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

Physics Hits the Street 
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Scholes model. Instrumental in this shift was the Black Monday stock 
market crash of 1987, during which world financial markets fell more 
than 20% literally overnight. Blame for the crash fell to a novel finan-
cial product based on options and the Black-Scholes model, known as 
portfolio insurance. Portfolio insurance was designed, and advertised, 
to curtail the risk of major losses. It was a kind of hedge that amounted 
to buying stocks and short selling stock market futures, the idea being 
that if stocks began to fall, the market futures would also fall, and so 
your short position would increase to offset your losses. the strategy 
was designed so that you wouldn’t sell too many futures short, because 
that would eat into your profits if the market went up. Instead, you 
would program a computer to gradually sell your stocks if the market 
fell, and you would short just enough market futures to cover those 
losses.
When the market crashed in 1987, though, everyone with portfolio 
insurance tried to sell their stocks at the same time. the trouble with 
this was that there were no buyers — everyone was selling! this meant 
that the computers trying to execute the trades ended up selling at 
much lower prices than the people who had designed the portfolio 
insurance had expected, and the carefully calculated short positions in 
market futures did little to protect investors. (In fact, investors holding 
portfolio insurance tended to do better than those who didn’t hold it; 
however, many people think the automated sell orders associated with 
portfolio insurance exacerbated the sell-off, and so everyone suffered 
because portfolio insurance was so prevalent.) the Black-Scholes-
based calculations underlying portfolio insurance didn’t anticipate the 
possibility of a crash, because the random walk model indicates that a 
major one-day drop like this wouldn’t happen in a million years.
Several things happened in light of the crash. for one, many prac-
titioners began to question the statistical predictions of the random 
walk model. this makes perfect sense — if your model says something 
is impossible, or virtually impossible, and then it happens, you need 
to start asking questions. But something else happened, too. Markets 
themselves seemed to change in the wake of the crash. Whereas in the 
years leading up to the crash the Black-Scholes model seemed to get 
options prices exactly right, in virtually all contexts and all markets, 

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after the crash certain discrepancies began to appear. these discrep-
ancies are often called the volatility smile because of their distinctive 
shape in certain graphs. the smile appeared suddenly and presented 
a major mystery for financial engineers in the early 1990s, when its 
prevalence was first recognized. notably, emanuel derman came up 
with a way of modifying the Black-Scholes model to account for the 
volatility smile, though he never came up with a principled reason why 
the Black-Scholes model had stopped working.
Mandelbrot’s work, however, offers a compelling explanation for 
the volatility smile. one way of interpreting the smile is as an indica-
tion that the market believes large shifts in prices are more likely than 
the Black-Scholes model assumes. this is just what Mandelbrot had 
been claiming all along: that probability distributions describing mar-
ket returns have fat tails, which means that extreme events are more 
likely than one would predict based on a normal distribution. In other 
words, market forces seemed to have brought prices into line with 
Mandelbrot’s theory. from the late 1980s on, Mandelbrot’s work has 
been taken much more seriously by investment bankers.
there’s an interesting, and rarely told, twist to the story of the rise 
and fall of Black-Scholes. the first major company to develop a quan-
titative strategy based on derivatives was a highly secretive chicago 
firm called o’connor and Associates. o’connor was founded in 1977 
by a pair of brothers named ed and Bill o’connor, who had made their 
fortune on grain futures, and Michael Greenbaum, a risk manager 
who had worked for them at first options, an options clearinghouse 
the brothers ran. Greenbaum had majored in mathematics at rensse-
laer Polytechnic Institute before joining first options, and so he had 
some background with equations. He was one of the first people to 
realize that the new options exchange in chicago offered a chance to 
make a killing, at least if you were mathematically sophisticated. He 
approached the o’connor brothers with the idea of a new firm that 
would focus on options trading.
this much of the story is well known. But given the timing, many 
people assume that o’connor was simply an early adopter of the 
Black-Scholes model. not so. Greenbaum realized from the start that 
the assumptions underlying Black-Scholes weren’t perfect, and that it 
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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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