## Random Walk Theory

## Definition

A random walk is a mathematical object, known as a stochastic or random process, that describes a path that consists of a succession of random steps on some mathematical space such as the integers. An elementary example of a random walk is the random walk on the integer number line, \mathbb Z, which starts at 0 and at each step moves +1 or −1 with equal probability. Other examples include the path traced by a molecule as it travels in a liquid or a gas, the search path of a foraging animal, the price of a fluctuating stock and the financial status of a gambler can all be approximated by random walk models, even though they may not be truly random in reality. As illustrated by those examples, random walks have applications to many scientific fields including ecology, psychology, computer science, physics, chemistry, biology as well as economics.

Source: Investopedia

*This Article has been Edited for Accessibility*

### Random Walk Theory

### What is the 'Random Walk Theory'

The random walk theory suggests that stock price changes have the same distribution and are independent of each other, so the past movement or trend of a stock price or market cannot be used to predict its future movement. In short, this is the idea that stocks take a random and unpredictable path.

### Explaining 'Random Walk Theory'

A follower of the random walk theory believes it's impossible to outperform the market without assuming additional risk. Critics of the theory, however, contend that stocks do maintain price trends over time – in other words, that it is possible to outperform the market by carefully selecting entry and exit points for equity investments.### Efficient Markets Are Random

This theory raised a lot of eyebrows in 1973 when author Burton Malkiel wrote "A Random Walk Down Wall Street." The book popularized the efficient market hypothesis, an earlier theory posed by University of Chicago professor William Sharp. The efficient market hypothesis says that stock prices fully reflect all available information and expectations, so current prices are the best approximation of a company’s intrinsic value. This would preclude anyone from exploiting mispriced stocks on a consistent basis because price movements are largely random and driven by unforeseen events. Sharp and Malkiel concluded that, due to the short-term randomness of returns, investors would be better off investing in a passively managed, well-diversified fund. In his book, Malkiel theorized that "a blindfolded monkey throwing darts at a newspaper's financial pages could select a portfolio that would do just as well as one carefully selected by experts."

### Enter the Dart-Throwing Monkeys

In 1988, the Wall Street Journal created a contest to test Malkiel's random walk theory by creating the annual Wall Street Journal Dartboard Contest, pitting professional investors against darts for stock-picking supremacy. Wall Street Journal staff members played the role of the dart-throwing monkeys. After 100 contests, the Wall Street Journal presented the results, which showed the experts won 61 of the contests and the dart throwers won 39. However, the experts were only able to beat the Dow Jones Industrial Average (DJIA) in 51 contests. Malkiel commented that the experts' picks were aided by the publicity jump in the price of a stock that tends to occur when stock experts make a recommendation. Passive management proponents contend that, because the experts could only beat the market half the time, investors would be better off investing in a passive fund that charges far lower management fees.