Random Walk Hypothesis

Origins and early research

Louis Bachelier (1900) modeled price changes on the Paris bourse as a random process and argued that the speculator's mathematical expectation is zero. Alfred Cowles (1933) reported that professional forecasters' stock market predictions did no better than chance, and Maurice Kendall (1953), analyzing British stock and commodity price series, remarked with surprise that price changes behaved almost as if a demon of chance drew them at random. The physicist Osborne (1959) showed that changes in log stock prices resemble Brownian motion. These studies challenged the conventional belief that price changes follow predictable patterns.

Theoretical foundations and market efficiency

In Proof that Properly Anticipated Prices Fluctuate Randomly, Paul Samuelson (1965) showed mathematically that if rational participants incorporate all information into prices, future price changes respond only to news that cannot be known today and are therefore unpredictable. Strictly, his conclusion is that prices follow a martingale, a weaker condition than a strict random walk. Eugene Fama (1965) documented that returns on Dow Jones stocks show almost no autocorrelation, and Fama (1970) systematized this as the efficient market hypothesis. Burton Malkiel's (1973) A Random Walk Down Wall Street brought the idea to a wide audience. The random walk is one implication of market efficiency, but the two concepts are not identical, a point that became central to later debate.

Challenges and recent perspectives

Lo and MacKinlay (1988) used a variance ratio test, based on the property that return variance should grow in proportion to the horizon, and found that weekly US stock indexes do not follow a random walk. Poterba and Summers (1988) reported mean reversion in long-horizon returns, and Jegadeesh and Titman (1993) documented momentum, with stocks that performed well over the past three to twelve months continuing to do so. Such predictability may not translate into actual excess profits, however, because of transaction costs, time-varying risk premia and data mining. Lo and MacKinlay (1999) collected this research in A Non-Random Walk Down Wall Street, and Lo (2004) proposed the adaptive markets hypothesis, in which market efficiency varies over time with the environment and the adaptation of participants. The random walk is also a basic assumption of option pricing models and continues to be studied in contrast to behavioral explanations such as information cascades.

FAQ

What is the random walk hypothesis in simple terms?

It holds that tomorrow's price move is random like a coin toss regardless of past moves, so past charts cannot consistently predict the future.

Is it the same as the efficient market hypothesis?

They are closely related but not identical. In an efficient market only news moves prices, producing near-random-walk behavior, but if risk premia vary over time some predictability can arise even in an efficient market.

Sources reviewed: 2026-10-26

References

1. Bachelier, L. (1900). Théorie de la spéculation. Annales scientifiques de l'École Normale Supérieure, 17, 21–86.
2. Cowles, A. (1933). Can stock market forecasters forecast? Econometrica, 1(3), 309–324.
3. Kendall, M. G. (1953). The analysis of economic time-series—Part I: Prices. Journal of the Royal Statistical Society Series A, 116(1), 11–34.
4. Osborne, M. F. M. (1959). Brownian motion in the stock market. Operations Research, 7(2), 145–173.
5. Samuelson, P. A. (1965). Proof that properly anticipated prices fluctuate randomly. Industrial Management Review, 6(2), 41–49.
6. Fama, E. F. (1965). The behavior of stock-market prices. Journal of Business, 38(1), 34–105.
7. Fama, E. F. (1970). Efficient capital markets: A review of theory and empirical work. Journal of Finance, 25(2), 383–417.
8. Malkiel, B. G. (1973). A Random Walk Down Wall Street. New York: W. W. Norton.
9. Lo, A. W., & MacKinlay, A. C. (1988). Stock market prices do not follow random walks: Evidence from a simple specification test. Review of Financial Studies, 1(1), 41–66.
10. Poterba, J. M., & Summers, L. H. (1988). Mean reversion in stock prices: Evidence and implications. Journal of Financial Economics, 22(1), 27–59.
11. Jegadeesh, N., & Titman, S. (1993). Returns to buying winners and selling losers: Implications for stock market efficiency. Journal of Finance, 48(1), 65–91.
12. Lo, A. W., & MacKinlay, A. C. (1999). A Non-Random Walk Down Wall Street. Princeton: Princeton University Press.
13. Lo, A. W. (2004). The adaptive markets hypothesis. Journal of Portfolio Management, 30(5), 15–29.