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Once every 7 millenia?


I write with some frequency about the role that psychology plays in negotiated financial markets. But making that statement presumes that current asset pricing models must be incomplete or wrong. So in an attempt to 'fill in' some of the background for the idea, I thought it might be helpful to describe - and debunk - the efficient market hypothesis, which is the standard academic asset pricing theory upon which most equilibrium economics rests. Onward.

No dissection of EMH can begin without first defining it. Though Louis Bachelier in the early 1900s is credited with developing the idea that stock prices are governed by a random walk, it wasn't until the 1960s that his theories for asset price fluctuations gained note, most popularly with Paul Samuelson. Ultimately though it was Eugene Fama, a professor of finance at the University of Chicago, that was credited with being the first to use the term "efficient market", about which he said this:

"In an efficient market, competition among the many intelligent participants lead to a situation where , at any point in time, actual prices of securities already reflects the effects of information based both on events that have already occurred and on events, as of now, the market expects to take place in the future. In other words, in an efficient market at any point in time the actual price of a security will be a good estimate of its intrinsic value."

To paraphrase Professor Fama, the hypothesis states that all relevant information is fully and immediately reflected in a security's market price. As a result of this, no investor will be able to earn anything more than an equilibrium rate of return on investments.

There are three forms of the efficient market hypothesis: (1) a weak form, (2) a semi-strong form, and (3) a strong form. The weak form of EMH states that all past prices, volumes and other market statistics (generally referred to as technical analysis) cannot provide any information that would prove useful in predicting future stock price movements. This is because stock price changes are random as a direct result of the fact that stock prices reflect new information and that new information arrives randomly. In short, the weak form of EMH says that technical analysis is fruitless in generating excess returns.

The semi-strong form suggests that stock prices fully reflect all publicly available information and all expectations about the future. "Old" information then is already discounted and cannot be used to predict stock price fluctuations. In sum, the semi-strong form suggests that fundamental analysis is also fruitless; knowing what a company generated in terms of earnings and revenues in the past will not help you determine what the stock price will do in the future. Lastly the strong form of EMH suggests that stock prices reflect all information, whether it be public (in SEC filings) or private (in the minds of the CEO and other insiders). So even with material non-public information, EMH asserts that stock prices cannot be predicted with any accuracy.

Academic studies have attempted to prove or disprove each of these forms of EMH, via testing of correlations (month-to-month and day-to-day returns), relative strengths, stock splits, earnings announcements, book value/market capitalization correlation studies, etc. In general, these tests have proven the strong and semi-strong forms to be entirely unacceptable, while the weak form has slightly more validity. That said, even the weak form has shown itself to be open to anomalies that make it, at best, sometimes operative.

We could detail the studies that show the various forms of EMH do not fit the empirical data but readers with any experience in the market will not need such data points. You already know that markets are, in fact, mostly inefficient and do not "fully reflect" all past and future information at all times. After all, what, precisely, was the stock market discounting in the spring of 2000? What was it discounting on September 6th 1929? Or for that matter the lows in 1974? Why do prices, on a statistically significant basis, generally outperform in January? That said, we think an important example will readily destroy the idea that markets are efficient all the time.

One of the central tenets of EMH is that one day's prices do not have any impact on the next day's prices. That is, price fluctuations are a function of a process of random information discounting and nothing more. And since information changes every day (or minute) today's stock price cannot have any impact on tomorrow's as tomorrow's price will be a function of new information.

The Bachelier-Samuelson model of efficient markets proposes a normal daily distribution of returns over any period that hews to a statistical bell curve. Such a statistical bell curve for the Dow Jones Industrial average, using a typical 10 year price history data set as the basis, shows a 1% standard deviation for expected daily returns. This implies that investors can expect the Dow to go up or down by 1% about every three days. Another way to say this is that investors can expect on any given day, a plus or minus 1% performance in the Dow with a probability of 0.317. Extending this bell-shaped probability into larger time frames yields interesting results. Specifically, the theory states that investors can expect a 2% up or down day for the Dow every 22 trading days or roughly once per month; a 3% up or down day for the Dow once every 1.5 years; a 4% +/- day once every 63 years, and a 5% +/- day can be expected once every 7 millennia.

Thus, applying the strict Bachelier-Samuelson expected return distribution, investors should never, theoretically, experience a single day of returns that were greater or less than 5% of the previous day's price. After all, the statistical model for such an event predicts it happening once every 7,000 years. Obviously, anyone who has lived through the last 4 years has seen more than a handful of these 5% +/- days, let alone several of the days surrounding the crashes of 1987 and 1929 that witnessed ever larger return deviations. What this tells us is that there are times when the market deviates from "normal" expected return distributions.

Above we only analyzed a single day of expected returns. What happens when we consider the probability of a series of back-to-back days of large (outlier) returns? The Nasdaq composite demonstrates a 10% return day approximately once every four years (or once every 1000 trading days). What then are the statistical probabilities of witnessing 3 back-to-back 10% down days, or a crash of 30% in 3 days? Statistics suggest that the probability of such a crash taking place would be 1/1000 days * 1/1000 days * 1/1000 days or 0.001*0.001*0.001 (which equals 0.0000000001). That corresponds to one crash of 30% over 3 consecutive days taking place once every 1 billion trading days or about 4 million years. Even a cursory glance at the price record illustrates a greater frequency of such a crash than 1 in 4 million years. We would note, parenthetically, that, for the Dow, the statistical probability of seeing any one of the three largest crashes in the Dow this century (1914, 1929, and 1987) are again, 1 in 7000 years.

In sum, looking at a series of expected consecutive returns as well as simply one expected daily return, we can see that the price record of stock trading over the last 100 years has produced events that, statistically speaking, were impossible. They never should have taken place if the Bachelier-Samuelson efficient market distribution pattern was operative.

What can we conclude based on these statistical examples of the actual price record? First, that the market is clearly not efficient at all times, since distribution returns do not hew to a normal bell-shaped curve as a random walk of asset price fluctuations would demand. Second, that there are times when prices correlate from one day to the next; that one day's prices can and do impact the next day's prices, such as during a crash. Both of these conclusions run counter to those of Bachelier and Samuelson. At best then we can only conclude that sometimes the EMH is at work, but clearly not all the time.

An analysis of extreme events - those statistical outliers - in the stock price record points to the fatal epistemological flaw in EMH. Whether one is analyzing the great crash of 1929 in the U.S., the Nikkei index crash in Japan from 1990 to present, or the crash of 1987 in the U.S., these extreme events illustrate why EMH is not an acceptable theory for asset price fluctuations. Acceptable models must work all the time and fit the empirical data. EMH does neither.

We will further investigate the importance and development of extreme events in complex systems (like the stock market) later in this paper. These statistical outliers are not anomalies as Bachelier and Samuelson's bell-curve return profile would predict. In fact, they are absolutely essential to understanding the forces at work in asset markets. Far from being worthless, these outliers - these rare and unusual events - help to define the complex forces at work in all manner of complex systems, from weather patterns, to sun spot creation, to thermodynamics, to asset markets.

Above and beyond the simple statistical refutation of EMH, the theory suffers from an internal logic flaw as well, and it is this. EMH assumes investors are rational and that the act of searching for discrepancies between true value and market value for a stock is futile since, according to EMH, such discrepancies would never exist in the first place. Thus, the very investors who search for discrepancies, and that is almost all of us, cannot be rational if we are searching for discrepancies that EMH purports do not exist. But for EMH to hold, investors must be rational. Thus, the internal flaws of logic with respect to EMH are clear.

Hopefully by now the above examination of EMH, both empirically and logically, has provided enough evidence to refute EMH as a workable model. Plenty of researchers have investigated the theory and found EMH wanting as well: in particular we would point readers interested in a more in depth dissection to Edgar Peters' book Chaos and Order in the Capital Markets (Wiley, 2nd ed., 1996). After reading his critique we suspect you will need no further convincing. In sum then, we believe we can state with confidence that the efficient market theory is wrong; it does not present a complete model for understanding what governs changes in asset prices.

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