The efficient markets hypothesis (EMH) has been the central proposition of finance for nearly thirty years. Fama (1970) defined an efficient financial market as one in which security prices always fully reflect the available information, any new or shock information being immediately incorporated into the share price. The efficient markets hypothesis then states that real-world financial markets are actually efficient according to this definition. As matters stood at the end of the 1970s, the efficient market hypothesis (EMH) was indeed one of the great triumphs of twentieth-century economics.

Standard economic theory - particularly the theory of arbitrage - predicted that financial markets were efficient. Mountains of empirical evidence based on some of the most extensive data available in economics, that on security prices, almost universally confirmed the predictions of the theory. Whenever researchers found small money-making opportunities, they could be easily explained away by a variety of arguments, the most pervasive of which was the failure to adjust properly for risk.

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It may be precisely because rationality is such a fundamental concept, in different areas, that it has in the past tended not to be closely examined: rationality is the main feature that has distinguished human beings from other animals; and irrationality is the main reason for which people have been dispatched to mental hospitals. It has been only recently that philosophers and economists have started to examine what mean by it: although the concept does get mentioned in various, mostly very technical contexts.

As a first approach, what is the meaning of investor rationality is a investor buying or investing shares logically for good reasons. Reasons for investing or buying shares are ''good,'' if we have taken into account the available facts and have thought through it logically and carefully; or perhaps if we would be able to explain them to other investors else, especially someone who at first might not agree with us. The opposite of being investor rationality is being investor irrationality.

The basic theoretical case for the efficient market hypothesis (EMH) rests on three arguments which rely on progressively weaker assumptions. First, investors are assumed to be rational and hence to value securities rationally. Second, to the extent that some investors are not rational, their trades are random and therefore cancel each other out without affecting prices. Third, to the extent that investors are irrational in similar ways, they are met in the market by rational arbitrageurs who eliminate their influence on prices.

When investors are rational, they value each security for its fundamental value: the net present value or its future cash flows, discounted using their risk characteristics. When investors learn something about fundamental values of securities, they quickly respond to the new information by bidding up prices when the news is good and bidding them down when the news is bad. As a consequence, security prices incorporate all the available information almost immediately and prices adjust to new levels corresponding to the new net present values of cash flows.

Samuelson (1965) and Mandelbrot (1966) proved some of the first theorems showing how, in competitive markets with rational risk-neutral investors, returns are unpredictable - security values and prices follow random walks. Since then, economists have characterized efficient securities prices for risk-averse investors, with both varying levels of risk over time and varying tolerances toward risk. In these more complicated models security prices are no longer predicted to follow random walks.

Still, investor rationally implies the impossibility of earning superior risk-adjusted returns, just as Fama wrote in 1970. The efficient market hypothesis (EMH) is thus first and foremost a consequence of equilibrium in competitive markets with fully rational investors. But remarkably, the efficient market hypothesis (EMH) does not live or die by investor rationality. In many scenarios where some investors are not fully rational, markets are still predicted to be efficient. In one commonly discussed case, the rational investors in the market trade randomly.

When there are large numbers of such investors, and when their trading strategies are uncorrelated, their trades are likely to cancel each other out. In such a market, there will be substantial trading volume as the irrational investors exchange securities with each other, but the prices are nonetheless close to fundamental values. This argument relies crucially on the lack of that reason, is quite limited. The case for the efficient market hypothesis (EMH), however, can be made even in situations where the trading strategies of investors are correlated.