  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 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 non-trivial manner on the other model parameters.
