Flavors of Randomness
By: Jørgen Veisdal
Tags: Economics, Finance, Stock Market, Money, Investing

Flavors of Randomness

Implications of the Efficient-Market Hypothesis

“The baseball announcer has it, of course, conveniently all wrong. Ted Williams is due to hit because he hasn’t hit for seven days. That’s red noise. Ted Williams is hot, he’s sure to hit tomorrow because he’s been hitting for seven days. That’s blue noise. The better description of an efficient market with random movements, which is white noise, is in between.” — Paul Samuelson

The above anecdote was made by economist Paul Samuelson in a 2004 interview conducted by fellow Nobel Laureate Robert C. Merton for the American Finance Association (AFA). Lauded for his many contributions and often hailed as the ‘last of the great general economists’, the interview regarded one of Samuelson’s main contributions to finance, work on the so-called efficient-market hypothesis (Fema, 1965). This essay relates the implications of that work to the later development of the field of behavioral economics.

The Efficient-Market Hypothesis

The efficient-market hypothesis (EMH) states that asset prices fully reflect all available information in a market. That is, it should in theory be impossible to “beat” an efficient market consistently on a risk-adjusted basis. Given the ability to profit from private information, the conjecture assumes that rational investors are motivated to act by buying or selling an asset. In doing so, they reveal the implications of their analysis (of their private information), and so contribute to increasingly efficient market prices. In the competitive limit, market prices will therefor reflect all available information (both public and private) and prices will only change in response to new information. What one is left with, is the noise of investors’ decisions in unfounded information — which is considered to behave essentially randomly (see “Brownian Motion in Financial Markets”).

What Samuelson’s anecdote above and the efficient-market hypothesis (EMH) hence spells out is essentially a taxonomy of human interpretations of what may statistically be interpreted as random events. Events such as the usefulness of a price trend in predicting the future value of a stock or the dependence of a future base hit on a history of striking out or hitting streaks. His point is that people’s interpretations vary wildly, and that it goes against human nature to imply randomness by default, which in turn leads to fallacious expectations.

History

Prior to its popularization in the mid-1960, the roots of the efficient market hypothesis (EMH) can be traced back to Louis Bachelier’s 1900 doctoral dissertation Théorie de la spéculation (“The Theory of Speculation”). Bachelier was the first to use the theory of Brownian motion to describe stock and option market fluctuations as essentially random movements. His advisor at the University of Paris was Henri Poincaré and he successfully defended his thesis in 1900.

Left: Louis Jean-Baptiste Alphonse Bachelier at the age of 20 in 1890. Right: Bachelier’s doctoral dissertation Théorie de la spéculation (1900).

The key insight of Bachalier’s dissertation was the realization that if asset prices in the short term show an identifiable pattern, speculators will find this pattern and exploit it, thereby eliminating it. He argued, essentially, that as soon as the price of a stock or option begins behaving according to a predictable pattern, that pattern will disappear as speculators find and exploit it. The notes from Bachelier’s thesis defense committee, co-signed by Poincaré, describe the thesis in the following way:

One could imagine combinations of prices on which one could bet with certainty. The author cites some examples. It is clear that such combinations are never produced, or that if they are produced they will not persist. The buyer believes in a probable rise, without which he would not buy, but if he buys, there is someone who sells to him and this seller believes a fall to be probable. From this it follows that the market taken as a whole considers the mathematical expectation of all transactions and all combinations of transactions to be null.

Now considered the quintessential pioneering work in financial mathematics, the work was largely forgotten until being rediscovered in 1956 by Leonard Savage and put to the attention of Paul Samuelson, who arranged to have it translated by his colleague Paul Cootner. Samuelson used it to further develop Bachelier’s ideas and in 1965 publish two now momentous papers in finance: Proof That Properly Anticipated Prices Fluctuate Randomly (Samuelson, 1965a) and Rational Theory of Warrant Pricing (Samuelson, 1965b), both in Industrial Management Review. There, he proposed a model of option pricing closely related to the key thesis in Bachelier’s work, citing his influence.