The coordinating role of a redundant security in frictional markets

In this paper, we show that even if a redundant security does not have the cost-saving role in markets with transaction costs, it may still be relevant to risk-sharing at equilibrium. We call this the coordinating role of the redundant security. We prove that at least five securities and three states are necessary for one of the securities to have the coordinating role. We also show that even if a redundant security requires a lower transaction cost and actively traded at an equilibrium, it need not be relevant to risk-sharing.