The Physics of Wall Street: a brief History of Predicting the Unpredictable
part of everyday trading life. even more importantly, Black and Scho-
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part of everyday trading life. even more importantly, Black and Scho- les pointed a way forward for modeling other derivatives contracts, too, which rapidly grew at the IMM as businesses sought new ways of protecting themselves against currency risk. Between the IMM and the cBoe, Black and Scholes found a world that was perfectly poised to take advantage of their new ideas. the options pricing formula that Black, Scholes, and Merton discov- ered was equivalent to the method that thorp had worked out in 1965 for pricing warrants — though thorp used a computer program to calculate options prices, rather than derive the explicit equation that bears Black’s, Scholes’s, and Merton’s names. But the underlying ar- guments were different. thorp’s reasoning followed Bachelier’s: he ar- gued that a fair price for an option should be the price at which the option could be interpreted as a fair bet. from here, thorp worked out what the price of an option should be, assuming that stock prices satisfy the log-normal distribution osborne described. once he had a way of calculating the “true” price of an option, thorp went on to work out the proportions of stocks and options necessary to execute the delta hedging strategy. Black and Scholes, meanwhile, worked in the opposite direction. they started with a hedging strategy, by observing that it should al- 118 • t h e p h y s i c s o f wa l l s t r e e t Physics Hits the Street • 119 ways be possible to construct a risk-free portfolio from a combination of stocks and options. they then applied cAPM to say what the rate of return on this portfolio should be — that is, the risk-free rate — and worked backward to figure out how options prices would have to de- pend on stock prices in order to realize this risk-free return. the distinction may seem inconsequential — after all, the two argu- ments are different paths to the same model of options prices. But in practice, it was crucial. the reason is that dynamic hedging, the basic idea behind the Black-Scholes approach, gave investment banks the tool they needed to manufacture options. Suppose you are a bank and you would like to start selling options to your clients. this amounts to selling your clients the right to buy or sell a given stock at a prede- termined price. Ideally, you don’t want to make a risky bet yourself — your profits are going to come from the commissions you will earn on the sales, not on the proceeds of speculation. In effect this means that when a bank sells an option, it wants to find a way to counterbalance the possibility that the underlying stock will become valuable, without losing money if the option doesn’t become valuable. Black and Scho- les’s dynamic hedging strategy gave banks a way to do exactly this: using the Black-Scholes approach, banks could sell options and buy other assets in such a way that (at least theoretically) they didn’t carry any risk. this turned options into a kind of product, something that banks could construct and sell. Black stayed in chicago until 1975, when MIt wooed him back to cambridge. for a few years, academia seemed like the perfect fit for Black. He could work on whatever he liked, and at least in the early heyday of exchange-based options trading, it seemed he could do no wrong. He was an academic celebrity of the highest order, which brought both respect and freedom. His personal life, however, was a growing disaster: his (second) wife, Mimi, hated their chicago life, which was an important part of the decision to move back to cam- bridge, nearer to her family. But the move east didn’t help much. In- creasingly alienated at home, Black devoted more and more time to his work, branching off now in new directions. He began to work on gen- eralizing cAPM to try to explain cycles in the economy: why, in a ra- tional world, would there be periods of growth, followed by periods of contraction? this led him to a new theory of macroeconomics, which he called “general equilibrium.” He also launched a crusade against the accounting industry, which he considered backward and unhelpful to investors. But these other strands of his work were terribly received. It was as though Black had used up all his luck and timing with the options paper, and the string of other papers on derivatives and financial mar- kets that followed it. His work on macroeconomics in particular was out of step with the times. economists in the 1970s and 1980s were deeply engaged in an ongoing debate about economic regulation and monetary policy. on one side were the chicagoans; on the other, the Keynesians, who favored government intervention throughout the economy. General equilibrium was a third way, thrust into a bipolar community. Black found himself attacked, and then ignored, by both sides. no one would publish his papers. His colleagues began to write him off as irrelevant. In less than a decade, he went from outsider to idol, and then back to outsider. By the early 1980s, Black was fed up with academia. He wanted out. In december 1983, robert Merton, Black’s old collaborator from the Black-Scholes days, was doing consulting work for the investment bank Goldman Sachs. Merton was doing at Goldman what Black and Scholes had been doing at Wells fargo back in 1970: bringing in the new ideas from academia and trying to implement them in a practical setting. In this capacity, he argued to robert rubin, then head of the equities division, that Goldman Sachs should hire a theorist, an aca- demic of its own, at a high enough level of the company that the new ideas would have a chance to seep through the culture. rubin was con- vinced, and so Merton went back to MIt, brainstorming who among their current crop of graduate students he would recommend for this important position. Merton asked Black for his advice and received a surprising answer: Black wanted the job himself. three months later, Black left academia for a new job at Goldman Sachs, to organize a Quantitative Strategies Group in the equities division. thus he be- came one of the first quants, a new kind of investment bank employee with an intensely quantitative and scientific focus, as interested in in- 120 • t h e p h y s i c s o f wa l l s t r e e t |
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