Equilibrium and welfare in markets with financially constrained arbitrageurs

Equilibrium and welfare in markets with financially constrained arbitrageurs

August 19, 2002 | Denis Gromb and Dimitri Vayanos
This paper analyzes equilibrium and welfare in financial markets with financially constrained arbitrageurs. The authors propose a multiperiod model where competitive arbitrageurs exploit price discrepancies between two identical risky assets traded in segmented markets. Arbitrageurs must collateralize positions in each asset, which imposes financial constraints that limit their positions based on wealth. While arbitrage activity benefits all investors by providing liquidity, arbitrageurs may not take a socially optimal level of risk. The paper shows that arbitrageurs can fail to take too much or too little risk, depending on market conditions. The model considers a multiperiod economy with a riskless asset and two risky assets with identical payoffs. Markets for the risky assets are segmented, with some investors able to invest in only one asset. Arbitrageurs, who can invest in both assets, act as intermediaries by exploiting price discrepancies and facilitating trade. The authors model financial constraints as requiring arbitrageurs to maintain positive margin accounts, which limits their ability to take positions based on their wealth. The paper shows that if arbitrageurs' wealth is insufficient, they may be unable to eliminate price discrepancies between the risky assets. The resulting price wedge increases with the relative demand of the two types of investors and decreases with the arbitrageurs' wealth. Arbitrageurs exploit the price wedge by holding opposite positions in the two assets. However, if the capital gain on the arbitrage opportunity is risky, arbitrageurs may choose not to invest up to the financial constraint for risk management reasons. The paper also analyzes welfare implications, showing that arbitrage activity is beneficial to all investors because arbitrageurs supply liquidity to the market. However, arbitrageurs may fail to take a socially optimal level of risk. When arbitrageurs are heavily invested in the arbitrage opportunity, a reduction in their positions can make all investors better off. Conversely, when arbitrageurs do not invest much in the arbitrage opportunity, an increase in their positions can be Pareto improving. The authors show that the mechanism for Pareto improvement arises because competitive arbitrageurs fail to internalize that changing their positions affects prices. Due to market segmentation and financial constraints, agents' marginal rates of substitution differ, and a redistribution of wealth induced by a change in prices can be Pareto improving. This mechanism was first pointed out by Geanakoplos and Polemarchakis (1986) in a general incomplete markets setting. The paper also discusses the implications of financial constraints for allocative inefficiency in financial markets. The authors show that the sources of inefficiency in their model seem quite realistic, as the liquidation of arbitrageurs' positions can reduce other arbitrageurs' net worth through price effects, a feature of the 1998 crisis. The paper relates their findings to other strands of the literature on financial markets with asymmetric information and financial constraints. It also discusses the implications of financial constraints for intertemporal wealth effects and the welfare analysis ofThis paper analyzes equilibrium and welfare in financial markets with financially constrained arbitrageurs. The authors propose a multiperiod model where competitive arbitrageurs exploit price discrepancies between two identical risky assets traded in segmented markets. Arbitrageurs must collateralize positions in each asset, which imposes financial constraints that limit their positions based on wealth. While arbitrage activity benefits all investors by providing liquidity, arbitrageurs may not take a socially optimal level of risk. The paper shows that arbitrageurs can fail to take too much or too little risk, depending on market conditions. The model considers a multiperiod economy with a riskless asset and two risky assets with identical payoffs. Markets for the risky assets are segmented, with some investors able to invest in only one asset. Arbitrageurs, who can invest in both assets, act as intermediaries by exploiting price discrepancies and facilitating trade. The authors model financial constraints as requiring arbitrageurs to maintain positive margin accounts, which limits their ability to take positions based on their wealth. The paper shows that if arbitrageurs' wealth is insufficient, they may be unable to eliminate price discrepancies between the risky assets. The resulting price wedge increases with the relative demand of the two types of investors and decreases with the arbitrageurs' wealth. Arbitrageurs exploit the price wedge by holding opposite positions in the two assets. However, if the capital gain on the arbitrage opportunity is risky, arbitrageurs may choose not to invest up to the financial constraint for risk management reasons. The paper also analyzes welfare implications, showing that arbitrage activity is beneficial to all investors because arbitrageurs supply liquidity to the market. However, arbitrageurs may fail to take a socially optimal level of risk. When arbitrageurs are heavily invested in the arbitrage opportunity, a reduction in their positions can make all investors better off. Conversely, when arbitrageurs do not invest much in the arbitrage opportunity, an increase in their positions can be Pareto improving. The authors show that the mechanism for Pareto improvement arises because competitive arbitrageurs fail to internalize that changing their positions affects prices. Due to market segmentation and financial constraints, agents' marginal rates of substitution differ, and a redistribution of wealth induced by a change in prices can be Pareto improving. This mechanism was first pointed out by Geanakoplos and Polemarchakis (1986) in a general incomplete markets setting. The paper also discusses the implications of financial constraints for allocative inefficiency in financial markets. The authors show that the sources of inefficiency in their model seem quite realistic, as the liquidation of arbitrageurs' positions can reduce other arbitrageurs' net worth through price effects, a feature of the 1998 crisis. The paper relates their findings to other strands of the literature on financial markets with asymmetric information and financial constraints. It also discusses the implications of financial constraints for intertemporal wealth effects and the welfare analysis of
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