Consensus Beliefs, Information Acquisition, and Market Information Efficiency

Abstract

In an attempt to provide a precise analytical interpretation for the notion of introduced by Eugene Fama (1970), Mark Rubinstein suggests that a necessary and sufficient condition for an individual to perceive all his information fully reflected in prices is that he have beliefs. That is, consensus beliefs are those beliefs which, if held by all individuals in an otherwise similar economy, would generate the same equilibrium prices as in the actual heterogeneous economy. However, the notion of information efficiency embodied in Rubinstein's discussion has been more broadly interpreted as follows.' A market is efficient with respect to an information set A, say, if the prices it generates are identical to those generated in an otherwise identical economy in which the set A accurately describes the information available to each and every market participant; the common, or homogeneous, belief induced by knowledge of A is the consensus belief.2 If the set of information A happens to be the union of the information sets privately available to each and every market participant, then efficiency with respect to A can be characterized as a situation in which the consensus belief is at least as correct an assessment (on the basis of A) as the assessment privately held by any single investor. Stated more informally, all investors perceive that no less information is fully reflected in prices than that which each individual investor privately knows. With regard to welfare implications, when the consensus belief is at least as correct, investors face a type of fair game in the market. That is, let returns be defined as the difference in the expected utility some well-informed investor achieves by trading at a price which reflects information inferior to his own visa-vis the expected utility he achieves when price reflects information at least as good. Then a price reflecting no less information than what is privately known prohibits excess returns. In effect, prices provide an effective barrier to the exploitation of less well-informed investors by better-informed investors, because no investor can exploit his superior information (in the classical price taking setting usually attributed to a securities market) whenever a price exists which reflects information which is in no way inferior to his own.3 *Graduate School of Business, University of Chicago. 1See, for example, Avraham Beja, William Beaver, and my 1979b paper. 2For example, suppose that a market consisted of two investors, the first of whom had as his sole source of information a set 0, say, which contained only optimistic bits and pieces of data about a security, and which consequently induced him to regard the future return of the security as abnormally high. Alternatively, the second investor had as his sole source of information a set P, say, which contained only pessimistic bits and pieces of data about the security, and which consequently induced him to regard the future return of the security as abnormally low. Suppose further that trading against one another in the market resulted in a price that appeared to reflect the fact that the future return for the security would be average; this is a natural supposition if both traders have equal weight in the market with regard to the supply and demand of the security. Now if in an otherwise identical market the set of information A, where A is the union of 0 and P, is substituted for both traders' original private sources, 0 and P, respectively, and if this knowledge induces them to regard the future return of the security as average, then this will likely cause no price change since prices have already averaged out their diverse opinions. Thus the market for the security will be efficient with respect to A, where A is the union of 0 and P. 3To illustrate this, consider the situation described in fn. 2 in which one investor knows 0, and another knows P. Suppose that a third investor enters the market who happens to know A, the union of 0 and P. Clearly, the third investor is better informed than either of the other two, where it will be assumed

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