Asset Pricing with Arbitrage Activity

Abstract

We study an economy populated by three groups of logarithmic agents: Constrained agents subject to a portfolio constraint that limits their risk-taking, unconstrained agents subject to a standard nonnegative wealth constraint, and arbitrageurs with access to uncollateralized credit. Such credit is valuable as it allows arbitrageurs to exploit the limited arbitrage opportunities that emerge endogenously in reaction to the portfolio imbalance generated by constrained agents. The model is solved in closed-form and we show that, in contrast to most equilibrium models with frictions and logarithmic agents, arbitrage activity has an impact on the price level and generates both excess volatility and the leverage effect. We show that these results are due to the fact that arbitrageurs lever up in good times and delever in bad times, and also investigate the effects of an unexpected tightening of the funding liquidity conditions of arbitrageurs.

Keywords: Limits of arbitrage; Rational bubbles; Wealth constraints; Excess volatility; Leverage effect

JEL Classification: D51, D52, G11, G12