Extracting Information from Trading Volume

Abstract

This paper shows how to extract information from equilibrium trading volume. The analysis is first carried out in a market- clearing framework with symmetrically (and later normally) distributed demands, and is then extended to include market-making models. The conclusions of this paper hence apply to the majority of the models developed in the noisy rational expectations literature. If a random variable is symmetrically distributed with the traders' demands around zero and the asset market clears, the volume-based conditional distribution of this variable is symmetric, and consequently its conditional expectation based on volume is zero. The random variable under consideration may be the true value of the asset, the price or, in a dynamic model, the price difference. The paper further proves that the covariance between the absolute value of any variable jointly normally distributed with the traders' demands and the equilibrium volume is positive, which agrees with the empirical evidence of a positive covariance between the absolute value of the price difference and volume. Furthermore, numerical examples indicate that, when the asset value is jointly normally distributed with the traders' demands, the probability ofextreme realizations for the asset true value conditioned on volume is increasing in volume. The paper's proposition hold in market-making frameworks as long as the price, the asset value and the traders' demands are symmetrically (resp. jointly normally) distributed. Finally, the paper develops a simple static model where transaction costs can induce a positive covariance between price and volume.

JEL Classification: G12, G14