Episodic Liquidity Crises: Cooperative and Predatory Trading

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. ∗Bruce Ian Carlin, Miguel Sousa Lobo, and S. Viswanathan are from the Fuqua School of Business at Duke University. The authors would like to thank Robert Almgren, Yacov Amihud, Kerry Back, Ravi Bansal, Michael Brandt, Markus Brunnermeier, Bhagwan Chowdry, Phil Dybvig, Simon Gervais, Milt Harris, Roy Henriksson, Ming Huang, Ron Kaniel, Arvind Krishnamurthy Pete Kyle, Leslie Marx, Atif Mian, David Mordecai, Lasse Pedersen, Matt Pritsker, Uday Rajan, Ioanid Rosu, Ronnie Sadka, Louis Scott, Duane Seppi, Jim Smith, Matt Spiegel, Curt Taylor, Jiang Wang, Huseyin Yildirim, an anonymous referee, and seminar participants in the 2005 World Congress of Economics, the 2005 New York Federal Reserve Bank conference on liquidity, the 2006 Atlanta Federal Reserve conference on risk, the IAFE Liquidity Risk Symposium, the 2006 Mitsui Life Financial Center Symposium, the Duke Finance and Duke Economics seminars, and the Indian School of Business for their comments. Why is illiquidity rare and episodic? Pastor and Stambaugh (2003) detect only 14 aggregate lowliquidity 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. 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, causing an adverse price impact for the trader. Cooperation involves refraining from predation and allows the distressed trader to transact at more favorable prices. In our model, traders cooperate most of the time through repeated interaction, providing “apparent liquidity” to one another. However, episodically this cooperation breaks down, especially when the stakes are high, which leads to opportunism and the loss of this apparent liquidity. The following quote provides a recent example of an episodic breakdown in cooperation between two cooperative periods in the European debt market (New York Times, Sept. 15, 2004): “...The bond sale, executed Aug. 2, caused widespread concern in Europe’s markets. Citigroup sold 11 billion euros of European government debt within minutes, mainly through electronic trades, then bought some of it back at lower prices less than an hour later, rival traders say. Though the trades were not illegal, they angered other bond houses, which said the bank violated an unspoken agreement not to flood the market to 1 drive down prices.” This quote suggests that market participants generally cooperate, though there is episodic predation that leads to acute changes in prices. Note that predatory behavior can involve either exploiting a distressed trader’s liquidity requirements or inducing another trader to be distressed. There exists some empirical evidence that cooperation affects price evolution and liquidity in financial markets. Cooperation and reputation have been shown to affect liquidity costs on the floor of the New York Stock Exchange (NYSE). Battalio, Ellul, and Jennings (2005) document an increase in liquidity costs in the trading days surrounding a stock’s relocation on the floor of the exchange. They find that brokers who simultaneously relocate with the stock and continue their long-term cooperation with the specialist obtain a lower cost of liquidity, which manifests in a smaller bid-ask spread. Cocco, Gomes, and Martins (2003) detect evidence in the Interbank market that banks provide liquidity to each other in times of financial stress. They find that banks establish lending relationships in this market to provide insurance against the risk of shortage or excess of funds during the reserve maintenance period. We model the effects of cooperation and predation on liquidity as follows. We start by establishing a predatory stage game in continuous time, and then model cooperation by embedding it in a repeated game framework. In the stage game, each trader faces a differential game with other strategic traders, in which trading has both a temporary and a permanent impact on the price of the asset. That is, the price of the asset is affected by the current rate of trading (temporary price impact) and by the total cumulative quantity traded over time (permanent price impact). Because we use a pricing equation that accounts for the effect of trading pressure on prices (in contrast to the model of Brunnermeier and Pedersen (2005)), in aggregate the strategic traders suffer a surplus loss in the presence of predatory trading. This surplus loss motivates the traders to cooperate and 2 provide liquidity to each other in our repeated game.7,8 In the equilibrium of our stage game, traders race to market, selling quickly in the beginning of the period, at an exponentially decreasing rate. Also in equilibrium, predators initially race the distressed traders to market, but eventually fade them and buy back. This racing and fading behavior is well known in the trading industry and is modeled by Foster and Viswanathan (1996). We model cooperation by embedding the predatory stage game in a dynamic game. We first consider an infinitely-repeated game in which the magnitude of the liquidity event is fixed. In this framework, there exists an extremal equilibrium that is Pareto superior for the traders. We then extend the model to episodic illiquidity by allowing the exogenous magnitude of the liquidity event in the repeated game to be stochastic. Given such stochastic liquidity shocks, we provide predictions as to the magnitude of liquidity event required to trigger liquidity crises and we describe how a breakdown in cooperation leads to price volatility. Finally, we allow for multimarket contact in the stochastic version of our dynamic game. This increases cooperation across markets, but leads to contagion of both predation and liquidity crises across markets. We note a few empirical implications of our model. We show that the need for liquidity over time needs to be sufficiently symmetric for the traders to cooperate; asymmetric distress probabilities lead to the abandonment of cooperation in equilibrium. We also show that traders are more likely to cooperate in markets in which the permanent price impact of trading is high and the temporary price impact of trading is low. These markets are also those in which the predatory equilibrium strategies are the most aggressive. We would expect liquidity in these markets to be smooth most of the time and the episodes of illiquidity to be the most marked. If the degree of asymmetric information associated with an asset is a good predictor of the permanent price impact of trading, then securities that have concentrated ownership, that have high insider ownership, or that are