We show that, surprisingly, the latter equilibrium Pareto-dominates the former because it saves on cash reserves, which are costly to carry.27 However, the delayed-trading equilibrium does not exist when the adverse selection problem is severe enough. The reason is that in this case prices are so depressed as to make it profitable for the agents holding good assets to carry them to maturity even when it is very costly to do so. We show that https://www.xcritical.com/ if they were able to do so, intermediaries would be better off committing ex ante to liquidating their assets at these depressed prices in the distressed states. Our model departs from the existing literature by considering the endogenous timing of asset sales and the deterioration of adverse selection problems over time. Financial intermediaries face the choice of raising liquidity early before adverse selection problems set in or in the midst of a crisis at more depressed prices. 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.

About Inside and Outside Liquidity

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 liquidity pools forex that the asset may ultimately pay off.

X. LONG-TERM CONTRACTS FOR LIQUIDITY

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.

IX.C. Arbitrage Contagion: The Price of the Long Run Asset

Parlour and Plantin (2008) consider a model where banks may securitize loans and thus obtain access to outside liquidity. As in our setting, the efficiency of outside liquidity is affected by adverse selection. But in the equilibrium they characterize liquidity may be excessive for some banks—as it undermines their loan origination standards—and too low for other banks, who may be perceived as holding excessively risky assets.

VI.C. Monopolistic Supply of Liquidity and Efficiency

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.

The only difference is that liquidity for SRs is held in the form of a tradable long-run asset instead of cash. Even if LRs can invest in risky assets at date 0, they may still choose not to hold these assets if the return on risky assets is low relative to the return on holding cash, as is the case for a large subset of our parameter values in our model. If, however, the supply of risky assets by SRs is so low that SRs earn a scarcity rent from investing in risky assets, then LRs may also invest a positive amount of their endowment in risky assets at date 0. Even in this case, LRs will continue to hold cash sufficient to equalize the return on the marginal dollar held in cash with the expected return on risky assets at date 0. The prospect of purchasing risky assets from SRs at distressed prices at dates 1 or 2 provides a sufficiently high expected return on cash to LRs to induce them to hold positive amounts of cash. Most closely related to our model is the framework considered in Fecht (2006), which itself builds on the related models of Diamond (1997) and Allen and Gale (2000).

Under complete information such a fund arrangement always dominates any equilibrium allocation achieved through future spot trading of assets for cash. Similarly, even if SRs buy long-run assets to sell them to LRs at date 1 or 2, as a substitute for holding cash, they may still choose to only hold cash and originate risky assets if the shadow cost of cash for LRs φ′(κ − M) is very large. Indeed, in this case SRs have to sell their long-run assets at such discounts at dates 1 or 2 that holding only cash and risky assets is preferred to holding long run assets that they sell at dates 1 or 2. The notion that adverse selection problems worsen during a liquidity crisis is intuitive, as originators learn more about the quality of their assets over time. It is also broadly consistent with how the financial crisis of 2007 and 2008 has played out. To be sure, the risk profile and asset quality of many financial intermediaries became difficult to ascertain as the residential real estate and mortgage markets’ implosion unfolded in 2007 and 2008 (see Gorton 2008a, 2008b).

Along the other axis, LRs also prefer to carry less outside liquidity (lower M) for a given supply of risky projects by SRs. In the figure we display the isoprofit lines for both the immediate- and delayed-trading equilibrium (this is why the isoprofit lines appear to cross in the plot; the lines that cross correspond to different dates). In our setup a higher total surplus can be achieved when the aggregate amount of cash held by investors is lower and when investment in risky and long-run projects is increased. But under Assumption 2, SRs only want to only hold cash in autarchy and do not want to originate risky projects.

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.

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 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.

But the opportunity cost of trading the risky asset for SRs is higher at date 1 than at date 2, as SRs forgo the option not to trade when they trade at date 1, and SRs can expect to sell their asset in state ω2L at an even higher price than at date 1. To compensate SRs for these forgone options, the price at date 1 has to be at least P1i ≥ ηρ, but at this price LRs do not want to carry cash to acquire risky assets at date 1. In sum, in the presence of asymmetric information the price at date 2 may be lowered sufficiently to make trade at date 1 attractive for both SRs and LRs. Third, we assume that there are gains from trading risky assets for cash at least at date 1 following an aggregate liquidity shock (the realization of state ω1L). This is the case when φ′(κ) is not so high to make it unattractive for LRs to carry cash to purchase risky assets at date 1. Our analysis sheds light on the recent transformation of the financial system toward more origination and greater reliance on distribution of assets as evidenced in Adrian and Shin (2009).

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.

• Another way of ensuring trade at date 2 in state ω2L is to have a monopoly LR set prices instead of an auctioneer in a competitive market.
• This change in information asymmetry is meant to capture in a simple way the idea that in liquidity crises the extent of asymmetric information grows over time.
• These assets will be traded at lower prices in the delayed-trading equilibrium, even taking into account the lemons problem.
• Here the bootstrap works in the other direction, as LRs decide to hold more cash in anticipation of a larger future supply of the assets held by SRs.
• It benefits from a unified approach, based on incentive theory, that delivers a coherent perspective on the elusive concept of liquidity.
• When sellers of secondhand cars can time their sales they tend to sell their cars sooner, when they are less likely to have become aware of flaws in their car, so as to reduce the lemons discount at which they can sell their car.

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.