by John Allen Paulos
Election season has put an increased focus on the stock market, but little attention is ever paid to the Efficient Market Hypothesis (the EMH, for short). As I’ve written in A Mathematician Plays the Stock Market, it is a fundamental and important notion, but it is also a little weird. Its recent formulation derives from the work of Eugene Fama, economist Paul Samuelson, and others in the 1960s. The basic idea, however, dates back more than 100 years when Louis Bachelier, a student of the great French mathematician Henri Poincare, formulated an early version. Roughly, the hypothesis maintains that stock prices reflect all relevant information about the stock. As Fama put it, “In an efficient market, competition among the many intelligent participants leads to a situation where, at any point in time, actual prices of individual securities already reflect the effects of information based both on events that have already occurred and on events which, as of now, the market expects to take place in the future.”
The EMH depends crucially on what information is assumed to be reflected in the stock price. The weakest version maintains that all information about past market prices is already reflected in a stock price. A stronger version maintains that all publicly available information about a company is already reflected in its stock price. The strongest version states that information of all sorts, even inside information, is already reflected in the stock price.
It was probably this last rather implausible and all-encompassing version of the hypothesis that underlies the joke about the two efficient market theorists walking through town. They notice a hundred dollar bill on the sidewalk and simply ignore it. If it were real, they conclude, someone would have been picked it up already. Even more risible is the question: How many efficient market theorists does it take to change a light bulb? Answer: The answer is none. If the bulb needed changing, the wisdom of the market would have insured that it had already been changed.
So why do people think that the market efficiently, and more or less immediately, responds to changes in the conditions for a particular stock or even for the market as a whole? The answer is that investors are always seeking an edge to increase their gains or decrease their losses, and they try to do so in a multitude of ways. They’re on the lookout for new bits of information possibly relevant to a company’s stock price that may be enough to quickly raise or lower it. Because of this swarm of profit-hungry and loss-averse investors, the market rapidly responds to new information, and efficiently – there’s that word again – adjusts prices to reflect it. The changes take place so rapidly, or so the story goes, that even utilizing technical rules or fundamental analyses aren’t fast enough to be fully exploited, and investors who pursue them will see their excess profits shrink to zero.
I mentioned above that the EMH is weird. The reason is that it leads to a conclusion that has something of the flavor of the Liar Paradox: “This sentence is false.” How specifically? Well, if a sufficiently large majority of investors believe the hypothesis, they naturally would assume that new information about a stock would very quickly be reflected in its price. They would conclude that since relevant news almost immediately moves the price up or down, and since new developments can’t be predicted, neither can price increases or decreases. Thus those investors who subscribe to the EMH and believe the market is efficient would further believe that looking for trends and analyzing companies’ fundamentals is a waste of time. Believing this, the majority of investors won’t pay much attention to new developments, leaving only the relatively few remaining investors actively searching for an edge. The result is that the market will not respond quickly to new information and thus it will not be efficient. In this way a strong belief in the EMH ensures its falsity.
And in the opposite case, if investors believe that the market is not efficient, their belief will induce them to use whatever tools (technical analysis, fundamental analysis, and so on) are at their disposal. They will search diligently for an edge and for opportunities that they believe exist in an inefficient market, and by so doing these profit-seeking investors will ensure that the market becomes efficient.
Reiterating and in summary, if a sufficiently large proportion of investors doesn’t believe the EMH, their actions will ensure that it is efficient, and if most investors do believe that the market is efficient, looking for an edge would seem pointless to them and so their inaction will likely result in an inefficient market. Alternatively stated, the Efficient Market Hypothesis is true if and only if a sufficiently large majority of investors believes it to be false. Pleasantly counterintuitive and a bit weird as I said.
Of course, I’ve made some big assumptions that may not hold. One is that it’s not clear what “sufficiently large” means, and I’ve ignored the fact that it occasionally requires very few investors to move the market.
Another gap in the argument is that any suspected deviations from the EMH can always be attributed to mistakes in pricing models or some other issue. There is also a potent psychological reason that people disbelieve the EMH. Believing it makes it harder to maintain an investor’s self-image as a brilliant financial gunslinger whose keen insight will make him rich.
Nevertheless, I think the point remains: the truth or falsity of the EMH is not immutable but depends critically on the beliefs of investors. Furthermore, as the percentage of investors who believe in the hypothesis itself varies, the truth of the hypothesis varies inversely with it.
On the whole, however, I suspect most investors disbelieve in it, and so for this reason I think it holds, but only approximately and only most of the time.
Post script: That exploitable opportunities tend to gradually disappear is a general phenomenon that occurs in other domains. Steven Jay Gould in his book Full House developed an example from baseball. The absence of .400 hitters in the years since Ted Williams hit .406 in 1941, he argued, was not due to any decline in baseball ability but just the opposite: a gradual increase in the athleticism of all players and a consequent decrease in the disparity between the worst and best players. As players have improved over time, the distribution of batting averages and earned run averages shows less variability. There are fewer bad pitchers facing hitters and fewer bad hitters facing pitchers. The consequence is that .400 batting averages are now rare. The improved athleticism of both hitters and pitchers makes the “market” between them more efficient.
This would hold true for other sports, especially newly minted ones that arise suddenly and sometimes even become Olympic events. One might even try to invoke the EMH to explain the variation and stability of so-called prediction markets that purport to estimate candidates’ chances in so-called prediction markets. Investors buy, sell, and borrow shares in candidates as they do with stocks, and, arguably at least, the prediction market becomes more efficient as the election nears.
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John Allen Paulos is an emeritus Professor of Mathematics at Temple University and the author of Innumeracy and A Mathematician Reads the Newspaper. These and his other books are available here.
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