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

Swimming Upstream 
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virginia to work in a government lab at the moment the government 
was most prepared to support creative, interdisciplinary research.
osborne began “Brownian Motion in the Stock Market” with a thought 
experiment. “Let us imagine a statistician,” he wrote, “trained perhaps 
in astronomy and totally unfamiliar with finance, is handed a page of 
the Wall Street Journal containing the n.Y. Stock exchange transac-
tions for a given day.” osborne began thinking about the stock market 
around 1956, after his wife, doris (also an astronomer), had given birth 
to a second set of twins — the osbornes’ eighth and ninth children, re-
spectively. osborne decided he had better start thinking about financ-
ing the future. one can easily imagine osborne going down to the 
store and picking up a copy of the day’s Wall Street Journal. He would 
have brought it home, sat down at the kitchen table, and opened it to 
the pages that reported the previous day’s transactions. Here he would 
have found hundreds, perhaps thousands, of pieces of numerical data, 
in columns labeled with strange, undefined terms.
the statistician trained in astronomy wouldn’t have known what the 
labels meant, or how to interpret the data, but that was fine. numerical 
data didn’t scare him. After all, he’d seen page after page of data record-
ing the nightly motions of the heavens. the difficulty was figuring out 
how the numbers related to each other, determining which numbers 
gave information about which other numbers, and seeing if he could 
make any predictions. He would, in effect, be building a model from 
a set of experimental data, which he’d done dozens of other times. So 
osborne would have adjusted his glasses, rolled up his sleeves, and 
dived right in. Lo and behold, he discovered some familiar patterns: 
the numbers corresponding to price behaved just like a collection 
of particles, moving randomly in a fluid. As far as osborne could 
tell, these numbers could have come from dust exhibiting Brownian 
motion.
In many ways, osborne’s first, and most lasting, contribution to the 
theory of stock market behavior recapitulated Bachelier’s thesis. But 
there was a big difference. Bachelier argued that from moment to mo-
ment stock prices were as likely to go up by a certain small amount as 

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to go down by that same amount. from this he determined that stock 
prices would have a normal distribution. But osborne dismissed this 
idea immediately. (Samuelson did, too — in fact, he called this aspect 
of Bachelier’s work absurd.) A simple way to test the hypothesis that 
the probabilities governing future stock prices are determined by a 
normal distribution would be to select a random collection of stocks 
and plot their prices. If Bachelier’s hypothesis were correct, one would 
expect the stock prices to form an approximate bell curve. But when 
osborne tried this, he discovered that prices don’t follow a normal dis-
tribution at all! In other words, if you looked at the data, Bachelier’s 
findings were ruled out right away. (to his credit, Bachelier did ex-
amine empirical data, but a certain unusual feature of the market for 
rentes — specifically, that their prices changed very slowly, and never 
by very much — made his model seem more effective than it actually 
was.)
So what did osborne’s price distribution look like? It looked like a 
hump with a long tail on one side, but virtually no tail on the other side. 
this shape doesn’t look much like a bell, but it was familiar enough to 
osborne. It’s what you get, not if prices themselves are normally dis-
tributed, but if the rate of return is normally distributed. the rate of 
return on a stock can be thought of as the average percentage by which 
the price changes each instant. Suppose you took $200, deposited $100 
in a savings account, and used the other $100 to buy some stock. A 
year from now, you probably wouldn’t have the $200 (you might have 
more or less), because of interest accrued in the savings account, and 
because of changes in the price of the stock that you purchased. the 
rate of return on the stock can be thought of as the interest rate that 
your bank would have had to pay (or charge) to keep the balances in 
your two accounts equal. It is a way of capturing the change in the 
price of a stock relative to its initial price.
the rate of return on a stock is related to the change in price by a 
mathematical operation known as a logarithm. for this reason, if rates 
of return are normally distributed, the probability distribution of stock 
prices should be given by something known as a log-normal distribu-
tion. (See figure 2 for what this looks like.) the log-normal distri-
bution was the funny-looking hump with a tail that osborne found 
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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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