The Quants: How a New Breed of Math Whizzes Conquered Wall Street and Nearly Destroyed It

by Scott Patterson

  Such obvious discrepancies in practice are rare and are often hidden in the depths of the financial markets like gold nuggets in a block of ore. That’s where the quants, the math whizzes, step in.

  Behind the practice of arbitrage is the law of one price (LOP), which states that a single price should apply to gold in New York as in London, or anywhere else for that matter. A barrel of light, sweet crude in Houston should cost the same as a barrel of crude in Tokyo (minus factors such as shipping costs and variable tax rates). But flaws in the information certain market players may have, technical factors that lead to brief discrepancies in prices, or any number of other market-fouling factors can trigger deviations from the LOP.

  In the shadowy world of warrants, Thorp and Kassouf had stumbled upon a gold mine full of arbitrage opportunities. They could short the overpriced warrants and buy an equivalent chunk of stock to hedge their bet. If the stock started to rise unexpectedly, their downside would be covered by the stock. The formula also gave them a method to calculate how much stock they needed to hold in order to hedge their position. In the best of all worlds, the warrant price would decline and the stock would rise, closing out the inefficiency and providing a gain on each side of the trade.

  This strategy came to be known as convertible bond arbitrage. It has become one of the most successful and lucrative trading strategies ever devised, helping launch thousands of hedge funds, including Citadel Investment Group, the mammoth Chicago powerhouse run by Ken Griffin.

  Forms of this kind of arbitrage had been in practice on Wall Street for ages. Thorp and Kassouf, however, were the first to devise a precise, quantitative method to discover valuation metrics for warrants, as well as correlations between how much stock investors should hold to hedge their position in those warrants. In time, every Wall Street bank and most hedge funds would practice this kind of arbitrage, which would become known as delta hedging (delta is a Greek term that essentially captures the change in the relationship between the stock and the warrant or option).

  Thorp understood the risks his strategy posed. And that meant he could calculate how much he was likely to win or lose from each bet. From there, he would determine how much he should wager on these trades using his old blackjack formula, the Kelly criterion. That allowed him to be aggressive when he saw opportunities, but it also kept him from betting too much. When the opportunities were good, like a deck full of face cards, Thorp would load the boat and get aggressive. But when the odds weren’t in his favor, he would play it safe and make sure he had lots of extra cash on hand if the trade moved against him.

  Thorp was also cautious almost to the point of paranoia. He was always concerned about out-of-the-blue events that could turn against him: an earthquake hitting Tokyo, a nuclear bomb in New York City, a meteor smashing Washington, D.C.

  But it worked. Thorp’s obsessive risk management strategy was at the heart of his long-term success. It meant he could maximize his returns when the deck was stacked in his favor. More important, it meant he would pull his chips off the table if he felt a chill wind blowing—a lesson the quants of another generation seemed to have missed.

  After launching in late 1969, Thorp and Regan’s fund was an almost immediate hit, gaining 3 percent in 1970 compared with a 5 percent decline by the S&P 500, which is a commonly used proxy for the market as a whole. In 1971, their fund was up 13.5 percent, next to a 4 percent advance by the broader market, and it gained 26 percent in 1972, compared with a 14.3 percent rise by the index. Thorp programmed formulas for tracking and pricing warrants into a Hewlett-Packard 9830A he’d installed in his office in Newport Beach, Keeping tabs on Wall Street thousands of miles away from the edge of the Pacific Ocean.

  In 1973, Thorp received a letter from Fischer Black, an eccentric economist then teaching at the University of Chicago. The letter contained a draft of a paper that Black had written with another Chicago economist, Myron Scholes, about a formula for pricing stock options. It would become one of the most famous papers in the history of finance, though few people, including its authors, had any idea how important it would be.

  Black was aware of Thorp and Kassouf’s delta hedging strategy, which was described in Beat the Market. Black and Scholes made use of a similar method to discover the value of the option, which came to be known as the Black-Scholes option-pricing formula. Thorp scanned the paper. He programmed the formula into his HP computer, and it quickly produced a graph showing the price of a stock option that closely matched the price spat out by his own formula.

  The Black-Scholes formula was destined to revolutionize Wall Street and usher in a wave of quants who would change the way the financial system worked forever. Just as Einstein’s discovery of relativity theory in 1905 would lead to a new way of understanding the universe, as well as the creation of the atomic bomb, the Black-Scholes formula dramatically altered the way people would view the vast world of money and investing. It would also give birth to its own destructive forces and pave the way to a series of financial catastrophes, culminating in an earthshaking collapse that erupted in August 2007.

  Like Thorp’s methodology for pricing warrants, an essential component of the Black-Scholes formula was the assumption that stocks moved in a random walk. Stocks, in other words, are assumed to move in antlike zigzag patterns just like the pollen particles observed by Brown in 1827. In their 1973 paper, Black and Scholes wrote that they assumed that the “stock price follows a random walk in continuous time.” Just as Thorp had already discovered, this allowed investors to determine the relevant probabilities for volatility—how high or low a stock or option would move in a certain time frame.

  Hence, the theory that had begun with Robert Brown’s scrutiny of plants, then led to Bachelier’s observations about bond prices, finally reached a most pragmatic conclusion—a formula that Wall Street would use to trade billions of dollars’ worth of stock and options.

  But a central feature of the option-pricing formula would come back to bite the quants years later. Practically stated, the use of Brownian motion to price the volatility of options meant that traders looked at the most likely moves a stock could make—the ones that lay toward the center of the bell curve. By definition, the method largely ignored big jumps in price. Those sorts of movements were seen as unlikely as the drunk wandering across Paris suddenly hopping from the cathedral of Notre Dame to the Sorbonne across the river Seine in the blink of an eye. But the physical world and the financial world—as much as they seem to have in common—aren’t always in sync. The exclusion of big jumps left out a key reality about the behavior of market prices, which can make huge leaps in the blink of an eye. There was a failure to factor in the human element—a major scandal, a drug that doesn’t pan out, a tainted product, or a panicked flight for the exits caused by all-too-common investor hysteria. History shows that investors often tend to act like sheep, following one another in bleating herds, sometimes all the way over a cliff.

  Huge, sudden leaps were a contingency no one bothered to consider. Experienced traders such as Thorp understood this and made adjustments accordingly—his paranoid hand-wringing about distant earthquakes or nuclear bomb attacks, as well as his constant attention to the real odds of winning essential for his Kelly calculations, kept him from relying too much on the model. Other quantitative traders, less seasoned, perhaps less worldly, came to see the model as a reflection of how the market actually worked. The model soon became so ubiquitous that, hall-of-mirrors-like, it became difficult to tell the difference between the model and the market itself.

  In the early seventies, however, the appearance of the Black-Scholes model seemed propitious. A group of economists at the University of Chicago, led by free market guru Milton Friedman, were trying to establish an options exchange in the city. The breakthrough formula for pricing options spurred on their plans. On April 26, 1973, one month before the Black-Scholes paper appeared in print, the Chicago Board Options Exchange opened for business. And soon after, Texas Instruments int
roduced a handheld calculator that could price options using the Black-Scholes formula.

  With the creation and rapid adoption of the formula on Wall Street, the quant revolution had officially begun. Years later, Scholes and Robert Merton, an MIT professor whose ingenious use of stochastic calculus had further validated the Black-Scholes model, would win the Nobel Prize for their work on option pricing. (Black had passed away a few years before, excluding him from Nobel consideration.) Thorp never received any formal recognition for devising essentially the same formula, which hadn’t fully published. He did, however, make hundreds of millions of dollars using it.

  Princeton/Newport Partners had garnered so much attention by 1974 that the Wall Street Journal ran a front-page article on the fund: “Playing the Odds: Computer Formulas Are One Man’s Secret to Success in the Market.”

  “Reliable brokerage-house sources close to the funds say they have averaged better than 20 percent a year in net asset growth,” the article said. More remarkable, such gains came at a time when the market was experiencing its worst decline since the Great Depression, rocked by high inflation and the Watergate scandal. In 1974, a year that saw the S&P 500 tumble 26 percent, Thorp’s fund gained 9.7 percent.

  The article went on to describe one of the world’s most sophisticated investing operations—and the germ for the quant revolution to come. Thorp, it said, “relies on proprietary mathematical formulas programmed into computers to help spot anomalies between options and other convertibles and their common stock. … Mr. Thorp’s funds are an example of an incipient but growing switch in money management to a quantitative, mechanistic approach, involving heavy use of the computer.”

  Starting in the mid-1970s, Princeton/Newport went on a hot streak, posting double-digit returns for eleven straight years (after the 20 percent incentive fees Thorp and Regan charged clients, typical for hedge funds). In fact, from its inception, the fund never had a down year or a down quarter. In 1982, Thorp quit his teaching job at UC Irvine and started working full-time managing money.

  The gains kept coming, even in down years. In the twelve months through November 1985, Princeton/Newport was up 12 percent, compared with a 20 percent decline by the S&P 500. By then, Thorp and Regan were managing about $130 million, a heady increase from the $10,000 stake Thorp had received from Manny Kimmel for his first blackjack escapade in 1961. (In 1969, when the fund opened its doors for business, it had a stake of $1.4 million.)

  But Thorp wasn’t resting on his laurels. He was always on the lookout for new talent. In 1985, he ran across a hotshot trader named Gerry Bamberger who’d just abandoned a post at Morgan Stanley. Bamberger had created a brilliant stock trading strategy that came to be known as statistical arbitrage, or stat arb—one of the most powerful trading strategies ever devised, a nearly flawless moneymaking system that could post profits no matter what direction the market was moving.

  It was right up Thorp’s alley.

  Gerry Bamberger discovered stat arb almost by accident. A tall, quick-witted Orthodox Jew from Long Island, he’d joined Morgan Stanley in 1980 after earning a degree in computer science at Columbia University. At Morgan, he was part of a group that provided analytical and technical support for the bank’s stock trading operations.

  In this capacity, Bamberger wrote software for Morgan’s block trading desk, which shuffled blocks of ten thousand or more shares at a time for institutional clients such as mutual funds. The block traders also used a “pairs strategy” to minimize losses. If the desk held a block of General Motors stock, it would sell short a chunk of Ford that would pay off if the GM stock took a hit. Bamberger’s software provided traders up-to-date information on the relative positions of the pairs.

  Bamberger noticed that large block trades would often cause the price of the stock to move significantly. The price of the other stock in the pair, meanwhile, barely moved. This pushed the typical gap between the two stock prices, the “spread,” temporarily out of whack.

  Suppose GM typically traded for $10 and Ford for $5. A large buy order for GM could cause the price to rise temporarily to $10.50. Ford, meanwhile, would stay at $5. The “spread” between the two stocks had widened.

  By tracking the historical patterns and moving with cheetah-quick speed, Bamberger realized he could take advantage of these temporary blips. He could short a stock that had moved upward in relation to its pair, profiting when the stocks returned to their original spread. He could also take a long (or short) position in the stock that hadn’t moved, which would protect him in case the other stock failed to shift back to its original price—if the historical spread remained, the long position would eventually rise.

  Much like Thorp’s delta hedging strategy, it was the old game of buy low, sell high, with a quant twist.

  After describing his ideas to his superiors, Bamberger was set up on Morgan’s equity desk in early 1983 with $500,000 and a small group of traders. He started making buckets of cash right out of the gate. By September, his group had $4 million worth of long and short positions. In early 1984, it had $10 million. The stake rose to $15 million in October. By 1985, the group was running a $30 million book.

  But almost as fast as Bamberger scaled the heights, he came crashing down. Morgan’s higher-ups, reluctant to leave such a money machine in the hands of a programmer, turned it over to a hired gun named Nunzio Tartaglia. Bamberger, outraged, quit the firm.

  The Brooklyn-born Tartaglia was a mass of contradictions. He’d earned a master’s degree in physics from Yale University in the early 1960s, then promptly joined the Jesuits. After five years, he left the seminary to earn a Ph.D. in astrophysics from the University of Pittsburgh. By the early 1970s, Tartaglia found himself working on Wall Street as a retail broker at Merrill Lynch. After Merrill, the peripatetic Tartaglia went to five other firms before landing at Morgan in 1984.

  He renamed the group he’d taken over Automated Proprietary Trading, or APT, and moved it to a single forty-foot-long room on the nineteenth floor in Morgan’s Exxon Building headquarters in mid-town Manhattan. Tartaglia added more automation to the system, linking the desk to the New York Stock Exchange’s Super Designated Order Turnaround System, or SuperDOT, which facilitated computerized trades. APT was soon trading so much that at times it accounted for 5 percent of the daily trading volume on the NYSE. The stat arb strategy earned $6 million in the first year Tartaglia ran the group. In 1986, it pulled in an eye-popping $40 million, then $50 million in 1987. The group started to gain legendary status on Wall Street, in part due to its CIA-like secrecy.

  In 1986, Tartaglia hired David Shaw, a computer whiz teaching at Columbia University, to head APT’s technology unit. The Stanford-educated Shaw was an expert in a hot new field called parallel processing, in which two or more mainframe computers crunched numbers on the same problem to ramp up speed and efficiency. Shaw had virtually no trading experience, but he was a quick learner, and soon became interested in the group’s unique trading strategies. His colleagues found him shy, nervous around women, and self-conscious about his looks. Tall, thin as a spider, Shaw dabbled in the early computer dating services springing up in the 1980s—in other words, he was a classic quant.

  Morgan had hired Shaw with the promise that he’d be able to develop his own trading strategies, where the real money was to be made. But as Tartaglia steadily took over the group, making every effort to keep the lucrative trading platform to a chosen few, Shaw realized that he wouldn’t have the opportunity to trade.

  He decided to take matters into his own hands. One day in September 1987, the group was giving a presentation about its business model and trading strategies to senior management. Shaw’s presentation on parallel processing and high-speed algorithms was proceeding normally. Suddenly, he started to expound on complex mathematical bond-arbitrage strategies. As the meeting ended, APT’s traders and researchers sat fuming in their chairs. Shaw had crossed the line. Programmers weren’t supposed to trade, or even think about trading. Back then, th
e line between programmer and trading strategist remained firmly in place, a boundary that steadily dissolved as trading became more and more computerized.

  For his part, Shaw had hoped that Morgan’s higher-ups would see the value of his ideas. He’d also approached upper management on his own about creating an entirely new research unit, a scientific laboratory for research on quantitative and computational finance. But his ideas fell on deaf ears, and Tartaglia wasn’t giving any ground. The weekend after the presentation, Shaw decided to quit, informing Tartaglia of his decision the following Monday. Tartaglia, possibly perceiving Shaw as a threat, was happy to see him go.

  It may have been one of the most significant losses of talent in the history of Morgan Stanley.

  Shaw landed on his feet, starting up his own investment firm with $28 million in capital and naming his fund D. E. Shaw. It soon became one of the most successful hedge funds in the world. Its core strategy: statistical arbitrage.

  Tartaglia, meanwhile, hit a rough patch, and in 1988, Morgan’s higher-ups slashed APT’s capital to $300 million from $900 million. Tartaglia amped up the leverage, eventually pushing the leverage-to-capital ratio to 8 to 1 (it invested $8 for each $1 it actually had in its coffers). By 1989, APT had started to lose money. The worse things got, the more frantic Tartaglia became. Eventually he was forced out. Shortly after, APT itself was shut down.

  In the meantime, Bamberger had found a new home. One day after he’d left Morgan, he got a call from Fred Taylor, a former Morgan colleague who’d joined a hedge fund that specialized in quantitative investing.