Liquidity misallocation in an over-the-counter market

Abstract

To understand the illiquidity of the over-the-counter market when dealers and traders are in long-term relationships, I develop a framework to study the endogenous liquidity distortions resulting from the profit-maximizing, screening behavior of dealers. The dealer offers the trading mechanism contingent on the aggregate history of his customers summarized by the asset allocation. The equilibrium distortion is type dependent: trade with small surplus breaks down; trade with intermediate surplus may be delayed; trade with large surplus is carried out with a large bid/ask spread but without delay. Because of dealers' limited commitment, the distortions become more severe when the valuation shock is frequent, the valuation dispersion is large or the matching friction to form new relationships is large. Calibrating the model and running a horse race between matching efficiency, trading speed and relationship stability, I found that the liquidity disruption in the market during the recent financial crisis is more consistent with declining matching efficiency of forming trading relationships. The optimal mechanism can be implemented by random quote posting.

Introduction

Many financial over-the-counter (OTC) markets are illiquid, with large bid-ask spreads and long delay in trade. For example, a typical municipal bond is traded in the OTC market once every 25 days with an average bid-ask spread of more than 50 basis point (Green et al., 2007), whereas an equity is typically traded more than once every second with bid-ask spreads an order of magnitude smaller (Pagnotta and Philippon, 2012). Standard theories of the OTC market such as Duffie et al. (2005), Lagos and Rocheteau (2009) and Hugonnier et al. (2014) show that liquidity distortions can arise from the search friction to locate trading counterparties. However, financial institutions typically maintain long-term relationships with each other.³ The friction to locate trading counterparties may not be so large as to explain all the distortions. In this paper, I show that even when broker-dealers maintain long-term relationships with traders, additional liquidity distortions may arise if they do not observe traders' private valuations. In this environment, dealers screen traders by controlling the speed of trade and the transaction price and keep track of the endogenous asset allocation across his customers. Although dealers provide immediacy to traders, the monopsony power of the dealer in the OTC market leads to imperfect allocation of liquidity.

In the model, traders search and match with dealers. Similar to equilibrium search models of the labor market (Pissarides, 1990), the match is long-term but subject to breakup shocks and forming new matches takes time. Each dealer is matched with a continuum of traders. By posting menus of contracts specifying trading probabilities and transaction prices for indivisible assets, dealers screen traders with heterogeneous gain from trade. In equilibrium, traders with large gain from trade value most immediacy. So, they are willing to pay a high premium relative to the market price to trade faster. Traders with intermediate gain from trade sacrifice trading speed for a lower spread. To induce traders with large gain to accept the high premium, dealers strategically exclude traders with small gain by charging a fixed spread on top of a variable spread increasing in the trading probability. Therefore, trade breaks down for those with small gains from trade. I show that these three types of distortions could coexist in equilibrium.

A theoretical contribution of the paper is to formalize and solve the dynamic programing problem of the dealer, in which the asset allocation to customers is a high-dimensional state variable and the contract menus are the control variable. The asset allocation is slow moving because of the strategic delay of the dealer and the physical limit on the trading frequency between the dealer and his customers. This induces the dynamic interaction between the trading mechanism and the asset allocation, especially for traders with intermediate gain from trade. Traders with large gains from trade are willing to pay a premium to trade immediately. But trading faster with them also means that less of those traders remain waiting. With less traders with large gain remaining, dealers have an incentive to trade faster with traders with intermediate gain. Meanwhile, the dealer also has limited commitment to contract menus he chooses: when he chooses date-t contract menus, he takes as given traders' reservation value, even though it depends on contract menus offered by the dealer in the future. A better deal in the future increases the reservation value, which in turn squeezes the dealer's current profit margin. The limited commitment induces dynamic competition within a long-term relationship, in the spirit of the Coase conjecture, that a dealer competes with his future self when trading with investors and this drives his monopsony rent to zero. In this rich dynamic environment, however, we will show the Coase conjecture only holds partially. Frictions in the dynamic environment, such as the persistence of the trading relationship, matching frictions to form long-term relationships, and trading speed limit, all affect market liquidity. As a result, qualitatively, for traders with intermediate gain from trade, trade may not break down but instead may be delayed. For traders with small gain, trade still breaks down as in a static screening problem.

The endogenous liquidity distortion also depends on the stability of trader–dealer relationships and the matching friction in relationship formation. In benchmark models of the OTC market such as Duffie et al. (2005) and Lagos and Rocheteau (2009), liquidity distortion arises because of search frictions to locate trading counterparties. I show that when it is hard to form new matches, dealers may also be more likely to delay trade. Therefore, the strategic delay of the dealer could amplify the matching friction. On the other hand, the stability of the trader–dealer relationship, measured by the breakup rate of the relationship, may or may not induce more delay by the dealer, depending on the matching friction. When I calibrate the model to the corporate bonds market and run a horse race between relationship stability, matching efficiency and trading speed limit, a friction similar to those in benchmark models, I found that increasing the matching friction is more consistent with stylized facts from the recent financial crisis, during which dealers charge higher markups to their clients without increasing liquidity provision.⁴

The theory also links the opacity of the OTC market to market liquidity, transaction costs and asset prices. Opacity leads to heterogeneous valuation over an asset. I show that more dispersed valuations lead to more delay in trade and larger spread for all traders.

The optimal trading mechanism can be implemented by lotteries over transaction prices. So, the assumption that the dealer offers the contract menus is not restrictive, even when the dealer can only use outright sales contract. My theory gives an alternative explanation for the price dispersion in opaque markets described in Green (2007).

Literature review  Since assets are durable and dealers have limited commitment to the trading mechanism they post. This paper is closely related to the literature on the Coase conjecture (see, for example, Gul et al., 1986). Recent developments in this literature include Fuchs and Skrzypacz (2010) and Garrett (2013). My model allows changing valuations and arrival of new buyers over time, as well as the frictions in forming and maintaining long-term relationships, none of which are trivial additions to the baseline setup. The literature studies the optimal trading mechanism contingent on the individual history. By summarizing by the asset allocation the aggregate history of the dealer' customers, which includes trading activities and other events in the past, the trading mechanism in the paper becomes more tractable and captures the effect of not only trading speed limit but also other frictions on the liquidity distortion in the market.

My paper is also related to the literation on strategic delay induced by asymmetric information. Guerrieri et al. (2010) and Chang (2011) combine directed search friction and asymmetric information. In these papers, delay in trade serves as a signaling device. One common issue with the signaling equilibrium is that it is sensitive to perturbation. For an environment with nearly complete information, the equilibrium allocation is the same as an environment with severe adverse selection as long as the support of the distribution remains the same. In this model, delay in trade serves as a screening device. Dealers take into account the effect of the type distribution on their profit when they optimize the menu of contracts they offer. A perturbation to the distribution will not affect qualitatively the equilibrium allocation. In this sense, the equilibrium allocation is more robust in this model. Chiu and Koeppl (2011), Camargo and Lester (2014), Guerrieri and Shimer (2014) and Chang (2011) study the effect of lemons problem on liquidity. These papers take the sales contract as given, while here I allow contracts consisting of two ingredients, the trading probability and the transaction price for sales.

Another related literature is about asymmetric information in the decentralized dynamic market. Lauermann and Wolinsky (2011), Wolinsky (1990) and Blouin and Serrano (2001) study information aggregation in the lemon market and its social welfare as the friction vanishes. Golosov et al. (2014) and Camargo and Lester (2014) are concerned with the trading dynamics. Hörner and Vieille (2009) studies the interaction of strategies of sequentially arriving short-lived buyers in a dynamic lemon market. Inderst (2005) studies limiting property of a matching market with adverse selection. Hendel and Lizzeri (1999) studies the durable goods market with lemons. These papers study the implications of asymmetric information about the quality of the goods or assets being traded, while this paper studies the implications of asymmetric information about private valuations. Most of these papers focus on the limiting results as frictions are asymptotically zero. My focus is to characterize the equilibrium with frictions to study the resulting liquidity misallocation. In Duffie et al. (2014), the authors characterize analytically the dynamics of information aggregation in segmented markets. I do not allow information propagation in the model. So valuations across traders do not interact. While my focus is on the liquidity distortion due to the interaction between asymmetric information and other frictions and shocks in the economy, it would be interesting to further study the interaction between these two channels: information aggregation and the liquidity distortion that arises from the dealer's screening strategies.

The rest of the paper is organized as follows. In Section 2, I lay out the model. In Section 3, I characterize the equilibrium. In Sections 4 and 5, I focus on distinct implications of the model on market liquidity and the quoting strategy of the dealer.