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

From Coastlines to Cotton Prices 
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(according to either theory), and so you usually won’t notice much of 
a difference between the two models.
for this reason — as we will see in the next several chapters — when 
it came time for economists interested in financial markets to try to 
extend the ideas presented in cootner’s book, to put the randomness 
of stock market prices to work by using statistics to predict derivatives 
prices or to calculate the amount of risk in a portfolio, they had to pick 
between the simple theory that gave good results the vast majority of 
the time and the more cumbersome one that better accounted for cer-
tain extreme events. It made perfect sense to start with the simpler one 
and see what happened. If you make good assumptions, if you idealize 
effectively, you can often solve a problem that otherwise couldn’t be 
solved — and get a solution that is quite close to correct, even if some 
of the details are wrong. of course, all along, you know you’ve made 
assumptions that aren’t quite right (markets are not perfectly efficient; 
returns and not prices follow a simple random walk). But they’re a 
start.
It is also too simple to say that Mandelbrot was ignored in the de-
cades immediately following his early papers on cotton. Most econo-
mists followed osborne’s lead when building on the randomness of 
markets to study related topics. But a dedicated core of mathemati-
cians, statisticians, and economists put Mandelbrot’s proposals to the 
test with ever more detailed data, and ever more sophisticated math-
ematical methods — most of which were developed specifically for 
the purpose of better understanding what it would mean if the world 
were really as wildly random as Mandelbrot said. this work confirmed 
Mandelbrot’s basic thesis, that normal and log-normal distributions 
are insufficient to capture the statistical properties of markets. rates of 
return have fat tails.
that said, there’s a wrinkle in the story. Mandelbrot made a very 
specific claim in his 1963 papers: he said that markets were Lévy-stable 
distributed. And except for the normal distribution, the volatility of 
Lévy-stable distributions is infinite, which means that most standard 
statistical tools don’t apply for analyzing such distributions. (this is 
what cootner was alluding to when he said that if Mandelbrot was 

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correct, the standard statistical tools were obsolete.) today, the best 
evidence indicates that this specific claim, regarding infinite variability 
and the inapplicability of standard statistical tools, is false. After al-
most fifty years of research, the consensus is that rates of return are fat-
tailed, but they aren’t Lévy-stable. If this is correct, as most economists 
and physicists working on these topics believe it is, then the standard 
statistical tools do apply, even though the simplest assumptions of nor-
mal and log-normal distributions do not. But evaluating Mandelbrot’s 
claims is an extremely tricky business — mostly because the important 
differences between his proposal and its nearest alternatives apply only 
in extreme cases, data for which are very hard to come by. And even 
today, there is disagreement about how to interpret the data we do 
have.
the fact that Mandelbrot’s claims were likely too aggressive makes 
his legacy a little more difficult to evaluate. Some writers today insist 
that Mandelbrot was never given his due, and that a proper apprecia-
tion of his ideas would solve all the world’s problems. While this is not 
entirely true, a few things are certain. extreme events occur far more 
often than Bachelier and osborne believed they would, and markets 
are wilder places than normal distributions can describe. to fully un-
derstand markets, and to model them as safely as possible, these facts 
must be accounted for. And Mandelbrot is singularly responsible for 
discovering the shortcomings of the Bachelier-osborne approach, and 
for developing the mathematics necessary to study them. Getting the 
details right may be an ongoing project — indeed, we should never 
expect to finish the iterative process of improving our mathematical 
models — but there is no doubt that Mandelbrot took a crucially im-
portant step forward.
After a decade of interest in the statistics of markets, Mandelbrot gave 
up on his crusade to replace normal distributions with other Lévy-sta-
ble distributions. By this time, his ideas on randomness and disorder 
had begun to find applications in a wide variety of other fields, from 
cosmology to meteorology. these fields were closer to his starting 
point in applied mathematics and mathematical physics. He remained 
affiliated with IBM for his entire career; in 1974, he was named an IBM 
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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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