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Random Walk Theory, Efficient Market Hypothesis (EMH), and Our Stock Trading Philosophy

Economic theory teaches the notion that in a perfectly efficient stock market, prices should follow a random walk. Under a random walk, historical data on prices and volume have no value in predicting future stock prices. In other words, statistical analysis and "technical analysis" is useless and trying to time the market is a fool's errand.

Pick up a book on technical analysis or how to time the stock market, on the other hand, and you will find contempt for the efficient market hypothesis and random walk hypothesis (if either is mentioned at all). These books dismiss the implications of efficient markets all too easily, and rarely state their claims in terms that can be subjected to objective empirical analysis. The well-defined trading rules that one does find discussed often fail to work as suggested once they are put to extensive analysis (see our tests in "Technical Indicators and Trading Systems" for examples).

Related Books

Inefficient Markets: An Introduction to Behavioral Finance by Andrei Shleifer

The New Finance: The Case Against Efficient Markets by Robert A. Haugen

A Non-Random Walk Down Wall Streetby Andrew W. Lo and Craig A. MacKinlay

(Mis)behavior of Markets by Benoit Mandelbrot and Richard Hudson

To their credit, we do believe that many books on technical analysis provide inspiration and raw materials that can be used to construct quantitative trading systems.

Many in the academic finance community now hold that stock prices do have some degree of predictability. Using the most rigorous and credible methods, the academic finance community now generally recognizes that stock returns can deviate from a random walk, which highlights the potential value in technical analysis or more sophisticated statistical forecasting methods. Nonetheless, efficient market hypothesis and/or random walk hypothesis should not be simply rejected as many writers of books on trading would have it. Rather, it should be treated as the base case to which alternatives can be compared.

Of course, it is one thing to know that stock prices contain some predictability. It is quite another to exploit this fact. And it is yet another thing to exploit it in a way that compensates for the transactions costs of trading. We began implementing many of the claims made in trading books and academic papers into trading systems and put them through extensive testing. The tests we ran included out of sample testing to avoid statistical pitfalls of over-fitting/data-snooping. We found that the systems that worked were robust, in that they were profitable over wide ranges of parameters.

Our broad conclusions about the stock market and effective trading can be summarized as follows:

  • Changes in stock prices are not completely random, though usually very close to it.

  • Investor psychology, time-varying investor preferences, over-reaction, under-reaction, transaction costs, informational constraints, and even widespread use of similar trading systems contribute to this nonrandomness.

  • Trading systems can be developed to effectively exploit deviations from the random walk. Mechanical trading systems can be profitable, in part, because they are immune to greed and fear.

  • Over-reaction (i.e. mean reversion, negative autocorrelation) is more prevalent for some types of stocks and for some time frames, and under-reaction (i.e. price momentum, positive autocorrelation) is more prevalent in others.

  • There are different ways to characterize risk, including volatility measured by a standard deviation and the probability of experiencing a drawdown of a given size. Academics focus on the former and many traders seem to focus on the latter. If stock returns followed a fixed normal distribution, there would be a direct mapping between these two types of risk. However, it is now well known that stock returns are "fat tailed," meaning that the probability of an abnormal return is typically larger than a normal distribution would imply. Stop losses can help shield against adverse "rare events."
These conclusions are drawn from our own experience testing many systems over a wide variety of stocks and evaluating competing claims from a wide variety of sources--academic and otherwise.

Finally, an important component of enjoyable, successful trading is that the trading method should match one's personality. As emphasized by Jack Schwager in The New Market Wizards, "If you don't want to watch the quote screen all day (or can't), don't try a day-trading method. If you can't stand the emotional strain of making trading decisions, then try to develop a mechanical trading system for trading the markets. The approach you use must be right for you; it must feel comfortable." Our trading systems are honed to our personalities, tolerance for risk, and confidence in statistics and our own analysis. We prefer trading systems that only need monitoring at the beginning and end of the day. Visitors and subscribers should consider their own personalities and trading objectives when considering following our trading systems or any others.