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random walk hypothesis

Contributor(s): Matthew Haughn

Random walk hypothesis is a mathematical theory where a variable does not follow an apparent trend and moves seemingly at random. The concept originated as a hypothesis theorizing that the movements of stock prices are largely random and cannot be based on past movements or trends, and are thus unpredictable. As a result, one can’t attempt to predict outcomes of markets without significant risk. Since its creation, the applied theory of random walk has been used to predict probabilities of events occurring in largely random movements.

One of the simplest examples of a random walk is integers. Starting from the point of origin, assumed as zero, a random walk can take either the direction of right into positive integers or left into negative. One can use a coin to perform a random decision for the movement. Even though the walk is random, some certainties exist. When applied to integers, a random walk can only be on odd numbers during odd turns and even numbers on even turns. One the first turn, there is a 50/50 chance that the position is either on -1 or 1. On the second turn, there is a 50% chance the position is zero, 25% that it could be -2 and 25% it could be +2 value. Subsequent turns follow the same fractional pattern of probable outcomes. An integer walk such as this is simple mostly because it is one-dimensional in movement and unit per movement. Things become much more complex with multi-dimensional systems such as 2D or 3D random walks.

Random walks are grouped into two types: Recurrent, which return to their origin, or transient, which do not or are unlikely to return to their starting point. Simpler random walks such as those of integers are much more likely to return home as their choice of direction involves more potential directions away from the origin. The difference in tendency between simple and complex random walks has resulted in a popular joke among mathematicians: A drunken man will eventually find his way home but a drunken bird will never find its way home.

The random walk hypothesis was originally formulated by mathematician Burton Malkiel in 1973. Malkiel compared the likelihood of predicting the performance of stocks accurately to chimpanzees playing darts successfully. Random walks can be used to describe and help predict the performance of stocks and other systems, such as biological movement, search engines and the study of evolution.

This was last updated in March 2018

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