On the Role of Arbitrageurs in Rational Markets

Abstract

Price discrepancies, although at odds with mainstream finance, are persistent phenomena in financial markets. These apparent mispricings lead to the presence of arbitrageurs, who aim to exploit the resulting profit opportunities, but whose role remains controversial. This article investigates the impact of the presence of arbitrageurs in rational financial markets. Arbitrage opportunities between redundant risky assets arise endogenously in an economy populated by rational, heterogeneous investors facing restrictions on leverage and short sales. An arbitrageur, indulging in costless, riskless arbitrage is shown to alleviate the effects of these restrictions and improve the transfer of risk amongst investors. When the arbitrageur lacks market power, he always takes on the largest arbitrage position possible. When the arbitrageur behaves non-competitively, in that he takes into account the price impact of his trades, he optimally limits the size of his positions due to his decreasing marginal profits. In the case when the arbitrageur is subject to margin requirements and is endowed with capital from outside investors, the size of the arbitrageur's trades and the capital needed to implement these trades are endogenously solved for in equilibrium.

Keywords: Arbitrage, asset pricing, margin requirements, non-competitive markets, risk-sharing

JEL Classification: C60, D50, D90, G11, G12