The Quants: How a New Breed of Math Whizzes Conquered Wall Street and Nearly Destroyed It (6 page)

Soon after Thorp announced his results in Washington, D.C., he was watching a TV program about gambling. A reporter asked a casino owner whether gambling ever paid off.

“When a lamb goes to the slaughter, the lamb might kill the butcher,” the owner said. “But we always bet on the butcher.”

Thorp smiled. He knew that he’d beaten the butcher. As he would later write: “The day of the lamb had come.”

After his
first excursion to Vegas, Thorp began work on
Beat the Dealer
. Published in 1962, the book quickly became a
New York Times
bestseller—and struck terror into the heart of casino bigwigs everywhere.

Thorp continued to rack up gains at blackjack tables on several return trips to Las Vegas. Dealers were on the lookout for the gambling professor. He began wearing disguises, well aware of stories about card counters getting hauled into side alleys or casino basements for brutal beatings.

One day in 1964, when he was playing at a baccarat table in Las Vegas, he was offered a cup of coffee with cream and sugar. He took a few sips, then started feeling odd.

A friend who’d traveled to Las Vegas with Thorp and his wife
happened to be a nurse. She peered into his eyes and recognized the look of drugged-out patients who landed in the emergency room. He walked it off, but the episode unnerved him. He decided he needed to find a fresh venue to test his strategies.

Thorp immediately set his sights on the biggest casino of all: Wall Street.

On a
typical day of desert sun and dry heat in Albuquerque, New Mexico, in the summer of 1965, Thorp settled into a lawn chair to read about an obscure corner of Wall Street: stock warrants.

Warrants are basically long-term contracts, much like a call option, that investors can convert into common stock. (A call option that gives an investor the right to purchase a stock at a future date is mathematically identical to a warrant.) At the time, warrants were thinly traded and generally considered the province of gamblers and bucket shops, the shadowy realm of off-exchange trading—not the typical domain of mathematically inclined professors. No one had figured out how to accurately price them.

In this obscure world, Thorp saw a vision of millions. Methods he’d used to win at blackjack, he realized, could be used to discern the value of warrants.

Soon after discovering this hidden gold mine, Thorp, who’d been teaching at New Mexico State, took a job at the University of California, Irvine. After arriving on campus, he heard about a finance professor at the university named Sheen Kassouf, a New York native of Lebanese descent, who’d also been plugging away at the problem of how to price warrants.

Kassouf had been dabbling in warrants since the early 1960s. He hadn’t cracked the code for how to price the securities, but he had a strong grasp of how they worked. The two professors began meeting several times a week and eventually devised one of the first truly rigorous quantitative investing strategies—what they called “a scientific stock market system.”

Their system enabled them to accurately price convertible bonds, which are a hybrid security made up of a bond, which spits out a regular interest payment, and those thinly traded warrants, which give the owner the right to convert the security to stock (hence the name of the bonds). Pricing a warrant was a difficult task, since its value depends on divining the likely price of the underlying stock at some future date. The system Thorp and Kassouf devised helped them make predictions about the future course of stock prices, allowing them to discover which convertible bonds were mispriced.

A key part of the answer, Thorp discovered, was found in a book he’d picked up after he’d switched his attention from blackjack to Wall Street. It was called
The Random Character of Stock Market Prices
, a collection of essays published in 1964, most of which argued that the market followed a so-called random walk. Essentially, that meant the future direction of the market as a whole, or any individual stock or bond, was a coin flip: there was a 50–50 chance that it could rise or fall.

The idea that the market moved in this fashion had been gaining ground since the mid-1950s, although the conceptual tool kit had been in the making for more than a century—all the way back, in fact, to June 1827 and a Scottish botanist and his love of flowers.

The botanist, Robert Brown, had been studying a species of pollen, called pinkfairies, through the lens of a brass microscope. The
magnified pollen grains, he observed, jiggled incessantly, like thousands of tiny Ping-Pong balls moving in a frenetic dance.

Brown couldn’t figure out what was causing the motion. After testing a range of other plant specimens, even the ground dust of rocks, and observing similar herky-jerky motion, he concluded that he was observing a phenomenon that was completely and mysteriously random. (The mystery remained unsolved for decades, until Albert Einstein, in 1905, discovered that the strange movement, by then known as Brownian motion, was the result of millions of microscopic particles buzzing around in a frantic dance of energy.)

The connection between Brownian motion and market prices was made in 1900 by a student at the University of Paris named Louis Bachelier. That year, he’d written a dissertation called “The Theory of Speculation,” an attempt to create a formula that would capture the movement of bonds on the Paris stock exchange. The first English translation of the essay, which had lapsed into obscurity until it resurfaced again in the 1950s, had been included in the book about the market’s randomness that Thorp had read in New Mexico.

The key to Bachelier’s analysis was his observation that bond prices move in a way identical to the phenomenon first discovered by Brown in 1827. Bonds trading on the Paris stock exchange followed a pattern that, mathematically, moved just like those randomly oscillating pollen particles. Like the jiggling pollen grains, the minute-by-minute movement of the price of bonds appeared to be completely random, pushed up, down, and sideways by thousands of investors trying to guess where the market was going next. According to Bachelier’s thinking, their guesses were futile. There was no way to know where the market would move next.

Bachelier’s formula describing this phenomenon showed that the future course of the market is essentially a coin flip—a bond is as likely to rise as it is to fall, just as a coin is as likely to land on heads as tails, or a grain of pollen quivering in a mass of liquid is as likely to zig left as right. With bond prices, that’s because the current price is “the true price: if the market judged otherwise, it would quote not this price, but another price higher or lower,” Bachelier wrote.

This discovery came to be called the
random walk
. It’s also called the
drunkard’s walk
. Imagine it’s late at night, and you’re walking home through a thick fog—let’s say a 1900 Parisian fog. You notice a drunk leaning against a lamppost in the bohemian quarter of Montmartre—perhaps some unknown artist celebrating a breakthrough. He’s had too much absinthe and is wavering as he tries to decide which direction home lies. Is it east, north, west, south? Suddenly he lurches from the pole in a southward direction with great conviction, stumbling that way for the next five seconds. Then he changes his mind. He has every right—he’s an artist in Paris, after all. Home, of course, lies to the west. Five seconds later, he changes his mind again—south. And so on.

According to Bachelier, the odds that the drunk will stagger five feet east, or five feet west, are the same, just as the odds that a 100-franc bond will rise 1 franc or fall 1 franc in a given time period are identical.

Visually, a chart of the various outcomes of a random walk is known as a
bell curve
, sloping gently upward to a rounded peak before sloping downward at the same rate. It’s much more likely that the confused drunkard will sway randomly in many directions as the night progresses (samples that would fall in the middle of the curve) than that he will move continuously in a straight line, or spin in a circle (samples that would fall in the ends of the curve, commonly known as the tails of the distribution). In a thousand coin flips, it’s more likely that the sample will contain roughly five hundred heads and five hundred tails (falling in the curve’s middle) than nine hundred heads and one hundred tails (outer edge of the curve).

Thorp, already well aware of Einstein’s 1905 discovery, was familiar with Brownian motion and rapidly grasped the connection between bonds and warrants. Indeed, it was in a way the same statistical rule that had helped Thorp win at blackjack: the law of large numbers (the more observations, the more coin flips, the greater the certainty of prediction). While he could never know if he’d win every hand at blackjack, he knew that over time he’d come out on top if he followed his card-counting strategy. Likewise, while he’d never know whether a stock would move up or down in the next week, he could determine how likely it was that the stock would rise or fall by, say, 2, 5, or 10 percent.

Thorp applied the formula to warrants. The future movement of a stock—a variable known to quants as
volatility
—is random, and therefore quantifiable. And if the warrant is priced in a way that underestimates, or overestimates, its likely volatility, money can be made.

Discovering how to price volatility was the key to unlocking the stock warrant treasure trove. Say you own a warrant for IBM. The current value of IBM’s stock is $100. The warrant, which expires in twelve months, will be valuable only if IBM is worth $110 at some point during that twelve-month period. If you can determine how volatile IBM’s stock is—how likely it is that it will hit $110 during that time period—you then know how much the warrant is worth. Thorp discovered that by plugging in the formula for Brownian motion, the random walk model, in addition to an extra variable for whether the stock itself tends to rise more or less than other stocks, he could know better than almost anyone else in the market what the IBM warrant was worth.

Gamblers make such time-dependent bets all the time. The time to expiration of the warrant is similar to the four quarters of a football game, baseball’s nine innings, or a lap around the racetrack. Investors are wagering on a certain outcome within a predefined time frame. Thorp simply used his math skills and his well-honed gambling instincts to quantify the problem.

But to the conservative crowd—think investors in Treasuries and blue chips—all of this seemed a sort of crystal ball divination of the future, an approach better left to hucksters and charlatans. A trained
physicist such as Thorp, however, saw that it was simply a matter of assigning a certain probability to a future outcome based on fixed parameters—a practice physicists and engineers engage in on a daily basis.

Using their
models and their ability to predict volatility, Thorp and Kassouf realized there were a number of warrants that appeared to be mispriced. Some were too expensive, while others were cheap. The two professors collaborated on a 1967 book that described their findings. It was called
Beat the Market: A Scientific Stock Market System
. A quant touchstone, it soon became one of the most influential how-to books on investing ever written.

It also flew in the face of an increasingly popular theory in academia that it was impossible to consistently beat the market. Spearheaded by University of Chicago finance professor Eugene Fama in the late 1960s, this theory was known as the efficient-market hypothesis (EMH). At bottom, EMH was based on the idea, as Bachelier had argued, that the market moves in a random fashion and that current prices reflect all known information about the market. That being the case, it’s impossible to know whether the market, or an individual stock, currency, bond, or commodity, will rise or fall in the future—the future is random, a coin flip. It’s a fancy way of saying there’s no free lunch. This idea eventually spawned the megabillion-dollar index fund industry, based on the notion that if active managers can’t consistently put up better returns than the rest of the market, why not simply invest in the entire market itself, such as the S&P 500, for a much lower fee?