The Quants

by Scott Patterson

  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 th
en 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?

  While Thorp fully understood the notion of random walks, which he’d used to price warrants, he thought EMH was academic hot air, the stuff of cloistered professors spinning airy fantasies of high-order math and fuzzy logic. Standard thinking had once been that it was also impossible to beat the dealer, and he’d proven the doubters wrong. He was convinced he could accomplish the same feats in the stock market.

  He and Kassouf were soon investing in all kinds of warrants using their scientific system, and raking in piles of cash. Other faculty members who’d heard of Thorp and Kassouf’s winning streak began asking to get in on the action. In short order, they were managing accounts for more than ten people, approaching the limit where they’d have to start filing with the government as investment advisors. It occurred to Thorp that the best way to invest for a number of people would be to create a single pool of assets, but he wasn’t sure how to go about it.

  The solution came from a man quickly gaining a reputation as one of the savviest investors in the world: Warren Buffett.

  In the summer of 1968, Thorp drove from Irvine to Buffett’s house in Laguna Beach, where Buffett often vacationed when he wasn’t accumulating millions from his office in Omaha, Nebraska. Buffett was in the process of winding down his investing pool, Buffett Limited Partnerships, and distributing its assets to his investors—including shares of a New England textile factory called Berkshire Hathaway. In the coming years, Buffett would transform Berkshire into a cash-generating powerhouse that would turn the legendary investor who came to be known as the “Oracle of Omaha” into the richest man in the world.

  At the time, however, Buffett wasn’t very enthusiastic. Market conditions were unfavorable, he’d decided, and it was time to call it quits. One of his investors was Ralph Gerard, dean of the University of California, Irvine, where Thorp taught. Gerard was looking for a new place to invest his money and was considering Thorp. He’d asked Buffett if he would size up the hotshot math professor who was making a killing on stock warrants.

  Buffett told Thorp about his partnership, which used a legal structure similar to the one created by his mentor, Benjamin Graham, author of The Intelligent Investor and father of value investing. The structure was also used by a former writer for Fortune magazine named Alfred Winslow Jones.

  It was called a hedge fund.

  In 1940, the U.S. Congress had passed the Investment Company Act, which was designed to protect small investors from devious mutual fund managers. But Congress made an exception. If a fund manager limited himself to no more than ninety-nine wealthy investors with assets of $1 million or more and didn’t advertise, he could do pretty much whatever he liked.

  Graham had been seared by brutal losses during the Great Depression and was a notoriously conservative investor who put his money only in companies he believed had a Grand Canyon-like “margin of safety.” Jones, an Australian native who had worked as a writer and editor for Time Inc., was much more of a cowboy trader, apt to bet on short-term swings in stocks or make speculative bets that a stock would plunge. In 1949, he founded A. W. Jones & Co. It was the first true hedge fund, with $100,000 in capital—$40,000 of it his own.

  To further sidestep government oversight, A. W. Jones was domiciled offshore. Jones charged a 20 percent annual performance fee. To lessen the volatility of his fund, he’d sell certain stocks short, hoping to profit from a decline, while at the same time going long on certain stocks, benefiting from rising prices. In theory, this would boost returns during good times and bad. The short positions hedged his long portfolio, hence the name hedge fund, though the term didn’t come into common parlance until the 1960s. His fund’s eye-popping gains—670 percent over the prior ten-year period, far better than the 358 percent return sported by the top mutual fund of that era—spawned a generation of copycats.

  Jones may have been a reporter, but he was also a primitive quant, deploying statistical analysis to better manage his fund’s risk. To amplify returns, he used leverage, or borrowed money. Leverage can be highly beneficial for funds that are properly positioned, but it can also be disastrous if prices move in the wrong direction.

  As the go-go sixties bull market roared to life, other rock star hedge fund managers, such as the Hungarian savant George Soros, appeared on the scene. By 1968, there were 140 hedge funds in operation in the United States, according to a survey by the Securities and Exchange Commission. Ed Thorp was about to add to that growing list.

  His chance came in August the following year, 1969. Hippies partied in Haight-Ashbury. The war in Vietnam raged. The New York Jets, led by “Broadway” Joe Namath, beat the Baltimore Colts to win the Super Bowl. But Ed Thorp focused like a laser on a single goal: making money.

  That’s when he happened to meet Jay Regan, a Dartmouth philosophy major working for a Philadelphia brokerage firm, Butcher & Sherrerd. A full decade younger than Thorp, Regan had read Beat the Market and was blown away by the book’s revolutionary trading strategy. Convinced the nerdy West Coast professors were onto something extremely lucrative, he called up Thorp and asked for a meeting.

  Regan said he had contacts on the East Coast who could help seed a fund, with the kicker that the contacts were reliable sources of valuable market information. The idea appealed to Thorp, who didn’t want to waste his time dealing with brokers and accountants.

  They struck a deal: Thorp would stay in Newport Beach, continue teaching at UC Irvine, and work on the fund’s investing strategies, while Regan would set up shop in Princeton, New Jersey, and keep tabs on Wall Street. Initially, the fund was called Convertible Hedge Associates. In 1975, they renamed it Princeton/Newport Partners.

  I
n the meantime, Thorp continued to work on his formula for pricing warrants, always on the hunt for lucrative opportunities to apply his new scientific stock market system. Using his methodology to scan hundreds of warrants, he realized most were overpriced. For whatever reason, investors were too optimistic that the warrant would expire “in the money”—that the IBM stock would hit $110 in the next twelve months—much like starry-eyed gamblers wagering on their favorite team.

  That opened up an exciting opportunity. Thorp could sell a presumably overpriced warrant short, borrowing it from a third party and selling it at the current price to another investor. His hope was that he could buy it back at a later date for a cheaper price, pocketing the difference. The risk was that the warrant would rise, possibly because the underlying stock gained in value. This could be crushing for a short seller, since there is theoretically no limit to how much a stock can increase in value.

  But he had a safety net for that scenario: arbitrage, a practice that lies at the heart of how the modern-day financial industry operates—and a skeleton key to the quants’ search for the Truth. Alfred Jones, with his long-short hedge strategy, had performed a primitive form of arbitrage, although it was the stuff of children compared to the quantitative method Thorp was devising.

  True arbitrage is virtually a sure thing. It involves buying an asset in one market and almost simultaneously selling that asset, or its near equivalent, in another. Say gold is trading for $1,000 in New York and $1,050 in London. A fleet-footed arbitrageur will buy that New York gold and sell it in London (instantaneously), pocketing the $50 difference. While this was difficult when traders were swapping stocks beneath a buttonwood tree on Wall Street in the eighteenth century, the invention of the telegraph—and the telephone, the high-speed modem, and a grid of orbiting satellites—has made it much easier to accomplish in modern times.