Dating back to work on the random walk hypothesis by French economist Louis Bachelier (1870-1946), efficient market hypothesis asserts that stock market prices are the best available estimates of the real value of shares since the market has taken account of all available information on an individual stock.

Also see: rational expectations theory, adaptive expectations

Source:

H Roberts, ‘Stock Market “Patterns” and Financial Analysis: Methodological Suggestions’, Journal of Finance, 14, 1 (March, 1959), 1-10

## Theoretical background

Suppose that a piece of information about the value of a stock (say, about a future merger) is widely available to investors. If the price of the stock does not already reflect that information, then investors can trade on it, thereby moving the price until the information is no longer useful for trading.

Note that this thought experiment does not necessarily imply that stock prices are unpredictable. For example, suppose that the piece of information in question says that a financial crisis is likely to come soon. Investors typically do not like to hold stocks during a financial crisis, and thus investors may sell stocks until the price drops enough so that the expected return compensates for this risk.

How efficient markets are (and are not) linked to the random walk theory can be described through the fundamental theorem of asset pricing. This theorem states that, in the absence of arbitrage, the price of any stock is given by^{[clarification needed]}

- {\displaystyle P_{t}=E_{t}[M_{t+1}(P_{t+1}+D_{t+1})]}

where {\displaystyle E_{t}} is the expected value given information at time {\displaystyle t}, {\displaystyle M_{t+1}} is the stochastic discount factor, and {\displaystyle D_{t+1}}is the dividend the stock pays next period. Note that this equation does not generally imply a random walk. However, if we assume the stochastic discount factor is constant and the time interval is short enough so that no dividend is being paid, we have

- {\displaystyle P_{t}=ME_{t}[P_{t+1}]}.

Taking logs and assuming that the Jensen’s inequality term is negligible, we have

- {\displaystyle \log P_{t}=\log M+E_{t}[\log P_{t+1}]}

which implies that the log of stock prices follows a random walk (with a drift).

## Empirical studies

Research by Alfred Cowles in the 1930s and 1940s suggested that professional investors were in general unable to outperform the market. During the 1930s-1950s empirical studies focused on time-series properties, and found that US stock prices and related financial series followed a random walk model in the short-term.^{[7]} While there is some predictability over the long-term, the extent to which this is due to rational time-varying risk premia as opposed to behavioral reasons is a subject of debate. In their seminal paper, Fama, Fisher, Jensen, and Roll (1969) propose the event study methodology and show that stock prices on average react before a stock split, but have no movement afterwards.

### Weak, semi-strong, and strong-form tests

In Fama’s influential 1970 review paper, he categorized empirical tests of efficiency into “weak-form”, “semi-strong-form”, and “strong-form” tests.^{[1]}

These categories of tests refer to the information set used in the statement “prices reflect all available information.” Weak-form tests study the information contained in historical prices. Semi-strong form tests study information (beyond historical prices) which is publicly available. Strong-form tests regard private information.^{[1]}

## Historical background

Benoit Mandelbrot claimed the efficient markets theory was first proposed by the French mathematician Louis Bachelier in 1900 in his PhD thesis “The Theory of Speculation” describing how prices of commodities and stocks varied in markets.^{[8]} It has been speculated that Bachelier drew ideas from the random walk model of Jules Regnault, but Bachelier did not cite him,^{[9]} and Bachelier’s thesis is now considered pioneering in the field of financial mathematics.^{[10]}^{[9]} It is commonly thought that Bachelier’s work gained little attention and was forgotten for decades until it was rediscovered in the 1950s by Leonard Savage, and then become more popular after Bachelier’s thesis was translated into English in 1964. But the work was never forgotten in the mathematical community, as Bachelier published a book in 1912 detailing his ideas,^{[9]} which was cited by mathematicians including Joseph L. Doob, William Feller^{[9]} and Andrey Kolmogorov.^{[11]} The book continued to be cited, but then starting in the 1960s the original thesis by Bachelier began to be cited more than his book when economists started citing Bachelier’s work.^{[9]}

The concept of market efficiency had been anticipated at the beginning of the century in the dissertation submitted by Bachelier (1900) to the Sorbonne for his PhD in mathematics. In his opening paragraph, Bachelier recognizes that “past, present and even discounted future events are reflected in market price, but often show no apparent relation to price changes”.^{[12]}

The efficient markets theory was not popular until the 1960s when the advent of computers made it possible to compare calculations and prices of hundreds of stocks more quickly and effortlessly. In 1945, F.A. Hayek argued that markets were the most effective way of aggregating the pieces of information dispersed among individuals within a society. Given the ability to profit from private information, self-interested traders are motivated to acquire and act on their private information. In doing so, traders contribute to more and more efficient market prices. In the competitive limit, market prices reflect all available information and prices can only move in response to news. Thus there is a very close link between EMH and the random walk hypothesis.^{[13]}

The efficient-market hypothesis emerged as a prominent theory in the mid-1960s. Paul Samuelson had begun to circulate Bachelier’s work among economists. In 1964 Bachelier’s dissertation along with the empirical studies mentioned above were published in an anthology edited by Paul Cootner.^{[14]} In 1965, Eugene Fama published his dissertation arguing for the random walk hypothesis.^{[15]} Also, Samuelson published a proof showing that if the market is efficient, prices will exhibit random-walk behavior.^{[16]} This is often cited in support of the efficient-market theory, by the method of affirming the consequent,^{[17]}^{[18]} however in that same paper, Samuelson warns against such backward reasoning, saying “From a nonempirical base of axioms you never get empirical results.”^{[19]} In 1970, Fama published a review of both the theory and the evidence for the hypothesis. The paper extended and refined the theory, included the definitions for three forms of financial market efficiency: weak, semi-strong and strong (see above)

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