1.1 Robert Lucas vs. “The Economist”

In July 2009, “The Economist” published an article titled “What went wrong with economics” that was trying to assess to what extent the accusations made against economists after the crisis had erupted were founded. Two other articles were detailing the respective cases of macroeconomics and financial economics. Three weeks later, the magazine published a guest article signed by prominent Chicago economist Robert Lucas (Lucas, 2009), who wanted to react to the previous articles in which he apparently saw an unjust attack on his profession.

The efficient market hypothesis was one of the main stakes of the debate. What “The Economist” was saying was that the theory was making people overconfident in capital markets: “Financial economists formalised theories of the efficiency of markets, fueling the notion that markets would regulate themselves and financial innovation was always beneficial.” It was also explaining how the efficiency theory had been abundantly criticised for 30 years, but also that this controversy had had little or no impact on market practitioners and regulators. The magazine recalled how behavioural economics had tried to show that individual psychology could explain bubbles and crashes and that arbitrage, that plays a crucial role in the efficiency theory to bring the prices back to intrinsic values when they depart from them, was in fact a limited and risky activity.

So the justification of the critique on efficiency theory in these articles was that financial asset prices should stick to their fundamental or intrinsic value: because efficiency theory was assuming they were, investors and regulators were also assuming it, so they could neither explain bubbles (that is, persistent deviations from the fundamentals) nor even recognize their very existence. The idea was that asset price bubbles and crashes do happen and that it’s a problem but that this problem cannot be solved as long as people believe in a theory that says it does not happen.

Now if we look at Robert Lucas’article, titled “In defence of the dismal science”, we can see the focus of his defence of efficiency theory was not on fundamental value but on forecastability. “If an economist had a formula that could reliably forecast crises a week in advance, say, then that formula would become part of generally available information and prices would fall a week earlier.” Even if bubbles and crashes exist, they can’t be forecasted anyway.

It seems Lucas answered a question that was not really asked, and didn’t answer the question that stemmed from the previous articles. These articles were treating bubbles as a problem in itself, and the question that logically arises, then, is “How could we prevent bubbles from happening?”. But Lucas answered another question, that is “Could we forecast bubbles?”.

1.2 Eugene Fama vs. Justin Fox

This kind of misunderstanding could also be found in Eugene Fama’s reaction to Justin Fox’s book “The myth of the rational market” (Fox, 2009), that was published the same year. In this text, that appeared on the blog he shares with Kenneth French on Dimensional Advisers’ website, Fama (2009) points out the fact that “80 % of mutual fund wealth is actively managed”, that is, they rely on the idea that market prices can be, one way or another, forecasted. Consequently, the efficiency theory, that says these prices are unforecastable, cannot be considered guilty. Fama even added that “if banks and investment banks took market efficiency more seriously, they might have avoided lots of their recent problems.”

But Fox’s book was not at all about passive management being the cause of the crisis; in fact it was not even about the crisis: it was a thorough investigation on the history of financial theory and the related developments of financial industry in the United States since the times of Irving Fisher, that the journalist began to write in 2002, long before the crisis. And even if we concentrate on what he says on efficiency theory, we can see he recalls that what was really new in what Fama called efficiency was a counter-intuitive linkage between the random walk hypothesis and the idea that stock prices were right or, as Fama put it at that time, “best estimates of intrinsic values”. What Fox wrote in his book about the crisis, that is the introduction and the epilogue, does not put any blame on the random walk hypothesis, nor does it accuses the more sophisticated versions of this idea that insist on the fact that financial asset prices are unpredictable and that, consequently, you can’t consistently make a profit on these markets on the basis of stale information. As in the articles published by “The Economist”, he rather accuses the other side of efficiency theory, that is, the idea that these asset prices correctly reflect at any time their intrinsic values.

1.3 A tale of two efficiencies

In both cases, we see on the one hand people who say prices are not right and that’s a problem, and on the other hand people who say prices are not predictable and the problem is too many people think they are.

This debate seems flawed, in the sense its participants don’t really agree on what it is about. Efficiency just doesn’t mean the same thing, apparently, when it is advocated and when it is criticized. What is the difference between the two meanings?

In his own reaction to Fox’s book, Richard Thaler (2009), a prominent figure of behavioural finance, gave us a clue. He said two components of efficiency could be distinguished: the “Price Is Right” component and the “No Free Lunch” component. Says Thaler: “The price is right principle says asset prices will, to use Fama’s words “fully reflect” available information, and thus “provide accurate signals for resource allocation”. The no free lunch principle is that market prices are impossible to predict and so it is hard for any investor to beat the market after taking risk into account.”

Going back to the debate, we can say the advocated efficiency was the No Free Lunch component and the criticized one the Price Is Right component. We propose to call the No Free Lunch component technical efficiency, because it’s about the technique investors should implement, and the Price Is Right component fundamental efficiency, because it’s about asset prices reflecting their fundamental value. ^[4] Technical efficiency implies an investor should not try to guess the market trend: the best strategy for him is to build a portfolio as representative as possible, in order to replicate this trend as closely as possible. Fundamental efficiency implies any kind of public intervention or regulation trying to influence, to weigh on asset prices can only be harmful, the price produced by the market mechanism being the best one, the more appropriate at any time. Table 1 makes the distinction more visible.

When critics of efficiency said fundamental efficiency did not hold, advocates of efficiency answered technical efficiency did hold. The only logical explanation for this is that, for these advocates, technical efficiency necessarily implies fundamental efficiency.

2.1 An untested inference

According to LeRoy (1989) and Guerrien and Gun (2011, p. 26), what is required for technical efficiency to imply fundamental efficiency is no less than the rational expectations hypothesis, which “means that investors use their information to make those inferences about future events that are justified by objective correlations between the information variables and the future events, and only those inferences. In other words, rational expectations models treat the agents being modelled as knowing the structure of the model and the value of its parameters” (LeRoy, 1989, p. 1595). A definition of market efficiency including this assumption clearly goes beyond the simple question of unforecastability. It leads us to fundamental efficiency, if we admit agents knowing the “true” model of the economy value financial assets at their “true” price.

As LeRoy pointed out, Fama referred to rational expectations in its 1976 definition of efficiency, whereas it was not the case in his famous 1970 article. In the meantime, indeed, the rational expectations assumption had gained traction, notably through several influential articles. In one of these, Robert Lucas tried to demonstrate “long-run neutrality of money, or independence of real and nominal magnitudes” (Lucas, 1972, p. 103) holds even if “the information conveyed to traders by market prices is inadequate to permit them to distinguish real from monetary disturbances” (ibid., p. 121–122). The demonstration relies on demanding assumptions: “the assumption that traders use the correct conditional distribution in forming expectations, together with the assumption that all exchanges take place at the market clearing price, implies that markets in this economy are efficient, as this term is defined by Roll. It will also be true that price expectations are rational in the sense of Muth” (ibid., p. 110).

As Roll had applied the notion of efficiency to Treasury bill rates, i. e., like Fama, to financial assets, this was already a way to connect the EMH in Fama’s terms to the rational expectations assumption, expressed earlier by Muth (1961). Some years later, Lucas, in an article devoted to asset prices, went further by in effect equalling the two:

“Most of our attention will be focused on the derivation and application of a functional equation in the vector of equilibrium asset prices […]. This equation is a generalization of the Martingale property of stochastic price sequences, which serves in practice as the defining characteristic of market “efficiency,” as that term is used by Fama and others. […] The analysis is conducted under the assumption that, in Fama’s terms, prices “fully reflect all available information,” an hypothesis which Muth had earlier termed “rationality of expectations.”

(Lucas, 1978, p. 1429)

We now understand more easily why the same author, in 2009, answered the claim fundamental efficiency did not hold by saying technical efficiency did hold: for him, the idea the second one implied the first one was relying on an assumption he had formulated 37 years earlier, which implied he didn’t consider, in effect, the difference between the two.

At this point, we can remark that what is discussed here is the validity of a proposition, which says that technical efficiency necessarily implies fundamental efficiency. Hence it can be useful to recall what is said about such a validity in the most influential epistemological work in economics, namely Milton Friedman’s “Methodology of positive economics”: “the only relevant test of the validity of a hypothesis is comparison of its predictions with experience” (Friedman, 1953, p. 8–9). In other words, what counts, what can be said valid or not, is a proposition tested against data. Now, looking at the literature on efficiency tests, we didn’t find any clear example of the inference we mentioned tested this way. In Friedman’s terms, however, what is really significant when assessing the validity of the EMH is, like for any other hypothesis, what is effectively tested. We will now see the rational expectations hypothesis is clearly not part of it.

For efficiency advocates, it is quite clear that what is tested in the empirical evidence they generally refer to is technical efficiency. Fama himself explained in 1976 what had to be tested and how. He first recalled a classical definition: “Market efficiency requires that in setting the price of securities at any time t-1, the market correctly uses all available informations.” (Fama, 1976, p. 143). Then he specified: “For simplicity, assume that the prices of securities at t–1 depend only on the characteristics of the joint distribution of prices to be set at t. Market efficiency then requires that in setting prices at t-1, the market correctly uses all available information to assess the joint distribution of prices at t.” (ibid., p. 143) To make this proposition testable, Fama explains we need a model of equilibrium. The underlying assumption, here, is that a price that fully reflects information is an equilibrium price and vice versa. Hence the testable definition of efficiency: “in an efficient market the true expected return on any security is equal to its equilibrium expected value.” (ibid., p. 144) If it is not, we’ve got what is generally called an abnormal return. The tests, consequently, are tests for abnormal returns. Fama then presented two kinds of such tests: tests to see if a trading rule gives abnormal returns, and tests choosing a specific piece of information to see if an investor can use it to get abnormal returns. This second kind corresponds to what is called event studies.

Fama also specified “the choice of a model of equilibrium is not restricted by the market efficiency condition.” (ibid., p. 144) This problem of the choice of the model has been known since then as the joint hypothesis problem. But it can be stressed the ongoing debate about these models has nothing to do with fundamental efficiency, because, whatever model you choose, what you test is always technical efficiency : the question is always to know if, as an investor, you can beat the market using a trading rule relying on available information. If market prices are not normally distributed, for example, this doesn’t contradict fundamental efficiency, but it also doesn’t necessarily contradict, in our view, technical efficiency, at least theoretically. ^[5] The issue, again, is forecastability.

Discussing the various acceptations of the EMH by focusing, like us, on the way it is tested, Hyme (2004) rightly points out that the nature of the debate is flawed by the fact that the kind of efficiency which is advocated differs from the one which is criticized, as illustrated by showing what is effectively tested in Malkiel (2003) clearly differs from what is tested in Shiller (2003). However, our view of the misunderstanding, of the way the debate is flawed clearly departs from hers: whereas, for Hyme, the difference between the two kinds of tests lies in the choice of the price formation model, opposing “fair game” models to a “fundamental value” model, for us it lies in the research design of the tests. This research design, in our view, determines by itself the kind of efficiency which is tested, regardless of the choice of the model.

Remember efficiency, be it technical or fundamental, is about the relationship between information and price. Technical efficiency says that information is instantaneously reflected in prices, hence an investor cannot use information to forecast prices. Fundamental efficiency says the price of a financial asset reflects its intrinsic value through information, hence only information related to this intrinsic value makes these prices move. To test technical efficiency, you have to check how prices react to information. To test fundamental efficiency, you have to check if price changes are explained by fundamental factors. In both cases, you study the information-price relationship but, whereas in the first case you take information as the starting point, in the second case you take price as the starting point. In the first case, you’ve got information and you want to know how prices react. ^[6] In the second, you’ve got prices and you want to know to what extent information on fundamental factors explains them. This distinction is expressed in Table 2.

What is crucial here is neither the kind of assumption made about agents’ rationality nor the kind of price formation model considered as “normal” but the starting point chosen when studying the information-price relationship, because it determines what is effectively tested. The famous distinction between strong, semi-strong and weak efficiency is based on the kind of information taken as a starting point, hence it is a distinction between several kinds of technical efficiency.

Hence the simple fact that nearly all efficiency tests take information as the starting point tells us that:

1. these are technical efficiency tests.

2. the rational expectations hypothesis is not, at least in this case, a tested assumption but an interpretative one, an assumption you use to interpret, to draw conclusions from your findings.

If we now come back to Friedman’s epistemology, we can recall a distinction he made about what is stated in a proposition whose validity has to be assessed: “We can regard the hypothesis as consisting of two parts: first, a conceptual world or abstract model simpler than the “real world” and containing only the forces that the hypothesis asserts to be important; second, a set of rules defining the class of phenomena for which “the model” can be taken to an adequate representation of the “real world” and specifying the correspondence between the variables or entities in the model and observable phenomena.” (Friedman, 1953, p. 24). While this second part clearly defines as precisely as possible what is tested and how and “cannot possibly be abstract and complete” (p. 25), the first part expresses the core assumptions, a “model” which doesn’t have to be realistic, but has to be unambiguous: “there is no place in the model for, and no function to be served by, vagueness, maybe’s, or approximations” (p. 24).

If we now try to apply these principles to the efficient markets hypothesis, we will first remark that, if what is effectively tested is technical efficiency, then the “rules for using the model” will simply recall that prices are unpredictable and, if necessary, how this can be measured; the way the model will explain this can be expressed as follows: the market mechanism makes the price of a financial asset react instantaneously only to new information, hence this price is unpredictable.

This proposition captures the Hayekian view of the market as the best information processor, better than any individual actor or organization (Hayek, 1945). The way the proposition is formulated can be compared to the famous example given by Friedman himself: “leaves seek to maximize the sunlight they receive” (p. 24). What is clearly measurable here is “the sunlight they receive”: what will be effectively tested is the hypothesis “the sunlight received by leaves is maximized”. Of course it is grossly unrealistic to assume leaves are actors that “seek to maximize” something, but this wording is justifiable, in Friedman’s terms, because it allows to describe both concisely and precisely a hypothesis, which, then, can be tested. In our formulation of the EMH, what will be effectively tested is the unpredictability of prices; the idea there is a market mechanism that “makes” something is unrealistic but understandable and logical.

Now, fundamental efficiency in itself doesn’t appear in this “friedmanian” formulation. Indeed, what can be said about the way it is related to technical efficiency is that:

1. it is consistent with it

2. it is implied by it only if the rational expectations hypothesis, which is not tested as such, is valid.

The inference we discussed here requires the rational expectations hypothesis to be valid, now this hypothesis is not only untested: it is also not part of the explanatory model, which, based on Hayek’s reasoning, doesn’t require such a demanding assumption. Consequently, it doesn’t seem to be valid in friedmanian terms. It is really nothing more than an interpretation and, as we shall see later, one possible interpretation among others, and arguably not the most defensible one. It may well be a “remarkable error”, as Shiller said. Now, this is not exactly the argument Shiller used to make this bold statement.

2.2 Shiller’s argument

The quotation comes from an article that was published in the Brookings Papers on Economic Activity, based on a conference pronounced at the Brookings Institution. ^[7] When you read this article, what is remarkable at first sight is that those who were defending the EMH more than 30 years ago were already using the same “unforecastibility” argument when they felt their theory was disputed. The point Shiller wanted to make was that investors’ psychology, and more specifically their propensity to follow fads or to herd, strongly influences and even determines financial assets prices. At the beginning of the article, he explains that this idea is not discussed seriously enough: the arguments against it are “confined to an oral tradition, tacitly accepted by all parties, and not discussed in the scholarly literature.” (p. 458) And the main argument of this “oral tradition” is that “Returns on speculative assets are nearly unforecastable” and that “because real returns are nearly unforecastable, the real price of stocks is close to the intrinsic value.” “This argument for the efficient market hypothesis”, Shiller adds, “represents one of the most remarkable errors in the history of economic thought. It is remarkable in the immediacy of its logical error and in the sweep and implications of its conclusion.” (p. 459)

Thus, as we said before, this “remarkable error” is the idea that technical efficiency implies fundamental efficiency. Then, how does Shiller challenge this inference? In fact, what he tries to show in the article is that unforecastability, or at least the fact that stock prices are not very forecastable, is consistent with a model that takes in account investors’ departures from rationality. ^[8] He does not show that prices consistently depart from their intrinsic value but that technical efficiency does not necessarily imply investors’ rationality. As, for him, it seems to demonstrate that to infer fundamental efficiency from technical efficiency is a “remarkable error”, then the underlying assumption of Shiller’s reasoning is that investors’ rationality necessarily implies fundamental efficiency. This is also the basic idea of behavioural finance since then: it explains financial assets prices depart from their intrinsic value because investors depart from rationality, and that implies that, were investors rational, then prices would be right.

To make the reasoning visible, we used the sign to mean “necessarily implies” and the sign to mean “does not necessarily imply”. Shiller’s reasoning can be summed up this way:

Proposition 1 Proposition 2

Where

Proposition 1 is: Technical efficiency		Investor’s rationality
Proposition 2 is: Technical efficiency		Fundamental efficiency

Hence Shiller’s underlying assumption is

Proposition 3: Investor’s rationality

Fundamental efficiency

One can first remark that it is not quite clear that the rationality Shiller evokes means precisely assuming rational expectations in Lucas’ sense. If, nevertheless, we admit it is the case, then the main difference between the two approaches is simple to describe: Shiller simply doesn’t make this assumption, which implies the discussed inference is a “remarkable error” indeed. In any case, irrationality is clearly at the heart of his argument, whereas he doesn’t mention the other question we raised, i. e. the research design of the tests.

This is somehow surprising, because his most famous previous article was precisely an attempt to take price as a starting point when studying the information-price relationship (Shiller, 1981). As we said previously, this means it was an attempt to test fundamental efficiency. And when we look more closely at the academic literature in finance, we indeed find some cases where the issue of fundamental efficiency is directly addressed. These are neither weak form efficiency tests nor semi-strong form efficiency tests nor strong form efficiency tests: this typology of efficiency as strong, semi-strong or weak is based on the kind of information taken as a starting point, whereas these articles take price as a starting point.

2.3 Attempts to test fundamental efficiency

Fundamental efficiency is the idea that financial asset prices reflect their fundamental value and that, consequently, when they move it’s because of some new information related to this fundamental value. Hence testing fundamental efficiency can be made either by comparing directly price changes and intrinsic value changes or by checking if informations that make prices move are the ones that make a difference on intrinsic value, that influence the fundamentals. In the first case, you have to define and measure intrinsic value, in the second you have to define relevant information in order to test its explanatory power on prices.

The first kind of test can be illustrated by Shiller’s (1981) article “Do stock prices move too much to be justified by subsequent changes in dividends?”. He chose a classical definition of the intrinsic value of a stock, that is the discounted value of future dividends. Hence he compared the movements of the S&P 500 to subsequent changes in dividends paid by S&P 500 companies. Stephen LeRoy and Richard Porter published the same year a similar study, based on earnings rather than dividends (LeRoy & Porter, 1981).

Richard Roll (1988) tried to run regressions on stock price movements on a five-year period on data generated by models of risk supposed to represent fundamental factors. We can consider it a case of the second kind of fundamental efficiency tests, a somewhat clearer example being the article “What moves stock prices” published by David Cutler, James Poterba and Lawrence Summers in 1989. Cutler, Poterba and Summers used regressions on stock returns to measure the explanatory power of seven measures of macroeconomic activity, “chosen to measure both real and financial conditions” (p. 5). They also identified the 50 largest one-day stock market movements in a 42-year period to check if significant news on fundamental factors had appeared in the media on these days or on subsequent days.

More recently, Bouveret & Di Filippo (2009) tried to test both technical and fundamental efficiency on forex markets. They defined three kinds of efficiency: “speculative efficiency”, “fundamental efficiency” and “macroeconomic efficiency”. To put it simply, speculative efficiency corresponds to our technical efficiency, fundamental efficiency means exchange rates are determined by differences between real interest rates and macroeconomic efficiency is a kind of fundamental efficiency which also takes in account other relevant indicators. Their tests of speculative efficiency are tests of investment strategies based on stale information, hence information is their starting point, whereas their tests of fundamental and macroeconomic efficiency are tests of the explanatory power of models based on fundamental factors. Bouveret & Di Filippo also tried to test the rational expectation hypothesis (REH) on these markets: assuming the REH implies agents don’t make systematic forecast errors, they tested the accuracy of the “Consensus Forecast” made by economists on forex markets. Interestingly enough, their empirical results showed these markets were “fundamentally inefficient” on all horizons, “speculatively efficient” at least in the mid-term, and “macroeconomically efficient” in the long term, although they were more cautious about this last point, the choice of the indicators and the model of “macroeconomic efficiency” being difficult and questionable. They also found the REH was not met, which is consistent, as we saw, with a situation where a market is technically but not fundamentally efficient.

A remarkable feature of these articles is that they are scarce. ^[9] The overwhelming majority of the literature on efficiency is only about the technical one, with tests taking information as the starting point. The greatest part of behavioural finance has accepted this methodological approach and made a difference by interpreting abnormal returns in psychological terms, by giving for deviations from technical efficiency an explanation based on assumptions about investors’ psychology (Shleifer, 2000). Thus, this literature has come to assume investors’ rationality necessarily implies technical efficiency and, when it draws conclusions from its evidence about fundamental efficiency, it means it also assumes technical efficiency necessarily implies fundamental efficiency, which is precisely the “remarkable error” pointed out by Shiller…

In other words, the confusion between the two efficiencies and the “remarkable error” have persisted, this specific problem being rarely raised.

We will now suggest possible explanations of this situation, and try to show what would be at stake if fundamental efficiency was clearly and directly addressed.