Why Is The Price Of A Stock Like A Random Walk
The discussion begins with the question “What is a random walk?” Mathematicians have come up with an interesting way to broach the subject. They say, imagine a drunk to who is trying to get home. He starts off at a lamp post, and then starts taking steps. Every step he takes is random in direction. Over time, he will start to drift away from the lamp post, but also occasionally return to it. This situation captures the essence of a random walk.
The price of a security such as a high yield mutual fund or even a money market deposit account moves up and down over time as evidenced by a time-series graph. Even tracking it minute-by-minute (should one be able to access such data) the up and down motion is evident although at smaller scales than over days or weeks. Based on this observation, it has been proposed by financial economists and statisticians that this fluctuating movement that goes up and down is akin to a random walk. Whereas the drunkard walked in two dimensions, the price of a stock executes a one dimensional random walk.
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.
In fact, the Black-Scholes theory of options pricing based on ideas drawn from random-walk mathematics was the reason for a Nobel Prize in economics. Readers will find the details of the theory daunting, but should keep in mind that it is no more than a formalization of the random walk idea.
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.
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.
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