Fortune's Formula (38 page)

A
T A
1998 UCLA
CONFERENCE,
Eugene Fama “pointed to me in the audience and called me a criminal,” said Robert Haugen. Haugen’s “crime” was that he was a prominent academic critic of the efficient market hypothesis. Fama “then said that he believed that God knew that the stock market was efficient.”

The efficient market hypothesis is far from dead. The rhetoric, as strident as ever, provides scant evidence that the track records of a few successful hedge funds have changed many minds.

The story of the Kelly criterion began with bookies and horse races. The one milieu where Kelly’s system has attained the status of orthodoxy is neither Wall Street’s canyons nor the groves of academe. It is Hong Kong’s racetracks.

In the past few decades, gamblers have begun to discover how inefficient the “market” of sports bets is. This realization began in the early 1980s with the Las Vegas–based “Computer Group” of Michael Kent, Ivan Mindlin, and Billy Woods. They had a factor-analysis system that looked at college football and basketball statistics and decided which teams to bet on, at what point spreads. News of the Computer Group’s predictions spread so quickly that it cut into the group’s profits. Others piggybacked on the group’s bets, affecting the point spread.

On Super Bowl Sunday of 1985, the FBI raided Computer Group affiliates at forty-three locations in sixteen states. The Computer Group had been placing bets at sports books all across the country in order to minimize the effect of its own wagers on the odds. The government argued that this constituted a bookmaking operation. People were indicted, the Computer Group dissolved, and ultimately the charges were dropped.

In 1993 Ed Thorp was approached by a secretive computer scientist who was just finishing his Ph.D. at UC Irvine. The computer scientist had a program to identify favorable wagers on basketball and other pro games. He had discovered, for instance, that teams that had to travel to the city in which a game was played tended to do poorer than a team that didn’t have to travel. A team that had to play a number of games in a row did poorer on average than a team given more rest between games. These variables were not properly weighted in bookies’ odds.

Thorp was impressed enough to put up $50,000 for an experiment. To minimize copycat betting, they decided that the person playing the bets should defy the stereotypes about what a successful bettor would look like. A female friend of the computer scientist agreed to play the role. She moved to Las Vegas for the term of the experiment.

Sports betting has several advantages over blackjack. It is possible to place very large bets, spreading among multiple bookies when necessary. There is no pressure to place camouflage bets when no favorable opportunity exists. The computer system identified wagers with a typical edge of 6 percent. They used the Kelly criterion to size the bets. Wagers ranged from a few hundred dollars into the thousands as the bankroll grew. They placed anywhere from five to fifteen bets a day.

Over a period of 101 days in early 1994, the team racked up a profit of $123,000 on the $50,000 bankroll. They almost literally broke the bank at one down-at-the-heels sports book called Little Caesar’s. It went out of business during the experiment, and Thorp suspects their winnings were a factor.

The team called it quits because the system required having someone in Las Vegas to place the bets. The bettor had to transport lots of cash, and that made everyone nervous.

The problem with winning at blackjack and sports betting is that sooner or later a big guy in a suit tells you to leave. The successful player is winning from the house.

In the 1970s Alan Woods was a professional blackjack player coping with this very issue. He had read Thorp’s blackjack book and wondered whether it would be possible to take a similar approach to horse racing. The winning purses come out of the pockets of the great mass of bettors. The track always gets its cut and has no reason to care who wins.

In 1984 economists William T. Ziemba and Donald B. Hausch published a book with the Thorp-inspired title
Beat the Racetrack
. In this and other publications, the authors showed how it was possible to find arbitrage opportunities at the racetrack and to use Kelly’s system for its ostensible purpose, of betting on horses.

Ziemba and Hausch’s experience was mainly with North American tracks. By 1984 Woods had determined that the best place to bet horses was Hong Kong. Horse racing is the only form of legal gambling in Hong Kong, and it is, according to an official web site, “by far the most popular form of recreation.” About $10
billion
is wagered on horses in Hong Kong each year. That averages to about $1,400 for every man, woman, and child in Hong Kong. More is wagered on some Hong Kong races than in an entire year of betting at some U.S. and European tracks. Bets are accepted by cell phone and Internet.

Racing in Hong Kong is run by the Jockey Club, a not-for-profit organization that takes in about $2 billion a year. The club has a squeaky-clean reputation. Fixed races are bad for the bottom line. The Jockey Club runs two racetracks, the British colonial Happy Valley and the newer, high-tech Sha Tin. The Hong Kong racing scene is relatively insular. Horses and jockeys have little reason to run elsewhere. That too is good for a computer system, for there are fewer “unknown” horses without track records.

Woods partnered with Bill Benter and Walter Simmons in the “Hong Kong Syndicate.” Benter wrote the software, Simmons assembled the historical data on horses and jockeys, and Woods put up the seed money, about $150,000. It took several years of labor to get the system operating. Benter’s computer model used a fractional Kelly system to prescribe the optimal portfolio of bets.

Kelly’s
edge
/
odds
formula ignores the effect of the bettor’s own wager on pari-mutuel odds. A bettor who places a large wager—large relative to how much is already riding on the horse—will lower the odds and the potential winnings. Benter had to use a more complex version of the Kelly formula that takes this into account. The effect of a successful betting operation’s own wagers on the odds limits profits more than the usual overbetting concerns. This was one reason for favoring Hong Kong and its large pari-mutuel pools.

Running a computer betting team is labor-intensive. Up to a hundred people are needed to hustle to the betting windows and to continually update the model’s database. Benter’s model uses not only published data like jockey and finish position but some 130 variables. The syndicate hired people to pore over videos of each race, gleaning data such as whether a horse was bumped in the turn and how well it recovered.

The first winning season was 1986–87. Almost as soon as the money started coming in, Benter and Woods fought over the division of profits. The syndicate split up, each partner taking a copy of the software. Within a few years, Benter, Woods, and Simmons were each multimillionaires.

Woods has a tragic flaw for a scientific bettor: he talks about his betting. “I would have benefited by not telling anybody about this—thus not tipping off the several other computer teams that have since come in here and made their own millions,” he told one journalist. “But that is an extremely difficult thing to do. I just could not keep my mouth shut.”

William Ziemba estimates that a first-rate Hong Kong computer team can make as much as $100 million in a good season, with about half that going to the team leader. Woods himself says he has made $150 million. To Ziemba, the races are an instructive model of the securities markets. It is the same fallible humans who set prices for technology stocks and show bets. Both sets of speculators are motivated by desire for gain. This does not guarantee perfect market efficiency.

Woods lives the life of one of the more benignly dissolute James Bond villains. He makes his home in Manila, close enough to Hong Kong in a world of fiber-optic cables transmitting bits that mean money. Now in his late fifties, Woods is a white-haired recluse who rarely leaves his luxury high-rise apartment and his shapely female entourage. If he needs anything, he has his maid or his Filipino girlfriend get it for him. “I like going to the seedy girlie bars in Makati,” he admitted in one interview. “I go out only a few nights per month, but on those nights, I tend to come home with two girls, or, usually, more.”

Woods takes a perverse pride in saying that he has not watched a horse race in person in the past eighteen years. He does not find horse races that interesting. Results arrive as instant messages from his agents at the track, punctuated by the appropriate smiling or frowning emoticons.

Near the top of the late 1990s stock market bubble, Woods sold short the NASDAQ index. It was an outright gamble that the bubble would burst, and the timing was wrong. Woods says he lost
$100 million
. “When you look at how much money I have consistently made from the horses, from 1987 onward, compared to what I’ve done in the market,” he said, “horses would seem to be a far safer investment than stocks.”

C
LAUDE
S
HANNON DIED
the same year as HAL—2001—on February 24. Among the hundreds of obituaries were a few that mentioned Shannon’s influence on thinking about gambling and investment. “Perhaps the impact Shannon and Kelly have had on finance can now best be measured by the number and quality of Wall Street firms that are actively recruiting mathematicians and information theorists,” wrote Elwyn Berlekamp.

Tragically, Shannon saw little of the 1990s’ developments in mathematical finance or the equally impressive developments in information theory. His memory lapses worsened and were diagnosed as symptoms of Alzheimer’s disease. Shannon would be driving in the car and realize he did not know where he was going. In collecting his scientific lifework for book publication by the IEEE, Shannon found it impossible to remember where he had put many of his files. When he did find papers, he often had no memory of writing them.

Still physically vigorous, Claude would take off and have trouble finding his way home. He failed to recognize his own children. By 1993 Betty had little choice but to put her husband in a Medford, Massachusetts, nursing home. She visited him daily. Shannon was a tinkerer to the end, customizing other patients’ walkers and taking apart the home’s fax machine.

Ed Thorp closed Ridgeline Partners in October 2002. He seems to have shown good timing. The return of statistical arbitrage operations has mostly been unexceptional since 2002. Perhaps the market has adapted—or perhaps it is only waiting for somebody’s new and improved software.

The Thorps recently endowed a chair at the University of California at Irvine mathematics department. The gift consists of one million dollars to be invested entirely in stocks, with the university limited to withdrawing only 2 percent a year. The fund is expected to compound exponentially in inflation-adjusted dollars. Ultimately, Thorp hopes, it will fund the most richly endowed university chair in the world, and will help draw exceptional mathematical talent to UC Irvine.

Besides running a fund of funds and managing his own investments, Thorp is exploring new investment and gambling opportunities. He cagily described one he had recently discovered. He told me it is a widespread form of gambling, “something available in the Eastern Hemisphere,” that can take a million-dollar bankroll. “You can make about $2,000 an hour, but it’s
work
. If I could figure out how to make it better, it would be a lot of fun. I’ve got a whole theory worked out, and nobody else anywhere knows this theory. The people who operate this gambling situation have no clue.”

People remain polarized over the Kelly criterion. Each side has defined the debate so narrowly that its own position is incontestable. Each believes its opponents are about to be swept aside by the good sense charitably ascribed to posterity.

In a recent letter, Samuelson told me that a heretic is born every minute. By “heretic” he meant someone subscribing to logarithmic utility and/or the false corollary. When I told Thomas Cover that I was writing a book on this subject, he said it was a story with everything except an ending. Like many of the Kelly people, Cover sees the story as incomplete because it does not include mainstream economists recanting their errors.

The Kelly cultists feel themselves surrounded by the indifferent and skeptical. Nils Hakansson estimates that no more than 10 percent of M.B.A. programs bother to mention the Kelly criterion (a situation he describes as “shameful”). “The Kelly criterion is integral to the way we manage money,” wrote chairman Bill Miller in the 2003 annual report of the Legg Mason Value Trust. But Miller says that “my guess is most portfolio managers are unaware of it, since it did not arise from the classic work of Markowitz, Sharpe, and others in the financial field.” Investment manager Jarrod Wilcox told me the subject is still “fringe.”

The idea pops up in the strangest places. It has gained currency in the cryonics subculture, those people who plan to have their bodies frozen at death for potential reanimation by the medical nano-technology of a remote future. (Thorp has arranged to have his body frozen.) The unlikely connection is the need to set up a trust fund to pay for ongoing refrigeration. Art Quaife, director of the International Cryonics Foundation and chairman of its Suspension Funds Investment Committee, argued that a Kelly investment policy “should handily beat the published investment policies of other cryonics organizations.”

To a limited extent, the Kelly criterion has entered the company of pi and the golden section as one of those rare mathematical ideas that captures the imagination of nonmathematicians. There is something numinous about Kelly’s “coincidental” link between gambling and the theory underpinning our digital age and the fact that a simple rule turns out to be optimal in several distinct ways. Thomas Cover compares the Kelly “coincidences” to the way that pi turns up in contexts that have nothing to do with circles. “When something keeps turning up like that,” he suggests, “it usually means it’s fundamental.”

Cover is getting into the hedge fund business himself. His plan is to use the universal data compression algorithms devised for the Internet to wring profits from pairs of volatile stocks. In marketing his fund, Cover has run into resistance from conventionally trained economists and financial advisers. For many people in finance, terms like
information theory
and the
long run
still raise red flags. A Wharton School professor was quizzing Cover on behalf of potential investor Gordon Getty (who did not invest). The Wharton professor objected to Cover’s talk of compound return rates as time goes to infinity. He informed Cover that “there’s a dark side to infinity.”

Paul Wilmott wrote that “life, and everything in it, is based on arbitrage opportunities and their exploitation.” This idiosyncratic view is interesting for its candor. The defenders of free markets are often at pains to insist that market prices are “fair” prices and no one “exploits” anyone. Wilmott proposes instead that 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. The operative model is Kelly’s gambler, or perhaps Dostoyevsky’s
The Gambler
(who finds that “people, not only at roulette, but everywhere, do nothing but try to gain or squeeze something out of one another”).

“You’ve heard of Kuhn’s paradigm shift? This is what’s going on here,” Jarrod Wilcox said recently of the ongoing Kelly criterion controversy. “Until you get one of the leading lights at MIT or Stanford to endorse it, you’re not going to have the paradigm shift…At one point I was so daring as to submit a paper to
The Journal of Finance
. The review said, ‘This contradicts everything we’ve learned in finance.’ Well, it really doesn’t. But it contradicts so many things that are so well established that the claws come out.”