Endogenous Noise Trackers in a Radner Equilibrium

Abstract

We prove the existence of an incomplete Radner equilibrium in a model with exponential investors and an endogenous noise tracker. We analyze a coupled system of ODEs and reduce it to a system of two coupled ODEs in order to establish equilibrium existence. As an application, we study the impact of the endogenous noise tracker on welfare by comparing it to a model with an exogenous noise trader. We show that the aggregate welfare in the endogenous noise tracker model is bigger for a sufficiently large stock supply, but the welfare comparison depends, in a nontrivial manner, on the other model parameters.