J Financ Serv Res (2012) 41:1–18 DOI 10.1007/s10693-011-0110-2

Liquidity Crunch in the Interbank Market: Is it Credit or Liquidity Risk, or Both? Angelo Baglioni

Received: 20 May 2010 / Revised: 4 April 2011 / Accepted: 19 April 2011 / Published online: 17 May 2011 © Springer Science+Business Media, LLC 2011

Abstract The interplay between liquidity and credit risks in the interbank market is analyzed. Banks are hit by idiosyncratic random liquidity shocks. The market may also be hit by bad news at a future date, implying the insolvency of some participants and creating a lemons problem; this may end up with a gridlock of the interbank market at that date. Anticipating such possible contingency, banks currently long of liquidity ask a liquidity premium for lending beyond a short maturity, as a compensation for the risk of being short of liquidity later and being forced to liquidate some illiquid assets. When such premium gets too high, banks currently short of liquidity prefer to borrow short term. The model is able to explain some stylized facts of the 2007–2009 liquidity crunch affecting the money market at the international level: (i) high spreads between interest rates at different maturities; (ii) “flight to overnight” in traded volumes; (iii) ineffectiveness of open market operations, leading the central banks to introduce some relevant innovations into their operational framework. Keywords Global financial crisis · Money market · Liquidity · Central banking JEL Classification G01 · G21 · E43 · E50 1 Introduction The liquidity crunch taking place in the interbank market during the 2007-2009 international financial turmoil raises some puzzling questions: –

why did the spread between the medium term and the short term interest rates jump to unprecedented levels?

A. Baglioni (B) Department of Economics and Finance, Catholic University of Milan, Largo Gemelli, no.1 – 20123 Milano, Italy e-mail: [email protected]

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Fig. 1 Spread 3 Month Euribor—Eonia Swap (daily data—b.p.)



why did the trading activity dry up, particularly on maturities longer than very short term (so called “flight to overnight”)?

There is wide evidence documenting such stylized facts, particularly for interest rates.1 A picture like the one shown in Fig. 1—reporting the spread between the 3 month interbank rate and the expected overnight rate over the same horizon—has become a sort of “standard view” of the liquidity crisis (the vertical lines mark two crucial dates: the start of the liquidity crunch in August 9th 2007, and the collapse of Lehman Brothers in September 15th 2008). Figure 2 shows the pattern of the trading activity in the euro area money market, in particular in the electronic platform e-MID.2 The daily number of trades dropped significantly since the start of crisis. The decline of traded volumes was even stronger, documenting a significant reduction of the mean value of the deals. Both larger spreads and fewer trades point to a higher liquidity risk in the money market. A useful indicator of the liquidity (funding) risk perceived by banks is their behavior in monetary policy operations. Figure 3 reports this kind of information for the euro area: (i) the difference between the weighted average rate and the minimum bid rate in the main refinancing operations conducted by the ECB; (ii) the “cover ratio” in the same operations, defined as the ratio between total bids and allotted amount. The picture documents a more aggressive behavior of European banks since August 2007, and even more so after the LB collapse, confirming the increasing difficulties faced by them in managing their liquidity position.

1 See: Cecchetti (2009), Taylor and Williams (2009), and Ashcraft et al. (2009) for the U.S.; Heider et al. (2009), Eisenschmidt and Tapking (2009), and ECB (2009a) for the euro area. 2 This

electronic interbank market is located in Italy, but most of its participants are from other countries of the euro area. So it is quite representative of the money market in this area.

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Fig. 2 Daily activity in the e-MID market (monthly average)

Two factors have played a crucial role in determining the liquidity crunch in the money market. First, the lack of information about the (cross-border) exposure of market participants to troubled institutions or “toxic” assets has created a classic “lemons problem”. Second, banks have become more uncertain about their liquidity

Fig. 3 ECB main financing operations

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needs, due to a higher volatility of liquidity shocks; this can be due to the complexity of financial conglomerates (for example, a vehicle unable to roll-over an outstanding issue of asset-backed commercial paper may draw on the bank credit line supporting such an issue). Therefore, the starting point of this paper is that we have to look at the interplay between credit and liquidity risks; they are indeed the two essential ingredients of the model presented below. Let me sketch the main features of the model here. Liquidity risk: banks are hit by a liquidity shock, which may be reversed at some future date; so an excess of liquid reserves now may be later converted into a shortage. Credit risk: the banking system may be hit by a negative shock, implying that some market participants suffer losses so large to become insolvent; the distribution of those losses is private information, implying an adverse selection problem, which can make the interbank market dry up. This framework leads to some interesting results for the equilibrium of the interbank market before the dry up of trades possibly occurs. Banks take into account the chance that the interbank market may no longer be there in the future, forcing those banks short of liquidity at that time to liquidate some illiquid assets. Hence banks currently long of liquidity ask a premium for lending it out in the interbank market on a long maturity, as a compensation for the liquidation cost they might suffer, should their liquidity position be reversed later. If this premium gets too large (this happens whenever the volatility of liquidity shocks is high enough), banks currently short of liquidity prefer to borrow short term. The model is then able to provide an answer to the questions raised at the start of this Introduction: first, the chance of a future gridlock in the interbank market adds a relevant component to the spread between long and short term interest rates, by introducing a liquidity premium; second, it provides an explanation for the “flight to overnight”. The plan of the paper is the following. After a brief review of the related literature (Section 2), the model is illustrated in Section 3. Some policy implications are derived in Section 4, and the main insights of the analysis are summarized in Section 5. Finally, the Appendix includes the proofs of all the propositions.

2 Related literature The theory of banking has for a long time built on the seminal contribution of Diamond and Dybvig (1983). Their key insight is that banks insure consumers against liquidity risk. Since they invest only a fraction of deposits in liquid reserves, banks bear the risk of being short of liquidity in some contingencies, including a coordination failure among retail depositors (“bank run”). This approach has generated a wide literature (surveyed in Allen and Gale 2007), and it has been applied to the analysis of the interbank market; see for example Bhattacharya and Gale (1987), Allen and Gale (2000), Freixas et al. (2010), and Heider et al. (2009). However, there is quite strong evidence that the global liquidity crunch, starting in August 2007, was not triggered by retail depositors. To the contrary, the hoarding behavior of financial institutions played a crucial role, making liquidity dry up in the money market (see Brunnermeier 2009 and Ashcraft et al. 2009). Banks more relying on wholesale (international) markets for their funding were more prone to a liquidity squeeze, contrary to those more relying on retail deposits. A remarkable example is the case of Northern Rock: the fundamental weakness of this bank was

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the reliance on institutional investors for short term funding, as Shin (2009) argues; moreover, the spillover effects of this bank run episode and of the subsequent bail out announcement have been significant for U.K. banks relying on wholesale funding, as opposed to those relying on retail deposits, as Goldsmith-Pinkham and Yorulmazer (2010) show. Another example is the Icelandic banking crisis: the huge amount of wholesale short term funding in foreign currency has been at the origin of the collapse of three large banks in that country (see Buiter and Sibert 2008).3 Therefore several recent studies abstract from retail deposits and focus on wholesale money markets. Huang and Ratnovski (2010) extend the Calomiris and Kahn (1991) framework to show that short term wholesale financiers can force an inefficient liquidation of bank assets. The same issue was tackled even before the recent crisis by Rochet and Vives (2004), pointing to the coordination failure among large CD holders. Acharya et al. (2010) show that the release of information may cause the market for asset-backed securities to dry up. Adrian and Shin (2010) and Brunnermeier and Pedersen (2009) study the mechanisms amplifying the impact of a (small) shock to the balance sheet of financial intermediaries (“loss spirals” and “margin spirals”). This growing body of literature generally studies the market for short term bank liabilities—including repos and commercial paper—held by nonbank financial institutions, like mutual and hedge funds. My paper shares with this literature the attention paid to the incentives and constraints faced by players in the money market, abstracting from the behavior of retail depositors. However my focus is on the role of the unsecured interbank market, where banks trade their reserves in response to idiosyncratic liquidity shocks. As we shall see, I assume perfect competition in the interbank market. Acharya et al. (2008) address the issue of imperfect competition in the interbank market, showing that the market power enjoyed by some banks enable them to strategically increase the interest rate they charge to banks needing liquidity, forcing the latter to inefficiently liquidate their illiquid assets. Thus they show that imperfect competition is a further reason—in addition to those analyzed here—that can explain why, even in presence of an aggregate surplus of liquidity, banks short of liquidity might not borrow in the interbank market and incur in liquidation costs, since the market is unable to channel the liquid funds from surplus to illiquid banks. Interestingly, they come to the conclusion that the central bank is able to avoid such inefficiency only provided it is willing to lend at subsidized terms to banks needing liquidity, bearing an expected loss (unless it has superior information than the market). This result will be derived here in a perfect competition context. Another crucial assumption is the presence of a “lemons problem” in the interbank market. This assumption has become standard in the banking literature after being introduced by Flannery (1996), who shows that credit risk together with adverse selection can lead to a break down of the market for interbank deposits. Other authors, like Rochet and Tirole (1996), have stressed the role of banks as peer monitors of each other in the interbank market. However, this monitoring role itself may be viewed as a way to control for the basic asymmetric information problem affecting the market for interbank loans, like any credit market more generally.

3 Norden

and Weber (2010) show that many German banks have been substituting retail customers’ deposits with interbank liabilities over time, and they discuss the implications of such evolution for the stability of the banking system.

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Under this regard, the interbank market is no exception: like the monitoring activity of banks over final borrowers is not in general assumed to completely overcome the asymmetric information between borrowers and lenders, so the peer monitoring among banks themselves cannot rule out completely the adverse selection issue. The latter has presumably become even more severe under the financial crisis, as the explosion of the interest rate spreads in the market confirms (see the evidence reported in the Introduction): this can be partially attributed to a jump of the “lemons premium” in the interbank market. The lack of information about bank risk exposures at the outset of the crisis has been stressed by regulators as well (see FSF 2008). Diamond and Rajan (2009) analyze a problem quite similar to that addressed here. They show that a liquidity shock may lead to a dry up of the market for bank assets. For different reasons, both potential buyers and sellers of those assets defer trading: the former because, in a “fire sale” context, they wait for a further drop of assets price; the latter because they prefer to bet on the recovery of assets price rather then selling at a loss. As a result, the market for bank assets gets gridlocked. My approach differs from theirs mainly for the inclusion of two ingredients: the possibility that the initial liquidity shock may be reversed later, and the analysis of the interaction between a “lemons problem” possibly arising in the future and the current equilibrium in the interbank market. Finally, there is a growing empirical literature related to this paper, trying to measure the two risk premia—credit and liquidity—incorporated in money market spreads since August 2007. It is difficult to say which of the two items prevails: while some authors provide evidence that credit risk is predominant (an example is Taylor and Williams 2009), others stress the importance of liquidity risk (an example is Eisenschmidt and Tapking 2009). The role of liquidity is documented also by those studies focussing on the intraday patterns of traded volumes and of interest rates in the interbank market (see Hansal et al. 2008, Baglioni and Monticini 2008, 2010). Overall, the evidence shows that both elements play a relevant role, supporting the view—taken here—that we should look at the interplay between the two sources of risk.

3 The model 3.1 Set-up Timeline of the model Before describing in detail the assumptions of the model, let me briefly sketch the timing of events. There are three dates: t = 0, 1, 2. •



t = 0. Banks are hit by a liquidity shock. Banks hit by a positive shock have to decide whether to lend in the interbank market or store liquidity. Banks hit by a negative shock have to decide whether to borrow in the interbank market or liquidate some loans. t = 1. With some probability, a credit risk shock can hit the banking sector, implying that some banks become “bad” (“lemons”), while the others are “good”; each bank observes her own type. If no shock occurs, all banks are “good”. Interbank claims maturing at this date are repaid. Again, banks long of liquidity decide whether to lend in the interbank market or store liquidity; banks

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short of liquidity decide whether to borrow in the interbank market or liquidate some loans. t = 2. All retail deposits and outstanding interbank claims have to be repaid. Good banks repay all their liabilities. Bad banks (if any) are insolvent.

Retail deposits All agents in the economy are risk-neutral. Each bank enters the model with an endowment of one unit of retail deposits, which have to be repaid at t = 2. This assumption captures the fact that retail depositors are a stable source of funding, thanks to their “passive” behavior. They are fully insured through a fairly priced deposit insurance scheme; thus banks pay the riskless rate of interest on deposits.4 (The insurance does not cover the interbank loans introduced below). Bank assets The initial deposit endowment is entirely invested in loans. Thus all banks enter the model without any liquid reserves.5 The rationale behind this assumption is that, for any target level of liquid reserves, a bank may be hit either by a positive shock creating excess (undesired) reserves, or by a negative shock leading to a reserve level below the target. So a bank may turn out to be either long or short of liquidity, due to random shocks. We are not interested here in determining ex ante the optimal target level of reserves. This is quite a complex problem, which can be addressed in two ways: (i) as the management of the compulsory reserve requirement, allowing for a day-to-day mobilization within the maintenance period;6 (ii) as the choice of the optimal point along a trade-off between liquid (safe) assets and illiquid (risky) assets providing a higher expected return than liquidity holdings.7 Both approaches show that in equilibrium banks hold only a fraction of thier balance sheet in liquid reserves; as a consequence they are prone to a liquidity shortage. Our interest is in how an ex post shortage or excess of liquidity, relative to a target level, is managed by a bank. Therefore it seems reasonable to set the target level of liquid reserves at an exogenous value (zero for simplicity), and to study banks’ reactions to any deviations of available reserves from such a level. Liquidity risk At t = 0, some banks are hit by a positive liquidity shock: they have a deposit inflow equal to x, so their retail deposits jump to 1 + x (where 0 < x < 1) and they have an excess reserve of x. Other banks are hit by an opposite shock −x: their deposits decline to 1 − x and they have a reserve shortage of x. Each of these liquidity shocks is either “permanent” or “transitory”. A permanent shock lasts for two periods (untill t = 2). To the contrary, a transitory shock lasts only for one period: at t = 1 the deposit level comes back to 1. A bank observes the nature of the shock

4 Fair

pricing of the deposit insurance is a technical assumption, introduced in order to avoid any incentive distortion (risk-taking attitude) arising from flat insurance premia.

5 The

same assumption is made by Diamond and Rajan (2009), who explain why banks may be unwilling to convert illiquid into liquid assets, despite the fact that by doing so they increase their risk of insolvency (see Section 2 above).

6 This

management problem was formalized by Campbell (1987). See also Spindt and Hoffmeister (1988), Hamilton (1996), and Bartolini et al. (2002).

7A

recent contribution within this approach has been given by Acharya et al. (2009). Interestingly, they find that the choice of bank liquidity is inefficiently low during economic booms and excessively high during crises.

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at t = 1, while at t = 0 she knows that it is permanent with probability p. Liquidity shocks are assumed to be publicly observable; thus our results do not depend on any opportunistic behavior due to asymmetric information about individual liquidity imbalances.8 Interbank market Banks long of liquidity can either lend in the interbank market or store liquidity in a riskless asset (e.g. Treasury Bills or reserves held at the central bank). Banks short of liquidity can either borrow in the interbank market or liquidate some loans.9 By assumption, there never is any liquidity shortage for the banking system as a whole, and there is competition among lenders in the interbank market: they demand an expected return on an interbank loan weakly larger than the riskless rate. This rate is set by the monetary policy authority, and its level is assumed to be zero for simplicity. At t = 0 both a short term (ST) and a long term (LT) interbank markets exist. A ST interbank loan at t = 0 is defined as a trade where a bank transfers at this date an amount x to another bank, and the latter promises to repay R1 at t = 1. Similarly, a LT interbank loan at t = 0 is defined as a trade where a bank transfers at this date an amount x to another bank, and the latter promises to repay R2 at t = 2. At t = 1 only a ST market is available by definition: an interbank loan at t = 1 is defined as a trade where a bank transfers at this date an amount x to another bank, and the latter promises to repay R at t = 2. We will determine below whether there are trades in the interbank market and, if so, at which rate of interest. If there is a positive volume of trades, the interbank market is said to be “active”. The alternative situation, where no trade takes place, is labelled “gridlock”. As we said, on one side banks long of liquidity can store it in a riskless asset as an alternative to lending it out in the interbank market; on the other side banks short of liquidity can liquidate loans as an alternative to borrowing from other banks. These outside options will enable us to identify their reservation prices for trading in the interbank market: the lowest repayment asked by a lending bank and the highest amount that a borrowing bank is willing to repay. The reservation prices for trades at t = 0 are labelled R1 , R2 and R1 , R2 , for a long and for a short bank respectively. Hence the feasibility conditions for the interbank market to be active are: R1 ≤ R1 and R2 ≤ R2 for the ST and the LT market respectively. Moreover, for both markets to be active at the same time all banks must be indifferent between trading in the ST and in the LT markets. The reservation prices for trades at t = 1 are labelled R, R, and the feasibility condition is R ≤ R. Credit risk The are two states of nature, high and low: s ∈ {h, l} (see Fig. 4). If s = h all banks are “good” (G): their loan portfolio is worth VG > 1, provided it is not liquidated until t = 2. To the contrary, if s = l a share α of the banking system is

8 The

alternative assumption that liquidity shocks are private information would strengthen the results below, since it would make a gridlock in the interbank market even more likely (see footnote 14).

9A

further alternative that could be considered is borrowing from the central bank. However this generally occurs at a penalizing interest rate, and this penalty would play in my framework much the same role as the liquidation cost introduced below. Therefore I do not consider it explicitly here. The role of the discount window policy is discussed in Section 4.

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Fig. 4 Loan portfolio value

made up of “bad” (B) banks: these have a loan portfolio which is worth V B < 1 in t = 2. In particular, VG is assumed to be large enough that a good bank is always solvent at t = 2 (i.e. able to repay all her retail deposits plus interbank liabilities). To the contrary, V B is assumed to be low enough that a bad bank is always insolvent at t = 2. Moreover, retail depositors (or equivalently the deposit insurer) have a senior claim, so an interbank debt maturing at t = 2 is never repaid by a bad bank.10 This framework formalizes the idea that with some probability (say k) a negative shock hits the market at t = 1, implying that some participants suffer losses large enough to become “lemons”. Everyone observes which state occurs, but each bank observes only her own type: the final value of the loan portfolio is a private information. Of course, this asymmetric information problem is relevant only in the low state; in this case an interbank claim maturing at t = 2 will be repaid with probability (1 − α), as far as the lender knows. In case of early liquidation at t = 1, a bank’s loan portfolio is worth either LG or L B , depending on her type, with LG > L B . We can think of “liquidation” in this context in two different (but not exclusive) ways. First, a bank calls back a credit line, asking a borrower to reduce or even to repay in full his outstanding debt. Under this interpretation, the liquidation cost is the difference between the value of a loan at maturity and the amount that a borrower is able to repay “at short notice”; it sounds reasonable to assume that a good borrower is able to repay more than a bad one. Second, a bank sells a portfolio of loans through a securitization deal. Loans are bank specific assets: their value is higher inside than outside the bank, which has accumulated through time some skills in monitoring and administering them; this is the reason why they are sold at a discount, implying a liquidation cost. In securitization deals, it is a common practice that loans are evaluated and assigned a rating by some intermediary; the latter is delegated to collect information about the quality of the assets under sale and to send a signal to the market, so that a good portfolio of loans can be sold at a higher price than a bad one. 11 At t = 0, the loans’ liquidation value is L0 for all banks, since the loan portfolio is worth the same for all banks with the information available at this date. For simplicity, the ratio between

10 This seniority assumption is introduced for simplicity: the recovery rate on an interbank loan to a bad bank is zero. Allowing for a positive recovery rate would not alter the results below. 11 Sometimes the liquidity of bank loans is limited through contractual arragements. This is the case in the syndicated loan market, as shown by Pyles and Mullineax (2008). They find that resale constraints are more likely when borrowers are more risky.

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the continuation and the liquidation value is assumed to be the same in all cases: l = VLGG = VLBB = VL00 > 1.12 As of t = 0 all banks are identical: each of them is aware that there can be a shock in the financial system at t = 1, making some banks—possibly including herself—to be lemons. Each bank’s loan portfolio is worth V0 = π VG + (1 − π )VB , where π = (1 − k) + k(1 − α) and V0 > 1 by assumption. A LT interbank claim will be repaid with probability π . To the contrary, a ST loan is riskless, since all banks are assumed to be always able to repay their interbank liabilities at t = 1, either by rolling over a ST debt or by liquidating part of their loan portfolio (formally: L B ≥ R1 ).13 3.2 The interbank market at t = 1 In the following, we are going to solve the model backwards. First, we identify the alternative equilibria prevailing in the interbank market at t = 1, depending on the state of nature governing the evolution of credit risk (s ∈ h, l ). Second, we determine the alternative equilibria at t = 0, which of course will depend on the outcomes obtained at t = 1. Let us begin by examining the simple case where the good state occurs: s = h. In this case, banks short of liquidity are able to borrow in the interbank market, and trades take place at the riskless rate of interest, since all banks are able to repay for sure at t = 2. Proposition 1 Let s = h at t = 1. The interbank market is active and the equilibrium price is Rh = x. The issue becomes more interesting in the low state: s = l. Proposition 2 Let s = l at t = 1. 1 , the interbank market is active and the pooling equilibrium price is (A) If l ≥ (1−α) x Rl = (1−α) . 1 , there is a gridlock in the interbank market. (B) If l < (1−α)

Proposition 2 shows that the emergence of a lemons problem in the interbank market ends up with two quite different outcomes, depending on the size of the liquidation cost relative to the share of “lemons” present in the banking system. For any value of α, if the liquidation cost is high enough, good banks short of liquidity prefer to borrow and the pooling equilibrium is feasible. In this case, the only consequence of the credit risk shock is a rise of the price charged on interbank loans, which has to incorporate a premium for the credit risk incurred by the lender. The (standard) implication is that—on the borrowing side—good banks subsidize

12 It must be stressed that this is only a simplifying assumption, not necessary to get the results below. The assumption that LG > L B is made also by Heider et al. (2009) (in their notation: ls > lr ). 13 Note that the above assumption, that retail deposits are a senior claim, is actually enforced only at t = 2. Due to the passive behavior of retail depositors, interbank loans are de facto —although not formally − senior at t = 1.

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bad ones.14 If the liquidation cost is instead low enough, good banks are no longer ready to pay the bill and they prefer to liquidate. In this case, the pooling equilibrium breaks down and no bank is able to raise funds in the interbank market. As a consequence, all banks short of liquidity suffer a liquidation cost. 3.3 The interbank market at t = 0 The equilibrium at t = 0 crucially depends on the outcome obtained at t = 1. As we have seen, a gridlock in the interbank market can occur at t = 1 when the following condition fails to hold: l≥

1 (1 − α)

(1)

Therefore I consider two separate cases: (A) condition (1) holds; (B) condition (1) does not hold. Case (A) no gridlock at t = 1 1 Proposition 3 Let l ≥ (1−α) . Both the ST and the LT interbank markets are active at t = 0. The equilibrium prices are R1 = x and R2 = πx respectively.

Proposition 3 shows that, given that the interbank market is active at t = 1, the spread between the LT and the ST interbank rates at t = 0 incorporates only a credit risk premium, due to the possibility that a LT loan will not be repaid, whereas a ST loan is risk-free. Thus the spread is:   1 R2 − R1 = x −1 (2) π The liquidity risk, namely the risk of being short of liquidity in the next period, plays no role in this context, since a bank is always able to raise funds in the interbank market. Both the ST and the LT markets are active, since the expected value of a bank—as of t = 0—does not depend on the maturity of her interbank trade, so she is indifferent between trading ST and LT.15 This expected value is V0 − 1 regardless of the sign of the liquidity shock, thanks to the redistribution of liquidity taking place through the interbank market. Things are going to change in case (B). Case (B) possible gridlock at t = 1

14 The assumption that liquidity shocks are public information rules out opportunistic behavior by bad banks, which are not short of liquidity, when the pooling equilibrium prevails. If these banks try to make a profit by borrowing and storing liquidity (exploiting the information that they will not repay the interbank debt), the other market participants are able to detect such banks and they do not lend to them. Allowing for such an opportunistic behavior—by assuming that liquidity shocks were privately observed—would increase the number of bad banks borrowing in the interbank market. As a consequence, lenders’ reservation price would increase, making a gridlock even more likely to occur. 15 This result contrasts the one obtained in Eisenschmidt and Tapking (2009), where a possible future rise of interest rates—reflecting a positive default probability—is enough to make the long term interbank market break down.

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1 Proposition 4 Let l < (1−α) . If p < (>) 21 , only the ST (LT) interbank market is active 1 at t = 0. If p = 2 , both the are active. The equilibrium prices  ST and the LT markets  are R1 = x and R2 = πx 1 + (1 − p)k(l − 1) respectively.

Proposition 4 highlights the main points of this paper. First, the spread between the LT and the ST interbank rates at t = 0 incorporates not only a credit risk premium, but also a liquidity risk premium. Thus the spread is now:    (1 − p)k(l − 1) 1 R2 − R1 = x −1 + (3) π π The second term in brackets is the compensation asked by a bank lending LT for the risk she incurs of being short of liquidity in the next period and being forced to liquidate part of her loan portfolio: this happens if the initial positive liquidity shock turns out later to be transitory and there is a gridlock in the interbank market at t = 1. Note that the liquidity premium is due to the interplay between credit and liquidity risks: both elements are necessary to generate a positive liquidity premium (it is immediate to see that the liquidity premium vanishes if either k = 0 or p = 1). Second, banks initially short of liquidity are not indifferent (in general) between borrowing ST and LT. They have to compare the liquidity premium charged on a LT loan with the liquidity risk they incur by borrowing ST: a ST debt should be rolled-over in the next period if the liquidity shock is permanent, but this is not possible if the interbank market is gridlocked at t = 1, implying a liquidation cost. The balance between these two costs depends on p. If the liquidity shock is more likely to be permanent ( p > 12 ), the liquidity premium charged on a LT loan is more than outweighed by the risk of being forced to liquidate at t = 1: than all banks short of liquidity at t = 0 prefer to pay the price of borrowing LT. The opposite happens if the liquidity shock is more likely to be transitory ( p < 12 ): in this case the liquidity premium on a LT loan is too high and all short banks prefer to borrow ST. Therefore trades drop to zero either in the ST or in the LT interbank market. Finally, note that none of the above results derives from an aggregate shortage of liquidity. Therefore, the management of aggregate liquidity—through central bank open market operations—does not seem to be the right answer to the issues raised here. The central bank’s intervention could still be effective within this context, but only by putting taxpayers’ money at risk. If, in case of a gridlock at t = 1, the central bank stands ready to lend to all banks short of liquidity, such banks would borrow x from the central bank instead of liquidating, provided the amount to be repaid to the central bank does not exceed xl (the reservation price of good banks). This kind of intervention would avoid an inefficient liquidation of bank assets. If anticipated, it would also avoid banks long of liquidity asking for a liquidity premium on LT interbank loans. However, the provision of this discount window facility would imply an expected loss for the central bank (equal to x − (1 − α)xl, if the highest feasible rate is applied).

4 Policy implications A key element of the model is the adverse selection issue raised by the lack of information about the quality of bank assets. The first policy implication is that the

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intervention of the authorities should be devoted to improving the transparency of financial institutions and markets. The complexity of large (international) financial groups have worsened the quality of the information released through their balance sheets. The opacity of the OTC markets has prevented market participants from having a clear picture of the distribution of losses arising from the crisis of specific market segments (like ABS). A regulatory and supervisory intervention in this area is needed.16 The second implication is that increasing the supply of bank reserves seems unable to solve issues which are ultimately related to the creditworthiness of counterparties, unless the central bank is willing to subsidize the banking system and incur some credit risk. Actually, this line of intervention has been adopted by some central banks, after observing the ineffectiveness of traditional open market operations. For example, in October 2008 the ECB has started to provide unlimited amounts of liquidity at fixed interest rate in the main refinancing operations; at the same time, the range of eligible collateral has been enlarged and the penalization applied to the marginal lending facility was halved (from 100 to 50 basis points). Moreover, the policy rate has been dramatically lowered (from 4.25% to 1% in several steps). Through these measures the ECB took up a relevant share of credit risk from the market.17 Similar actions have been taken by the Fed: (i) the penalty on the primary discount lending has been lowered from 100 to 25 b.p. above the federal funds target rate, which in turn has been substantially lowered in several steps; (ii) reserves have been directly supplied to all the U.S. banks through the Term Auction Facility (while only 19 primary dealers can participate in traditional open market operations); (iii) the range of eligible collateral has been broadened through the Term Securities Lending Facility; (iv) primary dealers have been given access to discount window through the Primary Dealer Credit Facility.18

5 Concluding remarks The lesson we can draw from the above analysis is that the chance of a bad news hitting the market in the future bears important consequences for the equilibrium prevailing in the interbank market. If market participants believe that such a bad news can lead to a gridlock (due to an adverse selection effect), they demand a liquidity premium for lending at maturities longer than very short ones. They fear that an excess of reserves turns later into a shortage: if this should happen, they would come back to the market and find that it is not there any more, forcing them to liquidate some illiquid assets. The liquidity premium can get so high that banks short

16 The Financial Stability Forum has stressed the role of transparency: financial institutions should release reliable information on their risk exposures (including off-balance sheet items and securitized products) to restore market confidence. Regulators and supervisors are invited to act in order to achieve that goal. See FSF (2008). 17 The credit risk incurred by the Eurosystem in providing liquidity became evident when—in autumn 2008—five counterparties defaulted on refinancing operations for a total amount of euro 10.3 billions. The ECB acknowledged that the ABSs submitted as collateral were not liquid. As a consequence, the Governing Council decided that the NCBs should establish a total provision of 5.7 billions in their annual accounts for 2008. See ECB (2009b). 18 See

Cecchetti (2009) for further details.

14

J Financ Serv Res (2012) 41:1–18

of liquidity prefer to borrow short term, originating a “flight to overnight” (despite the fact that by doing so they incur in a roll-over risk). The interplay between credit and liquidity risks plays a crucial role in this framework. The policy implication is twofold. First, more transparency is needed to enable market participants to have a more accurate picture of the distribution of losses following a negative shock. Second, the supply of aggregate liquidity through open market operations may become ineffective under a liquidity crunch; this explains why some central banks have introduced several innovations into their operational framework, which have implied a subsidy to the banking system. Acknowledgements I wish to thank the audience at the Amsterdam POLHIA Workshop (November 2009), the Editor and an anonymous referee of the JFSR for very helpful comments on a previous draft of this paper.

Appendix: The liquidity management problem The crucial decision a bank has to take at t = 0 is whether to trade ST or LT in the interbank market. This choice affects her liquidity position and the actions she has to take in the next period. An analysis of this choice is necessary as a preliminary step, in order to understand how the banks’ payoffs shown below are derived, particularly in the proofs of Propositions 3 and 4. Consider first a bank hit by a positive liquidity shock: she is long of liquidity at t = 0. Suppose she lends ST at this date: – –

if the shock is permanent, at t = 1 she is still long of liquidity: she has to roll over her trade (lend again); if the shock is transitory, her liquidity position is balanced at t = 1: the deposit outflow (from 1 + x to 1) is funded by the incoming repayment of the interbank loan. Now suppose that she lends LT at t = 0:

– –

if the shock is permanent, her position is balanced at t = 1: there is no inflow/outflow of liquidity at this date; if the shock is transitory, she is going to be short of liquidity at t = 1: she will have to fund the deposit outflow (from 1 + x to 1) by borrowing in the interbank market.

The same reasoning applies to a bank hit by a negative liquidity shock: she is short of liquidity at t = 0. Suppose she borrows ST at this date: – –

if the shock is permanent, she is still short of liquidity at t = 1 : she has to roll over her trade (borrow again); if the shock is transitory, her liquidity position is balanced at t = 1: she repays her interbank debt by the deposit inflow (from 1 − x to 1). Suppose instead that she borrows LT at t = 0:



if the shock is permanent, her position is balanced at t = 1: there is no inflow/outflow of liquidity at this date;

J Financ Serv Res (2012) 41:1–18



15

if the shock is transitory, she is going to be long of liquidity at t = 1: she will lend out the deposit inflow (from 1 − x to 1).

Table 1 summarizes the above discussion. It can be noted that if a bank trades LT at t = 0 and the shock turns out to be transitory, her liquidity position is reversed at t = 1 and she has to trade in a way opposite to what she did before. In particular, a bank initially hit by a positive liquidity shock turns out to be short of liquidity in the next period. To the contrary, if a bank trades ST at t = 0 and the shock is permanent, she has to roll over her trade at t = 1. Finally, if a bank trades ST at t = 0 and the liquidity shock is transitory, or alternatively if she trades LT and the shock is permanent, her liquidity position is balanced at t = 1: she does not need to take any action at this date. Proof of Proposition 1 Interbank loans are riskless, so lenders’ reservation price is Rh = x. As an alternative to borrowing, a short bank has to liquidate a share LxG of her loan portfolio, giving up a return LxG VG = xl, with l > 1; so Rh = xl. Hence Rh > Rh : the feasibility condition is met. Due to competition among lenders, the equilibrium price is Rh = x. At this price all banks short of liquidity borrow, since liquidating is more costly.   Proof of Proposition 2 (A) In a pooling equilibrium a lender in the interbank market is repaid with probability (1 − α), so lenders’ reservation price is given by (1 − α)Rl = x. A good bank borrowing in the interbank market has a reservation price Rl = xl. Hence Rl ≥ Rl : the feasibility condition is met. A bad bank never repays an interbank debt, so the expected cost of borrowing in the interbank market is zero, while liquidating would cost LxB V B = xl. Hence she is ready to (promise to) pay any price for borrowing and the feasibility condition is trivially met. x Due to competition among lenders, the equilibrium price is Rl = (1−α) . At this price all banks short of liquidity borrow, since liquidating is more costly. x (B) A good bank short of liquidity has a reservation price xl < (1−α) . Hence the pooling price—obtained in (A)—is not an equilibrium price, since the feasibility condition fails to hold for good banks. Banks long of liquidity are aware that only bad banks are ready to borrow (at any price) in the interbank market, so they do not lend.   Proof of Proposition 3 ST market

ST interbank loans are riskless, so lenders’ reservation price is R1 = x. As an alternative to borrowing, a short bank has to liquidate a share Lx0

Table 1 The liquidity management problem

t=0 Shock 1+x 1−x

Lend ST Lend LT Borrow ST Borrow LT

t=1 Permanent Roll-over (lend again) Do nothing Roll-over (borrow again) Do nothing

Transitory Do nothing Borrow Do nothing Lend

16

J Financ Serv Res (2012) 41:1–18

LT market

of her loan portfolio, giving up a return Lx0 V0 = xl, with l > 1; so R1 = xl. Hence R1 > R1 : the feasibility condition is met. Due to competition among lenders, the equilibrium price is R1 = x. LT interbank loans are repaid with probability π , so lenders’ reservation price is given by π R2 = x and borrowers’ reservation price is given by π R2 = xl. Hence R2 > R2 : the feasibility condition is met. Due to competition among lenders, the equilibrium price is R2 = πx .

At the equilibrium prices R1 and R2 , banks short of liquidity borrow, since liquidating is more costly. All banks are indifferent between trading ST and LT, since the expectation − as of t = 0 − of their final value is as follows.19 The expected value of a long bank lending ST is:20   p V0 + (1 − k)Rh + k(1 − α)Rl − (1 + x) + (1 − p) (V0 − 1) = V0 − 1 (4) The expected value of a long bank lending LT is:21 p [V0 + π R2 − (1 + x)] + (1 − p) {V0 + π R2 − [(1 − k)Rh + k(1 − α)Rl ] − 1} = V0 − 1

(5)

The expected value of a short bank borrowing ST is: p {V0 − [(1 − k)Rh + k(1 − α)Rl ] − (1 − x)} + (1 − p)(V0 − 1) = V0 − 1

(6)

The expected value of a short bank borrowing LT is: p [V0 − π R2 − (1 − x)] + (1 − p) {V0 − π R2 + [(1 − k)Rh + k(1 − α)Rl ] − 1} = V0 − 1

(7)  

Proof of Proposition 4 ST market LT market

The same as in Case (A). LT interbank loans are repaid with probability π . Lenders’ reservation price is given by π R2 − x(1 − p)k(l − 1) = x: the expected cost of funding a LT loan by liquidating at t = 1 must be subtracted from the expected return on such a loan. Borrowers’ reservation price is given by π R2 = xl. It is easy to check that R2 > R2 : the feasibility condition

19 The expectations below are computed by taking the difference between the values of assets and liabilities, including the positions to be taken at t = 1 in the interbank market, if any. Contrary to interbank debt, retail deposits appear in the expressions below with a repayment probability equal to one: this is due to the assumed fair pricing of the deposit insurance scheme, through which any expected liability of the deposit insurer is internalized to the bank issuing deposits. 20 This value is calculated by assuming that the bank rolls over the loan at t = 1, if the liquidity shock is permanent. The same result is obtained if the bank stores the excess liquidity at t = 1 (this could happen because of the aggregate excess liquidity assumed in our set-up).

that if the liquidity shock is transitory the bank has to borrow at t = 1. The probability of repaying this debt in the low state (s = l) is (1 − α), with the information available at t = 0.

21 Note

J Financ Serv Res (2012) 41:1–18

17

is met. Due to competition among lenders, the equilibrium price is R2 = πx 1 + (1 − p)k(l − 1) . Banks long of liquidity are indifferent between lending ST and LT, since the expectation—as of t = 0—of their final value is as follows. The expected value if lending ST is:22 p [V0 + x − (1 + x)] + (1 − p) (V0 − 1) = V0 − 1

(8)

23

The expected value if lending LT is:    p [V0 + π R2 − (1 + x)] + (1 − p) V0 + π R2 − (1 − k)Rh + kxl − 1 = V0 − 1 (9)   At the equilibrium prices R1 and R2 , banks short of liquidity borrow, since liquidating is more costly. They prefer to borrow either ST if p < 12 , or LT if p > 12 (they are indifferent if p = 12 ), since the expectation—as of t = 0—of their final value is as follows. The expected value if borrowing ST is:    p V0 − (1 − k)Rh + kxl − (1 − x) + (1 − p)(V0 − 1) = V0 − 1 − pkx(l − 1) (10) The expected value if borrowing LT is: p [V0 − π R2 − (1 − x)] + (1 − p) [V0 − π R2 + x − 1] = V0 − 1 − (1 − p)kx(l − 1) (11)

References Acharya V, Gromb D, Yorulmazer T (2008) Imperfect competition in the interbank market for liquidity as a rationale for central banking. CEPR Discussion Paper 6984 Acharya V, Shin H, Yorulmazer T (2009) Crisis resolution and and bank liquidity. NBER WP 15567 (forthcoming in Review of Financial Studies) Acharya V, Gale D, Yorulmazer T (2010) Rollover risk and market freezes. NBER WP 15674 Adrian T, Shin HS (2010) Liquidity and leverage. J Financ Intermed 19:418–437 Allen F, Gale D (2000) Financial contagion. J Polit Econ 108(1):1–33 Allen F, Gale D (2007) Understanding financial crises. Oxford University Press Ashcraft A, McAndrews J, Skeie D (2009) Precautionary reserves and the interbank market. FRB of New York Staff Report No.370 Baglioni A, Monticini A (2008) The intraday price of money: evidence from the e-MID interbank market. J Money, Credit Bank 40(7):1533–1540 Baglioni A, Monticini A (2010) The intraday interest rate under a liquidity crisis: the case of August 2007. Econ Lett 107:198–200 Bartolini L, Bertola G, Prati A (2002) Day-to-day monetary policy and the volatility of the Federal Funds interest rate. J Money, Credit Bank 34(1):137–159 Bhattacharya S, Gale D (1987) Preference shocks, liquidity and central bank policy. In: Barnett W, Singleton K (eds) New approaches to monetary economics. Cambridge University Press

the liquidity shock is permanent, the bank either lends x at t = 1 (in state s = h) or stores (in state s = l). In both cases the value of this excess liquidity is x.

22 If

23 Note that if the liquidity shock is transitory and the state is s = l, the bank has to liquidate at t = 1, giving up xl.

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Brunnermeier M (2009) Deciphering the liquidity and credit crunch 2007–2008. J Econ Perspect 23(1):77–100 Brunnermeier M, Pedersen L (2009) Market liquidity and funding liquidity. Rev Financ Stud 22(6):2201–2238 Buiter W, Sibert A (2008) The Icelandic banking crisis and what to do about it. CEPR Policy Insight No.26 Calomiris C, Kahn C (1991) The role of demandable debt in structuring optimal banking arrangements. Am Econ Rev 81(3):497–513 Campbell J (1987) Money announcements, the demand for bank reserves, and the behavior of the Federal Funds rate within the statement week. J Money, Credit Bank 19(1):56–67 Cecchetti S (2009) Crisis and responses: the Federal Reserve in the early stages of the financial crisis. J Econ Perspect 23(1):51–75 Diamond D, Dybvig P (1983) Bank runs, deposit insurance, and liquidity. J Polit Econ 91(3):401–419 Diamond D, Rajan R (2009) Fear of fire sales and the credit freeze. NBER WP 14925 (forthcoming in Quarterly Journal of Economics) ECB (2009a) Euro money market study 2008. European Central Bank ECB (2009b) Eurosystem monetary policy operations in 2008. Press release, March 5, European Central Bank Eisenschmidt J, Tapking J (2009) Liquidity risk premia in unsecured interbank money markets. ECB Working Paper no. 1025 Flannery M (1996) Financial crises, payment system problems, and discount window lending. J Money, Credit Bank 28(4):804–824 Freixas X, Martin A, Skeie D (2010) Bank liquidity, interbank markets and monetary policy. FRB of New York Staff Report No.371 FSF (2008) Report of the Financial Stability Forum on enhancing market and institutional resilience, April 7 Goldsmith-Pinkham P, Yorulmazer T (2010) Liquidity, bank runs, and bailouts: spillover effects during the Northern Rock episode. J Financ Serv Res 37(2–3):83–98 Hamilton J (1996) The daily market for Federal funds. J Polit Econ 104(1):26–56 Hansal C, Jackson J, Merrouche O (2008) Interest rate volatility and the timing of interbank loans in the Sterling money market 2003–2008. mimeo, Bank of England Heider F, Hoerova M, Holthausen C (2009) Liquidity hoarding and interbank market spreads: the role of counterparty risk. ECB, mimeo Huang R, Ratnovski L (2010) The dark side of bank wholesale funding. ECB Working Paper No.1223 (forthcoming in Journal of Financial Intermediation) Norden L, Weber M (2010) Funding modes of German banks: structural changes and their implications. J Financ Serv Res 38:69–93 Pyles M, Mullineax D (2008) Constraints on loan sales and the price of liquidity. J Financ Serv Res 33:21–36 Rochet J-C, Tirole J (1996) Interbank lending and systemic risk. J Money, Credit Bank 28(4):733–762 Rochet J-C, Vives X (2004) Coordination failures and the lender of last resort: was Bagehot right after all? J Europ Econ Ass 2(6):1116–1147 Shin HS (2009) Reflections on Northern Rock: the bank run that heralded the global financial crisis. J Econ Perspect 23(1):101–119 Spindt P, Hoffmeister R (1988) The micromechanics of the Federal Funds market: implications for day-of-the-week effects in funds rate variability. J Financ Quant Anal 23(4):401–416 Taylor J, Williams J (2009) A black swan in the money market. Americ Econ J: Macro 1(1):58–83

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