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One interpretation of this assumption is that once a scale is chosen, a risky project is indivisible. 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. An analogy with Akerlof ‘s famed market liquidity pools forex for secondhand cars is helpful to understand these results. 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. We first construct a candidate delayed-trading equilibrium and then establish the conditions on δ under which the candidate delayed-trading equilibrium is indeed an equilibrium. This is a very insightful book on a difficult and poorly understood topic at the center of the current financial crisis.
IX.C. Arbitrage Contagion: The Price of the Long Run Asset
This literature emphasizes the https://www.xcritical.com/ need for public liquidity to supplement private liquidity in case of aggregate demand shocks. Originating financial institutions also kept super senior tranches of asset-backed debt on their balance sheet. These tranches, as well as the special investment vehicles backed by commercial paper facilities, were asset risks that banks remained exposed to until the securities were sold to third parties. Another feature in Diamond and Rajan (2005) in common with our setup is the idea that financial intermediaries possess superior information about their assets, which is another source of illiquidity.
Basics of Leverage and Liquidity
They are only willing to invest in risky projects if enough outside liquidity is provided by LRs at either dates 1 or 2. SRs are endowed with an investment opportunity they do not want to exploit, unless they can distribute the investment to LRs in exchange for cash in some contingencies. Therefore, from a social point of view efficiency requires minimization of inside liquidity. Thus the key trade-off is between the efficiency gain from lowering inside liquidity and the efficiency loss from raising outside liquidity. One way of understanding these equilibrium portfolio choices is to note that in state ω1L the risky asset is of higher ex ante value to LRs (ηρ) than to SRs (θηρ + (1 − θ)δηρ) .
VI.C. Monopolistic Supply of Liquidity and Efficiency
Determining the extent of unsold inventory of assets was also difficult, and the value of any insurance or swap agreements was undermined by growing counterparty risk. The freezing up of the interbank loan market was one clear symptom of the difficulty of assessing the direct and indirect exposure of financial institutions to these toxic assets. In our model SRs invest in risky projects and a set of LR investors, those with sufficient knowledge to value and oversee the risky projects, may stand ready to buy them at a relatively good price. An important potential source of inefficiency in reality and in our model is asymmetric information between SRs and LRs about project quality. LRs cannot always tell whether the SR asset sale is motivated by a sudden liquidity need or whether the SR investor is trying to pass on a lemon. This problem is familiar to market participants and has been widely studied in the literature in different contexts.
X. LONG-TERM CONTRACTS FOR LIQUIDITY
We consider a model of liquidity demand arising from a possible maturity mismatch between asset revenues and consumption. This liquidity demand can be met with either cash reserves (inside liquidity) or via asset sales for cash (outside liquidity). The question we address is, what determines the mix of inside and outside liquidity in equilibrium? An important source of inefficiency in our model is the presence of asymmetric information about asset values, which increases the longer a liquidity trade is delayed. 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.
In contrast, under the expectation of delayed liquidity trading, SRs rely more on outside liquidity. 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. These assets will be traded at lower prices in the delayed-trading equilibrium, even taking into account the lemons problem. The reason is that in this equilibrium SRs originate more projects and therefore end up trading more assets following a liquidity shock. They originate more projects in this equilibrium because the expected return for SRs to investing in a project is higher, due to the lower overall probability of liquidating assets before they mature. Figure II represents the immediate- and delayed-trading equilibria in a diagram where the x axis measures M, the amount of cash carried by LRs, and the y axis m, the amount of cash carried by SRs.
The models of Diamond (1997) and Fecht (2006) seek to address an important weakness of the Diamond and Dybvig theory, which cannot account for the observed coexistence of financial intermediaries and securities markets. Liquidity trading in secondary markets undermines liquidity provision by banks and obviates the need for any financial intermediation in the Diamond and Dybvig setting, as Jacklin (1987) has shown. In Diamond (1997) banks coexist with securities markets because households face costs in switching out of the banking sector and into securities markets. Fecht (2006) extends Diamond (1997) by introducing segmentation between financial intermediaries’ investments in firms and claims issued directly by firms to investors though securities markets.
It is immediate from these constraints that LR cannot replicate the delayed-trading equilibrium allocation under a long-term contract. In sum, a unit of output from the long-run project at date 3 has to trade at a discount at dates 1 and 2 because of arbitrage. Thus, in our setup cash-in-the-market pricing is necessarily transmitted in the form of arbitrage contagion across different secondary asset markets, even if no trading of the long-run asset actually occurs in equilibrium. In other words, liquidity events affect prices of assets other than the ones where distressed sales are taking place. Liquidity crises thus cannot be contained across markets and time when these markets are linked via arbitrageurs. Diamond and Dybvig (1983) and Bryant (1980) provide the first models of investor liquidity demand, maturity transformation, and inside liquidity.
Our current research attempts to understand how different knowledge capital gets “earmarked” to specific markets. What arises is a theory of market segmentation and contagion that may shed new light on the behavior of financial markets in crisis situations. Our model also highlights that by supporting secondary market trading and the reliance on outside liquidity by banks, monetary authorities can encourage banks to do new lending. All these interventions are aimed at restoring the outside liquidity channel for banks and make new origination of loans more attractive. The clear Pareto-ranking of the two equilibria is somewhat surprising, because delayed trade is hampered by the information asymmetry at date 2 and takes place at lower equilibrium prices. Although lower prices clearly benefit LRs it is not obvious a priori that they also benefit SRs.
- 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.
- In this subsection we explore the consequences of restricting LRs to buying an integer number of indivisible projects.
- That being said, an important concern with origination and distribution that is omitted from our model is the greater moral hazard in origination that arises with greater distribution.
- The constraints simply state that SRs cannot invest more in the risky asset than their endowment and that they cannot sell more than what they hold.
- When and to what extent can the state and international financial markets make up for a shortage of liquid assets, allowing agents to save and share risk more effectively?
- 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.
- 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.
The reason is that the amount of outside liquidity that LRs hold in the delayed-trading equilibrium is not that much larger than the amount of cash they hold in the immediate-trading equilibrium. LRs don’t need to hold much more cash as they expect to acquire only risky assets in states ω2L and ω20. In other words, they expect that SRs retain the risky asset in state ω2ρ in the delayed-trading equilibrium. In contrast, in the immediate-trading equilibrium the price of the risky asset must be relatively high, and the expected returns to LRs relatively low, to compensate SRs for the forgone option that the asset may pay off at date 2. This lowers the amount of outside liquidity that LRs are willing to hold to trade at date 1 , and this in turn decreases the incentives of SRs to invest in risky assets. The first line in (3) is simply what the LR investor gets by holding an amount of cash M until date 3 without ever trading in secondary markets at dates 1 and 2.
We show that, when it exists, the delayed-trading equilibrium is Pareto superior to the immediate-trading equilibrium, despite the presence of adverse selection. However, the presence of adverse selection may inefficiently accelerate asset liquidation. We also show that the delayed-trading equilibrium features more outside liquidity than the immediate-trading equilibrium although it is supplied in the presence of adverse selection. If however, the shadow cost of cash for LRs is not too high then SRs may choose to buy long-run assets to sell them to LRs at date 1 or 2, as a substitute for holding cash. In this case our analysis with respect to SRs demand for liquidity with respect to the risky assets they originate would still go through virtually unchanged. In this case, cash is a dominated asset for SRs but not for LRs, as the latter continue to benefit from buying risky assets in secondary markets at distressed prices.
The reason is that under delayed trading, SR is constrained by different incentive constraints at date 2 than those faced by LR under the long-term contract. Under delayed trading, SR must trade the risky asset at the same price in both states ω20 and ω2L, and in state ω2ρ there is no trade between SR and LR. Under the long-term contract, however, LR promises transfers Ct(ω) to SR, which must satisfy the incentive compatibility constraints (21) and (22).
In our model inefficiencies arise through distortions in the ex ante portfolio decisions of SRs and LRs and through the particular timing of liquidity trades they give rise to. When agents anticipate trade in state ω1L, SRs lower their investment in the risky asset and carry more inside liquiditymi . In contrast LRs, carry less liquidity Mi as they anticipate fewer units of the risky asset to be supplied in state ω1L.
Banks were aware that the longer they waited in trading assets the more they would be perceived to be trading based on superior information about asset quality. Under full information the price of the risky asset at date 2 must be bounded below by the price at date 1. The reason is that the expected gross value of a risky asset to LRs is always ηρ whether it is traded at date 1 (in state ω1L) or at date 2 (in state ω2L).
Given that neither financial markets nor long-term contracts for liquidity can achieve a fully efficient outcome, the question naturally arises whether some form of public intervention may provide an efficiency improvement. An ex post inefficiency, which arises when the delayed-trading equilibrium fails to exist, and an ex ante inefficiency in the form of an excess reliance on inside liquidity. It is worth noting that a common prescription against banking liquidity crises—requiring that banks hold cash reserves or excess equity capital—would be counterproductive in our model. Such a requirement would only force SRs to rely more on inefficient inside liquidity and would undermine the supply of outside liquidity. That is, conditional on trade occurring at either dates there is no reallocation of the risky asset that would make both sides better off. Figure II shows that it is not possible to improve the ex post efficiency of either equilibrium, as in each case the equilibrium allocation is located at the tangency point of the isoprofit curves.
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. The goal of this article is to propose a tractable model of origination and contingent distribution of assets by financial intermediaries, and the liquidity demand arising from the maturity mismatch between asset payoffs and desired redemptions. When financial intermediaries invest in long-term assets they may face redemptions before these assets mature. Early redemptions can be met either with an intermediary’s own reserves—what we refer to as inside liquidity—or with the proceeds from asset sales to other investors with a longer horizon—what we refer to as outside liquidity. The purpose of our analysis is to determine the relative importance of inside and outside liquidity in a competitive equilibrium of the financial sector. The model captures key elements of the financial crisis and yields novel policy prescriptions.
An important remaining task is to analyze the benefits of public policy in our model under the assumption that the public agency may be ignorant about the true state of nature in which it is intervening. Claims to date 3 output from the long-run asset also trade at depressed prices at date 1, even if fire sales of risky assets only take place at date 2. 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. A monopoly LR would internalize the effect of an excessively low price on the quality of assets exchanged by SRs and may choose to keep its price P2M above δηρ to support the market at date 2 .
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.
The obvious question then is whether a monopoly LR may be more efficient ex ante than a competitive market. Given that all SRs are ex ante identical, we restrict attention to equilibria that treat all SRs symmetrically. We also restrict attention to pooling equilibria, in which observable actions cannot be used to distinguish among SRs with worthless risky assets (in state ω20) and SRs with valuable assets maturing at date 3 (in state ω2L). Our model is also related to the literature on liquidity and the dynamics of arbitrage by capital or margin-constrained speculators as in Dow and Gorton (1994) and Shleifer and Vishny (1997). However, models in this literature do not address the issue of deteriorating adverse selection and the timing of liquidity trading, nor do they explore the question of the optimal mix between inside and outside liquidity.