We describe how episodic illiquidity arises from a breakdown in cooperation between market participants. We first solve a one-period trading game in continuous-time, using an asset pricing equation that accounts for the price impact of trading. Then, in a multi-period framework, we describe an equilibrium in which traders cooperate most of the time through repeated interaction, providing apparent liquidity to one another. Cooperation breaks down when the stakes are high, leading to predatory trading and episodic illiquidity. Equilibrium strategies that involve cooperation across markets lead to less frequent episodic illiquidity, but cause contagion when cooperation breaks down.WHY IS ILLIQUIDITY RARE and episodic? Pastor & Stambaugh (2003) detect only 14 aggregate low-liquidity months over the time period 1962 to 1999. Despite being of significant magnitude, most of the episodes were short-lived and were followed by long periods of liquidity.1 The origin of this empirical observation still remains a puzzle. In this paper, we attempt to shed light on this puzzle by developing a theoretical model in which a breakdown in cooperation between traders in the market manifests itself in predatory trading. This mechanism leads to sudden and short-lived illiquidity.We develop a dynamic model of trading based on liquidity needs. During each period, a liquidity event may occur in which a trader is required to liquidate a large block of an asset in a relatively short time period. This need for liquidity is observed by a tight oligopoly, whose members may choose to predate or cooperate. Predation involves racing and fading the distressed trader to the market, * Bruce Ian Carlin is from the Anderson Graduate School of Management, University of California at Los Angeles. Miguel Sousa Lobo and S. Viswanathan are from the Fuqua School of Business at Duke University. The authors would like to thank
W e analyze the problem of an investor who needs to unwind a portfolio in the face of recurring and uncertain liquidity needs, with a model that accounts for both permanent and temporary price impact of trading. We first show that a risk-neutral investor who myopically deleverages his position to meet an immediate need for cash always prefers to sell more liquid assets. If the investor faces the possibility of a downstream shock, however, the solution differs in several important ways. If the ensuing shock is sufficiently large, the nonmyopic investor unwinds positions more than immediately necessary and, all else being equal, prefers to retain more of the assets with low temporary price impact in order to hedge against possible distress. More generally, optimal liquidation involves selling strictly more of the assets with a lower ratio of permanent to temporary impact, even if these assets are relatively illiquid. The results suggest that properly accounting for the possibility of future shocks should play a role in managing large portfolios.
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