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Although our model is highly stylized and abstracts from many institutional aspects of financial markets, it does shed light on the unfolding of the current crisis. Our model builds on the interconnections between the reversal in real estate price growth and the liquidity shock to financial intermediaries over this period. The central source of uncertainty in our model comes from SRs’ origination of risky projects. In the delayed-trading equilibrium, inside liquidity is liquidity pools forex lower and the amount of risky projects originated is larger than in the immediate-trading equilibrium. The higher amount of risky projects originated is an efficiency gain, whereas the larger amount of outside liquidity is an efficiency loss.
X.B. Feasibility, Participation, and Incentive Compatibility Constraints
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 https://www.xcritical.com/ 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 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.
X. LONG-TERM CONTRACTS FOR LIQUIDITY
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).
- 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.
- 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.
- We establish existence of an immediate-trading equilibrium, in which asset trading occurs in anticipation of a liquidity shock, and sometimes also of a delayed-trading equilibrium, in which assets are traded in response to a liquidity shock.
- Besides capturing an important aggregate economic effect, this formulation also makes it easier to accommodate the discreteness of long-run projects.
- 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.
- As we postulate rational expectations, the LR investor’s information set, ℱ, includes the particular equilibrium that is being played.
Basics of Leverage and Liquidity
Thus, the expectation of future asymmetric information can bring about an acceleration of trade, which we show in the next section is inefficient. Under our assumptions about asset returns and observability of idiosyncratic states, SRs and LRs have symmetric information at date 1 but asymmetric information at dates 2 and 3 about expected and realized returns of risky assets. In other words, although there is no adverse selection at date 1 , there will be at dates 2 and 3. 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. Finally, in our model LRs are those agents with sufficient knowledge to be able to value and absorb the risky assets for sale by financial intermediaries. Only their capital and liquid reserves matter for equilibrium pricing to the extent that they are the only participants with the knowledge to perform an adequate valuation.
The basic point is that what makes an investor an SR or LR is almost by definition the investor’s preferences for short versus long-maturity assets. These preferences in turn drive portfolio choices whether or not we assume that asset markets are segmented. When the immediate- and delayed-trading equilibrium coexist, an interesting question to consider is whether the two equilibria can be Pareto-ranked. We are able to establish that indeed the delayed-trading equilibrium Pareto-dominates the immediate-trading equilibrium. When the delayed-trading equilibrium does not exist we show, however, that a more efficient outcome can be attained under LR monopoly.
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).
Another central theme in our analysis is the particular timing of the liquidity crisis that we propose. In our framework the onset of the liquidity event starts with a real deterioration of the quality of the risky asset held by financial intermediaries. The assumption that adverse selection problems worsen during the liquidity crisis is a feature of our analysis that, as we have argued, seems plausible in the context of the current crisis. Our model captures the fact that intermediaries were holding securities that had a degree of complexity that made for a costly assessment of the actual risk that they were exposed to (see Gorton (2008b) for an elaboration of this point). Once problems in the mortgage market were widely reported in early 2007 banks turned to an assessment of the actual risks buried in their books.
In their model a bank run may occur if there is insufficient inside liquidity to meet depositor withdrawals. In contrast to our model, investors are identical ex ante, and are risk averse with respect to future liquidity shocks. The role of financial intermediaries is to provide insurance against investors’ idiosyncratic liquidity shocks. Over time, SRs learn (asymmetrically) more about the value of the assets they originated. Therefore, when at the onset of a liquidity shock they choose to hold on to their assets in the hope of riding out a temporary liquidity need, SRs run the risk of having to go to the market in a much worse position later. Yet it makes sense for SRs not to rush to sell their projects, as these may mature and pay off soon enough so that SRs ultimately may not face a liquidity shortage.
As we have shown, the delayed-trading equilibrium in our model Pareto-dominates the immediate-trading equilibrium, even though secondary market prices for risky assets are higher under early trading. The reason is although some SRs are forced to sell at even lower prices in the delayed-trading equilibrium, others are able to hold on to their assets as they learn that their liquidity needs are only temporary. The important implication of this observation is that lower secondary market prices do not imply that the liquidity crisis is more severe.
In other words, such an institution in practice would be constrained by the same informational problems present in competitive bilateral exchange, but this time inside the organization. Explicitly modeling these informational frictions and solving for the optimal informationally efficient multilateral organization is beyond the scope of this article. More formally, we could have written P1(ω1L) and P2(ω1L) to denote the prices of the risky asset at dates 1 and 2 and similarly Q1(ω1L) and Q2(ω1L) to denote the quantities acquired by LRs at different dates. Given that all trading occurs in the “ lower branch” of the tree we adopt the simpler notation as there is no possible ambiguity.
The answer to this question is crucially related to the amount of risky projects originated by the SRs. In a nutshell, under the expectation of immediate liquidity-trading, LRs expect to obtain the assets originated by SRs at close to fair value. In this case the returns of holding outside liquidity are low and the LRs hold little cash. On the other side of the trade, SRs will then expect to be able to sell a relatively small fraction of assets at close to fair value, and therefore respond by relying more heavily on inside liquidity and originating fewer projects. In an immediate-trading equilibrium there is less cash-in-the-market pricing (to borrow a term from Allen and Gale (1998)) and a lower supply of outside liquidity. The anticipated reduced supply of outside liquidity causes SRs to originate fewer projects and, thus, bootstraps the relatively high equilibrium price for the assets.
This trade-off is unrelated to the incentives that may force institutions to liquidate at particular times, due to accounting and credit quality restrictions in the assets they can hold, that have featured more prominently in the literature. Understanding the effect these restrictions have on the portfolio decisions of the different intermediaries remains an important question to explore in future research. Two other closely related models are Gorton and Huang (2004) and Parlour and Plantin (2008). As we do, Gorton and Huang consider liquidity supply in a general equilibrium model and argue that publicly provided liquidity can be welfare enhancing if the private supply of liquidity involves a high opportunity cost. However, in contrast to our analysis, they do not look at the optimal composition of inside and outside liquidity, nor do they consider the dynamics of liquidity trading.
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.
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.
The fundamental gains from trade in our model are between SRs who undervalue long-term assets and LRs. The more SRs can be induced to originate projects, the higher the gains from trade and therefore the higher welfare is. Because the delayed-trading equilibrium relies more on outside liquidity, it is more efficient. There may then come a point when the cost is so high that SRs are better off postponing the redemption of their investments altogether rather than realize a very low fire-sale price for their valuable projects. At that point the delayed-trading equilibrium collapses, as only lemons are traded for early redemption.
Under this interpretation, every LR is indifferent between holding cash or investing in the long-run project in equilibrium. Besides capturing an important aggregate economic effect, this formulation also makes it easier to accommodate the discreteness of long-run projects. Finally, one natural interpretation of the parameter δ in the model is that it equals 11+r where r is the interest rate faced by SRs at date 2. Lowering r, that is increasing δ, makes it more likely that SRs with good projects will choose to hold on to their assets rather than trade them for outside liquidity at date 2, undermining the delayed trading equilibrium.
We show that when the adverse selection problem is not too severe there are multiple equilibria, an immediate-trading and a delayed-trading equilibrium. In the first equilibrium, intermediaries liquidate their positions in exchange for cash early in the liquidity crisis. In the second equilibrium, liquidation takes place late in the liquidity event and in the presence of adverse selection problems. Why does an immediate-trading equilibrium emerge under asymmetric information when it does not exist under full information?