Asset Pricing in General Equilibrium with Constraints

Abstract

We evaluate the impact of portfolio constraints on financial markets in a dynamic equilibrium pure exchange economy with one consumption good and heterogeneous investors. Despite numerous applications, portfolio constraints are notoriously difficult to incorporate into dynamic equilibrium analysis unless constrained investors are assumed to have logarithmic preferences. Our solution method yields new insights on the impact of constraints on stock prices without relying on this assumption. We compute the equilibrium when both investors have (identical for simplicity) CRRA preferences, one of them is unconstrained while the other faces an upper bound constraint on the proportion of wealth invested in stocks. We show that tighter constraints lead to higher price-dividend ratios and lower stock-return volatilities when the intertemporal elasticity of substitution (IES) is less than one, and lower price-dividend ratios and higher volatilities when IES is greater than one. Moreover, in the latter case the model generates countercyclical market prices of risk and stock return volatilities, procyclical price-dividend ratios, excess volatility and other patterns consistent with empirical findings. Finally, the baseline analysis is extended to study the impact of various portfolio constraints when investors disagree on mean dividend growth rates. In particular, we explicitly characterize the equilibrium in the unconstrained benchmark economy as well as in the economy with unconstrained pessimist and optimist facing no-borrowing constraint.

Keywords: asset pricing, dynamic equilibrium, heterogeneous investors, portfolio constraints, risk sharing, stock return volatility

JEL Classification: D52, G12