Information in equity markets with ambiguity averse investors

In this paper, I show that persistent pricing anomalies are consistent with a market that includes ambiguity averse investors. In particular, I show that ambiguity averse investors may prefer to trade based on aggregate signals that reduce ambiguity at the cost of a loss in information. Because the aggregate signals preferred by ambiguity averse investors are not sufficient statistics for the components from which they are constructed, equilibrium prices may fail to impound publicly available information. This provides opportunities for investors whose preferences satisfy the Savage (1954) axioms to generate profitable trading strategies since they are neutral to ambiguity. Ambiguity averse investors perceive that the benefit of using aggregate signals outweighs the costs of trading against investors who have superior information. The model can explain both under-reaction such as that evident in post-earnings announcement drifts and momentum and over-reaction to accounting accruals. JEL Classification: D81, G11, G14 This study examines how the aggregation of information affects equity prices when some investors are ambiguity averse while others have preferences that satisfy the Savage (1954) axioms (hereafter Savage investors). Ambiguity aversion refers to a distaste for uncertainty about the joint distribution of informative signals and security payoffs. I demonstrate that ambiguity aversion can cause investors to prefer aggregate information even when the aggregate signal is not a sufficient statistic for its components and therefore entails a loss of information in a Blackwell (1953) sense. Whereas Savage investors weakly prefer an aggregate signal only if it is a sufficient statistic for its components, ambiguity averse investors are willing to trade sufficiency for a reduction in ambiguity. It is possible for aggregate signals that deviate from sufficiency to provide greater reductions in ambiguity than those that do not. As a consequence, ambiguity averse investors’ preference for aggregate information implies that equilibrium prices may fail to impound public information. I model an exchange economy in which investors observe informative signals prior to trading shares in a firm and a riskless asset. I examine two information regimes. I first model an economy in which all investors view the same aggregate signal that is a linear combination of two components. I then model an economy in which investors select whether to view an aggregate signal or its components. The structure of the model allows for an aggregate signal that is a sufficient statistic for inferring the firm’s terminal dividend and thus entails no loss of information relative to viewing the components. I treat the sufficient statistic as a benchmark case and demonstrate that ambiguity averse investors prefer an aggregate signal that is a non-sufficient statistic if a reduction in ambiguity adequately compensates for a loss in information due to non-sufficiency. The impact of the ambiguity averse investors’ preference for aggregate information The Savage (1954) axioms are fairly standard and imply that a person maximizes expected utility with respect to a unique prior belief. See Ellsberg (1961) and Karni and Schmeidler (1991) for descriptions and definitions of ambiguity aversion.