An Examination of Heterogeneous Beliefs With a Short-Sale Constraint in a Dynamic Economy

Abstract

We study the effects of a market-wide short-sale constraint in a dynamic general equilibrium economy populated by optimistic and pessimistic investors. Imposing the constraint reduces the stock price if the optimist's intertemporal elasticity of substitution is less than one and increases the stock price if the optimist's intertemporal elasticity of substitution is greater than one. In all cases, the presence of the constraint implies that the pessimist's stock price marginal valuation is lower than the equilibrium price. In parameterized examples, the pessimist finds the stock most overvalued when the optimist's intertemporal elasticity of substitution is greater than one which is exactly when imposing the constraint reduces the equilibrium stock price. Additionally, the optimist's market price of risk falls and the instantaneous interest rate rises when the short-sale constraint is imposed. Imposing the constraint leads to a higher stock volatility when the optimist's intertemporal elasticity of substitution is less than one and a lower stock volatility when the optimist's intertemporal elasticity of substitution is greater than one.