The Quants: How a New Breed of Math Whizzes Conquered Wall Street and Nearly Destroyed It (7 page)

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.

In 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.

Such obvious discrepancies in practice are rare and are often hidden in the depths of the financial markets like gold nuggets in a block of ore. That’s where the quants, the math whizzes, step in.

Behind the practice of arbitrage is the law of one price (LOP), which states that a single price should apply to gold in New York as in London, or anywhere else for that matter. A barrel of light, sweet crude in Houston should cost the same as a barrel of crude in Tokyo (minus factors such as shipping costs and variable tax rates). But flaws in the information certain market players may have, technical factors that lead to brief discrepancies in prices, or any number of other market-fouling factors can trigger deviations from the LOP.

In the shadowy world of warrants, Thorp and Kassouf had stumbled upon a gold mine full of arbitrage opportunities. They could short the overpriced warrants and buy an equivalent chunk of stock to hedge their bet. If the stock started to rise unexpectedly, their downside would be covered by the stock. The formula also gave them a method to calculate how much stock they needed to hold in order to hedge their position. In the best of all worlds, the warrant price would decline and the stock would rise, closing out the inefficiency and providing a gain on each side of the trade.

This strategy came to be known as convertible bond arbitrage. It has become one of the most successful and lucrative trading strategies ever devised, helping launch thousands of hedge funds, including Citadel Investment Group, the mammoth Chicago powerhouse run by Ken Griffin.

Forms of this kind of arbitrage had been in practice on Wall Street for ages. Thorp and Kassouf, however, were the first to devise a precise, quantitative method to discover valuation metrics for warrants, as well as correlations between how much stock investors should hold to hedge their position in those warrants. In time, every Wall Street bank and most hedge funds would practice this kind of arbitrage, which would become known as delta hedging
(delta
is a Greek term that essentially captures the change in the relationship between the stock and the warrant or option).

Thorp understood the risks his strategy posed. And that meant he could calculate how much he was likely to win or lose from each bet. From there, he would determine how much he should wager on these trades using his old blackjack formula, the Kelly criterion. That allowed him to be aggressive when he saw opportunities, but it also kept him from betting too much. When the opportunities were good, like a deck full of face cards, Thorp would load the boat and get aggressive. But when the odds weren’t in his favor, he would play it safe and make sure he had lots of extra cash on hand if the trade moved against him.

Thorp was also cautious almost to the point of paranoia. He was always concerned about out-of-the-blue events that could turn against him: an earthquake hitting Tokyo, a nuclear bomb in New York City, a meteor smashing Washington, D.C.

But it worked. Thorp’s obsessive risk management strategy was at the heart of his long-term success. It meant he could maximize his returns when the deck was stacked in his favor. More important, it meant he would pull his chips off the table if he felt a chill wind blowing—a lesson the quants of another generation seemed to have missed.

After launching
in late 1969, Thorp and Regan’s fund was an almost immediate hit, gaining 3 percent in 1970 compared with a 5 percent decline by the S&P 500, which is a commonly used proxy for the market as a whole. In 1971, their fund was up 13.5 percent, next to a 4 percent advance by the broader market, and it gained 26 percent in 1972, compared with a 14.3 percent rise by the index. Thorp programmed formulas for tracking and pricing warrants into a Hewlett-Packard
9830A he’d installed in his office in Newport Beach, Keeping tabs on Wall Street thousands of miles away from the edge of the Pacific Ocean.

In 1973, Thorp received a letter from Fischer Black, an eccentric economist then teaching at the University of Chicago. The letter contained a draft of a paper that Black had written with another Chicago economist, Myron Scholes, about a formula for pricing stock options. It would become one of the most famous papers in the history of finance, though few people, including its authors, had any idea how important it would be.

Black was aware of Thorp and Kassouf’s delta hedging strategy, which was described in
Beat the Market
. Black and Scholes made use of a similar method to discover the value of the option, which came to be known as the Black-Scholes option-pricing formula. Thorp scanned the paper. He programmed the formula into his HP computer, and it quickly produced a graph showing the price of a stock option that closely matched the price spat out by his own formula.

The Black-Scholes formula was destined to revolutionize Wall Street and usher in a wave of quants who would change the way the financial system worked forever. Just as Einstein’s discovery of relativity theory in 1905 would lead to a new way of understanding the universe, as well as the creation of the atomic bomb, the Black-Scholes formula dramatically altered the way people would view the vast world of money and investing. It would also give birth to its own destructive forces and pave the way to a series of financial catastrophes, culminating in an earthshaking collapse that erupted in August 2007.

Like Thorp’s
methodology for pricing warrants, an essential component of the Black-Scholes formula was the assumption that stocks moved in a random walk. Stocks, in other words, are assumed to move in antlike zigzag patterns just like the pollen particles observed by Brown in 1827. In their 1973 paper, Black and Scholes wrote that they assumed that the “stock price follows a random walk in continuous time.” Just as Thorp had already discovered, this allowed investors to determine the relevant probabilities for volatility—how high or low a stock or option would move in a certain time frame.

Hence, the theory that had begun with Robert Brown’s scrutiny of plants, then led to Bachelier’s observations about bond prices, finally reached a most pragmatic conclusion—a formula that Wall Street would use to trade billions of dollars’ worth of stock and options.

But a central feature of the option-pricing formula would come back to bite the quants years later. Practically stated, the use of Brownian motion to price the volatility of options meant that traders looked at the most likely moves a stock could make—the ones that lay toward the center of the bell curve. By definition, the method largely ignored big jumps in price. Those sorts of movements were seen as unlikely as the drunk wandering across Paris suddenly hopping from the cathedral of Notre Dame to the Sorbonne across the river Seine in the blink of an eye. But the physical world and the financial world—as much as they seem to have in common—aren’t always in sync. The exclusion of big jumps left out a key reality about the behavior of market prices, which can make huge leaps in the blink of an eye. There was a failure to factor in the human element—a major scandal, a drug that doesn’t pan out, a tainted product, or a panicked flight for the exits caused by all-too-common investor hysteria. History shows that investors often tend to act like sheep, following one another in bleating herds, sometimes all the way over a cliff.