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What does it mean for stock market prices to be like a random walk? What is a random walk? Financial economists have come up with an interesting scenario to introduce the random walk to laymen. Imagine if you will, they say, a drunk who has been left at a lamp post. The drunk wants to get home, but every step he takes is in a random direction. What emerges is a very erratic trail, where the position of the drunk over time starts drifting away from lamp post but occasionally coming back to where he started.

Investors are well-aware that the price of a stock, high yield mutual fund, money market deposit account, fluctuates on a daily basis. These fluctuations do not go away upon zooming in to shorter times. That is, over the scale of hours and even minutes, the prices continue to fluctuate up and down. These same observations compelled mathematicians and statisticians to label stock prices as having the same behavior as the drunkard, albeit in one dimension.

Being able to map the behavior of a stock price to a mathematical theory means that the stock price should have certain statistical properties. For example, the price of a stock, bond, or mutual fund (and its yield we suppose) should move around a mean value. Moreover, the deviation away from this mean on a daily basis should never be too positive or too negative, but instead fits into a normal distribution. Interestingly many securities show these statistical behaviors which gives credence to the theory.

The random walk idea underlies an important equation in mathematical finance known as the Black-Scholes equation. It was even the basis for the Nobel Prize in economics for two researchers Scholes and Merton. Those who are interested may find the mathematics a bit daunting as it ventures into stochastic calculus and partial differential equations.

Despite the success of the random walk theory, it turns out that there are some observations that do not match the idea of the random walk. For example, many companies have increasing or decreasing stock prices over the long time period as they become successful or fail at their business. Companies also experience the negative effects of broad decline during recessionary times. Clearly the random walk theory is not applicable for these times.

The normal person who is more worried about a 401K or IRA account that contains high yield mutual funds, GNMA investments and bonds may find the discussion very theoretical. Indeed, it is likely that these mathematical concepts are only useful for a day-trader who must contend with making profits from swings in stock prices on the short term.

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