Random Walk in Stock Market Prices

For many years, economists, statisticians,and teachers of finance have been interested in developing and testing models of stock price behavior. One important model that has evolved from this research is the theory of random walks. This theory casts serious doubt on many other methods for describing and predicting stock price behavior-methods that have considerable popularity outside the academic world.

For example, we shall see later that, if the random-walk theory is an accurate description of reality, then the various “technical” or “chartist” procedures for predicting stock prices are completely without value.

In general, the theory of random walks raises challenging questions for anyone who has more than a passing interest in understanding the behavior of stock prices. Unfortunately,however, most discussions of the theory have appeared in technical academic journals and in a form which the non-mathematician would usually find incomprehensible.

Common Predictive Techniques
In order to put the theory of random walks into perspective, we first discuss, in
brief and general terms, the two approaches to predicting stock prices that are commonly espoused by market professionals. These are (1) “chartist” or “technical” theories and (2) the theory of fundamental or intrinsicvalue analysis.

The basic assumption of all the chartist or technical theories is that history tends to repeat itself, that is, past patterns of price behavior in individual securities will tend to recur in the future. Thus the way to predictstock prices (and, of course, increase one’s potential gains) is to develop a familiarity with past patterns of price behavior in order to recognize situations of likely recurrence.

Essentially, then, chartist techniques attempt to use knowledge of the past behavior
of a price series to predict the probable future behavior of the series. A statistician would characterize such techniques as assuming that successive price changes in individual securities are dependent. That is,the various chartist theories assume that the sequence of price changes prior to any given day is important in predicting the price change for that day.

The techniques of the chartist have always been surrounded by a certain degree
of mysticism, however, and as a result most market professionals have found them suspect.

Thus it is probably safe to say that the pure chartist is relatively rare among stockmarket analysts. Rather the typical analyst adheres to a technique known as fundamental analysis or the intrinsic value method.

Next, we look at fundamental analysis or the intrinsic value method of determining stock market prices