The Quants: How a New Breed of Math Whizzes Conquered Wall Street and Nearly Destroyed It by Scott Patterson
Authors: Scott Patterson
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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,
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,
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