The foundations

In nineteen hundred, in Paris, a young mathematician defended a thesis on the stock exchange. His name was Louis Bachelier.

His thesis was called Theory of Speculation. On the jury sat the great mathematician Henri Poincaré.

Bachelier described prices as a series of small random steps. From it he drew the mathematics of Brownian motion.

Five years before Albert Einstein did it, independently, to explain the jiggling of particles in a liquid.

Yet Bachelier was almost forgotten for half a century. Economists rediscovered him in the fifties.

His idea has a name: the random walk. Tomorrow's price is today's, plus unpredictable noise.

Toss a coin every day. Heads, the price gains one euro. Tails, it loses one. And draw the curve.

It looks surprisingly like a real stock chart. With trends, peaks, troughs. Yet it is all chance.

If prices follow a random walk, then the patterns of the past say nothing about the future.

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In nineteen seventy, the economist Eugene Fama gave this idea its modern form: market efficiency.

A market is efficient if prices already reflect the information available. You do not beat the market with what everyone knows.

Fama distinguished three forms. The weak form: past prices do not let you predict future prices.

The semi-strong form: all public information, results, news, announcements, is already in the price. It gets in within moments.

The strong form: even secret information would be in the price. Almost nobody believes it. Insider trading pays, hence its ban.

An old joke sums up the idea. An economist sees a banknote on the ground. He does not bend down: if it were real, someone would have picked it up.

The joke exaggerates. But in markets, banknotes on the ground are rare, and quickly picked up.

Practical consequence: most active managers do worse than their index, once fees are paid.

That is the argument that carried index funds. If you cannot beat the market, you might as well buy all of it, cheaply.

But bubbles raise a question. If prices are always right, how can they double, then collapse?

Robert Shiller answers that markets get carried away, and that you can sometimes see it coming, over long periods.

In two thousand thirteen, the Nobel prize rewarded Fama, Shiller and Lars Peter Hansen together. For partly opposing theses.

It is not a contradiction. Over a few days, prices are almost unpredictable. Over years, excesses often end up correcting.

Both are right, each on his own time scale.

For the saver, the lesson is twofold: do not bet on tomorrow, and be wary of prices that look too good to last.