The Informational Content of Transactions

This paper studies the price discovery process in security markets. In particular, it analyzes the incorporation of information into security prices in a quote-driven security market from the perspective of information theory. In essence, it draws on a sequential trading mechanism, which is standard in market microstructure theory, and in which information is processed on the basis of individual transactions. It is demonstrated that the ex-ante information content of a transaction is proportionate to the average Kullback–Leibler distance of the prior and the posterior probability measures that quantify the uncertainty on the state of nature prior to and after that transaction, respectively. It is shown that the information on the state of nature, reflected in the security price, never decreases ex-ante by an upcoming transaction, which in turn accounts for the fact that the order flow is informationally valuable. Finally, it is pointed out that security markets in which the order flow is completely uninformative for the state of nature feature maximum depth; that is, those security markets are maximally liquid.Acknowledgements: I am grateful to David R. Wolf for his valuable guidance concerning some subtleties of information theory. The precious comments of an anonymous referee are appreciated.