in the conceptual issues behind information theory and financial markets, Fortune’s Formula will be an informative and entertaining read.