The random walk hypothesis is a financial theory which states that the prices of financial assets, particularly those in the stock market, follow a random walk. According to this hypothesis, price variations occur in an essentially random manner, which implies that they cannot be systematically predicted or consistently exploited to achieve returns above those of the overall market.

The concept can be traced to French broker Jules Regnault who published a book in 1863, and then to French mathematician Louis Bachelier whose Ph.D. dissertation titled "The Theory of Speculation" (1900) included some remarkable insights and commentary. The same ideas were later developed by MIT Sloan School of Management professor Paul Cootner in his 1964 book The Random Character of Stock Market Prices. The term was popularized by the 1973 book A Random Walk Down Wall Street by Burton Malkiel, a professor of economics at Princeton University, and was used earlier in Eugene Fama's 1965 article "Random Walks In Stock Market Prices", which was a less technical version of his Ph.D. thesis. The theory that stock prices move randomly was earlier proposed by Maurice Kendall in his 1953 paper, The Analysis of Economic Time Series, Part 1: Prices. In 1993 in the Journal of Econometrics, K. Victor Chow and Karen C. Denning published a statistical tool (known as the Chow–Denning test) for checking whether a market follows the random walk hypothesis.

Whether financial data can be considered a random walk is a venerable and challenging question. One of two possible results are obtained, the data does fall under random walk or the data does not. To investigate whether observed data follows a random walk, some methods or approaches have been proposed, for example, the variance ratio (VR) tests, the Hurst exponent and surrogate data testing.

Burton G. Malkiel, an economics professor at Princeton University and author of A Random Walk Down Wall Street, performed a test where his students were given a hypothetical stock that was initially worth fifty dollars. The closing stock price for each day was determined by a coin flip. If the result was heads, the price would close a half point higher, but if the result was tails, it would close a half point lower. Thus, each time, the price had a fifty-fifty chance of closing higher or lower than the previous day. Cycles or trends were determined from the tests. Malkiel then took the results in chart and graph form to a chartist, a person who "seeks to predict future movements by seeking to interpret past patterns on the assumption that 'history tends to repeat itself'." The chartist told Malkiel that they needed to immediately buy the stock. Since the coin flips were random, the fictitious stock had no overall trend. Malkiel argued that this indicates that the market and stocks could be just as random as flipping a coin.

Modelling asset prices with a random walk takes the form:

${\displaystyle S_{t+1}=S_{t}+\mu \Delta {t}S_{t}+\sigma {\sqrt {\Delta {t}}}S_{t}Y_{i}}$

where

${\displaystyle \mu }$ is a drift constant