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

Swimming Upstream 
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to find places where your simplifying assumptions break down and try 
to figure out, again by focusing on the data, how these failures of your 
assumptions produce problems for the model’s predictions.
When osborne described his original Brownian motion model, he 
specifically indicated what assumptions he was making. He pointed 
out that if the assumptions were no good, there was no guarantee that 
the model would be, either. What osborne and other physicists under-
stood was that a model isn’t “flawed” when the assumptions underly-
ing it fail. But it does mean you have more work to do. once you’ve 
proposed a model, the next step is to figure out when the assumptions 
fail and how badly. And if you discover that the assumptions fail regu-
larly, or under specific circumstances, you try to understand the ways 
in which they fail and the reasons for the failures. (for instance, os-
borne showed that price changes aren’t independent. this is especially 
true during market crashes, when a series of downward ticks makes it 
very likely that prices will continue to fall. When this kind of herding 
effect is present, even osborne’s extended Brownian motion model is 
going to be an unreliable guide.) the model-building process involves 
constantly updating your best models and theories in light of new evi-
dence, pulling yourself up by the bootstraps as you progressively un-
derstand whatever you’re studying — be it cells, hurricanes, or stock 
prices.
not everyone who has worked with mathematical models in fi-
nance has been as sensitive to the importance of this methodology as 
osborne was, which is one of the principal reasons why mathemati-
cal models have sometimes been associated with financial ruin. If you 
continue to trade based on a model whose assumptions have ceased 
to be met by the market, and you lose money, it is hardly a failure of 
the model. It’s like attaching a car engine to a plane and being disap-
pointed when it doesn’t fly.
despite the patterns in stock prices that osborne was able to discover, 
he remained convinced that in general, there was no reliable way to 
make profitable forecasts about future market behavior. there was, 
however, one exception. Ironically, it had nothing to do with the so-

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phisticated models that he developed during the 1960s. Instead, his 
optimism was based on a way of reading the mind of the markets, by 
studying the behavior of traders.
osborne noticed that a great preponderance of ordinary investors 
placed their orders at whole-number prices — $10, or $11 say. But stocks 
were valued in units of 1/8 of a dollar. this meant that a trader could 
look at his book and see that there were a lot of people who wanted to 
buy a stock at, say, $10. He could then buy it at $10 1/8, knowing that 
at the end of the day the stock wouldn’t drop below $10 because there 
were so many people willing to buy at that threshold. So at worst, the 
trader would lose $1/8; at best, the stock would go up, and he could 
make a lot. conversely, he could see that a lot of people wanted to sell 
at, say, $11, and so he could sell at $10 7/8 with confidence that the most 
he could lose would be $1/8 if the stock went up instead of down. this 
meant that if you went through a day’s trades and looked for trades at 
$1/8 above or below whole-dollar amounts, you could gather which 
stocks the experts thought were “hot” because so many other people 
were interested.
It turned out that what the experts thought was hot was a great in-
dicator of how stocks would do — a much better indicator than any-
thing else osborne had studied. Based on these observations, osborne 
proposed the first trading program of a sort that could be plugged into 
a computer to run on its own. But in 1966, when he came up with the 
idea, no one was using computers to make decisions. It would take de-
cades for osborne’s idea and others like it to be tested in the real world.
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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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S
zolem mandelbrojt was the very model of a modern 
mathematician. An expert in analysis (the area of abstract 
mathematics that includes, among other things, standard col-
lege calculus), he had studied in Paris with the best of the best, includ-
ing emile Picard and Henri Lebesgue. He was a founding member of a 
group of french mathematicians who, under the pseudonym nicolas 
Bourbaki, endeavored to bring the highest possible level of rigor and 
abstraction to the field; the group’s collected works set the tone for two 
generations of mathematicians. When his mentor, Jacques Hadamard, 
one of the most famous mathematicians of the late nineteenth century, 
retired from his position at the prestigious collège de france, the col-
lège invited Mandelbrojt to replace him. He was a serious man, doing 
serious work.
or at least he would have been doing serious work if his nephew 
hadn’t been constantly hounding him. In 1950, Benoît Mandelbrot 
was a doctoral student at the University of Paris, Szolem’s alma mater, 
seeking (Szolem imagined) to follow in his eminent uncle’s footsteps. 
When Szolem first learned that Benoît wanted to pursue mathematics, 
he was thrilled. But gradually, Szolem began to question Benoît’s se-
From Coastlines to Cotton Prices
c H A P t e r 3

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riousness. despite his uncle’s advice, Benoît showed no interest in the 
pressing mathematical matters of the day. His work lacked the rigor 
that had brought Szolem such success. Worst of all, Benoît seemed in-
tent on geometrical methods, which every self-respecting mathemati-
cian knew had been abandoned a century before because they had led 
so many people astray. real mathematics couldn’t be done by drawing 
pictures.
Benoît’s father, Szolem’s oldest brother, had helped raise Szolem. He 
had supported Szolem through graduate school, creating opportuni-
ties Szolem would never have had otherwise. to Szolem, then, Benoît 
was more like a brother than a nephew, and Szolem felt that he owed 
Benoît his continued patience and support. But Szolem was at the end 
of his rope. Benoît just wasn’t getting it. He had as much mathemati-
cal aptitude as anyone, but when it came to picking projects, he was 
hopeless.
one day, while Benoît was in his office talking about his crazy disser-
tation ideas, Szolem snapped. He reached into his trash can and pulled 
out a discarded paper. If Benoît wanted to work on trash, Szolem had 
plenty of it to give him — a whole bin filled with papers of no interest 
or importance. “this is for you,” he said dismissively. “that’s the kind 
of silly stuff you like.”
Szolem must have hoped his dramatic gesture would knock some 
sense into his young nephew. But the plan backfired magnificently. 
Benoît took the paper — a review of a recent book by a Harvard lin-
guist named George Kingsley Zipf — and studied it carefully on his 
way home. Zipf was a famously eccentric character and few took him 
seriously. He had spent his career arguing for a universal law of physi-
cal, social, and linguistic phenomena. Zipf’s law said that if you con-
structed a list of all of the things in some natural category, say, all of the 
cities in france, or all of the libraries in the world, and ranked them ac-
cording to their size — you might rank cities by population; libraries, 
by collection size — you would always find that the size of each thing 
on the list was related to its rank on the list. In particular, the second 
thing on each list would always be about half the size of the first thing, 
the third thing on the list would be about a third the size of the first 
thing, and so on. the review that Benoît read focused on a particular 
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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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