Just What Exactly Is a Random Walk?

Just What Exactly Is a Random Walk?

To many people this appears to be arrant nonsense. Even the most casual reader of the financial pages can easily spot patterns in the market.

The persistence of the belief in repetitive patterns in the stock market is due to statistical illusion. To illustrate, let me describe an experiment in which I recently asked my students to participate. The students were asked to construct a norm stock charts showing the movements of a hypothetical stock initially selling at $50 per share. For each successive trading day, the closing stock price would be determined by the flip of a fair coin. If the toss was a head, the students assumed that the stock closed 1/2 point higher than the preceding close. If the flip was a tail, the price was assumed to be down by 1/2. The chart derived from random coin tossing looks remarkably like a normal stock price chart and even appears to display cycles. Of course, the pronounced “cycles” that we seem to observe in coin tossing do not occur at regular intervals as true cycles do, but neither do the ups and downs in the stock market.

It is this lack of regularity that is crucial. The “cycles” in the stock charts are no more true cycles than the runs of luck or misfortune of the ordinary gambler. And the fact that stocks seem to be in an uptrend, which looks just like the upward move in some earlier period, provides no useful information on the dependability or duration of the current uptrend. Yes, history does tend to repeat itself in the stock market, but in an infinitely surprising variety of ways that confound any attempts to profit from a knowledge of past price patterns.

In other simulated stock charts derived through student coin tossing, there were head-and-shoulders formations, triple tops and bottoms, and other more esoteric chart patterns. One of the charts showed a beautiful upward breakout from an inverted head and shoulders (a very bullish formation). I showed it a chartist friend of mine who practically jumped out of his skin. “What is this company?” he exclaimed. “We’ve got to buy immediately. This pattern’s classic. There’s no question the stock will be up 15 points next week.” He did not respond kindly to me when I told him the chart had been produced by flipping a coin. Chartists have no sense of humor. I got my comeuppance when Business Week hired a technician who was adept at hatchet work, to review the first edition of this book.

Just What Exactly Is a Random Walk? Photo by Elena

My students used a completely random process to produce their stock charts. With each toss, as long as the coins used were fair, there was a 50 percent chance of heads, implying an upward move in the price of the stock, and a 50 percent chance of tails and a downward move. Even if they flip ten heads in a row, the chance of getting a head on the next toss is still 50 percent. Mathematicians call a sequence of numbers produced by a random process (such as those on our simulated stock chart) a random walk. The next move on the chart is completely unpredictable on the basis of what has happened before.

To a mathematician, the sequence of numbers recorded on a stock chart behaves no differently from that in the simuated stock charts – with one exception. There is a long-run uptrend growth of earnings and dividends. After adjusting for this trend, there is essentially no difference. The next move in a series of stock prices is unpredictable of past price behavior. No matter what wiggle or wobble the prices have made in the past, tomorrow starts out fifty-fifty. The next price change is no more predictable than the flip of a coin.

Now, in fact, the stock market does not quite measure up to the mathematician’s ideal of the complete independence of present price movements from those in the past. There have been some dependencies found. But any systematic relationships that exist are small that they are not useful for an investor. The brokerage charges involved in trying to take advantage of these dependencies are far greater than any advantage that might be obtained. This is the consistent finding of the academic research on stock prices. Thus, an accurate statement of the “weak” form of the random-walk hypothesis goes as follows:

The history of stock price movements contains no useful information that will enable an investor consistently to outperform a buy-and-hold strategy in managing a portfolio.

In the weak form of the random-walk hypothesis is a valid description of the stock market, then, as Richard Quandt says, “Technical analysis is akin to astrology and every bit as scientific.”

I am not saying that technical strategies never make money. They very often do make profits. The point is rather that a simple “buy-and-hold” strategy (that is, buying a stock or group of stocks and holding on for a long period of time) typically makes as much or more money.

When scientists want to test the efficacy of some new drug they usually run an experiment where two groups of patients are administrated pills – one containing the drug inn question, the other a worthless placebo (a sugar pill). The results of the administration to the two groups are compared and the drug is deemed effective only if the group receiving the drug did better than the group getting the placebo. Obviously, if both groups got better in the same period of time the drug should not be given the credit, even if the patients did recover.

In the stock-market experiments, the placebo with which the technical strategies are compared is the buy-and-hold strategy. Technical schemes often do make profits for their users, but so does a buy-and-hold strategy. Indeed, as we shall see later, a naïve buy-and-hold strategy using a dart-board-selected portfolio has provided investors with an average annual rate of return of approximately 10 percent over the past sixty years. I believe that return will continue at roughly that level for the reminder of the century. Only if technical schemes produce better returns than the market can they be judged effective. To date, none has consistently passed the test.

Devotees of technical analysis may argue with some justification that I have been unfair. The simple tests I have just described do not do justice to the “richness” of technical analysis. Unfortunately for the technician, even some of his more elaborate trading rules have been subjected to scientific testing.

Burton G. Malkiel. A Random Walk Down Wall Street, including a life-cycle guide to personal investing. First edition, 1973, by W.W. Norton and company, Inc