Wednesday, January 7, 2009

Bachelier's Insight

Most people would never have heard of Louis Bachelier before. Bachelier was an academic who set himself the ambitious goal of offering a formula which expresses the likelihood of a market fluctuations - that is the move upwards or downwards of a stock price.

He was an unknown during his time but laid the ground work on which later mathematicians constructed a full-fledge theory of probability.

So what exactly did Bachelier propose?

Simply this: that the interval / size of a market fluctuation grows larger as the time horizon stretches out. During minutes, the fluctuations are small. In a single day, the fluctuation is big. In a single week, even bigger. An of course, needless to say, the price range for a year/years will be much much larger.

So how rapidly does this range expand? Bachelier came to the conclusion that the interval was proportional to the square root of time.

This prediction has held up with fairly accurate precision.

What does this mean?

It means stock prices resemble molecules randomly colliding with one another or what we now know as Brownian motion. Over time, in the literature of finance, this similarity of the stock prices to Brownian motion came to be known as random walk.

In the later years, the primary focus of much research on finance and capital markets was on determining whether this random walk is a valid description of security price movements.

This post was adapted by the author from the book Capital Ideas by Peter L.Bernstein

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