Disagreement, Information, and Trade

Abstract

Asymmetries in information among rational traders are widely recognized as unable to explain observed levels of speculative trade in financial markets. Heterogeneous priors—in which agents “agree to disagree” about the likelihoods of different events, even contingent on the same information—have been posited to explain such trade. In a contractually rich, zero-sum setting, we explore some of the patterns relating trade generated by heterogeneous priors to the distribution of traders’ information. Fixing an information structure, virtually any trade can be supported by some heterogeneous priors, provided no trader knows that they can only lose from the trade. However, the comparative-static patterns when fixing traders’ prior be- liefs and varying the assignment of information are far more restrictive. We establish a series of results showing that gainful trade flows in the direction of disagreements rather than pri- vate information. For instance, when traders’ information is swapped, the signs of a mutually agreeable trade can reverse only if traders are not taking maximal advantage of their disagree- ment; in some cases, reversing the signs of mutually agreeable trade is impossible altogether. Thus, heterogeneous priors on their own cannot rationalize traders systematically trading in the direction of randomly assigned information.