The Quants: How a New Breed of Math Whizzes Conquered Wall Street and Nearly Destroyed It by Scott Patterson Page A
Authors: Scott Patterson
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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-Packard9830A 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.
Huge, sudden leaps were a contingency no one bothered to consider.
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.
Huge, sudden leaps were a contingency no one bothered to consider.
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