\documentstyle[portada,11pt]{article}This paper shows that the presence of private information in aneconomy can be a source of market incompleteness even when it is feasibleto issue a set of securities that completely eliminates the informationalasymmetries in equilibrium. We analyze a simple security design model in which avolume maximizing futures exchange chooses not only the characteristics ofeach individual contract but also the number of contracts. Agents have rationalexpectations and differ in information, endowments and, possibly, attitudestoward risk. The emergence of complete or incomplete markets in equilibriumdepends on whether the {\it adverse selection effect} is stronger or weakerthan the {\it Hirshleifer effect}, as new securitiesare issued and prices reveal more information. When the Hirshleifer effectdominates, the exchange chooses an incomplete set of financial contracts, andthe equilibrium price is partially revealing.