The Quants: How a New Breed of Math Whizzes Conquered Wall Street and Nearly Destroyed It (10 page)

But the damage had been done. The mood around the country turned decidedly anti–Wall Street as the junk bond scandals hit the front pages of newspapers. An October 1987
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
Wall Street:
“Greed is good.” A series of popular books reflecting the anti–Wall Street sentiment hit the presses:
Bonfire of the Vanities
by Tom Wolfe,
Barbarians at the Gate
by
Wall Street Journal
reporters Bryan Burrough and John Helyar,
The Predators’ Ball
by Connie Bruck,
Liar’s Poker
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 Nazis 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 competition. 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 destitute. 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 competition 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 institutions of higher education, the École Normale Supérieure and the École 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 Institute 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.

The bizarre leaps and plunges in cotton prices had proved too wild for Houthakker. Either the data were bad—unlikely, as there were a lot of data, going back more than a century from records kept by the New York Cotton Exchange—or the models were faulty. Either way, he was on the verge of giving up.

“I’ve had enough,” he told Mandelbrot. “I’ve done everything I could to make sense of these cotton prices. I try to measure the volatility. It changes all the time. Everything changes. Nothing is constant. It’s a mess of the worst kind.”

Mandelbrot saw an opportunity. There might be a hidden relationship between his own analysis of income distributions—which also displayed wild, disparate leaps that didn’t fall within the normal bell curve—and these unruly cotton prices that had driven Houthakker to his wits’ end. Houthakker happily handed over a cardboard box full of computer punch cards containing data on cotton prices.

“Good luck if you can make any sense of these.”

Upon returning to IBM’s research center in Yorktown Heights, Mandelbrot began running the data through IBM’s supercomputers.
He gathered prices from dust-ridden books at the National Bureau of Economic Research in Manhattan and from the U.S. Agriculture Department in Washington. He looked into wheat prices, railroad stocks, and interest rates. Everywhere he looked he saw the same thing: huge leaps where they didn’t belong—on the outer edges of the bell curve.

After combing through the data, Mandelbrot wrote a paper detailing his findings, “The Variation of Certain Speculative Prices.” Published as an internal research report at IBM, it was a direct attack on the normal distributions used to model the market. While praising Louis Bachelier, a personal hero of Mandelbrot’s, the mathematician asserted that “the empirical distributions of price changes are usually too ‘peaked’ relative to samples” from standard distributions.

The reason: “Large price changes are much more frequent than predicted.”

Mandelbrot proposed an alternative method to measure the erratic behavior of prices, one that borrows a mathematical technique devised by the French mathematician Paul Lévy, whom he’d studied under in Paris. Lévy investigated distributions in which a single sample radically changes the curve. The average of the heights of 1,000 people won’t change very much as a result of the height of the 1,001st person. But a so-called Lévy distribution can be thrown off by a single wild shift in the sample. Mandelbrot uses the example of a blindfolded archer: 1,000 shots may fall close to the target, but the 1,001st shot, by happenstance, may fall very wide of the mark, radically changing the overall distribution. It was an entirely different way of looking at statistical patterns—all previous results could be overturned by one single dramatic shift in the trend, such as a 23 percent drop in the stock market in a single day. Lévy’s formulas gave Mandelbrot the mathematical key to analyzing the wild moves in cotton prices that had befuddled Houthakker.

When plotted on a chart, these wild, unexpected moves looked nothing like the standard bell curve. Instead, the curve bubbled out on both ends, the “tails” of the distribution. The bubbles came to be known as “fat tails.”

Word of Mandelbrot’s paper spread through the academic community. In late 1963, he got a call from Paul Cootner, an MIT finance professor. Cootner was putting together a book of published material on recent mathematical insights into the workings of the market, including a translation of Bachelier’s thesis on Brownian motion. He wanted to include Mandelbrot’s paper. He called the book
The Random Character of Stock Market Prices
. It was the same book Ed Thorp read a year later when he was trying to figure out a formula to price warrants.

In the book, Cootner attacked Mandelbrot’s submission in a vicious five-page critique. Mandelbrot “promises us not utopia but blood, sweat, toil, and tears.” The wild gyrating mess of Lévy’s formulas, the sudden leaps in prices, simply wouldn’t do. The result would be chaos. While several economists briefly glommed on to Mandelbrot’s analysis, it soon fell out of favor. Some said the approach was too simplistic. Others simply found the method too inconvenient, incapable of predicting prices, as if one were trying to forecast the direction of a Mexican jumping bean. Critics said that while it may work for brief time periods when price action can be erratic, over longer time periods, prices appear to move in a more orderly Brownian fashion. An eyeball test of long-term trends in the stock market shows that prices of an entire market do tend to move in more regular, less erratic patterns.

Mandelbrot agreed that over long periods, equilibrium tends to rule the day. But that misses the point. Prices can gyrate wildly over
short
periods of time—wildly enough to cause massive, potentially crippling losses to investors who’ve made large, leveraged wagers.

As Nassim Nicholas Taleb, a critic of quant models, later argued in several books, investors who believe the market moves according to a random walk are “fooled by randomness” (the title of one of his books). Taleb famously dubbed the wild unexpected swings in markets, and in life itself, “black swans,” evoking the belief long held in the West that all swans are white, a notion exploded when sailors discovered black swans in Australia. Taleb argued that there are far more black swans in the world than many people believe, and that models based on historical trends and expectations of a random walk are bound to lead their users to destruction.