A Primer On Random Walks In The Stock Market

A Primer On Random Walks In The Stock Market

Jun.10, 2010

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.

Most economists and investors are acutely cognizant of the fact that high yield mutual funds, money market deposit accounts, and general security prices have erratic up-and-down movements from day to day. Furthermore, looking at security prices from hour to hour and minute to minute continue to show these fluctuations albeit at reduced magnitudes. These observations provided the basis for the idea that like the drunkard’s walk, stock prices move up and down and drift while adhering to strict statistical properties.

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 proposal that the stock market (specifically in the options market) has these mathematical properties is the basis the Nobel Prize in economics being awarded to the economists Merton and Scholes. Interested readers may find that brushing up on calculus and venturing into the field of differential equations will be helpful to understanding the mathematics.

While the success of the random walk theory is not arguable, the extent to which it is true is very much in contention. Instead of strictly fluctuating around a mean, many stock prices show “trending” or consistent movement up or down ove time. And instead of fluctuation, during stock market crashes, the price of stocks, bonds, mutual funds show precipitous declines. These inconsistencies have driven development of more accurate models but the issue is not resolved.

To the regular, layman investor who is engaged in low risk investments, mutual funds, and GNMA mutual funds over the long term, such information is not so useful for calculating returns and yields. On the other hand the veteran day trader who moves in and out of positions within hours may derive some value from these ideas.