"The only serious criticism of my work, expressed by Cootner, was that if I am right, all of our previous work is wrong," Mandelbrot said, staring out his window at the Charles. "Well, all of their previous work is is wrong. They've made a.s.sumptions which were not valid." wrong. They've made a.s.sumptions which were not valid."

He paused a moment and shrugged. "The models are bad."

In February 2008, Ed Thorp gazed out of the windows of his twelfth-floor corner office in the exclusive city of Newport Beach, California. The glistening expanse of the whitecapped Pacific Ocean stretched far into a blue horizon past Newport Harbor toward the green jewel of Catalina Island. "Not a bad view," he said to a reporter with a smile. 2008, Ed Thorp gazed out of the windows of his twelfth-floor corner office in the exclusive city of Newport Beach, California. The glistening expanse of the whitecapped Pacific Ocean stretched far into a blue horizon past Newport Harbor toward the green jewel of Catalina Island. "Not a bad view," he said to a reporter with a smile.

Thorp was angry even though the full fury of the crisis was yet to strike. The banks and hedge funds blowing up didn't know how to manage risk. They used leverage to juice returns in a high-stakes game they didn't understand. It was a lesson he'd learned long before he founded his hedge fund, when he was sitting at the blackjack tables of Las Vegas and proving he could beat the dealer. At bottom, he learned, risk management is about avoiding the mistake of betting so much you can lose it all-the mistake made by nearly every bank and hedge fund that ran into trouble in 2007 and 2008. It can be tricky in financial markets, which can exhibit wild, Mandelbrotian swings at a moment's notice. Banks juggling billions need to realize the market can be far more chaotic over short periods of time than standard financial models reflect.

Thorp stood ramrod straight from his habit of continual exercise. Until 1998, when he injured his back, he ran a few marathons a year. He was trim, six feet tall, with the etched features of an aging athlete. His gaze was clear and steady behind a pair of square gold-framed gla.s.ses. Thorp had been taking a large number of pills every day, as part of his hope that he will live forever. After he dies, his body will be cryogenically frozen. If technology someday advances far enough, he'll be revived. Thorp estimates that his odds of recovering from death are 2 percent (he's quant.i.tative literally to the end and beyond). It is his ultimate shot at beating the dealer.

Even if corporeal immortality was unlikely, Thorp's mark on Wall Street was vast and indelible. One measure of that influence lay in a squat chalk-white building, its flat-topped roof flared like an upside-down wedding cake, a short walk from his office in Newport Beach.

The building houses Pimco, one of the largest money managers in the world, with nearly $1 trillion at its disposal. Pimco is run by Bill Gross, the "Bond King," possibly the most well-known and powerful investor in the world besides Warren Buffett. A decision by Gross to buy or sell can send shock waves through global fixed-income markets. His investing prowess is legendary, as is his physical stamina. When he was fifty-three, he decided to run a series of marathons-five of them, in five days. On the fifth day, his kidney ruptured. He saw blood streaming down his leg. But Gross didn't stop. He finished the race, collapsing into a waiting ambulance past the finish line.

Gross would never have become the Bond King without Ed Thorp. In 1966, while a student at Duke University, Gross was in a car accident that almost killed him-he was nearly scalped, as a layer of skin was ripped from the top of his head. He spent six months recovering in the hospital. With lots of time to kill, he cracked open Beat the Dealer Beat the Dealer, testing the strategy in his hospital room over and over again.

"The only way I could know if Ed was telling the truth was to play," said Gross later that day in a conference room just off Pimco's expansive trading floor. His red tie hung jauntily untied around his neck like a scarf. A tall, lanky man with combed-back orange-tinted hair who meditates daily, Gross appeared so relaxed it was as if he were getting an invisible ma.s.sage as he sat in his chair. "And lo and behold, it worked!" Thorp, sitting to Gross's right, gave a knowing chuckle.

After he recovered from his accident, Gross decided to see if he could make the system pay off in the real world, just as Thorp had done in the early 1960s. With $200, he headed out to Las Vegas. In rapid fashion, he parlayed that into $100,000. The wad of cash helped pay for graduate school at the University of California, Los Angeles, where Gross studied finance. That's where he came across Beat the Market Beat the Market. Gross's master's thesis was based on the convertible-bond investment strategies laid out in the book-the same strategies Ken Griffin used to build Citadel.

Soon after reading Thorp's book, Gross had an interview at a firm then called Pacific Mutual Life. He had no experience trading and had little chance of landing a job. But his interviewer noticed that his thesis was on convertible bonds. "The people who hired me said, 'We have a lot of smart candidates, but this guy is interested in the bond market.' So I got my job because of Ed," said Gross.

As Gross and Thorp sat together in Pimco's conference room, they got to musing about the Kelly criterion, the risk management strategy Thorp used starting with his blackjack days in the 1960s. Pimco, Gross noted, uses a version of Kelly. "Our sector concentration is predicated on that-blackjack and investments," he said, gesturing toward the trading floor. "I hate to stretch it, but professional blackjack is being played in this trading room from the standpoint of risk management, and that ultimately is a big part of our success."

Thorp nodded in agreement. The key behind Kelly is that it keeps investors from getting in over their heads, Thorp explained. "The thing you have to make sure of is that you don't overbet," he said.

The conversation turned to hedge funds and leverage. A river of money had flowed into hedge funds in recent years, turning it from an industry with less than $100 billion under management in the early 1990s to a $2 trillion force of nature. But the amount of actual investing opportunities hadn't changed very much, Thorp said. The edge had diminished, but hedge fund managers' and bankers' appet.i.te for gigantic profits had only grown more voracious. That led to ma.s.sive use of leverage-in other words, overbetting. The inevitable end result: gambler's ruin on a global scale.

"A cla.s.sic example is Long-Term Capital Management," Thorp said. "We'll be seeing more of that now."

"The available edge has been diminished," Gross agreed, noting that Pimco, like Warren Buffett's Berkshire Hathaway, used very little leverage. "And that led to increased leverage to maintain the same returns. It's leverage, the overbetting, that leads to the big unwind. Stability leads to instability, and here we are. The supposed stability deceived people."

"Any good investment, sufficiently leveraged, can lead to ruin," Thorp said.

After about an hour, Gross stood, shook hands with the man responsible for getting him started, and walked onto Pimco's trading floor to keep an eye on the nearly $1 trillion in a.s.sets he ran.

Thorp walked back to his own office. It turned out that he was doing a little trading himself.

Sick and tired of watching screwups by managers he'd hired to care for his money, Thorp had decided to take the reins himself once again. He'd developed a strategy that looked promising. (What was it? Thorp wasn't talking.) In early 2008, he started running about $36 million with the strategy.

By the end of 2008, the strategy-which he called System X to outsiders-had gained 18 percent, with no leverage with no leverage. After the first week, System X was in positive territory the entire year, one of the most catastrophic stretches in the history of Wall Street, a year that saw the downfall of Bear Stearns, AIG, Lehman Brothers, and a host of other inst.i.tutions, a year in which Citadel Investment Group coughed up half of its money, a year in which AQR fell more than 40 percent and Saba lost nearly $2 billion.

Ed Thorp was back in the game.

DARK POOLS

On a sultry Tuesday evening in late April 2009, the quants convened for the seventh annual Wall Street Poker Night in the Versailles Room of the St. Regis Hotel in midtown Manhattan. sultry Tuesday evening in late April 2009, the quants convened for the seventh annual Wall Street Poker Night in the Versailles Room of the St. Regis Hotel in midtown Manhattan.

It was a far more subdued affair than the heady night three years earlier when the elite group of mathematical traders stood atop the investing universe. Many of the former stars of the show-Ken Griffin, Cliff Asness, and Boaz Weinstein-were missing. They didn't have time for games anymore. In the new landscape, the money wasn't pouring in as it used to. Now they had to go out and hustle for their dollars.

Griffin was in Beverly Hills hobn.o.bbing with former junk bond king Michael Milken at the Milken Inst.i.tute Global Conference, where rich people gathered for the primary purpose of reminding one another how smart they are. His IPO dreams had evaporated like a desert mirage, and he was furiously trying to chart a new path to glory. But the wind was blowing against him in early 2009. Several of his top traders had left the firm. And why not? Citadel's main fund, Kensington, had lost more than half its a.s.sets in 2008. In order to collect those lucrative incentive fees-the pie slice managers keep after posting a profit-the fund would need to gain more than 100 percent just to break even. That could take years years. To instant-gratification hedge fund managers, you might as well say forever. Or how about never?

Griffin wasn't shutting down the fund, though. Instead, he was launching new funds, with new strategies-and new incentive fees. He also was venturing into the investment banking world, trying to expand into new businesses as others faded. The irony was rich. As investment banks turned into commercial banks after their failed attempt to become hedge funds, a hedge fund was turning into an investment bank.

Some saw it as a desperate move by Griffin. Others thought it could be another stroke of genius. The toppled hedge fund king from Chicago was moving to take over business from Wall Street as his compet.i.tors were shackled by Washington's bailouts. His funds had made something of a comeback, advancing in the first half of the year as the chaos of the previous year abated. Whatever the case, Griffin hoped investors would see the debacle of 2008 as a one-time catastrophe, never to be repeated. But it was a tough sell.

Weinstein, meanwhile, was in Chicago hustling for his hedge fund launch. He was busy trying to convince investors that the $1.8 billion hole he'd left behind at Deutsche Bank was a fluke, a nutty mishap that could only happen in the most insane kind of market. By July, he'd raised more than $200 million for his new fund, Saba Capital Management, a big fall from the $30 billion in positions he'd juggled for Deutsche Bank. Setting up shop in the Chrysler Building in mid-town Manhattan, Saba was set to start trading in August.

Asness stayed home with his two pairs of twins and watched his beloved New York Rangers lose to the Washington Capitals in the decisive game seven of the National Hockey League's Eastern Conference playoff series. He was also busy launching new funds of his own. AQR had even ventured into the plain-vanilla-and low-fee-world of mutual funds. In a display of confidence in his strategies, Asness put a large chunk of his own money into AQR funds, including $5 million in the Absolute Return Fund. He also put $5 million into a new product AQR launched in 2008 called Delta, a low-fee hedge fund that quant.i.tatively replicated all kinds of hedge fund strategies, from long-short to "global macro." Several of AQR's funds had gotten off to a good start for the year, particularly his convertible bond funds-the decades-old strategy laid out by Ed Thorp in Beat the Dealer Beat the Dealer that had launched Citadel and hundreds of other hedge funds in the 1990s. Asness even dared to think the worst, finally, was behind him. He managed to find a bit of time to unwind. After working for months straight with barely a weekend off, Asness took a vacation in March to hike the craggy hills of Scotland. He even left his BlackBerry behind. But there were still reminders of his rough year. A newspaper article about AQR mentioned Asness's penchant for smashing computers. To his credit, he was now able to laugh at the antics he'd indulged in at the height of the turmoil, writing a tongue-in-cheek note to the editor protesting that it had "happened only three times, and on each occasion the computer screen deserved it." that had launched Citadel and hundreds of other hedge funds in the 1990s. Asness even dared to think the worst, finally, was behind him. He managed to find a bit of time to unwind. After working for months straight with barely a weekend off, Asness took a vacation in March to hike the craggy hills of Scotland. He even left his BlackBerry behind. But there were still reminders of his rough year. A newspaper article about AQR mentioned Asness's penchant for smashing computers. To his credit, he was now able to laugh at the antics he'd indulged in at the height of the turmoil, writing a tongue-in-cheek note to the editor protesting that it had "happened only three times, and on each occasion the computer screen deserved it."

But there was Peter Muller, walking briskly among the poker crowd in a brown jacket, well tanned, slapping old friends on the back, beaming that California smile.

Muller seemed calm on the outside, and with good reason: having earned north of $20 million in 2008, he was one of Morgan's highest earners for the year. Inside, he was seething. The Wall Street Journal Wall Street Journal had broken a story the week before that PDT might split off from Morgan Stanley, in part because its top traders were worried that the government, which had given the bank federal bailout funds, would curb their ma.s.sive bonuses. Muller had been working on a new business model for PDT for more than a year but was biding his time before he went public with his plans. The had broken a story the week before that PDT might split off from Morgan Stanley, in part because its top traders were worried that the government, which had given the bank federal bailout funds, would curb their ma.s.sive bonuses. Muller had been working on a new business model for PDT for more than a year but was biding his time before he went public with his plans. The Journal Journal article beat him to the punch, causing him no end of bureaucratic headaches. PDT had, in a flash, become a p.a.w.n in a game of giants-Wall Street versus the U.S. government. The move looked to some as if Morgan had crafted a plan to have its cake and eat it, too-spin off PDT, make a big investment, and get the same rewards while none of the traders lost a dime of their fat bonuses. article beat him to the punch, causing him no end of bureaucratic headaches. PDT had, in a flash, become a p.a.w.n in a game of giants-Wall Street versus the U.S. government. The move looked to some as if Morgan had crafted a plan to have its cake and eat it, too-spin off PDT, make a big investment, and get the same rewards while none of the traders lost a dime of their fat bonuses.

To Muller, it was a nightmare. Ironically, Morgan insiders even accused Muller of leaking the story to the press. Of course, he hadn't: Muller didn't talk to the press unless he absolutely needed to.

But he had one thing to look forward to: poker. And when it came to poker, Muller was all business.

Jim Simons, now seventy-one years old, was in attendance, hunched over a crowded dining table in a blue blazer and gray slacks, philosophically stroking his scraggly gray beard. But all was not well in Renaissance land. While the $9 billion Medallion fund continued to print money, gaining 12 percent in the first four months of the year, the firm's RIEF fund-the fabled fund that Simons once boasted could handle a whopping $100 billion (a fantasy it never even approached)-had lost 17 percent so far in 2009, even as the stock market was rising, tarnishing Simons's reputation as a can't-lose rainmaker. RIEF investors were getting upset about the disparity between the two funds, even though Simons had never promised that it could even approach the performance of Medallion. a.s.sets in Renaissance had fallen sharply, sliding $12 billion in 2008 to $18 billion, down from a peak of about $35 billion in mid-2007, just before the August 2007 meltdown.

There were other big changes in Simons's life, hints that he was preparing to step down from the firm he'd first launched in 1982. In 2008, he'd traveled to China to propose a sale of part of Renaissance to the China Investment Corp., the $200 billion fund owned and run by the Chinese government. No deal was struck, but it was a clear sign that the aging math whiz was ready to step aside. Indeed, later in the year Simons retired as CEO of Renaissance, replaced by the former IBM voice recognition gurus Peter Brown and Robert Mercer.

Perhaps most shocking of all, the three-pack-a-day Simons had quit smoking.

Meanwhile, other top quants mixed and mingled. Neil Chriss, whose wedding had seen the clash of Taleb and Muller over whether it was possible to beat the market, held session at a table with several friends. Chriss was a fast-rising and brilliant quant, a true mathematician who'd taught for a time at Harvard. He'd recently launched his own hedge fund, Hutchin Hill Capital, which received financial backing from Renaissance and had knocked the cover off the ball in 2008.

In a back room, before play began, a small private poker game was in session. Two hired-gun poker pros, Clonie Gowen and T. J. Cloutier, looked on, wincing from time to time at the clumsy play.

The crowd, still well heeled despite the market trauma, was dining on rack of lamb, puff pastry, and lobster salad. Wine and champagne were served at the bar, but most were taking it slow. There was still a lot of poker to play. And the party atmosphere of years gone by was diminished.

A chime rang out, summoning the players to the main room. Rows of tables with cards fanned out across them and dealers prim in their vested suits awaited them. Simons addressed the gathering crowd, talking about how the tournament had been getting better and better every year, helping advance the cause of teaching students mathematics. The quants in attendance somehow didn't think it ironic that their own profession amounted to a ma.s.sive brain drain of mathematically gifted people who could otherwise find careers in developing more efficient cars, faster computers, or better mousetraps rather than devising clever methods to make money for the already rich.

Soon enough play began. The winner that night was Chriss, whose hot hand at trading spilled over to the poker table. Muller didn't make the final rounds.

It had been a wildly tumultuous three years on Wall Street, drastically changing the lives of all the traders and hedge fund managers who'd attended the poker tournament in 2006. A golden era had come and pa.s.sed. There was still money to make, but the big money, the been a wildly tumultuous three years on Wall Street, drastically changing the lives of all the traders and hedge fund managers who'd attended the poker tournament in 2006. A golden era had come and pa.s.sed. There was still money to make, but the big money, the insane insane money, billions upon billions ... that train had left the station for everyone but a select few. money, billions upon billions ... that train had left the station for everyone but a select few.

Muller, ensconced in his Santa Barbara San Simeon, was hatching his plans for PDT. Its new direction wasn't just a change for Muller and company; it marked a seminal shift for Morgan Stanley, once one of the most aggressive kill-or-be-killed investment banks on Wall Street. By 2009, PDT, even in its shrunken state, was the largest proprietary trading operation still standing at Morgan. Its departure, if it happened, would cement the historic bank's transformation from a cowboy, risk-hungry, money-printing hot rod into a staid white-shoe banking company of old that made money by making loans and doing deals-not by flinging credit default swaps like so many Frisbees through the Money Grid and trading billions in other tangled derivatives through souped-up computers and clumsy quant models.

Most a.s.suredly, it would be a big change for PDT, once Morgan's secret quant money machine, and its mercurial captain.

Griffin, Muller, Asness, and Weinstein were all intent on making it work again, looking boldly into the future, chastened somewhat by the monstrous losses but confident they'd learned their lessons.

But more risk lurked. Hedge fund managers who've seen big losses can be especially dangerous. Investors, burned by the losses, may become demanding and impatient. If big gains don't materialize quickly, they may bolt for the exits. If that happens, the game is over.

That means there can be a significant incentive to push the limits of the fund's capacity to generate large gains and erase the memory of the blowup. If a big loss is no worse than a small loss or meager gains-since either can mean curtains-the temptation to jack up the leverage and roll the dice can be powerful.

Such perverse and potentially self-destructive behavior isn't countenanced by the standard dogmas of modern finance, such as the efficient-market hypothesis or the belief that the market always trends toward a stable equilibrium point. Those theories were increasingly coming under a cloud, questioned even by staunch believers such as Alan Greenspan, who claimed to have detected a flaw in the rational order of economics he'd long championed.

In recent years, new theories that captured the more chaotic behavior of financial markets had arisen. Andrew Lo, once Cliff Asness's teacher at Wharton and the author of the report on the quant meltdown of August 2007 that warned of a ticking Doomsday Clock, had developed a new theory he called the "adaptive market hypothesis." Instead of a rational dance in which market prices waltz efficiently to a finely tuned Bach cantata, Lo's view of the market was more like a drum-pounding heavy-metal concert of dueling forces that compete for power in a Darwinian death dance. Market partic.i.p.ants were constantly at war trying to squeeze out the last dime from inefficiencies, causing the inefficiencies to disappear (during which the market returns briefly to some semblance of equilibrium), after which they start hunting for fresh meat-or die-creating a constant, often chaotic cycle of destruction and innovation.

While such a vision seems unnerving, it appeared to many to be far more realistic, and certainly captured the nature of the wild ride that started in August 2007.

Then there were the behavioral finance theories of Daniel Kahneman, who picked up a n.o.bel Prize for economics in 2002 (his colleague, Amos Tversk, had pa.s.sed away years earlier). The findings of behavioral finance-often studies conducted on hapless undergraduate students in stark university labs-had shown time and again that people don't always make optimal choices when it comes to money.

A similar strand of thought, called neuroeconomics, was delving into the hardwiring of the brain to investigate why people often make decisions that aren't rational. Some investors pick stocks that sound similar to their own name, for instance, and others pick stocks with recognizable ticker symbols, such as HOG (Harley-Davidson). Evidence was emerging that certain parts of the brain are subject to a "money illusion" that blinds people to the impact of future events, such as the effect of inflation on the present value of cash-or the possibility of a speculative bubble bursting.

A small group of researchers at a cutting-edge think tank called the Sante Fe Inst.i.tute, led by Doyne Farmer (the hedge fund manager and chaotician who briefly met Peter Muller in the early 1990s), was developing a new way to look at financial markets as an ecology of interacting forces. The hope was that by viewing markets in terms of competing forces vying for limited resources, much like Lo's evolutionary vision, economists, a.n.a.lysts, and even traders will gain a more comprehensive understanding of how markets work-and how to interact with those markets-without destroying them.

And while quants were being widely blamed for their role in the financial crisis, few-aside from zealots such as Taleb-were calling for them to be cast out of Wall Street. That would be tantamount to banishing civil engineers from the bridge-making profession after a bridge collapse. Instead, many believed the goal should be to design better bridges-or, in the case of the quants, better, more robust models that could withstand financial tsunamis, not create them.

There were some promising signs. Increasingly, firms were adapting models that incorporated the wild, fat-tailed swings described by Mandelbrot decades earlier. J. P. Morgan, the creator of the bell curvebased VAR risk model, was pushing a new a.s.set-allocation model incorporating fat-tailed distributions. Morningstar, a Chicago investment-research group, was offering retirement-plan partic.i.p.ants portfolio forecasts based on fat-tailed a.s.sumptions. A team of quants at MSCI BARRA, Peter Muller's old company, had developed a cutting-edge risk-management strategy that accounted for potential black swans.

Meanwhile, the markets continued to behave strangely. In 2009 the gut-churning thousand-point swings of late 2008 were a thing of the past, but stocks were still mired in a ditch despite an early-year rally; the housing market looked as if it would keep cratering until the next decade. Banks had dramatically reduced their leverage and promised their new investor-the U.S. government-that they would behave. But there were signs of more trouble brewing.

As early as the spring of 2009, several banks reported stronger earnings numbers than most expected-in part due to clever accounting tricks. Talk emerged about the return of big bonuses on Wall Street. "They're starting to sin again," Brad Hintz, a respected bank a.n.a.lyst, told the New York Times New York Times.

Quant funds were also suffering another wave of volatility. In April, indexes that track quant strategies suffered "some of the best and worst days ever ... when measured over approximately 15,000 days," according to a report by Barclays quant researcher Matthew Rothman (formerly of Lehman Brothers).

Many of the toxic culprits of the meltdown were dying away. The CDOs were gone. Trading in credit default swaps was drying up. But there were other potentially dangerous quant gadgets being forged in the dark smithies of Wall Street.

Concerns about investment vehicles called exchange-traded funds were cropping up. Investors seemed to be piling into a number of highly leveraged ETFs, which track various slices of the market, from oil to gold mining companies to bank stocks. In March 2009 alone, $3.4 billion of new money found its way into leveraged ETFs. Quant trading desks at banks and hedge funds started tracking their behavior using customized spreadsheets, attempting to predict when the funds would start buying or selling. If they could predict the future-if they knew the Truth-they could antic.i.p.ate the move by trading first.

The worry was that with all the funds pouring money into the market at once-or pulling it out, since there were many ETFs that shorted stocks-a ma.s.sive, destabilizing cascade could unfold. In a report on the products, Minder Cheng and Ananth Madhavan, two top researchers at Barclays Global Investors, said the vehicles could create unintended consequences and potentially pose systemic risk to the market. "There is a close a.n.a.logy to the role played by portfolio insurance in the crash of 1987," they warned.

Another concern was an explosion in trading volume from computer-driven, high-frequency funds similar to Renaissance and PDT. Faster chips, faster connections, faster algorithms-the race for speed was one of the hottest going. Funds were trading at speeds measured in microseconds-or one-millionth of a second. In Mahwah, New Jersey, about thirty-five miles from downtown Manhattan, the New York Stock Exchange was building a giant data center three football fields long, bigger than a World War II aircraft carrier, that would do nothing but process computerized trades. "When people talk about the New York Stock Exchange, this is it," NYSE co-chief information officer Stanley Young told the Wall Street Journal Wall Street Journal. "This is our future."

But regulators were concerned. The Securities and Exchange Commission was worried about a rising trend of high-frequency trading firms that were getting so-called naked access to exchanges from brokerages that lent out their computer identification codes. While high-frequency firms were in many ways beneficial for the market, making it easier for investors to buy and sell stocks since there always seemed to be a high-frequency player willing to take the other side of a trade, the concern was that a rogue fund with poor risk-management practices could trigger a destabilizing sell-off.

"We consider this dangerous," said one executive for a company that provided services to high-frequency trading firms. "My concern is that the next LTCM problem will happen in less than five minutes."

The world of high-frequency trading leapt into the media spotlight in July 2009 when Sergey Aleynikov, a quant who'd just quit a job writing code for Goldman Sachs, stepped off a plane at Newark Liberty Airport after a trip to Chicago. Waiting for him at the airport were FBI agents. Aleynikov was arrested and charged with stealing code from Goldman's secretive high-frequency trading group, a charge he fought in court.

Adding to the mystery was a connection to a powerful quant Chicago hedge fund: Citadel. Aleynikov had just taken a position at Teza Technologies, which had recently been founded by Misha Malyshev, who'd been in charge of Citadel's highly lucrative Tactical Trading outfit. Six days after Aleynikov's arrest, Citadel sued Malyshev and several of his colleagues-also former Citadel employees-alleging that they'd violated noncompete agreements and could also be stealing code, allegations the defendants denied.

The suit spelled out previously unknown details about Citadel's superfast trading operation. The Tactical Trading offices, which required special codes to enter, came equipped with ranks of cameras and guards to ensure no proprietary information was stolen. The firm had spent hundreds of millions to develop the codes over the years and alleged that Malyshev and his cohorts were threatening the investment.

The suit also revealed that Tactical was a money-making machine, having raked in more than $1 billion in 2008, capitalizing on the market's volatility, even as Citadel's hedge funds lost about $8 billion. It raised questions about Griffin's decision in late 2007 to spin off Tactical from the hedge fund operations, a move that effectively increased his stake in a unit that printed money at a time his investors were getting clobbered. Princ.i.p.als at Citadel, mostly Griffin, owned about 60 percent of the $2 billion fund, according to people familiar with its finances.

All of the controversy alarmed regulators and everyday investors, who'd been largely unaware of the lightning-fast trading that had become a central component of the Money Grid, strategies first devised in the 1980s by innovators such as Gerry Bamberger and Jim Simons and furthered in the following decade by the likes of David Shaw and Peter Muller. But there were legitimate concerns that as computer-driven trading reached unfathomable speeds, danger lurked.

Many of these computer-driven funds were gravitating to a new breed of stock exchange called "dark pools"-secretive, computerized trading networks that match buy and sell orders for blocks of stocks in the frictionless ether of cybers.p.a.ce. Normally, stocks are traded on public exchanges such as the Nasdaq and the NYSE in open view of anyone who chooses to look. Trades conducted through dark pools, as the name implies, are anonymous and hidden from view. The pools go by names such as SIGMA X, Liquidnet, POSIT, CrossFinder, and NYFIX Millennium HPX. In these invisible electronic pools, vast sums change hands beyond the eyes of regulators. While efforts were afoot to push the murky world of derivatives trading into the light of day, stock trading was sliding rapidly into the shadows.

Increasingly, hedge funds had been crafting new systems to game the pools, hunting for price discrepancies between them in the eternal search for arbitrage or even causing causing price changes with dubious tactics and predatory algorithms. Hedge funds were "pinging" the dark pools with electronic signals like submarines hunting prey, searching for liquidity. The behavior was largely invisible, and light-years ahead of regulators. price changes with dubious tactics and predatory algorithms. Hedge funds were "pinging" the dark pools with electronic signals like submarines hunting prey, searching for liquidity. The behavior was largely invisible, and light-years ahead of regulators.

Dark pools were also opening up to superfast high-frequency trading machines. The NYFIX Millennium pool had narrowed its response time to client orders to three milliseconds. A flier Millennium sent to potential clients claimed that traders with "ninja skills succeed" in dark pools at "dangerously high speeds for the unprepared."

Mom and Pop's retirement dreams, meet Ninja Hedge Fund.

Whether such developments posed a broader risk to the financial system was unknown. Users of the technology said faster trades boosted "liquidity," making trading easier and cheaper. But as the financial panic of 2007 and 2008 had shown, liquidity is always there when you don't need it-and never there when you do.

Meanwhile, congressmen, President Obama, and regulators were making noise about reining in the system with new rules and regulations. Progress had been made in setting up a clearinghouse for credit default swaps to keep better track of the slippery contracts. But behind the scenes, the financial engineers were hard at work devising new methods to operate in the shadows.

Just look: exotic leveraged vehicles marketed to the ma.s.ses worldwide, hedge funds gaming their returns, lightning-fast computerized trading robots, predatory ninja algorithms hunting liquidity in dark pools ...

Here come the quants.

Notes.

1[image] ALL IN ALL IN Simons had pocketed $1.5 billion: Alpha Alpha, May 2006.

That night at the St. Regis: Several details of the poker event were gleaned from Several details of the poker event were gleaned from MFA News MFA News 2, 1 (Spring 2006). 2, 1 (Spring 2006).

In 1990, hedge funds held $39 billion: Based on data from Hedge Fund Research, a Chicago research group. Based on data from Hedge Fund Research, a Chicago research group.

2[image] THE G.o.dFATHER: ED THORP THE G.o.dFATHER: ED THORP Just past 5:00 A.M A.M.: I conducted numerous interviews with Ed Thorp and exchanged many emails. Many details about Ed Thorp's blackjack career, including a description of his foray into blackjack in 1961, were found in his colorful book Beat the Dealer: A Winning Strategy for the Game of Twenty-One Beat the Dealer: A Winning Strategy for the Game of Twenty-One (Vintage, 1962). (Vintage, 1962).

Other details were found in the excellent Fortune's Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street Fortune's Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street, by William Poundstone (Hill and w.a.n.g, 2005). I confirmed details I used from this book with Thorp.

The strategy was from a ten-page article: "Getting a Hand: They Wrote the First Blackjack Book but Never Cashed In," by Joseph P. Kahn, "Getting a Hand: They Wrote the First Blackjack Book but Never Cashed In," by Joseph P. Kahn, Boston Globe Boston Globe, February 20, 2008.

He'd kept his roulette strategy largely secret: "The Invention of the First Wearable Computer," by Edward O. Thorp ( "The Invention of the First Wearable Computer," by Edward O. Thorp (http://graphics.cs.columbia.edu/courses/mobwear/resources/thorp-iswc98.pdf.) Science-fiction writer Arthur C. Clarke: Voice Across the Sea Voice Across the Sea, by Arthur C. Clarke (HarperCollins, 1975).

3[image] BEAT THE MARKET BEAT THE MARKET On a typical day of desert sun: Much like the blackjack chapter, many details of this chapter derive from interviews with Thorp, Much like the blackjack chapter, many details of this chapter derive from interviews with Thorp, Fortune's Formula Fortune's Formula, and Thorp's second book, Beat the Market: A Scientific Stock Market System Beat the Market: A Scientific Stock Market System. That book is out of print, but Thorp kindly provided a Web-accessible version.

Huge, sudden leaps: For more than a decade, Na.s.sim Taleb has been criticizing quant models for leaving out huge market events, or black swans, and he deserves much credit for warning about such shortcomings of the models. I had numerous conversations with Taleb while writing this book. For more than a decade, Na.s.sim Taleb has been criticizing quant models for leaving out huge market events, or black swans, and he deserves much credit for warning about such shortcomings of the models. I had numerous conversations with Taleb while writing this book.

Gerry Bamberger discovered stat arb: The section on the discovery of statistical arbitrage is based almost entirely on interviews with Gerry Bamberger, Nunzio Tartaglia, and several other members of the original Morgan Stanley group that discovered and spread stat arb across Wall Street. Previous mention of this group can be found in The section on the discovery of statistical arbitrage is based almost entirely on interviews with Gerry Bamberger, Nunzio Tartaglia, and several other members of the original Morgan Stanley group that discovered and spread stat arb across Wall Street. Previous mention of this group can be found in Demon of Our Own Design Demon of Our Own Design, by Richard Bookstaber (John Wiley & Sons, 2007).

Morgan had hired Shaw: The account of Shaw's departure from Morgan are based on interviews with Nunzio Tartaglia and others who were at APT. The account of Shaw's departure from Morgan are based on interviews with Nunzio Tartaglia and others who were at APT.

4[image] THE VOLATILITY SMILE THE VOLATILITY SMILE Sometime around midnight: Many details of Black Monday were found in numerous Many details of Black Monday were found in numerous Wall Street Journal Wall Street Journal articles written during the time, including "The Crash of '87-Before the Fall: Speculative Fever Ran High in the 10 Months Prior to Black Monday," by James B. Stewart and Daniel Hertzberg, December 11, 1987. articles written during the time, including "The Crash of '87-Before the Fall: Speculative Fever Ran High in the 10 Months Prior to Black Monday," by James B. Stewart and Daniel Hertzberg, December 11, 1987.

Other details, including the description at the opening of the chapter, were found in An Engine, Not a Camera: How Financial Models Shape Markets An Engine, Not a Camera: How Financial Models Shape Markets, by Donald MacKenzie (MIT Press, 2006), and The Age of Turbulence: Adventures in a New World The Age of Turbulence: Adventures in a New World, by Alan Greenspan (Penguin 2007), 105.

On the evening of September 11, 1976: The best description of the invention of portfolio insurance that I know of can be found in The best description of the invention of portfolio insurance that I know of can be found in Capital Ideas: The Improbable Origins of Modern Wall Street Capital Ideas: The Improbable Origins of Modern Wall Street, by Peter L. Bernstein (John Wiley & Sons, 2005). Another source is "The Evolution of Portfolio Insurance," by Hayne E. Leland and Mark Rubinstein, published in Portfolio Insurance: A Guide to Dynamic Hedging Portfolio Insurance: A Guide to Dynamic Hedging, edited by Donald Luskin (John Wiley & Sons, 1988).

"Even if one were to have lived": The age of the universe is 13.5 billion years, not 20 billion. The age of the universe is 13.5 billion years, not 20 billion.

When German tanks rumbled into France: Some details of Mandelbrot's life come from a series of interviews with Mandelbrot in the summer of 2008. Many also come from the book Some details of Mandelbrot's life come from a series of interviews with Mandelbrot in the summer of 2008. Many also come from the book The (Mis)Behavior of Markets: A Fractal View of Financial Turbulence The (Mis)Behavior of Markets: A Fractal View of Financial Turbulence, by Benoit Mandelbrot and Richard L. Hudson (Basic Books, 2006).