Random Walk

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Random Walk

A random walk is one in which future steps or directions cannot be predicted on the basis of past actions. When the term is applied to the stock market, it means that short-run changes in stock prices cannot be predicted: Investment advisory services, earnings predictions, and complicated chart patterns are useless to the investor.

ORIGINS AND RATIONALES

The application of the random walk hypothesis to stock prices usually is associated with Samuelson (1965), although the general idea that security prices change randomly goes back at least to the time of Bachelier (1900). The basic rationale for the hypothesis is that securities markets are very efficient at digesting information. When information arises about a particular security or about the market in general, the news spreads quickly and is incorporated into the price of that security without delay. Armies of investment managers pounce on any news that could affect the value of a security. By their trading, they ensure that security prices fully reflect all available information. As a result it is not possible to make profitable trades on the basis of that information because any potential profit will have been realized already. Changes in the prices of securities will be random and unpredictable.

The random walk hypothesis does not imply that movements in security prices are erratic or capricious. However, tomorrow’s price change in securities markets will reflect only tomorrow’s “news” and will be independent of the price change today. True news by definition is unpredictable, and thus the resulting price change also must be unpredictable and random.

The term random walk usually is used loosely in the finance literature to characterize a price series in which all subsequent price changes represent random departures from previous prices. Thus, changes in price essentially are not related to past price changes. It is believed that the term was used first in an exchange of correspondence in Nature in 1905. The subject was the optimal search procedure for finding a drunk who had been left in the middle of a field. The solution was simply to start where the drunk had been left. That point provides the best unbiased estimate of the drunk’s future position because presumably he will have staggered along in an unpredictable and random fashion.

If stock price movements approximate those of a random walk, technical analysis (the making and interpretation of stock charts to divine the future) is unlikely to offer investors a guide to making above-average profits. Moreover, trading strategies that seek to buy and sell stocks on the basis of charting signals will not help investors outperform a simple buy-and-hold strategy.

Considerable statistical work has supported the random walk hypothesis. Changes in stock prices from day to day are essentially uncorrelated, and news seems to be reflected in the prices of securities without delay. Although markets sometimes overreact to news, they underreact at other times. Several technical trading systems have been tested, and they do not produce greater profits after transactions costs than does a simple buy-and-hold strategy.

The stock market does not fully meet all the conditions for a random walk, however. Some slight dependencies have been found, and there is a small degree of momentum in stock prices. Some seasonal patterns have been discovered. However, the dependencies that have been found are very small relative to the transactions costs that would be required to exploit them, and they are not dependable from period to period.

Logic suggests that any patterns that might have existed in the past are likely to self-destruct in the future. Suppose, for example, there was a dependable Christmas rally; that is, the stock market consistently rose in the trading days between Christmas and New Year’s Day. Traders attempting to profit from that pattern would plan to buy the day before Christmas and sell the day before New Year’s Day. However, pre-Christmas buying would make stock prices rise the day before Christmas and fall the day before New Year’s as traders unloaded their positions to realize profits. Hence, to beat the gun, traders would have to buy two days before Christmas and sell two days before New Year’s Day. Before long all the buying would take place before Christmas and the selling would occur after Christmas, and the year-end rally would disappear. Any dependable pattern that could be exploited for profit would self-destruct. This is the logical reason why dependable patterns in stock prices are unlikely to persist.

IMPLICATIONS FOR INVESTORS

The random walk hypothesis has important implications for investors in the stock market. Visually, charts of stock prices appear to display some obvious patterns, but those patterns are simply a manifestation of a statistical illusion. The “cycles” in stock charts are no more true cycles than are the runs of luck or misfortunes of the ordinary gambler. History tends to repeat itself best in an infinitely surprising variety of ways that confound any attempts to profit from knowledge of past price patterns. Although the market does not meet the statistician’s ideal of a perfect random walk, any systematic relationships that exist are so small and undependable that they are not useful for an investor. 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.

Attempting to use past patterns of stock prices to ascertain the times when investors should be out of the market is especially dangerous. Because there is a long-term uptrend in the stock market, it can be very risky to be in cash. An investor who frequently carries a large cash position to avoid periods of market decline is very likely to be out of the market during some periods when it rallies smartly. Market timers risk missing the infrequent big gains that are the main contributors to performance, and they also pay more in taxes and transactions costs than does an investor who simply buys and holds a diversified portfolio.

SEE ALSO Efficient Market Hypothesis; Expectations, Implicit; Expectations, Rational; Financial Markets; Information, Economics of; Stocks