نقدینگی بازار، قیمت دارایی ها، و رفاه

This paper represents an equilibrium model for the demand and supply of liquidity and its impact on asset prices and welfare. We show that, when constant market presence is costly, purely idiosyncratic shocks lead to endogenous demand of liquidity and large price deviations from fundamentals. Moreover, market forces fail to lead to efficient supply of liquidity, which calls for potential policy interventions. However, we demonstrate that different policy tools can yield different efficiency consequences. For example, lowering the cost of supplying liquidity on the spot (e.g., through direct injection of liquidity or relaxation of ex post margin constraints) can decrease welfare while forcing more liquidity supply (e.g., through coordination of market participants) can improve welfare.

Liquidity is of critical importance to the stability and the efficiency of financial markets. The lack of it has often been blamed for exacerbating market crises such as the 1987 stock market crash, the 1998 near collapse of the hedge fund Long Term Capital Management (LTCM), and the current upheaval in the credit market.1 Yet much less consensus exists about what market liquidity is, what determines it, and how it affects asset prices and welfare. Views become even more divergent when it comes to appropriate policies with respect to liquidity, such as lowering barriers of entry in securities trading, setting margin and capital requirements for broker-dealers, coordinating market participants, and supplying liquidity during crises. The ongoing debate on the interventions by the central banks and the US Treasury to inject liquidity into the market during the current credit market crisis is an excellent case in point. The purpose of this paper is to present a simple theoretical framework to facilitate the discussions on these issues. We start with the observation that the lack of full participation in a market is at the heart of illiquidity. Imagine a situation in which all potential buyers and sellers are constantly present in the market and can trade without constraints and frictions, i.e., fully participate. Then all agents face the full demand and supply at all times and security prices depend only on the fundamentals such as payoffs and preferences. To the extent that illiquidity reflects forces beyond these fundamentals, a market with full participation can be considered perfectly liquid. Thus, illiquidity arises only when frictions prevent full participation of all agents. To capture this notion of illiquidity in a simple way, we assume that agents face participation costs that prevent them from constant, active, and unfettered participation in the market. We then develop an equilibrium model of both liquidity demand and supply in the presence of such costs. The endogenous demand for liquidity arises when participation costs prevent potential buyers and sellers with matching trading needs from coordinating their trades. The same costs also hinder the supply of liquidity. As a result, purely idiosyncratic shocks can cause infrequent but large deviations in prices from the fundamentals. Moreover, we show that, in general, market forces fail to achieve efficient supply of liquidity. However, different policy interventions can lead to divergent consequences. For example, direct injection of liquidity when it is in shortage can reduce welfare, while coordinated supply of liquidity by market participants can improve welfare. We also show that different costs of market presence give rise to distinctively different market structures and price and volume behavior, and the welfare consequences of the same policy interventions heavily depend on the structure of the market. To model the need for and the provision of liquidity in a unified framework, we start with an economy in which agents face both idiosyncratic and aggregate risks. The desire to share the idiosyncratic risks gives rise to their need to trade in the asset market. By definition, idiosyncratic risks sum to zero across all agents. Thus, underlying trading needs are always perfectly matched among agents. When market presence is costless, all agents stay in the market at all times. The market price adjusts to coordinate all buyers and sellers. Buy and sell orders, driven by idiosyncratic risks, are always in balance. In this case, asset prices are fully determined by the fundamentals, in particular, the level of aggregate risk, and are independent of agents’ idiosyncratic trading needs. When market presence is costly, however, not all agents are in the market at all times. We assume that agents can participate in the market in two ways: either incur an ex ante cost to be a market maker and then trade constantly, or pay a spot cost to trade after learning about their trading needs. Such a cost structure is motivated by the market structure we observe: A subset of agents (such as dealers, trading desks, and hedge funds) maintain a constant market presence and act as market makers, while most agents (such as the majority of individual and institutional investors, whom we refer to as traders) enter the market only when they need to trade. By the cost of market presence we intend to capture not only the costs of being in the market, but also any costs associated with raising needed capital or adjusting existing positions, in other words, any costs or hurdles that prevent the free flow of capital in the market. As they trade only infrequently, traders are forced to bear certain idiosyncratic risk. This extra risk makes them less risk tolerant and less willing to hold their share of the aggregate risk. For traders receiving an additional idiosyncratic risk in the same direction as the aggregate risk, they are further away from their desired position and thus are more eager to trade. Consequently, more of them enter the market than those with the opposite idiosyncratic risk (which partially offsets their exposure to the aggregate risk). Thus, despite perfectly matching trading needs, traders fail to coordinate their trades, leading to order imbalances. The endogenous order imbalances exhibit several distinctive properties. First, they are always in the same direction as the impact of the aggregate risk on asset demand, as traders with higher than average risk are more likely to enter the market. Second, order imbalances are always of significant magnitudes when they occur. This is because, for small idiosyncratic shocks, gains from trading are small and all traders choose to stay out of the market. It is only with sufficiently large idiosyncratic shocks that gains from trading exceed participation costs for some traders, leading to the mismatch in their trades. The resulting order imbalance is also large. Third, the magnitude of possible order imbalances depends on the level of the aggregate risk, which affects the asymmetry in trading gains between different traders. By endogenizing the order imbalance, we are able to characterize the impact of liquidity on asset prices. In particular, purely idiosyncratic shocks can generate aggregate liquidity needs and cause price to deviate from its fundamental value. Moreover, the impact of liquidity on price is in the same direction as that of the aggregate risk and is of significant magnitude. Consequently, it leads to high price volatility and fat tails. Under exogenous liquidity demand, Grossman and Miller (1988) find that higher costs of market making lead to lower levels of liquidity in the market and more volatile prices. We show that, when liquidity demand is endogenously determined, it becomes interdependent with liquidity supply and prices are not necessarily more volatile in less liquid markets. In particular, we obtain two different market structures. Only when the cost of market making is below a threshold do we have the usual market structure in which liquidity is supplied by market makers. When the cost of market making exceeds this threshold, a different market structure emerges: No market makers are in the market, and all liquidity is supplied by traders themselves on the spot. Under such a market structure, the liquidity supply is extremely low but so is the observed need for liquidity. Traders choose to stay out of the market most of the time. They enter only when shocks are large and participation is sufficiently symmetric. In this case, prices become less volatile. In such a market, conventional measures of price impact fails to be informative about liquidity. Instead, the lack of trading volume properly reveals the low level of liquidity. Thus, our results also provide a theoretical justification for incorporating trading volume into measures of market liquidity.2 In our model, trading and liquidity provision generate externalities. A trader's participation in the market also benefits his potential counterparties, and a market maker's supply of liquidity helps all potential traders. We show that, in general, market mechanism fails to properly internalize these externalities and thus leads to inefficient supply of liquidity in the market. Such an inefficiency leaves room for policy interventions. However, given the endogenous nature of both liquidity demand and supply, we show that different policy choices can lead to surprising consequences. On the one hand, the overall welfare of the economy can be improved by forcing all agents to pay the participation cost. In this case, the extra liquidity generated by broad participation yields benefits for all agents, which can outweigh the extra costs they pay. On the other hand, in a market with insufficient liquidity supply, decreasing participation costs (in particular, the cost to enter the market on the spot) can reduce welfare. This is because lowering the cost to enter the market on the spot reduces the incentive to be in the market a priori, i.e., to become a market maker. The level of liquidity in the market then decreases, which hurts everyone, including those who now pay lower costs. During market crises, such as the 1998 LTCM debacle and the current credit market upheaval, central banks have resorted to relaxing their lending conditions, e.g., by cutting the rates charged and broadening the collateral accepted, to increase liquidity into the market. This can be interpreted as cutting the cost of spot market participation in our model. Government agencies, such as the New York Federal Reserve Bank in the case of LTCM crisis and the US Treasury in the case of current credit market crisis, have also coordinated market participants to collectively supply pools of liquidity. Such an action is related to the forced spot participation in our analysis. Similarly, regulations such as designated market makers and high capital requirements can be interpreted as increasing ex ante participation in our model. By relying on an equilibrium setting in which both the demand and the supply of liquidity are endogenously determined, we are able to identify the sources of market inefficiencies and examine the overall welfare implications of various policy tools under different circumstances. The paper proceeds as follows. Section 2 describes the basic model. Section 3 solves for the intertemporal equilibrium of the economy. In Section 4, we examine how the need for liquidity affects asset prices and trading volume. Section 5 describes the endogenous determination of liquidity provision in the market and how it influences prices and volume. In Section 6, we consider the welfare implications of liquidity need and provision. Section 7 further explores the policy implications of our analysis. Section 8 gives a more detailed discussion on the related literature, and Section 9 concludes. The Appendix contains all the proofs.

In this paper, we show that frictions such as participa- tion costs can induce imbalances in agents’ trades even when their trading needs are perfectly matched. Each trader, when arriving at the market, faces only a partial demand and supply of the asset. The mismatch in the timing and the size of trades creates temporary order imbalance and the need for liquidity, which causes asset prices to deviate from the fundamentals. By endogenously determining both the demand and supply of liquidity, we are able to show that purely idiosyncratic liquidity shocks can affect prices, introducing additional price volatility. The price deviations always amplify the price impact of aggregate shocks and is of large sizes whenever they occur, leading to fat tails in returns. Moreover, we find that traders optimally refrain from participating in less liquid market, leading to lower observed liquidity needs. As a result, prices do not necessarily exhibit higher liquidity impact or higher volatility in less liquid markets, rendering it necessary to incorporate trading volume into measures of market liquidity. Finally, we show that partial participation in the market by a subset of traders can have important welfare implications. In particular, the withdrawal of a subset of traders from the market reduces market liquidity, which further reduces the incentive for others to participate in the market. The fact that participating agents cannot fully internalize the benefit from their liquidity provision leadsto suboptimal provision of liquidity despite the optimizing behavior at the individual level. This inefficiency in the market mechanism leaves room for policy intervention. However, the design of efficient intervention is far from obvious as it affects the demand and supply of liquidity in intricate ways. For example, lowering the cost of supplying liquidity on the spot (e.g., through direct injection of liquidity or relaxation of ex post margin constraints) can decrease welfare by reducing the profit opportunities for market makers and thus the ex ante incentive for them to be there. However, forcing more liquidity supply (e.g., through coordination of market participants) during times of crises can improve welfare. The key distinction is that agents do not expect to be subsidized during crises, and hence the anticipation of future interventions does not hinder their ex ante incentive to supply liquidity.