The algorithms that describe Medallion’s lucrative patterns were and have remained a secret. But the reason for their discovery, and for the phenomenal profits that they brought, can be understood, at least roughly. Part of the success lay in the choice of the short term. By examining a commodity’s behavior over brief periods, Laufer could collect thousands of observations, boosting his chances of finding repetitive patterns that were statistically significant. Moreover, short-term signals were likely to be more valuable as well as easier to find. If you can predict which way a commodity will move over the next few days, it takes only that long to place your wager and collect your reward; a Tiger investor aspires to buy a company that will double its value in two years, but a statistical trader who makes a quarter of a percent in twenty-four hours will end up considerably richer. Finally, predictions over the short term tend to inspire more confidence than the long-term sort. There’s less time for unforeseen factors to knock the forecast off target. Because it was dealing in short-term predictions that were relatively robust, the Simons team could leverage its bets and magnify its profits.
When Simons and Ax launched the Medallion Fund in 1988, about 15 percent of its capital was driven by the short-term signals, with the rest allotted to traditional trend-following models.5 The fund began promisingly, then dipped into a terrifying nosedive; by May 1989 it was down almost a quarter from its peak, and Simons decided to suspend trading. James Ax insisted passionately that the model would soon resume its profitable run, but Simons was so convinced that Ax was wrong that he ended the partnership. Enlisting the help of Berlekamp and Laufer, he embarked on a “study period” to decide Medallion’s future.
The trouble, Simons and his team decided, was that the trend-following mainstay of Medallion’s system had run out of juice. Too many Commodities Corporation wannabes had crowded in; brokers such as Dean Witter were marketing dozens of commodity funds to their clients; trend following had grown trendy.6 After some months of deliberation, Simons and his colleagues resolved to make Laufer’s short-term signals the new heart of the system. In 1990, the first full year of trading after the relaunch, Medallion notched up 56 percent after subtracting fees. It was a good beginning.
Elwyn Berlekamp reacted to this bonanza by cashing out. He sold his share of the management company that ran Medallion and returned to his research interests at Berkeley. But Simons responded with the entrepreneurial conviction that distinguished him. For more than a decade, he had charmed a shifting cast of mathematicians into collaborating on his ventures, believing that the cryptographer’s methods could crack the market’s code eventually. Now he felt he had been proven right, and he was determined to press his advantage. Having bought Berlekamp’s share of the management company, he rolled what was left of it into his operations at Renaissance Technologies. Armed with the profits that Medallion was now generating, he redoubled his efforts to hire mathematicians onto his team, installing his brain trust in the Long Island High Technology Incubator building near the Stony Brook hospital. Pretty soon, the investment paid off. The expanding research team discovered that the patterns that worked in American commodities markets often worked in foreign markets too. And, after some setbacks, the Simons team’s ghost-hunting methods discovered patterns in equity markets.
As the Long Island brain trust expanded, Simons added computer scientists, physicists, and astronomers to his roster, though he never hired economists. He wanted people who would approach the markets as a mathematical puzzle, unconnected to the flesh and blood and bricks and mortar of a real economy. Of course, the scientists’ abstraction could sometimes lead to strange results. On one occasion, a member of the faculty gave a presentation on how Medallion had performed over the past week; he presented Friday’s results first, followed by Monday’s, Thursday’s, Tuesday’s, and then Wednesday’s, assuming that his colleagues would find this bizarre sequencing natural, since computers sort days alphabetically. Another time Renaissance hosted a dinner for five hundred investors. A scientist volunteered to help Simons write a program to figure out the seating plan; he would assign probabilities to which sorts of people would get along best with which others, then let the computer optimize the table settings. For a while the blackboard in Simons’s office was covered with estimates for the likelihood that a single female algebraic geometer would get along with a married male judo instructor, and so on. When the big night arrived, the program seated one of Renaissance’s long-time investors next to a woman he may have liked too much. She had sued him for sexual harassment.
Most of the time, though, the mathematical approach to the world proved gloriously successful. Simons invested heavily in computers, which were fed with every conceivable form of data: prices from financial markets, economic releases, information from newswires, even time series on weather. The deeper the team went with its ghost hunting, the more it succeeded in discovering profitable patterns. In one simple example, the brain trust discovered that fine morning weather in a city tended to predict an upward movement in its stock exchange. By buying on bright days at breakfast time and selling a bit later, Medallion could come out ahead—except that the effect was too small to overcome transaction costs, which is why Renaissance allowed this signal to be public.
Many of the patterns that Renaissance discovered were individually modest; to a first approximation, after all, markets are efficient. But by discovering a large number of minor inefficiencies and blending them into a single trading program, Renaissance built a system that racked up profits year after year, especially during periods of turbulence. In 1994, the year Michael Steinhardt lost billions in the bond-market meltdown, Medallion returned 71 percent after subtracting fees. In the crash of 2008, it was up 80 percent after fees—and almost 160 percent before them.
By the time Simons retired, in 2009, he had become a billionaire many times over. In 2006 alone, his personal earnings reportedly came to $1.5 billion, as much as the corporate profits generated by the 115,000 employees of Starbucks and the 118,000 employees of Costco put together. The secretive code cracker found his photograph on magazine covers: a comb-over of white hair and a grizzled white beard framing the lined face of an inveterate smoker. And to the astonishment of others in the hedge-fund universe, Medallion’s magic proved resilient to competitive pressure throughout the 1990s and 2000s. As of this writing, in early 2010, it shows no sign of diminishing.
THE FIRST COMPETITIVE CHALLENGE TO RENAISSANCE came from David Shaw, a computer scientist from Columbia University. Shaw launched his eponymous company, D. E. Shaw, in 1988—the same year that Medallion began trading. Much like the Simons team, Shaw focused on fairly short time scales, and he hired mathematicians and scientists rather than traders and economists. Much like the Simons team, he pursued numerical precision with a zealous intensity: His staff soon discovered that it was no good telling him that a programming task might take three to eight weeks; you had to say that it would take 5.25, but with an error of two weeks.7 Yet for all these similarities, there were differences between Shaw and Simons too. These proved to be significant.
Shaw got into finance via Morgan Stanley’s proprietary trading desk, which hired him to create a computer system to support its quantitative trading. It was 1986, and big things were stirring at Morgan. The firm’s secretive Analytical Proprietary Trading unit ran a computerized effort to profit from short-run liquidity effects in stock markets. As Michael Steinhardt had discovered in the 1970s, a big sell order from a pension fund could push a stock’s price out of line; provided that there was no information behind the sale—that is, provided that the pension fund was selling because it needed cash rather than because it was reacting to bad news—Steinhardt could profit by buying and holding the stock until it rose back to its previous level. Morgan Stanley’s Analytical Proprietary Trading unit aimed to beat Steinhardt at this game. To identify price moves that were not based on information, a team of quants sorted stocks into pairs: Ford’s movements tended to track those of GM, American Ai
rlines tracked United Airlines, International Paper tracked Georgia-Pacific, and so on. If one of these stocks fell while the paired one stayed put, it was probably being pushed by an institutional block trader that needed to raise cash—in which case the price would soon revert, creating an opportunity to profit.8 Of course, Morgan Stanley’s method was not infallible, but it did not need to be. The firm just had to be right more than half the time in order to generate profits.
After a couple of years at Morgan, Shaw wanted to do more than build a bank unit’s computer system. He had been struck by the limits to Morgan’s approach. Having figured out how to profit from simple pairs trading, the Analytical Proprietary Trading group had invested in all manner of research: It brought in physicists who sought to apply chaos theory to the markets, mathematicians who tried to develop complex differential equations to model stock movements, and even, according to one veteran’s account, systems that used 3-D glasses to hunt for patterns in prices.9 But to a person with Shaw’s computer-science training, Morgan was ignoring some potentially interesting avenues. The way Morgan’s team tried to find anomalies in financial data was nothing like the way that a university computer-science team would have approached the challenge, and the techniques used to combine the anomalies into trading models were also different. Not knowing exactly where his hunch would lead, Shaw quit Morgan, rented an office above a communist bookshop in Greenwich Village, and launched his own company.
Within six months of opening his doors, Shaw’s distinctive approach began to yield progress. Whereas Morgan had searched for complex nonlinear patterns and found little of interest, Shaw quickly identified promising anomalies. Much as with the Simons team, the ghosts that Shaw discovered were hard to explain: When he found recurring patterns and printed them out, there were no familiar terms that could be used to make sense of the squiggles on the paper. The effects were so far from being intuitive that Shaw had no need for high-speed trading systems: He did not need to get orders to market faster than rivals because he was confident that he would have none.10 Pretty soon, the profits started to roll in, and Shaw outgrew the premises in Greenwich Village. He moved to a loft in the Flatiron District in 1989 and then to a futuristic tower on West Forty-fifth Street two years later; meanwhile, Morgan Stanley’s frustrated bosses closed down the Analytical Proprietary Trading unit. A magazine writer who visited Shaw’s outfit in 1994 was struck by what he saw: By now the firm employed 135 people and accounted for as much as 5 percent of the daily turnover on the New York Stock Exchange. The dress code was casual and the firm had a faintly Bohemian feel. Staffers rolled out sleeping bags to stay over at night. “It is easier to focus if you don’t go home,” explained a young employee named Jeffrey Bezos, who went on to found the Internet retailing giant Amazon.11
Like other quantitative traders, Shaw’s approach to markets differed fundamentally from that of economists. The economists generally started from the assumption of perfect arbitrage: If two bonds or two equities were theoretically the same, then they should be worth the same; if they were not, the economists tended to presume that they ought to converge eventually. But the scientists were not looking for relationships between prices that ought to exist. They were looking at the data and asking what relationships did exist.12 Moreover, the data that they looked at had been painstakingly swept for typing glitches and errors—it was cleaner than anything available to most finance professors. Time and again, an eager academic would contact D. E. Shaw, claiming to have discovered a profitable anomaly in the markets. Time and again, Shaw’s faculty would find that the anomaly consisted merely of misreported numbers. The academic’s strategy might consist, for example, of buying stocks whose price had cratered suddenly. But if a price series shows IBM trading at $60, then at $61, and then at $16, that last number is not a buy signal. It is a typo.
Once Shaw had created his quantitative team, he reached beyond the modeling of stock prices. Options proved to be a fertile field. The early options models, created among others by the two LTCM Nobel laureates, Robert Merton and Myron Scholes, assumed that stock-price changes were distributed normally. The 1987 crash had demonstrated that this assumption was not merely shaky; it was dangerously wrong—the truth was that extreme price moves happened far more frequently than the normal distribution anticipated. The challenge was to come up with a better pricing model, and Shaw saw his chance: His mathematicians were better at modeling than other market players; but as market participants themselves, they had better access to price data than mathematicians at universities. Sure enough, Shaw’s team came up with an options-pricing model that gave him an edge in multiple markets. The firm milked misalignments in various kinds of equity derivatives, notably in Japan.13 It branched into “convertibles”—bonds with stock options attached. It opened an options market-making operation and soon came to account for half the trades in some parts of this business.
By 1995 Shaw’s outfit had swelled to more than two hundred employees, and there was no doubting his achievement. Yet it was not the same sort of achievement as the Medallion fund. Shaw had created a machine to discover anomalies in stock prices, much as Renaissance had done for futures and then later also for equities, and Shaw’s firm claims that some of its strategies produced Medallion-sized returns of 40 percent plus.14 But although the Shaw team is secretive about the details, it cannot have harnessed as much capital to those golden algorithms, since otherwise its total returns would have been higher. Meanwhile, Shaw has been more willing to branch out. In 1995 the firm launched the Internet service provider Juno Online, as well as FarSight, an early venture in online banking and brokerage. Alongside its efforts in options market making, Shaw waded into the so-called third market, in which listed equities were traded away from the stock exchange. This business was dominated by a genial networker named Bernie Madoff, and so Shaw’s team jumped in, figuring that its quantitative edge would allow it to make decent money. But Madoff had ways of making up for his lack of cutting-edge analysis, and Shaw’s quants failed to turn a profit.
Shaw’s willingness to experiment was both a strength and a weakness. By launching multiple ventures, he diversified his risks, and some of the new ventures paid off handsomely. But Shaw was sometimes moving into fields that were already popular, running the risk of getting stuck in crowded trades when markets turned turbulent. In 1997, his firm formed an alliance with Bank of America, which aimed among other things to mine anomalies in bonds. Unfortunately, its strategies turned out to overlap with the sorts of arbitrage practiced by LTCM and its imitators. The result was that D. E. Shaw got hurt in the bond-market turbulence that accompanied Long-Term Capital’s collapse in 1998—“It could have been the end of the game for Shaw at that point,” one of the firm’s traders said later. The company sold part of its trading book, taking a loss that wiped out that year’s gains in all its other strategies combined. Having learned how highly leveraged fixed-income strategies could get hit in a liquidity crunch, Shaw abandoned bond arbitrage for a few years, though by 2002 it had tiptoed back into it.
WHILE SHAW WAS BUILDING HIS MACHINE, ANOTHER effort was under way in a surprising corner of the industry. Paul Tudor Jones, rock-and-roll trader and Robin Hood founder, was investing the fruits of his winnings in a computer-trading project. The early phases of this effort were in keeping with Jones’s exuberant youth. The trading systems had names like Madonna and Material Girl; they were statistically crude and their results were less exciting than their namesakes. But in the early 1990s Jones’s style changed. Having been cockily public, he lowered his profile. Having been a hot Manhattan bachelor, he married and settled down in Greenwich. His company became more grown-up, too. The Bruce Willis sneakers were put away, and Tudor changed from a single-trader outfit to a sleek institutional platform that supported multiple portfolio managers. Jones brought in James Pallotta, a Boston-based stock picker who would complement his macro trading; he brought in a London-based wizard named Mark Heffernan, who had once been described as the great
est discretionary trader in the Goldman Sachs empire. Tudor’s expanding ambitions affected its computer-trading aspirations too, particularly after the arrival in 1995 of Sushil Wadhwani.
Wadhwani was at once an accomplished economist and a creature of the markets. He had taught economics and statistics at the London School of Economics, and he went on to serve on the monetary policy committee of the Bank of England. But he came to Tudor via Goldman Sachs, where he had worked as an investment strategist. His work at Goldman involved advising the bank’s proprietary traders and its external clients, not least Paul Tudor Jones; and by rubbing shoulders with these players he had learned the limits of pure economic thinking.15 Contrary to what a team of modern-portfolio theorists might imagine, identifying an illogical price anomaly was only the start of a trader’s thought process; the next step was to identify a trigger—a reason why the anomaly might correct—since otherwise it might persist indefinitely. The trigger could be an upcoming election, a psychological tipping point identified in the charts, or some factor that would change the behavior of large institutional investors. Whether consciously or otherwise, the great discretionary traders were acting on signals from this blend of inputs. Wadhwani’s mission at Tudor was to build a machine that mimicked their eclectic thinking.
Wadhwani’s system drew on careful observation of Paul Jones and his ex-Goldman colleague, Mark Heffernan. He began by creating a naive model: For example, the system might buy the stock-market index if economic indicators were positive, if institutions were sitting on large pools of uninvested cash, and if signals from the options market suggested that sentiment was ready to turn upward. Then he would watch Jones and Heffernan trading and probe them on the reasons for their moves. Why had one of them put a certain position on at ten o’clock? Why had he increased it three hours later? The traders were generally considering the same factors that were already in Wadhwani’s program, but they were combining them in different ways. The more Wadhwani listened, the more he refined his model.16
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