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What is the random walk theory? Definition and meaning

The definition and meaning of the random walk theory, also known as the random walk hypothesis, says it is impossible to predict which way prices will go in the world of investments. Shares and some other financial assets follow a **random walk – it is not possible to know whether the next price movement will be up or down, or how steeply that increase or decline might be. According to many economists, this unpredictability means that investors will never be able to outperform the market consistently. Some economists, however, disagree, and claim that asset prices do follow a non-random walk – they can be predictable – they insist that it is possible to outperform the markets consistently.

** A random walk is a mathematical process that describes a path that consists of a succession of random steps. For example, a molecule travels in a gas or liquid – we have no idea of predicting where it might go next, and after that, and then after that, etc. It is the same with a foraging animal, a drunkard walking, the financial status of a gambler, or a fluctuating stock.

According to the random walk theory, stock price changes have the same distribution and are completely independent of one another. So, it is not possible to use the past trend or movement of a market or stock price to predict where it will go. Put simply, random walk theory is the idea that stocks and shares take a random, haphazard and totally unpredictable path.

According to BusinessDictionary.com, to define the random walk hypothesis is:

“Stockmarket analysis theory that stock prices (and the capital markets in general) follow a pattern-less (random) path such as that of a drunkard’s walk.”

“Therefore, their future course is unpredictable and the best forecast of a stock’s price is equal to its present value plus an unpredictable negative or positive random error.”

Random walk theoryOur chances of outperforming the stock market are no better than our probability of predicting accurately where the drunkard in the image above will walk to next. Stock prices move randomly – it is impossible to predict – so says the random walk theory.

The random walk theory – a brief history

The concept of the random walk hypothesis can be traced back to a book published by Jules Regnault (1834-1894), a French stock broker’s assistant, one of the first authors who attempted to create a ‘stock exchange science’ based on probabilistic and statistical analysis.

Louis Bachelier (1870-1946), a French mathematician, who is credited with being the first individual to model the stochastic process, now known as Brownian motion, included some remarkable insights and commentary in his 1900 Ph.D. dissertation – The Theory of Speculation.



Paul Cootner (1930-1978), an American financial economist who taught at the MIT Sloan School of Management, developed Bachelier’s ideas in his 1964 book – The Random Character of Stock Market Prices.

In a 1953 paper – The Analysis of Economic time Series, Part 1: Prices – British statistician Maurice Kendall (1907-1983) put forward the theory that share prices moved randomly.

The term ‘random walk hypothesis’ was popularized by Princeton University Economics Professor Burton Malkiel in his 1973 book – A Random Walk Down Wall Street.

Non-Random Walk TheorySupporters of the non-random walk theory believe it is possible to make predictions about which way stock prices will go after observing past trends.

As random as flipping a coin

Prof. Malkiel carried out a test in which his students were given a hypothetical stock worth $50. A coin flip determined the closing stock price for each day. Heads meant that the price closed half-a-point up, while tails meant it closed half-a-point down.

Therefore, there was a 50-50 chance each time that the end-of-day closed higher or lower than the previous close-of-day. Trends or cycles were determined from the tests.



Prof. Malkiel then went with the results of his tests in a chart and graph form to a chartist. A chartist is somebody who tries to predict future movements by attempting to interpret past patterns on the assumptions that history has a tendency to repeat itself.

Malkiel was told by the chartist to buy the stock immediately. As the coin flips were random, the fictitious stock used in the test had no overall trend. Prof. Malkiel argued that this indicated that the stocks and the markets could be as random as flipping a coin.

The non-random walk theory

A significant number of investors, academics and economists believe that the market is to some degree predictable. They believe that prices may follow certain trends and that the study of previous prices can be used to predict which way stock values will go.

Some economic studies have been carried out to support this view. Andrew Wen-Chuan Lo, the Charles E. and Susan T. Harris Professor of Finance at the MIT Sloan School of Management, and A. Craig MacKinlay, Joseph P. Wargrove Professor of Finance at the Wharton School at the University of Pennsylvania wrote a book – A Non-Random Walk Down Wall Street – that attempts to prove that the random walk theory is wrong.

Princeton University Press wrote the following comment regarding Mackinlay’s and Lo’s book:

“Lo and MacKinlay find that markets are not completely random after all, and that predictable components do exist in recent stock and bond returns.”

“Their book provides a state-of-the-art account of the techniques for detecting predictabilities and evaluating their statistical and economic significance, and offers a tantalizing glimpse into the financial technologies of the future.”

Prof. Martin Weber, a leading researcher in behavioral finance, who works at the University of Mannheim in Germany, has carried out several studies and tests on finding trends in stock prices and the stock market.

In one of his studies, Prof. Weber observed the stock market for a whole decade. Throughout those ten years, he looked at market prices for detectable trends and found that stocks with significant price increases in the first five years tended to under-perform during the second-half of the decade.

Prof. Weber, together with many other supporters of the non-random walk theory, cite this observation as a key contradictor to the random walk theory.

Video – Random walk theory – Definition and Meaning

In this Ayn Rand Institute video, Yaron Brook answers the question: “What do you think of the random walk theory?”