The Physics of Wall Street: a brief History of Predicting the Unpredictable

Physics Hits the Street 
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to control risk. the difference was that thorp’s delta hedge strategy 
aimed to guarantee a profit, provided that the underlying stock’s price 
didn’t change too dramatically. this approach controlled risk, but it 
didn’t eliminate it altogether. (Indeed, if cAPM-style reasoning is cor-
rect, you shouldn’t be able to both eliminate risk and still make a sub-
stantial profit.) Black’s approach was to find a portfolio consisting of 
stocks and options that was risk-free, and then argue by cAPM rea-
soning that this portfolio should be expected to earn the risk-free rate 
of return. Black’s strategy of building a risk-free asset from stocks and 
options is now called dynamic hedging.
Black had read cootner’s collection of essays on the randomness of 
markets, and so he was familiar with Bachelier’s and osborne’s work 
on the random walk hypothesis. this gave him a way to model how 
the underlying stock prices changed over time — which in turn gave 
him a way to understand how options prices must change over time, 
given the link he had discovered between options prices and stock 
prices. once Black had found this fundamental relationship between 
the price of a stock, the price of an option on that stock, and the risk-
free interest rate, it was just a few steps of algebra for him to derive an 
equation for the value of the option, by relating the risk premium on 
the stock to the risk premium on the option. But now he was stuck. 
the equation he derived was a complicated differential equation — an 
equation relating the instantaneous rate of change of the price of the 
option to the instantaneous rate of change of the price of the stock —
and Black, despite his background in physics and mathematics, didn’t 
know enough math to solve it.
After struggling for several months, Black gave up. He didn’t tell 
anyone about the options problem, or his partial solution, until later in 
1969, when Scholes mentioned that one of his master’s students at MIt 
was interested in options pricing. Scholes began to speculate about 
whether cAPM could be used to solve the problem — at which point 
Black opened his desk drawer and pulled out a sheet of paper with the 
crucial differential equation written on it, and from then on the two 
men worked on the problem together. they had solved it by summer 
1970, and the Black-Scholes equation for the price of an option made 
its debut in July, at a conference that Scholes organized at MIt, spon-

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sored by Wells fargo. In the meantime, a new colleague of Scholes’s at 
MIt, robert Merton (himself an engineer by training, though he went 
on to earn a Phd in economics), had rederived the same differential 
equation and the same solution from an entirely different starting 
point. With two different approaches giving the same answer, Black, 
Scholes, and Merton were convinced they were on to something big.
Black and Scholes submitted their paper to the Journal of Political 
Economy, one of the most important publications in the field, soon 
after they had solved the problem. the paper was promptly rejected, 
without so much as a note of explanation (suggesting it wasn’t even 
seriously considered). So they tried again, this time with Review of 
Economics and Statistics. Again, they received a rapid rejection with no 
articulation of what was wrong with the article. Merton, meanwhile, 
held off on sending his alternative approach to journals, so that Black 
and Scholes could receive appropriate credit for their discovery.
despite the early setbacks, however, Black and Scholes were not 
destined to labor in obscurity. Powerful forces in academia, in finance, 
and in politics were aligning in their favor. And some of the then-
reigning academic gods were ready to intervene. After the second re-
jection, University of chicago professors eugene fama and Merton 
Miller, two of the most influential economists at the time and leaders 
of the then-nascent chicago School of economics, successfully urged 
the Journal of Political Economy to reconsider, and in August 1971 the 
article was accepted for publication, pending revisions.
In the meantime, fischer Black had attracted attention at the Uni-
versity of chicago. economists there were familiar with his work with 
Scholes, both on options and at Wells fargo; they’d seen him in ac-
tion at the Wells fargo conference. A few years earlier, in 1967, Black 
had traveled to chicago with treynor to present some of their collab-
orative work to the graybeards. chicago economists didn’t need fancy 
journals to vet young academics: they knew talent when they saw it, 
and Black certainly had talent. And so in May 1971, they offered Black 
a job. At this point, Black had already been out of graduate school for 
seven years, yet he had only four publications, just two of which were 
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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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