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Indeed, the fund manager’s private information then constrains the fund to make only incentive-compatible state-contingent transfers to the SR investor, thus raising the cost of providing liquidity. We show in particular that the fund allocation is https://www.xcritical.com/ dominated by the delayed-trading equilibrium in parameter regions for which there is a high level of origination and distribution of risky assets. Our model predicts the typical pattern of liquidity crises, where asset prices progressively deteriorate throughout the crisis.2 Because of this deterioration in asset prices one would expect that welfare is also worse in the delayed-trading equilibrium.
V.D. Outside and Inside Liquidity in the Immediate and Delayed Trading Equilibria
Why do financial institutions, industrial companies, and households hold low-yielding money balances, Treasury bills, and other liquid assets? When and to what extent can the liquidity pools forex state and international financial markets make up for a shortage of liquid assets, allowing agents to save and share risk more effectively? These questions are at the center of all financial crises, including the current global one.
- The outcome is that in the immediate-trading equilibrium most of the liquidity is inside liquidity held by SRs, whereas the delayed-trading equilibrium features relatively more outside liquidity than inside liquidity.
- This indivisibility is consistent with our assumption that each risky project has at most one SR owner, who is the only agent that observes the state of the risky project in period 2.
- If we assume instead that λρ + (1 − λ)[θ + (1 − θ)δ]ηρ ≥ 1, then SRs would always choose to put all their funds in a risky asset irrespective of the liquidity of the secondary market at date 1.
- In the delayed-trading equilibrium, inside liquidity is lower and the amount of risky projects originated is larger than in the immediate-trading equilibrium.
- The benefit of delaying asset sales and attempting to ride through the crisis is that the intermediary may be able to entirely avoid any sale of assets at distressed prices should the effect of the crisis on its portfolio be mild.
IX.C. Arbitrage Contagion: The Price of the Long Run Asset
The most closely related articles to the present article, besides Kyle and Xiong (2001) and Xiong (2001), are Gromb and Vayanos (2009), Brunnermeier and Pedersen (2009), and Kondor (2009). In particular, Brunnermeier and Pedersen (2009) also focus on the spillover effects of inside and outside liquidity, or what they refer to as funding and market liquidity. More recently, Allen and Gale (2000) and Freixas, Parigi, and Rochet (2000) (see also Aghion, Bolton, and Dewatripont 2000) have analyzed models of liquidity provided through the interbank market, which can give rise to contagious liquidity crises. The main mechanism they highlight is the default on an interbank loan, which depresses secondary-market prices and pushes other banks into a liquidity crisis. Subsequently, Acharya (2009) and Acharya and Yorulmazer (2008) have, in turn, introduced optimal bailout policies in a model with multiple banks and cash-in-the-market pricing of loans in the interbank market. Allowing for bilateral contracts between an SR and LR expands the set of allocations that can be attained as transfers can be made contingent on the realization of ω2ρ, ω20, and ω2L.
X. LONG-TERM CONTRACTS FOR LIQUIDITY
The reason is simply that under full information SRs get to trade the risky asset at date 2 at a sufficiently attractive price to make it worthwhile for them to delay trading until that date. By trading at date 1, SRs give up a valuable option not to trade the risky asset at all. This option is available if they delay trading to date 2 and has value in the event that the asset matures at date 2 with a payoff ρ. Under asymmetric information the price at which risky assets are traded at date 2 may be so low (due to lemons problems) that SRs prefer to forgo the option not to trade and to lock in a more attractive price for the risky asset at date 1 .
The second line is the net return from acquiring a position Q1 in risky assets at unit price P1 at date 1. This net return depends on the expected realized payoff of the risky asset at date 3, or in other words on the expected quality of assets purchased at date 2. As we postulate rational expectations, the LR investor’s information set, ℱ, includes the particular equilibrium that is being played. In computing conditional expectations, LRs assume that the mix of assets offered at date 2 corresponds to the one observed in equilibrium.
Therefore, the optimal long-term contract weakly (and sometimes strictly) dominates the equilibrium allocation under immediate trading. Note that we do not allow for more general multilateral contracts such that, for example, a giant financial intermediary contracting with all LRs and SRs simultaneously. In the absence of any organizational frictions in managing such a large institution, this arrangement is bound to achieve a better outcome, as it can pool all the idiosyncratic risks and thereby virtually eliminate asymmetric information between the parties. It is clearly unrealistic, however, to suppose that such an institution can be run without a hitch, and that it can magically overcome all existing informational constraints.
The government has an active role to play in improving risk-sharing between consumers with limited commitment power and firms dealing with the high costs of potential liquidity shortages. From this perspective, private risk-sharing is always imperfect and may lead to financial crises that can be alleviated through government interventions. When SR expects the delayed-trading equilibrium, then the long-term contract cannot always replicate the allocation under delayed trading.
It therefore seems to follow that ex ante contracting will always give rise to more efficient outcomes than under the immediate- and delayed-trading equilibria. A key and surprising observation of this section, however, is that optimal incentive-compatible, ex ante contracts do not generally give rise to strict efficiency improvements over the equilibrium allocations in the delayed-trading equilibrium. We begin by showing that when all agents are fully informed about the realization of idiosyncratic shocks at date 2, the unique equilibrium is the delayed-trading equilibrium. Thus, suppose for now that both SRs and LRs can observe whether a risky project is in state ω2L or ω20. In Inside and Outside Liquidity, leading economists Bengt Holmström and Jean Tirole offer an original, unified perspective on these questions. In this perspective, private risk-sharing is always imperfect and may lead to financial crises that can be alleviated through government interventions.
In addition we asked whether the provision of market liquidity can be Pareto-improved on by long-term contracts between those with potential liquidity needs and those who are likely to supply it. In this subsection we explore the consequences of restricting LRs to buying an integer number of indivisible projects. This restriction parallels the constraint we imposed on SRs and is similarly motivated by the fact that assets may in practice be physically indivisible, and more important, that information about each risky project is itself indivisible.
It benefits from a unified approach, based on incentive theory, that delivers a coherent perspective on the elusive concept of liquidity. But it is in fact unrelated to the idea of excess risk taking as SRs will choose to delay whether they are levered, or not.
Also, in his model banks have local (informational) monopoly power on the asset side, and subsequently can trade their assets in securities markets for cash—a form of outside liquidity. Finally, Fecht (2006) also allows for a contagion mechanism similar to Allen and Gale (2000) and Diamond and Rajan (2005),3 whereby a liquidity shock at one bank propagates itself through the financial system by depressing asset prices in securities markets. When two different rational expectations equilibria can coexist, one naturally wonders how they compare in terms of efficiency.
As emphasized by Holmstrom (2008) the opacity of these securities was also initially the source of their liquidity. Once the crisis started, banks and intermediaries started the costly process of risk discovery in their books, which immediately led to an adverse selection problem. Financial institutions faced a choice of whether to liquidate early or ride out the crisis in the hope that the asset may ultimately pay off.
We discuss policy interventions and use this model to interpret the current crisis in Section VII and, in greater depth, in Bolton, Santos, and Scheinkman (2009). We point out that the best form of public liquidity intervention relies on a complementarity between public and outside liquidity. Public liquidity in the form of a price support (or guarantee) for SR assets can restore existence of the delayed-trading equilibrium and thereby induce LRs to hold more outside liquidity. Such a policy would induce long-term investors to hold more cash in the knowledge that SRs rely less on inside liquidity, and thus help increase the availability of outside liquidity. However, when the investor who manages the fund also has private information about the realized returns on the fund’s investments then, as we show, the long-term contract cannot always achieve a more efficient outcome than the delayed-trading equilibrium.
In this excellent book, Holmstrom and Tirole put together a unified theory of liquidity, with applications ranging from the impact of liquidity on asset prices to the liquidity enhancing role of government debt, and the importance of international liquidity. In addition to academics and students of economics, it will appeal to people who work at central banks and international organizations. Two leading economists develop a theory explaining the demand for and supply of liquid assets. We now consider the more plausible situation where only the originating SR can observe whether its risky asset is in state ω2L or ω20. LRs at date 2 can only tell that if an asset is put up for sale it can be in either state ω2L or ω20. This Pareto-dominance must be qualified by the fact that we ignore the greater moral hazard problems at origination that may arise in the delayed-trading equilibrium.