Louis Bachelier - Random Thoughts (2)

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The Efficient Market Hypothesis ("EMH") was developed in the 1960s by a University of Chicago economist, Professor Eugene F. Fama.  Although Fama first coined the term Random Walk, our old friend, Professor Burton G. Malkiel, brought it into the popular consciousness with his first edition of A Random Walk Down Wall Street.  Some attribute the concept to a French broker, Jules Regnault, who wrote about the randomness of stock prices in 1863.  The more recent theory of random prices is based on a doctoral thesis written by a French mathematician, Louis Bachelier, in 1900 entitled The Theory of Speculation.  The basic concept of EMH is that financial markets, at any given point, set a price for a stock with such a degree of speed and efficiency that no investor can earn more from his or her investing strategy than the average market return.

Bachelier wrote the following about market movements:

Past, present, and even discounted future events are reflected in market price, but often show no apparent relation to price changes.....[A]rtificial causes also intervene: the Exchange reacts on itself, and the current fluctuation is a function, not only of the previous fluctuations, but also of the current state.  The determination of these fluctuations depends on an infinite number of factors; it is, therefore, impossible to aspire to mathematical predictions of it....[T]he dynamics of the Exchange will never be an exact science. *

Peter L. Berstein was an economist, university educator, investment manager and famous author of financial history.  In his 1992 book, Capital Ideas / The Improbable Origins of Modern Wall Street, Peter L. Berstein had the following to say about Bachelier:

The key to Bachelier's insight is his observation, expressed in a notably modern manner, that "contradictory opinions concerning [market] changes diverge so much that at the same instant buyers believe in a price increase and sellers believe in a price decrease."  Convinced that there is no basis for believing that - on the average - either sellers or buyers consistently know any more about the future than the other, he arrived at an astonishing conjecture: "It seems that the market, the aggregate of speculators, at a given instant, can believe in neither a market rise nor a market fall, since, for each quoted price, there are as many buyer as sellers." **
(Author's emphasis in bold)


Bachelier followed his thesis to its logical conclusion: the probability of a price rise is the same as the probability of a price decline at any given moment in time.  He stated, "Clearly the price considered most likely by the market is the true current price: if the market judged otherwise, it would quote not this price, but another price higher or lower." *

Bachelier studied the degree of fluctuation in stock prices and constructed a set of mathematical equations which demonstrated that the variations in price are proportional to the length of time in which those variations occur.  His equations resulted in the finding that the range of fluctuations (up or down) was linked to the square root of the time interval of the fluctuations.


In his book, Berstein points out that the stock price variations over time shown by Bachelier's equations are eerily similar to the action of molecules crashing into each other, which is known in physics as Brownian motion, which played a role in Albert Einstein's theories about the atom.

It is, indeed, humbling to consider the similarity between the prices generated by actions of investors in the market and the movement of molecules in nature.  We will continue looking into Random Walk in the next blog.

*  Quotations from Louis Bachelier's 1900 doctoral thesis, The Theory of Speculation, are contained in Capital Ideas / The Improbable  Origins of Modern Wall Street by Peter L. Bernstein.

**  Excerpts from Capital Ideas / The Improbable  Origins of Modern Wall Street, Peter L. Bernstein, copyright 1992, published by The Free Press, a division of Macmillan, Inc.  A new edition of the book was published in 2005 by John Wiley & Sons, Inc.

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