Imagine an aeronautics engineer designing a state-of-the-art jumbo jet. In order for it to fly, the engineer has to rely on the same aerodynamics equation devised by physicists 150 years ago, which is based on Newton's second law of motion: force equals mass times acceleration. Problem is, the engineer can't reconcile his elegant design with the equation. The plane has too much mass and not enough force. But rather than tweak the design to fit the equation, imagine if the engineer does the opposite, and tweaks the equation to fit the design. The plane still looks awesome, and on paper, it flies. The engineer gets paid, the plane gets built, and soon thousands just like it are packed full of people and sent out onto runways. They fly for a while, but eventually, because of that fatal tweak, they all end up crashing.
In a way, this is what's happened in quantitative finance. The planes are the complex derivatives—like collateralized debt obligations—that now lie smoldering on the balance sheets of banks. The engineers are the "quants": those math and science Ph.D.s who flocked to Wall Street over the past decade and used mathematical models to build these new investment products. These are the people Warren Buffett was talking about when he said, "Beware of geeks bearing formulas" in his letter to shareholders this year. The quants aren't entirely to blame for the financial meltdown; there's plenty of guilt to be shared by regulators, top executives and the investors who bought the instruments the quants created. Yet while aeronautical engineers who willfully designed a faulty plane might be on trial for criminal negligence, Wall Street's math gurus are, for the most part, still employed. Strangely, the banks need quants more than ever right now. If anyone's going to figure out how to price these toxic assets, it's them. Quantitative finance isn't going away, but it is in desperate need of reform. And one man—a math geek himself—thinks he knows where to start.
Paul Wilmott is a 49-year-old Oxford-trained mathematician and arguably the most influential quant today, the brightest star in their insular, nerdy universe. The Financial Times calls him a "cult derivatives lecturer." Nassim Taleb, the mathematician and author of the bestseller The Black Swan, calls him the smartest quant in the world. "He's the only one who truly understands what's going on ... the only quant who uses his own head and has any sense of ethics," says Taleb. Wilmott stands atop a veritable quant empire. His wonk-made-simple textbooks sell for hundreds of dollars. A subscription to his bimonthly magazine, Wilmott, costs $695 a year. His Web site, Wilmott.com, is the nerve center of the quant community, with 65,000 registered users and a chat forum that buzzes over such topics as geodesic stochastic manifolds and swaption vol arbitrage.
Over the past decade, and increasingly since the crash, Wilmott has cultivated a loyal following of truth-seeking converts from the failed school of thought that the entire world can be turned into Greek symbols, plugged into equations, priced and predicted. He's especially critical of the notion that math can forecast human behavior, essentially the basis of finance. "This," says Wilmott, "is absolute rubbish." To rectify the situation, he's started his own training program, the Certificate in Quantitative Finance, or CQF. It's the gem of his empire, the key, he hopes, to saving the quants from themselves, not to mention all of us from their future destruction. In essence, the course is rehab for quants, a six-month, $18,000 program designed to break them of the abstract, theoretical approach to finance they learned in their Ph.D. or financial-engineering programs, and replace it with a more practical set of skills that are actually used on Wall Street. "What banks really need are quants who can translate theoretical math and tell them how it applies," says Wilmott. "Because what good is being fluent in geek if you can't apply it? You might as well stay in university."
Ever since Ed Thorp, the first true quant, left his job teaching math at UC Irvine to start a hedge fund in the 1970s, math and science types have been setting out from academia to try their hand at finance. The watershed came in the mid-1970s when MIT-trained economist Robert Merton along with Myron Scholes, a University of Chicago economist, and Fischer Black of Harvard developed the Black-Scholes equation for pricing options, which eventually garnered a Nobel Prize. Over the past 20 years, quantitative methods gradually spread into commercial and investment banks, fueling a huge demand for math savants. Since the mid-1990s, dozens of master's-degree programs in financial engineering have sprouted up at top universities. (The highest-rated ones are at Carnegie Mellon, Columbia, Stanford and Princeton.) Along with physics Ph.D. programs, these are the primary breeding grounds for the many thousands of quants who have found their way to Wall Street. It's these programs that Wilmott has taken direct aim at with his CQF. "I'm building a new army of quants," he says. His ranks currently stand at 1,273: the number of CQF alumni who have graduated since the program was founded in 2003. Wilmott realizes he's vastly outnumbered, but he's undaunted. "Ever see the movie Zulu?" he asks, referring to the 1964 Michael Caine film about a battalion of 140 British soldiers besieged by 4,000 African warriors in 1879. The Brits won, mostly because they were better-trained and -equipped, just as Wilmott wants his graduates to be.
The CQF is taught at night in London's financial district by Wilmott and a handful of his buddies, most of whom have worked in finance. These instructors are miles away from the stereotypical math or finance professors. Among them is Espen Haug, a Norwegian former JPMorgan options trader who looks like a cross between James Bond and Arnold Schwarzenegger, and often lectures in sunglasses and a tuxedo. One evening this spring, Wilmott is wrapping up the final class on interest rates and fixed income. He stands at a podium, looking out at about 30 students, most of whom have just gotten off work from their jobs at banks: Citigroup, Deutsche Bank, Credit Suisse. Another 100 or so watch the lecture streaming over the Internet. The official topic of the evening is how to decompose the random movements of the forward rate curve into its principal components—i.e., how to predict random fluctuations in interest rates in order to determine bond prices. "There's nothing difficult here," Wilmott says without irony. "If you can keep your head, you'll be fine."
He's just scribbled a handful of equations on a whiteboard, including one called the Heath-Jarrow-Morton model. Developed in the late 1980s, the formula looks horrifically complicated to the layman. But to a mathematician it's elegant, simple—and dangerous. Behind its simplicity lie hidden mistakes, unobservable variables like volatility and correlation that can provide a false sense of security. "With models, you want to see where things go wrong," says Wilmott. "You want to see the dirt. But HJM is actually just a big rug for [mistakes] to be swept under." For the next half hour, Wilmott deconstructs the thing, cautioning students on overreliance. "In the end, we should all like models that wear their faults on their sleeves," he tells the class.
Two hours later, Wilmott is treating his students to beers at a nearby pub. Among them are half a dozen fresh-faced Citigroup employees, all in their mid-20s, all recent physics or engineering Ph.D. graduates, and all being sponsored by Citigroup to take the CQF. (Banks have only recently started sponsoring students to take Wilmott's classes, a tacit acknowledgment that quants need more holistic training.) "There's an arms race going on in quantitative finance," says one of the students. "The CQF gives us another weapon in our arsenal."
On a typical April weekday, Wilmott spends the morning in his office, a small, gray room that's completely nondescript save for the giant blackboard filled with mathematical notation. There he goes over the final touches of an options formula he's getting ready to publish with a former student. He then takes the tube across town to London's posh Grosvenor Square to meet with three former investment bankers who want to hire him as a quant on call for their consultancy startup. They pitch Wilmott while sitting in the modern dining room of Gordon Ramsay's Maze Grill restaurant. Wilmott tells them he'll think about it, then sets off down Oxford Street, a stretch of shops that's swarming with tourists.
Picking his way through, on and off his cell phone, Wilmott talks about the contradictions in his life: he's a car enthusiast who hates to drive; he goes on Swiss ski trips but doesn't ski. Though he's nearly 50, he could pass for 30-something, especially when dressed in skinny jeans, black Chuck Taylors, Gucci eyeglasses and a retro zip-up cardigan. This is his outfit of choice so long as he's not giving a speech somewhere, in which case he might change his shoes and throw on a jacket.
Born in Birkenhead, a small town outside Liverpool, Wilmott studied applied math at Oxford. In his spare time, he dabbled in juggling and competitive ballroom dancing. After earning a Ph.D. in fluid mechanics from Oxford in 1985, he got his start as an applied mathematician, working on jet-engine turbines for Rolls-Royce and calculating detonation sites for an explosives company. In the late 1980s, he started applying math to finance. His first burst of fame came in 1993 when he co-wrote a textbook on derivatives. Soon he'd made a name for himself as a contrarian guru, writing more textbooks, and giving speeches around the world to rooms full of bankers. From 2001 to 2005 he ran a $170 million hedge fund that returned an average of 15 percent a year.
Back on Oxford Street, Wilmott walks by several tube stops, deep in conversation on the topic that gets him most agitated these days: structured credit, the area of finance most at fault in the crash, and where quants inflicted the most damage by applying mathematical models they swore could predict default rates. "A complete lapse of ethics and responsibility," he calls it.
A collateralized debt obligation (CDO) is the most common form of structured credit. Banks build CDOs by putting together a bunch of loans, slicing them into little pieces (tranches) and selling them off to investors. Think of it as disassembling a cow into different cuts of meat—from prime steaks to ground beef—that are priced according to their quality. The first CDO was issued in 1987 by Drexel Burnham Lambert, the same firm that went bust in 1990. After the fall of Drexel, CDOs went away for a while, until the quants came along. In 2000, the CDO market was jump-started by David X. Li, who, while working at JPMorgan, created the Gaussian copula function, a formula for determining the correlation between the default rates of different securities. In theory, the model tells you the odds that, if one CDO goes bad, others will too. The apparent genius of the Gaussian copula is its abstraction. Rather than relying on the immense amount of data used to figure the odds that a CDO might default, Li appeared to have discovered a law of correlation. That is, you didn't need the data; the correlation was just there. Armed with it, quants could price CDOs much faster, and traders could buy and sell them at record speeds. Gaussian was rocket fuel for the CDO market. The global volume of CDO deals went from $157 billion in 2004 to $520 billion in 2006. As more banks got in on the game, the once large profit margins started to shrink. In order for banks to make the same kind of returns, they had to pack more and more loans into a CDO, essentially making bigger bombs. Li was on his way to a Nobel Prize when the world blew up. Wilmott marvels at the carelessness of it all. "They built these things on false assumptions without testing them, and stuffed them full of trillions of dollars. How could anyone have thought that was a good idea?"
To Wilmott, Gaussian is an example of how dangerously abstract quant finance has become. "We need to get back to testing models rather than revering them," he says. "That's hard work, but this idea that there are these great principles governing finance and that correlations can just be plucked out of the air is totally false." Wilmott spends a lot of time with another former student trying to tackle the biggest problem facing quant finance right now: how to price all those CDOs sitting on the balance sheets of banks, the toxic assets we hear so much about. "We don't have the tools yet to truly price them," Wilmott says. "People thought we did, but they were nowhere near robust enough."
The optimist in Wilmott thinks that people realize these models don't work. But he's not really an optimist. "What I think is going to happen is that people will forget and we'll just keep going on the way we have been with nothing really changing," he says. Wilmott is encouraged by President Obama's proposals to tighten regulation of derivatives; he thinks it'll keep quants on a shorter leash. But he's also stunned by the lack of outrage over the financial mess. The violence that erupted at this year's G20 summit wasn't anywhere near what he thought it should've been. "Where the hell was everybody? If people aren't angry now, they'll never be."
Wilmott realizes he's fighting a losing battle, and that changing finance will take a lot more than a few thousand better-prepared quants. As long as banks get paid in the first year for selling a CDO that doesn't mature for 30 years, little will change. Still, he does sense a tidal shift. "I've been helped by recent events, but I don't really take solace in that. I'm not gonna say I told you so."
For now, Wilmott will go about the hard work of retraining his merry band of quant soldiers, hoping his attempts at remedial education can help minimize the odds of a future derivatives-fueled melt-down. Waiting for traffic in the shadow of St. Paul's Cathedral, having walked the three miles from Grosvenor Square, Wilmott realizes he's late for the CQF class. "My God, I'm lecturing in 10 minutes!" For investors who hope to be protected from these "financial weapons of mass destruction," it's not a moment too soon.