The Quants Part 2

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 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 Ka.s.souf's delta hedging strategy, which was described in Beat the Market 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 a.s.sumption that stocks moved in a random walk. Stocks, in other words, are a.s.sumed 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 a.s.sumed 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. methodology for pricing warrants, an essential component of the Black-Scholes formula was the a.s.sumption that stocks moved in a random walk. Stocks, in other words, are a.s.sumed 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 a.s.sumed 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 quant.i.tative 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 introduced 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 n.o.bel Prize for their work on option pricing. (Black had pa.s.sed away a few years before, excluding him from n.o.bel 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 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." 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 a.s.set 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 quant.i.tative, 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 a.n.a.lytical and technical support for the bank's stock trading operations. 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 a.n.a.lytical 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 inst.i.tutional 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 s.h.i.+ft 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 cras.h.i.+ng 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 ma.s.s 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 cla.s.sic 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, the 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 quant.i.tative 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 pus.h.i.+ng 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 quant.i.tative investing.

"What's it called?" Bamberger asked.

"Princeton/Newport Partners," Taylor told him. "Run by a guy named Ed Thorp."

Thorp, Taylor explained, was always interested in new strategies and was interested in looking at stat arb. Taylor introduced Bamberger to Jay Regan, and the two hit it off. Thorp and Regan agreed to back a fund called BOSS Partners, an acronym for Bamberger and Oakley Sutton Securities (Oakley and Sutton are Thorp and Regan's middle names, respectively). Bamberger set up shop in a 120-square-foot twelfth-floor office on West 57th Street in New York. With $5 million in capital, he hit the ground running, cranking out an annualized return of about 30 percent his first year in operation. By 1988, BOSS was running about $100 million in a.s.sets and generating consistent double-digit returns.

BOSS, like APT, hit a dry spell in early 1988. Toward the end of the year, Bamberger decided he'd had enough of Wall Street. He wound down BOSS and moved upstate to teach finance and law at the State University of New York at Buffalo. He never again traded stocks on a large scale.

But his strategy lived on, and not just at Princeton/Newport. Traders who'd worked for Bamberger and Tartaglia fanned out across Wall Street, bringing stat arb to hedge funds and investment banks such as Goldman Sachs. As D. E. Shaw raked in profits, other funds started trying to copy its superfast trading style. Robert Frey, who'd worked as an APT researcher, took stat arb to Jim Simons's fund, Renaissance Technologies, in the early 1990s. Peter Muller, the singing quant who triumphed at Wall Street Poker Night in 2006, appeared on the scene at Morgan a few years after Tartaglia was ousted and started up his own stat-arb money machine, one that proved far more robust. Ken Griffin, who kept a keen eye on everything Thorp was doing, adopted the strategy at Citadel. Stat arb soon became one of the most popular and consistent ways to make money on Wall Street-too popular, in fact, as its pract.i.tioners would discover in August 2007.

Ed Thorp's influence was spreading across the financial universe in other ways as well. At MIT, a team of blackjack card counters sprung up, the group that would eventually inspire the bestselling book Bringing Down the House Bringing Down the House. An early member of the group was a young math hotshot named Blair Hull, who'd read Beat the Dealer Beat the Dealer in the early 1970s. By the end of the decade, he'd parlayed $25,000 in winnings to jump-start a trading career in the Chicago options trading pits, having also read in the early 1970s. By the end of the decade, he'd parlayed $25,000 in winnings to jump-start a trading career in the Chicago options trading pits, having also read Beat the Market Beat the Market. In 1985, he founded Hull Trading, which specialized in using quant.i.tative models and computers to price options on a rapid-fire basis. Hull eventually became one of the most advanced trading operations in the world, a quant mecca that transformed the options world. In 1999, Goldman Sachs sh.e.l.led out $531 million for Hull, which it developed into one of Wall Street's premier high-frequency trading outfits.

For Thorp and Regan, meanwhile, everything had been running smoothly. The fund had posted solid gains in 1986 and was surging ahead in the first half of 1987, helped by BOSS's gains. Then stocks started to wobble. By early October, cracks were forming in the market that would turn into a full-blown earthquake. At the heart of the disaster: the quants and the Black-Scholes option-pricing formula.

THE VOLATILITY SMILE

Sometime around midnight, October 19, 1987, Leo Melamed reached out a sweaty-palmed hand, picked up the phone in his nineteenth-floor office at the Chicago Mercantile Exchange, and dialed Alan Greenspan. The newly appointed chairman of the Federal Reserve, Greenspan was staying at the upscale Adolphus Hotel in Dallas to address the American Bankers a.s.sociation's annual convention the next day. It was to be his first major speech as chairman of the central bank. midnight, October 19, 1987, Leo Melamed reached out a sweaty-palmed hand, picked up the phone in his nineteenth-floor office at the Chicago Mercantile Exchange, and dialed Alan Greenspan. The newly appointed chairman of the Federal Reserve, Greenspan was staying at the upscale Adolphus Hotel in Dallas to address the American Bankers a.s.sociation's annual convention the next day. It was to be his first major speech as chairman of the central bank.

The speech would never happen. The Dow industrials had crashed, losing 23 percent in a single day. Other exchanges, including the Merc, were in chaos. Many players in the market were bankrupt and couldn't settle their bills. Greenspan had been fielding calls from executives at nearly every major bank and exchange in the country. His single goal: make sure the markets were up and running Tuesday morning.

Greenspan wanted to know if the Merc would make it. Melamed, the exchange's president, wasn't sure. The Merc had become a trading hub for a new financial product, futures contracts linked to the S&P 500. At the end of a typical trading day, traders who'd lost money on any contracts would transfer cash to the Merc's clearinghouse, which would deposit the money into the winners' accounts. Typically $120 million would change hands every day. But that Monday, buyers of S&P futures owed sellers an amount in the range of $2 billion to $3 billion. Some couldn't pay.

If the Merc couldn't open its doors for business, the panic would spread. The whole system could come cras.h.i.+ng down. That night, Melamed made frantic phone calls to inst.i.tutions around the country trying to settle accounts. By morning, $2.1 billion in transfers had been completed, but a single client still owed $400 million to Continental Illinois, the Merc's financing agent.

Melamed still wasn't sure if the Merc could open without that $400 million. Around 7:00 A.M A.M. he decided to call Wilma Smelcer, Continental's financial officer in charge of the bank's account with the Merc. If Smelcer couldn't help him, his next call would be to Greenspan ... with very bad news.

Smelcer didn't think she could look past $400 million in missing funds. It was a deal killer. "Wilma, I am certain your customer is good for it," Melamed pleaded. "You're not going to let a stinking couple of hundred million dollars cause the Merc to go down the tubes, are you?"

"Leo, my hands are tied."

"Please listen, Wilma. You have to take it upon yourself to guarantee the balance, because if you don't, I've got to call Alan Greenspan, and we're going to cause the next depression."

After a few moments of tense silence, Smelcer said, "Hold it a minute, Leo. Tom Theobald just walked in." Theobald was chairman of Continental.

After a few minutes, Smelcer was back. "Leo, we're okay. Tom said go ahead. You've got your money."

It was 7:17 A.M A.M., three minutes before the opening of the Merc's currency markets. The world had little idea how close the financial system had come to a catastrophic seizure.

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The critical factor behind the crash of Black Monday on October 19, 1987, can be traced to a restless finance professor's sleepless night more than a decade earlier. The result of that night would be a feat of financial engineering called portfolio insurance. Based on the Black-Scholes formula, portfolio insurance would scramble the inner workings of the stock market and set the stage for the single largest one-day market collapse in history. factor behind the crash of Black Monday on October 19, 1987, can be traced to a restless finance professor's sleepless night more than a decade earlier. The result of that night would be a feat of financial engineering called portfolio insurance. Based on the Black-Scholes formula, portfolio insurance would scramble the inner workings of the stock market and set the stage for the single largest one-day market collapse in history.

On the evening of September 11, 1976, Hayne Leland, a thirty-five-year-old professor at the University of California at Berkeley, was having trouble sleeping. He'd recently returned from a trip to France. A weak dollar had made the trip excessively pricey. Stagflation, a crippling mix of high inflation and slow growth, was rampant. The economy and the stock market were in the tank. California governor Ronald Reagan was threatening cutbacks in the salaries of academics such as Leland, who worried that the prosperous American lifestyle of his parents' generation was in danger.

As he pondered this bleak reality, Leland recalled a conversation he'd had with his brother, John, who worked at an investment management company in San Francisco. Stocks had cratered in 1973, and pension funds had pulled out en ma.s.se, missing out on a bounce that followed. "If only insurance were available," John had said, "those funds could be attracted back to the market."

Leland was familiar with the Black-Scholes formula and knew that options behaved in ways like insurance. A put option, which pays off if a stock drops, is akin to an insurance policy on a stock. He thought of it step by step. Say I own IBM at $50 and am worried about it losing value. I can buy a put for $3 that pays off if IBM falls to $45 (allowing me to unload it for $50), essentially insuring myself against the decline for a premium of $3 Say I own IBM at $50 and am worried about it losing value. I can buy a put for $3 that pays off if IBM falls to $45 (allowing me to unload it for $50), essentially insuring myself against the decline for a premium of $3.

Leland realized his brother had been describing a put option on an entire portfolio of stocks. He sat down at his desk and started to scribble out the implications of his revelation. If the risk of an entire portfolio of stocks declining could be quantified, and if insurance could cover it, then risk would be controlled and managed, if not effectively eliminated. Thus portfolio insurance was born. No more sleepless nights for jittery professors.

Over the next few years, Leland and a team of financial engineers, including Mark Rubinstein and John O'Brien, created a product that would provide insurance for large portfolios of stocks, with the Black-Scholes formula as a guidepost. In 1981, they formed Leland O'Brien Rubinstein a.s.sociates Inc., later known simply as LOR. By 1984, business was booming. The product grew even more popular after the Chicago Mercantile Exchange started trading futures contracts tied to the S&P 500 index in April 1982. The financial wizards at LOR could replicate their portfolio insurance product by shorting S&P index futures. If stocks fell, they would short more futures contracts. Easy, simple, and sweet. And enormously profitable.

By the autumn of 1987, the company's portfolio insurance protected $50 billion in a.s.sets held by inst.i.tutional investors, mostly pension funds. Add in LOR copycats and the total amount of equity backed by portfolio insurance was roughly $100 billion.

The Dow industrials had soared through the first half of 1987, gaining more than 40 percent by late August. The so-called Reagan Revolution had restored confidence in America. Inflation was in retreat. j.a.panese investors were flooding the United States with yen. New Agers around the country discovered the healing power of crystals. A new, young Fed chairman was in town. The New York Mets were the Cinderella world champions of baseball, having won the 1986 World Series in seven games, led by a young power hitter named Darryl Strawberry and a dazzling pitcher named Dwight Gooden. What could go wrong?

Plenty. By mid-October, the market had been knocked for a loop, tumbling 15 percent in just a few months. The block trading desk at Shearson Lehman Brothers installed a metal sign with an arrow that read: "To the Lifeboats."

The mood was grim. Traders talked of chain reaction declines triggered by mysterious computer-a.s.sisted trading strategies in stocks and futures markets. As trading wound down on Friday, October 16, a trader in stock index options on the floor of the American Stock Exchange shrieked, "It's the end of the world!"

Early on Monday, October 19, investors in New York were bracing for an onslaught well before trading began. Over in the Windy City, it was eerily quiet in the stock index futures pit at the Chicago Mercantile Exchange as traders waited for the action to begin. All eyes were on Chicago's "shadow markets," whose futures antic.i.p.ate the behavior of actual prices. Seconds after the open at the Merc-fifteen minutes ahead of trading in New York-S&P 500 index futures dropped 14 points, indicating a 70-point slump in the Dow industrials.

Over the next fifteen minutes before trading began on the NYSE, ma.s.sive pressure built up on index futures, almost entirely from portfolio insurance firms. The big drop by index futures triggered a signal for another new breed of trader: index arbitrageurs, investors taking advantage of small discrepancies between indexes and underlying stocks. When trading opened in New York, a brick wall of short selling slammed the market. As stocks tumbled, pressure increased on portfolio insurers to sell futures, racing to keep up with the widely gapping market in a devastating feedback loop. The arbs scrambled to put on their trades but were overwhelmed: futures and stocks were falling in unison. Chaos ruled.

Fischer Black watched the disaster with fascination from his perch at Goldman Sachs in New York, where he'd taken a job managing quant.i.tative trading strategies. Robert Jones, a Goldman trader, dashed into Black's office to report on the carnage. "I put in an order to sell at market and it never filled," he said, describing a frightening scenario in which prices are falling so fast there seems to be no set point where a trade can be executed. "Wow, really?" Black said, clapping his hands with glee. "This is history in the making!"

In the final seventy-five minutes of trading on October 19, the decline hit full throttle as portfolio insurance sellers dumped futures and sell orders flowed in from brokerage accounts around the country. The Dow snapped, sliding 300 points, triple the amount it had ever dropped in a single day in history and roughly the equivalent of a 1,500-point drop in today's market. The blue chip average finished the day at 1738.74, having dropped 508 points.

In the new globally interlaced electronic marketplace, the devastation wound around the globe like a poisonous serpent Monday night, hitting markets in Tokyo, Hong Kong, Paris, Zurich, and London, then making its way back to New York. Early Tuesday, during a brief, gut-wrenching moment, the market would lurch even deeper into turmoil than Black Monday. The blue-chip average opened down more than 30 percent. Stocks, options, and futures trading froze. It was an all-out meltdown.

Over in Newport Beach, Thorp's team was scrambling. Thorp had watched in dismay Monday as the market fell apart. By the time he got back from a hastily s.n.a.t.c.hed lunch, it had lost 23 percent. Trading was closed, and Thorp had a severe case of heartburn. But he quickly figured out that portfolio insurance was behind the market meltdown.

As trading opened Tuesday, a huge gap between S&P futures and the corresponding cash market opened up. Normally, that meant a great trading opportunity for arbs, including Thorp, always attracted to quant.i.tative strategies. The ma.s.sive gap between futures contracts, created by the heavy selling by portfolio insurers, and their underlying stocks was a sign to buy futures and short stocks.

By Tuesday, most of the arbs were terrified, having been crushed on Black Monday by the plummeting market. But Thorp was determined. His plan was to short the stocks in the index and buy the futures, gobbling up the big spread between the two.

The trouble was getting the orders through in the fast-moving market. As soon as a buy or sell order was placed, it was left behind as the market continued to tumble. In the heat of the crisis, Thorp got Princeton/Newport's head trader on the phone: "Buy $5 million worth of index futures at the market and short $10 million worth of stocks."

His best guess was that only half of the stock orders would be filled anyway because, due to technical reasons, it was hard to short stocks in the free-falling market.

At first his trader balked. "Can't, the market's frozen."

Thorp threw the hammer down. "If you don't fill these orders I'm going to do them in my own personal account. I'm going to hang you out to dry," Thorp shouted, clearly implying that the trader's firm wouldn't share any of the profits.

The trader reluctantly agreed to comply but was only able to make about 60 percent of the short sales Thorp had ordered up due to the volatility. Soon after, he did the trade again, pocketing more than $1 million in profits.

Thorp's calm leap into the chaos wasn't the norm. Most market players were in a this-is-the-big-one hand-wringing frenzy.

Then it stopped. Sometime Tuesday afternoon, the market landed on its feet. It started to climb as the Federal Reserve pumped ma.s.sive sums of money into the system. The Dow finished the day up 102 points. The next day, it soared 186.84 points, its biggest one-day point advance in history at the time.

But the damage had been done. The mood around the country turned decidedly antiWall Street as the junk bond scandals. .h.i.t the front pages of newspapers. An October 1987 Newsweek Newsweek cover queried, "Is the Party Over? A Jolt for Wall Street's Whiz Kids." In December 1987, audiences in movie theaters listened to Gordon Gekko, the slimy takeover artist played by Michael Douglas, proclaim the mantra for the decade in Oliver Stone's cover queried, "Is the Party Over? A Jolt for Wall Street's Whiz Kids." In December 1987, audiences in movie theaters listened to Gordon Gekko, the slimy takeover artist played by Michael Douglas, proclaim the mantra for the decade in Oliver Stone's Wall Street: Wall Street: "Greed is good." A series of popular books reflecting the antiWall Street sentiment hit the presses: "Greed is good." A series of popular books reflecting the antiWall Street sentiment hit the presses: Bonfire of the Vanities Bonfire of the Vanities by Tom Wolfe, by Tom Wolfe, Barbarians at the Gate Barbarians at the Gate by by Wall Street Journal Wall Street Journal reporters Bryan Burrough and John Helyar, reporters Bryan Burrough and John Helyar, The Predators' Ball The Predators' Ball by Connie Bruck, by Connie Bruck, Liar's Poker Liar's Poker by Michael Lewis. by Michael Lewis.

The quants were licking their wounds. Their wondrous invention, portfolio insurance, was roundly blamed for the meltdown. Fama's efficient-market theory was instantly called into question. How could the market be "right" one day, then suffer a 23 percent collapse on virtually no new information the next day, then be fine the day after?

The now-you-see-it-now-you-don't math wizards had a unique retort: Black Monday never happened. Jens Carsten Jackwerth, a postdoctoral visiting scholar at the University of California at Berkeley, and Mark Rubinstein, coinventor of portfolio insurance, offered incontrovertible proof that October 19, 1987, was statistically impossible. According to their probability formula, published in 1995, the likelihood of the crash was a "27-standard-deviation event," with a probability of 10 to the 160th power: "Even if one were to have lived through the entire 20 billion year life of the universe and experienced this 20 billion times (20 billion big bangs), that such a decline could have happened even once in this period is a virtual impossibility."

Still, the very real crash on Black Monday left very real scars on the psyches of the traders who witnessed it, from the trading pits of Chicago to the exchange floors of lower Manhattan. Meltdowns of such magnitude and ferocity were not supposed to happen in the world's most advanced and sophisticated financial marketplace.

They especially weren't supposed to happen in a randomized, Brownian motion world in which the market obeyed neat statistical rules. A 27-standard-deviation event was tantamount to flipping a coin a hundred times and getting ninety-nine straight heads.

Was there a worm in the apple, a fatal flaw in the quants' theory? This haunting fear, brought on by Black Monday, would hover over them like a bad dream time and time again, from the meltdown in October 1987 until the financial catastrophe that erupted in August 2007.

The flaw had already been identified decades earlier by one of the most brilliant mathematicians in the world: Benoit Mandelbrot.

When German tanks rumbled into France in 1940, Benoit Mandelbrot was sixteen years old. His family, Lithuanian Jews, had lived in Warsaw before moving to Paris in 1936 amid a spreading economic depression. Mandelbrot's uncle, Szolem Mandelbrojt, had moved to Paris in 1929 and quickly rose to prominence among the city's mathematical elite. Young Mandelbrot studied under his uncle and entered a French secondary school. But his life was upended when the n.a.z.is invaded. tanks rumbled into France in 1940, Benoit Mandelbrot was sixteen years old. His family, Lithuanian Jews, had lived in Warsaw before moving to Paris in 1936 amid a spreading economic depression. Mandelbrot's uncle, Szolem Mandelbrojt, had moved to Paris in 1929 and quickly rose to prominence among the city's mathematical elite. Young Mandelbrot studied under his uncle and entered a French secondary school. But his life was upended when the n.a.z.is invaded.

As the Germans closed in, the Mandelbrot family fled to the small hill town of Tulle in southwest France, where they had friends. Benoit enrolled in the local school, where there was little compet.i.tion. The freedom from the fierce head-to-head pressure of Paris nurtured his creative side. He soon developed the unique ability to picture complex geometric images in his mind and make intuitive leaps about how to solve difficult equations.

Mandelbrot's father, a clothing wholesaler, had no job, and the family was dest.i.tute. He knew a shopkeeper who had a bundle of coats from before the war with a strange Scottish design. The coats were so hideous that the shopkeeper had trouble giving them away. The senior Mandelbrot took one for his son, who welcomed it.

One day a group of French partisans blew up a nearby German outpost. A witness noticed that one of the attackers wore a strange-looking jacket with a Scottish design-the same jacket young Mandelbrot wore around the town. When a villager denounced him, he went into hiding, joined by his brother. During the next year, Mandelbrot, innocent of the attack, managed to avoid the German patrols. By the time Allied troops liberated Paris in 1944, he was twenty years old.

Those nomadic years spent in the countryside of France were crucial in the development of Mandelbrot's approach to mathematics. The absence of strict guidelines and compet.i.tion from peers created an environment in which his mind could freely explore the outer limits of mathematical territories most students his age could never dream of.

He took the entrance examination for Paris's elite inst.i.tutions of higher education, the ecole Normale Superieure and the ecole Polytechnique. With no time to prepare, he took it cold. The mathematical section of the test was a complex riddle involving algebra and geometry in which the result (after a great deal of calculation) comes out to zero. Mandelbrot landed the highest score in the country, earning him a ticket to either school. He completed his Ph.D. in 1952.

After graduating, Mandelbrot entered a period of professional limbo, working for a time with the French psychologist Jean Piaget before spending a year at Princeton's Inst.i.tute for Advanced Study in 1953.

In 1958, he took a job at IBM's Thomas J. Watson Research Center, the company's primary laboratory north of Manhattan. By then, his work on issues such as income distributions in various societies had captured the attention of economists outside the cloistered IBM research lab, and in 1961 he went to give a talk at Harvard. When he arrived on campus, he made a beeline to the office of his host for the event, the economics professor Hendrik Houthakker. Soon after entering, he was stunned by a strange diagram on the professor's blackboard, a convex V that opened out to the right. Mandelbrot sat down. The image on the blackboard loomed over Houthakker's shoulder. Mandelbrot couldn't keep his eyes off it.

"I'm sorry," he said after a few minutes' chitchat. "I keep looking at your blackboard because this is a strange situation. You have on your blackboard a diagram from my lecture."

Houthakker turned and gazed at the diagram. "What do you mean?" he said. "I have no idea what you're going to talk about."

The diagram came from a student's research project on the behavior of cotton prices, an obsession of Houthakker's. The student was trying to discern how the patterns in cotton prices fit into the standard Brownian motion models that dominated financial theory. But to his great frustration, nothing worked. The data didn't fit the theory or the bell curve. Prices flitted about too erratically. The stunning coincidence for Mandelbrot was that the diagram of cotton prices on Houthakker's chalkboard exactly matched the diagram of income distributions Mandelbrot had prepared for his talk.