Mathias Drehmann and Kleopatra Nikolaou · Mathias Drehmann (corresponding author): Bank for International Settlements, Centralbahnplatz 2, CH-4002 Basel, Switzerland, [email protected].

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Funding Liquidity Risk: Definition and Measurement

Mathias Drehmann and Kleopatra Nikolaou

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Funding Liquidity Risk: Definition and Measurement *

Mathias Drehmanna and Kleopatra Nikolaoub

a: Bank for International Settlements b: European Central Bank

July 2008

Abstract: In this paper we propose definitions of funding liquidity and funding liquidity risk and present a simple, yet intuitive, measure of funding liquidity risk based on data from open market operations. Our empirical analysis uses a unique data set of 135 main refinancing operation auctions conducted at the ECB between June 2005 and December 2007. We find that our proxies for funding liquidity risk are typically stable and low, with occasional spikes, especially during the recent turmoil. We are also able to document downward spirals between funding liquidity risk and market liquidity.

JEL classification: E58, G21 Keywords: funding liquidity, liquidity risk, bidding data, money market auctions, interbank markets

* The views expressed in the paper do not represent the views of the BIS or the ECB. We would like to thank Ben Craig, Charles Goodhart, Philipp Hartmann, Bill Nelson, Christian Upper and Götz von Peter as well as seminar participants at the BIS, the Norges Bank and the University of Pireus, Finance Division for helpful comments. The authors alone are responsible for any errors that may remain. Mathias Drehmann (corresponding author): Bank for International Settlements, Centralbahnplatz 2, CH-4002 Basel, Switzerland, [email protected]. Kleopatra Nikolaou: European Central Bank, Kaiserstrasse 29, 60311 Frankfurt am Main, Germany, [email protected].

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1. Introduction The events in August 2007 bore all the hallmarks of a funding liquidity crisis as interbank markets collapsed and central banks around the globe had to undertake massive liquidity injections. Many commentators referred to Bagehot (1873), who understood already in the 1880s that funding liquidity risk can be detrimental for banks. However, notwithstanding more than 100 years of research into funding liquidity risk, a concrete measure using accessible data remains so far elusive. This paper addresses this gap by developing a measure based on banks’ bids during open market operations. Our empirical analysis uses a unique data set of 135 main refinancing operation auctions conducted at the ECB between June 2005 and December 2007. We find that our proxies for funding liquidity risk are typically stable and low, with occasional spikes, especially during the recent turmoil. Our measure also allows us to assess the interactions of market liquidity and funding liquidity risk. Even though downward spirals between both have been a key concern for most policy makers during the turmoil and have been shown theoretically (see Brunnermeier and Petersen, 2007), we are the first to empirically support this theory.

However, measurement without definition is difficult if not impossible. In this paper we define funding liquidity as the ability to settle obligations with immediacy. Consequently, a bank is illiquid if it is unable to settle obligations in time. In this case the bank fails, resulting in losses to shareholders and possibly depositors. Given this definition, it can be said that funding liquidity risk is driven by the possibility that over a specific horizon the bank will become unable to settle obligations with immediacy. In particular we show that funding liquidity risk has two components: future (random) in- and outflows of money and future (random) prices of obtaining funding liquidity from different sources. In contrast to other definitions used by academics and practitioners we show in the first part of the paper that our definitions have important properties, shared by definitions of other risks. First, like solvency, funding liquidity is point-in- time and a zero-one concept as a bank is either able to settle obligations or not. Funding liquidity risk on the other hand can take infinitely many values depending on the funding position of the bank. As any other risk, it is forward looking and measured over a specific horizon.

Our analysis also highlights that funding liquidity is best understood as a flow concept, i.e. a bank is liquid as long as outflows of money are less or equal to inflows and the stock of money. We argue that for funding liquidity risk management not gross but net flows matter. Above all, net in- and outflows of central bank money are crucial, as central bank money underpins the most important settlement and payment

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systems in a modern economy (see CPSS, 2003).1 Therefore, funding liquidity can even be more tightly defined as the ability to settle obligations with central bank money with immediacy. One way to obtain central bank money is to participate in open market operations (OMO) conducted by the central bank. OMOs are conducted in an auction format and we use data from these auctions to measure funding liquidity risk.

In the second part of the paper we show that higher funding liquidity risk leads banks to submit higher bids. We start by reviewing the literature on the underlying sources of funding liquidity risk. This shows that funding liquidity risk is driven by aggregate shocks, incomplete markets and information asymmetries which lead to stochastic prices and stochastic volumes of central bank funds. For severe shocks these swings can actually lead to funding illiquidity and the failure of the bank. If banks are risk averse they would certainly be willing to pay an insurance premium ex-ante to avoid this risk. For severe shocks, asymmetric information can lead to a break down of interbank markets and also implies that banks face credit or informational limits which prevent them from borrowing what they may need. In periods when this constraint is likely to bind, obtaining liquidity from other sources may also be difficult. Attracting retail deposits would be a possibility but it takes time and a large branch network is required to obtain sufficient funds. Asset sales are an alternative but as funding liquidity risk and market liquidity can feed each other in a downward spiral (see Brunnermeier and Petersen, 2007), this may not be optimal.

None of these restrictions apply in the central bank auction where banks can obtain as much central bank funds as they want as long as they provide sufficient collateral. In contrast to other secured markets collateral requirements in the euro area are also very broad, as the ECB accepts a wide range of collateral including some illiquid loans. Furthermore, when bidding the bank in question does not have to fear any reputational effects, which may damage their funding position even further. Taken together these effects imply that, higher funding liquidity risk leads to a higher marginal valuation for obtaining funding liquidity directly from the central bank, especially in periods of stress.

However, bidding in the auction is not only determined by banks’ marginal valuations of liquidity but also by the auction set-up. So far the theoretical literature on OMOs is limited. Overall, the empirical and theoretical evidence strongly supports that a higher marginal value for funding liquidity, which is equivalent to higher funding liquidity risk, leads to higher bids in terms of prices and quantities. Even though bid shading

1 Central bank money consists mainly of reserves held by banks at the central bank.

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will take place (i.e. banks will bid less than their marginal valuation), bids in OMOS are therefore a very good proxy measure for funding liquidity risk.

Our measure significantly improves on other measures used for funding liquidity risk so far. Banks’ own funding liquidity risk measurement such as gap analysis or stress testing is essentially equivalent to a very detailed analysis of the stock flow constraint we suggest in the first part of the paper (see Matz and Neu, 2007, or Banks, 2005). This is very data intensive and relies entirely on confidential information. Whilst we also use confidential data from the ECB, similar data is accessible to other central banks. Furthermore, a second best measure can be constructed from purely public data by simply looking at the difference between the marginal and policy rate.

Aggregate funding liquidity risk has also been measured by the spread between interest rates in the interbank market and a risk free rate (e.g. see IMF, 2008). This is the average price for obtaining liquidity in the interbank market. Even though banks’ own funding costs may differ because of different credit premia, prices in the interbank market are centred round this rate (see Furfine, 2002). In this sense it reflects a key component of funding liquidity risk. But as it is purely a price measure it does not reveal anything about market access, which maybe severely impaired during crisis, nor the volume of net-liquidity demand – the second component of funding liquidity risk. Furthermore, severe doubts have been raised about the quality of interbank market rates during the recent turmoil, as it seems that some banks may have underreported their funding costs.2

Our empirical analysis is based on a unique data set of 135 main refinancing operation (MRO) auctions conducted between June 2005 and December 2007 in the euro area. We effectively have information on the bidding schedules of each of the 877 participating banks in the relevant auctions. We find that our proxies have intuitive properties. Namely, they show persistence at low levels with occasional spikes that funding liquidity risk is supposed to have according to market practitioners (see Matz and Neu, 2007). Moreover, these properties are also shared by measures for market liquidity (e.g. see Amihud, 2002; Chordia et al., 2000, 2002; Pastor and Staumbaugh, 2003). As already discussed, we are also able to show that there are strong negative interrelationships between our measure of funding liquidity risk and a measure for market liquidity. In this sense higher funding liquidity risk implies lower market liquidity. We are able to show that this effect is only present during the turmoil. This

2 See The Wall Street Journal, “Bankers cast doubt on key rate amid crisis”, 16 April 2008. Interbank rates such as LIBOR are fixed by surveying a set of banks each day about their own funding costs. Findings by the Wall Street Journal indicated that actual interbank interest rates have been even higher than indicated by LIBOR during the recent turmoil.

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is exactly what the theoretical work of Brunnermeier and Petersen (2007) would suggest as interactions should only occur once banks face funding liquidity risk.

The remainder of the paper is structured as follows. In Section 2 we introduce our definition of funding and funding liquidity risk. In Section 3 we analyse the sources of funding liquidity risk and show that higher funding liquidity risk will result in higher bids during OMOs. Section 4 introduces our measures. In Section 5 we discuss our data and provide a short overview over open market operations in the euro area. Section 6 analyses the results. Section 7 concludes.

2. Definition of funding liquidity and funding liquidity risk

2.1. Funding liquidity and funding liquidity risk

We define funding liquidity as the ability to settle obligations with immediacy. Consequently, a bank is illiquid if it is unable to settle obligations in time. In this case the bank fails resulting in losses to shareholders and possibly depositors. Obligations should be understood in a very broad sense here as it is not only paying for example depositors but it also includes increases in assets such as new loans or asset purchases. Given this definition it can be said that funding liquidity risk is driven by the possibility that over a specific horizon the bank will become unable to settle obligations with immediacy. In particular we show that funding liquidity risk has two components: future (random) in- and outflows of money and future (random) prices of obtaining funding liquidity from different sources.

It is worth to highlight two important differences between funding liquidity and funding liquidity risk. First, funding liquidity is essentially a zero-one concept, i.e. a bank can either settle obligations or it cannot. This is equivalent to the definition of solvency, where a bank is said to be solvent if the current value of the assets is higher than the value of liabilities. Funding liquidity risk on the other hand can take infinite many values. Second, and more importantly, funding liquidity is a point-in-time concept whilst funding liquidity risk is forward looking. As long as the bank is not in the absorbing state – which in this case is (funding) illiquidity – both states of the world (i.e. being liquid or illiquid) are possible. The likelihood of either depends on the future time horizon considered and the nature of the funding position of the bank. In this respect, concerns about the future ability to settle obligations or the future ability to raise cash at short notice, i.e. future funding liquidity, will impact on current funding liquidity risk. The funding position and the time frame considered will also impact on possible costs the bank has to incur to avoid illiquidity.

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In our opinion a clear distinction between funding liquidity and funding liquidity risk is important and mirrors definitions of other risks. For example a borrower can be in default or not. Looking forward, the borrower has a likelihood of default and in case default materialises the bank will incur losses terms of loss given default.3 Whilst default is a zero-one, point-in-time concept, credit risk is not. The latter is always used as forward looking measure and can take infinite many values, depending on the underlying position of the borrower.

Surprisingly a distinction in the definition of funding liquidity and funding liquidity risk is not made by practitioners and academics. In terms of funding liquidity, the IMF defines it as “the ability of a solvent institution to make agreed-upon payments in a timely fashion” (p. xi, IMF, 2008). This is very similar to ours, even though we argue that it may well be the case that an institution is liquid but solvent. Borio (2000), Strahan (2008) or Brunnermeier and Pedersen (2007) define funding liquidity as the ability to raise cash at short notice either via asset sales or new borrowing. Whilst it is the case that banks can settle all their obligations in a timely fashion if they can raise cash at short notice, the reverse is not true as a bank may well be able to settle its obligations as long as its current stock of cash is large enough. As the ability can vanish (Borio, 2000) this definition is implicitly forward looking and therefore closer associated to funding liquidity risk. The definition of the Basel Committee of Banking Supervision is close to our definition even though it mixes the concepts of funding liquidity and funding liquidity risk. In their view liquidity is “the ability to fund increases in assets and meet obligations as they come due” and they argue that “within this definition is an assumption that obligations will be able be met at a ‘reasonable cost’ ” (p.2, BCBS, 2008).4 While the first part is essentially equivalent to our definition of funding liquidity, the second part is in our view more related to funding liquidity risk even though it is unclear what ‘reasonable’ really means.

Considering the implementation side of the above definitions it is important to consider a more operational definition. In a modern economy many different settlement assets exist (see CPSS, 2003). Generally this is not realised as for example different forms of money in one currency are close substitutes and can be converted into each other at par. The most visible money constitutes of banknotes and coins, but this only plays a minor role as settlement asset. On the other hand, liabilities of commercial banks – which are also referred to as commercial bank money – represent the largest stock of money in the economy. Most transactions, especially those involving private agents, are settled in commercial bank money. However, for banks 3 In addition broader definitions can also incorporate gains and losses from changes in the underlying credit quality and changes in exposure at default. 4 Even though it is implicit that the BCBS is defining funding liquidity it is interesting that this definition talks about liquidity in general.

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funding liquidity risk management central bank money plays a crucial role as this is the one of the most, if not the most, important settlement asset. In the Eurosystem, but also in most other economies, large value payment and settlement systems rely on central bank money as the ultimate settlement asset (see CPSS, 2003).5 Hence, the ability to settle is crucially linked with the ability to satisfy the demand for central bank money. Central bank money, in turn, constitutes mainly of deposits held by commercial banks with the central bank.6 In the Annex the role of central bank money is elaborated further when we talk about funding liquidity as a flow concept. Given its importance in settlement systems and because our measure is directly linked to the availability of central bank money a more narrow view can be taken in the sense that funding liquidity is the ability to settle obligations with central bank money with immediacy.

2.2 Funding liquidity risk as a flow concept

Given the tighter definition it is easy to see that funding liquidity is related to flows, as has been pointed out by Drehmann, Elliot and Kapadia (2007). A bank is able to satisfy the demand for central bank money, and hence is liquid, as long as at each point in time outflows of central bank money are smaller or equal to inflows and the stock of central bank money held by the bank. Following this reasoning, a stock flow constraint provides an easy and straightforward representation:

Outflowst ≤ Inflowst + Stock of Moneyt (1)

A detailed breakdown of the stock flow constraint is given in Annex 1 and identifies four different sources of in- and outflows: depositors, the interbank market, financial markets and the central bank. In- and outflows can also be triggered by on- or off-balance sheet obligations. The constraint highlights therefore the interrelations between the various agents of the financial system in greater detail and offers a broad idea of the various liquidity sources of banks. Importantly, this exposition reveals the substitutability of obtaining liquidity from the central bank or other sources. This motivates the intuition behind the use of the CB auction data as proxies for a measure of liquidity risk.

The net volume of liquidity (i.e. central bank money) needed in order to avoid illiquidity can be represented by a new variable which we call the net-liquidity demand (NLD). We construct this variable from the stock flow constraint. Namely we take the difference between all outflows (Outflows) and contractual (i.e. known) inflows (Inflowsdue) net of the stock of central bank money (M): 5 For a history of central banks’ role in interbank payment systems see Norman et al (2006). 6 Cash and central bank reserves have also be labelled as high powered money in the monetary economics literature (e.g. see Friedman and Schwarz, 1963).

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( )

tnewtsoldIB

tnewD

tnew

tduettt

CBALL

MInflowsOutflowsNLD

,,,, +++≤

−−= (2)

NLD is the net amount of central bank money the bank needs to remain liquid. In case of a deficit (i.e. outflows are larger than inflows and the stock of money), the inequality highlights that NDLt has to be financed either by new borrowing from

depositors ( DnewL ), from the interbank market (IBnewL ), selling assets or accessing the

central bank (CBnew). If there is a positive net liquidity demand which cannot be funded with new inflows, the bank will become illiquid and fail. Conversely, if the bank has an excess supply of liquidity, no borrowing is necessary and liquidity risk is zero.

NDL is uncertain from an ex-ante perspective and random volumes of NDL are the first component of funding liquidity risk.7 Contractual obligations and their maturities are known, even though defaulting counterparties can lead to some randomness. Other components can be rather volatile. As seen during the sub-prime turmoil, off-balance sheet commitment and interbank borrowing can induce large swings in cash flows. Also note that outflows are partly endogenously determined. Under severe stress the bank may decide to cut back on new lending or reduce asset purchases.

Prices of liquidity are also uncertain and depend on the availability of funds from the different liquidity sources. Random prices are the second component of funding liquidity risk. Equation 2 highlights different potential funding sources the bank can access to obtain central bank money. These sources are depositors, the asset markets, the interbank market and the central bank. Ultimately, the choice of the funding source will be determined by the prices of obtaining liquidity from each of the sources.

The underlying sources of random volumes and random prices are further explored in the next section. In addition, we provide greater detail on the stochastic nature of each sub-component in Annex 1 when discussion the stock flow constraint in full.

3. Sources of funding liquidity risk and bidding behaviour In this section we show that banks’ bids during central bank auctions can be used as a proxy for measuring funding liquidity risk. We make this argument in two stages. 7 Ex-post inflows always equal to outflows as long as the bank does not fail. High inflows are always absorbed by asset purchases or new lending, for example in the interbank market. If at the end of the period banks have excess inflows of central bank money they will deposit them with the marginal deposit facility at the central bank.

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First, we show that higher liquidity risk implies a higher marginal value of obtaining liquidity from the central bank. In the second stage we argue that higher marginal valuation results in a higher bid during the central bank auction.

3.1. Sources of funding liquidity risk

The reader may not need a literature survey to be convinced that funding liquidity risk is associated with uncertain volumes and uncertain prices of obtaining liquidity in different markets. Nonetheless, this section provides a brief overview over the underlying reasons for funding liquidity risk which have been identified by the literature.

Importantly, the literature shows that as long as there are no aggregate shocks to funding liquidity and smoothly functioning interbank markets funding liquidity risk is zero. This is for example the case in Allen and Gale (2000) who show that in a fully connected interbank market with no aggregate shocks all idiosyncratic shocks (i.e. shocks to NDL) cancel each other out in aggregate as banks trade liquidity (or in our context central bank money) between each other. Similarly, early papers analysing interbank markets (e.g. Poole, 1968) already establish that prices for central bank liquidity, for example in the Fed’s fund market, equal the policy rate as long as the central bank provides sufficient central bank money and banks can trade freely. Hence, any volume of central bank money desired can be obtained from the interbank market at a fixed price in these models. From an ex-ante perspective the risk is therefore zero as banks cannot become illiquid. A similar argument can also be made for markets in general. If markets are efficient and there is not asymmetric information, banks could never be illiquid but solvent as they could always satisfy the demand for money with immediacy by simply selling assets at their fair value. Hence, the stock flow constraint could never bind as outflows could always be matched by inflows from asset sales.

Clearly the assumptions of no aggregate shocks and smoothly working interbank markets are very strong. Trading in the interbank market may not always be possible especially amid departures from the complete markets and perfect information paradigm. For example, interbank markets can break down because of a “lemons problem” due to asymmetric information (see Flannery, 1996). Co-ordination failures and asymmetric information may also lead to banks hoarding liquidity (e.g. Rochet and Vives (2004) as do doubts about their own ability to borrow in the future (Freixas et al., 2004; Holmstrom and Tirole, 2001). These effects may get strengthened in the presence of Knightian uncertainty (Caballero and Krishnamurthy, 2007). These papers suggest that banks can be rationed out of the system and support the common finding that banks face credit limits in the interbank market. Asymmetric information

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also implies that unusually large requests for funding liquidity can be seen as a negative signal about the solvency and funding position of the borrower. As rumours can spread quickly through interbank market, such a request in turn could trigger further outflows by deposit holders and therefore worsen the funding position of the bank (see Aghion and Dewatripont, 2000).

The structure of the interbank market itself may also aggravate funding liquidity shocks. In Allen and Gale (2000) an incomplete interbank market where not all banks are connected to each other implies that shocks to liquidity can spread through the system. Evidence strongly supports that such a network structure is more realistic than the assumption of an interbank system which is fully connected (e.g. see Pröpper et al, 2008).8 Contagion driven by interlinkages among banks can also arise from highly inter-connected bank payment systems (see Freixas et al., 1999), balance sheet linkages (for a survey see Upper, 2007,) or the cross-holdings of liabilities (see Drehmann et al., 2007; Brusco and Castiglinesi, 2007 and Strahan, 2008). In additional, informational interdependencies may also lead to contagion of funding liquidity shocks from one bank to others (e.g. see Chen, 1999). In addition, banks with excess holdings of central bank money may take advantage of their oligopoly power and strategically under-provide lending in order to exploit the others' failure (Acharya, Gromb and Yorulmazer, 2007), thereby aggravating the illiquidity in the interbank market.

In the literature aggregate liquidity shocks also play a crucial role. For example, in the models of Allen and Gale (2004a, 2004b) these shocks cannot be hedged because of missing (incomplete) markets. In aggregate it is impossible for banks to sell liquidity (i.e. central bank money) when it is plentiful and buy it when it is scarce. Banks have to rather rely on asset sales. Asset prices in turn are determined by ‘cash-in the market pricing’ and asset prices fall below their fundamental value for severe aggregate liquidity shocks. Similarly, Diamond and Rajan (2005) show that individual bank failures can create or exacerbate aggregate liquidity shortages as they shrink the common pool of liquidity (thereby lead to increases in interest rates) and therefore propagate the liquidity shortage to other banks.

Kashyap et al. (2002) focus on the stochastic nature of the net liquidity demand. They argue that banks can reduce this source of funding liquidity risk by offering demandable deposits and credit lines to customers. As long as both are not too strongly correlated liquidity shocks to the asset side are on average partly off-set by liquidity shocks on the asset side. Gatev and Strahan (2006) strengthen their argument

8 There is also evidence that banks need to have credit lines or strong relationships in place to obtain funding from the interbank markets. These relationships are often limited to a few numbers of banks rather than the whole market.

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by showing that banks indeed receive deposit inflows in times of stress when committed credit lines are withdrawn.9 Obviously, committed credit lines to off-balance sheet vehicles have played a central role during the recent turmoil.

The above papers focus mostly on severe shocks leading to liquidity crises and central banks only role is to act as a lender of last resort.10 Following Poole (1968), another strand of the literature focuses on the role of OMOs (regularly undertaken by central banks), marginal facilities and (small) shocks to the aggregate demand for central bank money (for example if government deposits or aggregate cash holdings change). These models rely on functioning interbank markets so that banks are able to trade out individual shocks. However, at the end of the period, after interbank markets close, the market in aggregate may be short (or long) and hence some banks need to access the marginal lending (deposit) facility. The prices for those in turn are fixed. In case of the euro area, banks pay 100bp on-top of (below) the policy rate to access the marginal lending (deposit) facility. These prices constitute an upper and lower bound for the interest rate in the interbank market, which therefore, in these models, purely reflects the expectations about the likelihood of accessing either facility. Generally, the volatility of changes in autonomous factors is very low and in addition can be smoothed out via reserve averaging in the euro area. Nonetheless, as can be observed daily, interest rates in the interbank market fluctuate, which is one of the potential sources of funding liquidity risk.

To conclude, the literature has shown that funding liquidity risk can for example be driven by aggregate shocks, incomplete markets and information asymmetries which lead to stochastic prices and stochastic volumes of central bank funds. Bidding in the central bank auction is one mechanism to partly hedge this risk as it allows the bank to obtain central bank money before liquidity shocks materialise.

Even with functioning interbank markets volatile volumes and prices imply that a risk averse bank would be willing to pay an (insurance) premium to obtain funding in these auctions. But as discussed, interbank market may break down or, more commonly, asymmetric information implies that banks face credit or informational limits which prevent them from borrowing what they may need. In periods when this constraint is likely to bind, obtaining liquidity from other sources may also be difficult. Attracting retail deposits would be a possibility but it takes time and a large 9 The rational for this is a flight to quality as banks have access to emergency liquidity from the central bank and depositors are sheltered from bank failures by the deposit insurance scheme. Pennachi (2006) shows that the negative correlation between deposit inflows and draw down of committed credit lines cannot be observed prior to the introduction of deposit insurance. 10 There is a debate in the literature whether the LLOR should only lend to the market (e.g. Goodfriend and King, 1989) or frictions in the interbank market require bank specific assistance (e.g. Furfine, 1996). This assessment crucially depends on the importance of moral hazard and the underlying frictions in the banking system.

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branch network is required to obtain sufficient funds. Asset sales are an alternative but as funding liquidity risk and market liquidity can feed each other in a downward spiral (see Brunnermeier and Petersen, 2007), this may not be optimal.

None of these restrictions apply in the central bank auction where banks can obtain as much central bank funds as they want as long as they provide sufficient collateral. In contrast to other secured markets collateral requirements in the euro area are also very broad, as the ECB accepts a wide range of collateral including some illiquid loans. Furthermore, when bidding the bank in question does not have to fear any reputational effects, which may damage their funding position even further. Taken together these effects imply that, higher funding liquidity risk leads to a higher marginal valuation for obtaining funding liquidity directly from the central bank. In the next section shows that this higher marginal valuation also translates into higher bids – our proxy for funding liquidity risk.

3.2 Bidding in the interbank market

Bidding behaviour is not only determined by marginal valuations but also by the auction set-up. A detailed discussion of OMOs in the euro area is given in Section 5. For the moment it is important to know that, technically speaking, auctions are organised as price-discriminating multi-unit auctions. In practice it means that bidders can submit multiple bids at different price-quantity pairs subject to a minimum bid rate. Every successful bidder then has to pay her bid. At the marginal rate (or stop-out rate) bids may be rationed so that everyone takes the same pro-rate amount of the remaining available central bank money. The quantity auctioned is announced by the ECB before banks submit bids.

Most theoretical auction models for this type of auction are based on highly stylised set ups and rely on several important assumptions, most importantly that banks are risk neutral and interbank markets are fully functional. Furthermore central banks are assumed to make no policy mistakes and always accurately provide the (expected) amount of aggregate (central bank) liquidity. We have already seen that in such a world, liquidity risk is zero and we conjectured that the marginal value for obtaining liquidity from the central bank is no higher than obtaining it from the interbank market. Indeed Välimäki (2002) and Ayuso and Repullo (2003) show that the optimal strategy for banks in such an environment is to only bid at the expected interbank market rate, which in turn equals the policy rate as the central bank provides the right amount of aggregate central bank money. Hence no bids should be observed above the marginal (which equals the policy rate) minimum bid rate.

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Nautz and Wolfstetter (1997) analyse bidding behaviour of risk averse agents in a multi-unit auction. They assume downward sloping marginal valuation function and show that bid shading occurs – i.e. agents do not bid their full marginal value to realise some gains from the auction. However, in contrast to risk neutrality bid shading is less strong with risk aversion. Their theoretical set-up is not fully applicable to open market operations as no secondary market exists in their model. Hence, the auction is characterised by private rather than common values.

If there is common value set-up and asymmetric (private) information, the well-known “winner’s curse” arises: In single unit auction where bidders do not adjust their bid schedules, the bidder who is most optimistic about the value wins the auction and is therefore likely to overpay relative to the common value of the good.11 Rational bidders will therefore scale their bids downwards. For multi-unit auctions Ausubel (2004) refers to this problem as “champion’s plague” and shows that bidders adjust to this by submitting lower demand schedules. Nyborg et al (2002) argue that with a minimum bid rate, higher uncertainty will lead to greater bid shading and a reduction in the quantity demanded. Furthermore, higher bid dispersion is to be expected. Wang and Zender (2002) show that with risk aversion marginal valuations are downward sloping and bid-shading will occur. The greater the winner’s curse problem the greater the bid-shading will be.

However, there may also be a “loser’s nightmare” in settings where agents who are long after the auction have market power in the secondary market to squeeze players which are short (Nyborg and Strebulaev, 2004).12 Given initial differences in allocations, this implies that bidders with large short positions bid more aggressively during the central bank auction. In our context it means that banks which are short of central bank liquidity (i.e. face higher liquidity risk) submit higher bids. Välimäki (2006) explores a model with risk averse banks which aim to achieve a target level of central bank balances. This seems realistic to assume as banks aim to ensure a certain degree of liquid balances for risk management purposes. Even though Välimäki cannot fully solve the model, he shows that a higher liquidity deficit by the bank and higher the risk aversion leads to a steeper bid curves.

Bindseil et al (2005) find empirical evidence in ECB auctions that bid shading decreases as volatility increases. Other tests also support that the winner’s curse problem in the repo market is less important than risk aversion or the loser’s nightmare. They conclude from this evidence that borrowing from the interbank

11 In a multi-unit set-up the winner’s curse problem is also referred to as champion’s plague (Ausubel, 2004) 12 Acharya et al. (2008) show that this can happen in the interbank market. They cite several historical episodes of severe funding pressures where this effect seems to have played a role.

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market is not a perfect substitute from borrowing from the central bank directly as the interbank market maybe characterised by too many frictions to smooth out all shocks.

4. Measuring funding liquidity risk Overall, the theoretical and empirical literature shows that higher funding liquidity risk implies a higher marginal valuation which in turn is linked to higher bids during OMOs. As bid-shading occurs these bids do not perfectly reflect the marginal value for funding liquidity. Nonetheless bids provide an ordinal measure of funding liquidity risk.

To construct this measure we use normalised individual bank bids (price and quantity submitted in the MROs) which we name the adjusted bid. We define the adjusted bid (AB) of bank i at auction t as a normalised variable of the bid price times the bid volume for successful bids, that is

t

tibtibti allotmenttotal

volumespreadAB

_* ,,,,

, = (4)

where, tibspread ,, is the bid price and the (allotted) tibvolume ,, the bid volume of bank

i, submitting from bid b (from 1 to B) at time (auction) t. spreadi,b,t equals the bid_rate i,b,t minus the policy_ratet. We only consider successful bids, i.e. the prices for which the demanded volume was granted by the central bank, albeit rationed. The bids are normalised by the total allotment supplied by the central bank during auction t. The normalization of bids is necessary to remove changes in the monetary policy stance and ensure consistency across auctions which can differ in size.

Based on the individual normalised bids we can construct an aggregate proxy of funding liquidity risk by summing across the adjusted bids of all banks. Following that reasoning, our first liquidity risk proxy (LRP) is simply the sum of all individual adjusted bids across banks for each auction.

∑∑==

=B

bti

N

it ABLRP

1,

1

, (5)

where b (from b=1 to B) are the bids of each bank i (from i=1 to N ) for each time (auction) t.

This proxy contains two categories of bidders: The ones who bid at the marginal rate and the ones who bid above the marginal. As discussed above without frictions and risk neutral banks all banks should bid at the marginal rate (see e.g. Ayuso and Repullo, 2002). It is therefore not certain to what extent the first group of bidders

15

paying a premium to acquire liquidity. Therefore we look at a second proxy for funding liquidity risk only capturing bids above the marginal rate13, namely

( )∑ ∑∑= =

−==

i

N

i

B

b t

tibtibtit allotmenttotal

volumeratemarginalratebidABLRP

1 1

,,,,, _

*)__(1_1_

Figure 1: A central bank auction and the funding liquidity risk measures.

Area A

Area B

Total allotment

Volumes

Note: Thick black line is the aggregate demand curve. LRP=[(Area A + Area B)/ total allotment], LRP_1=[Area A / total allotment]

Figure 1 provides a graphical representation of our two measures using one auction as an example. The two axes present the bid price (vertical) and the bid volumes (horizontal). The aggregate demand curve is the downward sloping, kinked thick black curve. LRP is nothing else than the normalised area under this demand curve as it equals Area A plus Area B divided by the total allotment. The figure also shows that LRP nests LRP_1 (Area A divided by the total allotment). Given our normalisation by the total allotment, it can be easily shown that the difference between the LRP and LRP_1 equals the spread between the marginal rate (at this time 2.3%) and the policy rate which is also the minimum bid rate (at this time 2.25%).

5. Data and open market operations in the euro area Our analysis is based on a unique data set of 135 MROs conducted by the ECB from June 2005 to December 2007. ECB data for MRO auctions allow us to follow the bidding behaviour of each of the 877 banks that took part at least once those years.

13 However, in cases of turmoil, the marginal rate can be well above the policy rate, therefore eliciting a premium in all successful banks. This is currently happening in the eurosystem’s auctions.

16

Information includes an anonymous but unique code for each bidder, the submitted bid schedule (bid rate and bid volume) of each bank and the allotted volume. These data are not publicly available. Further data on the policy rate (minimum bid rate), the marginal rate, the maintenance periods and the settlement dates of the auctions are taken from the ECB's internet site.

Before discussion our results it may be useful to provide more a more thorough discussion on the institutional background of open market operations in the euro area for those who are less familiar with OMOs. In the euro area around 95% of central bank money is provided via the main financing operations (MROs), which are conducted weekly and have a maturity of one week and the long term refinancing operations (LROs), which are conducted less frequently and have a maturity of 3months.14 These OMOs are conducted as standard flexible rate tenders.

As MROs form the basis of our measure we discuss them in more detail. During each MRO auction eligible banks can submit bids (volume and price) at up to ten different bid rates at the precision of one basis point (0.01%). Prices and volumes are unconstrained, except for the minimum bid rate, which equals the policy rate set by the Governing Council. Banks are only required to submit sufficient collateral for the allotted liquidity. The auction is price-discriminating, i.e. every successful bidder has to pay its bid. At the marginal rate, depending on the bid schedule, bids may be rationed, so that everyone takes the same pro rata amount of the remaining liquidity.

To calibrate the allotment volume in the weekly MROs, the ECB takes the sum of the outstanding autonomous factors (such as banknotes, government deposits and net foreign assets) and banks' reserve requirements.15 The allotment volume that satisfies exactly these needs for central bank money in aggregate is called the "benchmark allotment". An ECB forecast of the autonomous factors on which basis the benchmark allotment is calculated is published prior to the bidding of the banks in the MRO.

During a maintenance period when reserve requirements are fixed, the aggregate demand for central bank money can only change in line with autonomous factors such as for example a change in the demand for banknotes. As already discussed, all

14 Additionally the ECB conducts fine tuning operations, if there is a need for an additional and extraordinary injection or absorption of central bank money. 15 In the Euro area individual banks have to fulfil reserve requirements. Banks are allowed to hold positive or negative (relative) reserve balances with the CB within a specified period (i.e. relative to their requirements banks can hold more or less. Negative current accounts, so-called intraday credit, have to be collateralised and will be referred to the marginal lending facility at the end of the day). However reserve requirements have to be fulfilled on average across the maintenance period (usually between 28 and 35 days). At the start of the maintenance period the reserve requirements are determined by the Eurosystem for each bank and remain fixed during the period. The settlement day of the first MRO marks the start of the maintenance period. In addition, since April 2004, this is the day on which interest rate decisions of the Governing Council of the ECB become effective.

17

transactions between banks are settled with central bank money, at least if we consider the large important banks in the euro area. An outflow of central bank money of one institution is the liquidity inflow of another. Hence, the total sum of reserves does not change just the distribution within the system. This holds even during extreme liquidity stress scenarios such as a bank run. In this case depositors withdraw all their (matured) funds from the bank. If they deposit it with another bank, then this constitutes an inflow at another institution and hence the aggregate volume of reserves does not change.

6 Results

6.1 Funding liquidity risk

Our results are presented in Figure 2. In general we observe that funding liquidity risk is time varying and persistent, but subject to occasional spikes. These properties bode well with measures for market liquidity (Amihud, 2002; Chordia et al., 2000, 2002; Pastor and Staumbaugh, 2003; Brunnemeier and Pedersen, 2007).

For both our proxies, however, we see that liquidity risk is elevated in the recent turmoil period. The biggest spikes of our measures are at the end of our sample, when we observe the reaction of the banking system to the credit market turmoil (especially in August and December 2007). Most practitioners would certainly agree that the recent months have been the most risky event in terms of funding liquidity in our sample.16

Figure 2. LPR and LRP_1

16 By including a separate dummy for 2007 in the regression the high spike is essentially removed from the LRP_s.

18

0.1

.2.3

01jul2005 01jan2006 01jul2006 01jan2007 01jul2007 01jan2008date

LRP LRP_1

Year end effects are very pronounced especially at the end of 2005 and 2006. These effects are well known by practitioners and in the literature. For example, Bindseil et al (2003) argue that banks may engage in window-dressing to establish favourable end of year balances. Clearly, these seasonality effects are unrelated to liquidity risk as they are driven by bank managers’ desire to signal a specific balance sheet to the market rather than by a reaction to funding pressures.

In Figure 3 we therefore report the measures when simply dropping the date for the three year ends.17 Table 1 provides the summary statistics for this data. It is apparent that both LPR and LPR_1 increase during the turmoil following 9 August 2007. Both more than double on average. The increase in volatility is also enormous, especially for LRP which increases more than ten-fold.

Figure 3. LPR and LRP_1 (excluding year ends)

17 This is essentially equivalent to running a regression of the measure on three dummy variables for each year end.

19

0.1

.2.3

01jul2005 01jan2006 01jul2006 01jan2007 01jul2007 01jan2008date

LRP LRP_1

Note: Light blue horizontal line indicates the beginning of the turmoil (here 14 August when the first MRO was undertaken after the turmoil started). Red horizontal lines indicate changes in the policy rate. Green dots indicate starting dates of new maintenance periods. Year ends not shown.

Table 1: Statistics (excluding year ends)

LRP LRP_1Turmoil Normal Ratio Turmoil Normal Ratio

mean 0.167 0.064 2.59 0.021 0.009 2.34variance 0.00234 0.00021 11.07 0.00012 0.00003 3.65min 0.090 0.025 3.63 0.001 0.0001 3.79max 0.294 0.107 2.74 0.041 0.032 1.30 Note: Normal indicates the period from June 2005 until 7 August 2007. Turmoil is the remaining period until December 2007. Ratio equals Turmoil/Normal.

It is also interesting to note that bid rates initially did not pick up significantly after the turmoil started in 9 August 2007. This can be explained by the fact that in the first few days the ECB undertook several significant fine tuning operations. By the beginning of September both measures increase. However, the larger wedge than normal starts to appear. This suggests that banks on average faced significant funding pressures which lead to a rise in the spread of the marginal rate above the policy rate

20

(see Figure A1 in Annex 2, which shows the policy rate, the marginal rate and their spread). By construction this effect cannot be picked up by LRP_1, which highlights that certain bids were even more aggressive despite the already increased level of the marginal rate).

This suggests that the marginal rate provides an important – but second best – signal about aggregate funding liquidity risk in the market. Whilst individual bids are not publicly observed, the marginal rate is published by the ECB immediately after each auction and can be downloaded from its website. In an environment where publicly available data on funding liquidity risk are scarce, this provides a valuable source of information. The statistics in Table 1 highlight what is obvious from the graph: there are several peaks prior to the turmoil which are nearly as high as during it. The maximum during the latter period is only a factor 1.3 higher than during normal times (for LRP it is nearly three). This is initially surprising but can partly be explained. First most of these spikes happen at dates when the marginal rate was equal or very close to the policy rate and all bidding banks were more or less satisfied. As a result, the area captured by the two measures was approximately the same, which is why we observe a drop in LRP for the same dates.

A closer inspection of Figure 2 also reveals that spikes in LRP_1 prior to the turmoil are generally associated with the end of maintenance periods (green dots indicate the start of a new maintenance period) and or changes in the monetary stance (indicated by the red horizontal lines). Given the clear communication by the ECB the market certainly anticipated the latter. Theoretically, these changes in the stance should not impact on bidding behaviour as changes in the policy rate only become effective with the first MRO of a maintenance period. However, it appears to be the case the changes in the monetary policy rate impact on the bidding behaviour of banks.

6.2 Funding liquidity risk and market liquidity

Brunnemeier and Petersen (2007) have shown theoretically that there should be strong interactions between funding liquidity risk and market liquidity. Once, banks (or brokers in their model) become funding constraint a downward spiral of falling asset prices and higher funding liquidity risk can emerge. In this case falling asset prices will lead to higher margin calls, i.e. increase funding liquidity risk as outflows increase. To remain liquid banks have to sell assets, which depresses market prices even further (because of a lack of market liquidity), leading to further margin calls and so forth. This downward spiral can also start with higher marginal calls initially.

21

Whilst the theoretical exposition is clear and many observers attribute the recent turmoil to these interactions, it has not been shown empirically due to a lack of measures for funding liquidity risk. Using our measure we are able to empirically support these interactions by looking at the interrelationships between our measure LRP and an index of market liquidity used by the ECB Financial Stability Review in June 2008 (see ECB, 2008) (see Figure A2 Annex 2 for a time series). This index is a weighted average of different market liquidity measures such as bid-ask spreads in FX, equity, bond and money markets.

Figure 4 shows a scatter plot of LRP and the ECB market liquidity index. A clear negative relationship can be seen, i.e. when market liquidity is drying up (i.e. is low), funding liquidity risk is high (which would be equivalent to saying that high funding liquidity risk is associated with high market liquidity risk). The red line shows the predicted values based on a simple regression of the index on LRP. These results are shown in Table 2. The scatter plot already suggests that the negative relationship is primarily driven by the turmoil. The econometric analysis supports this as there is no significant relationship between our measure of funding liquidity risk and market liquidity prior to the turmoil.18 However, once the turmoil unfolds a significant negative relationship emerges. This is exactly what the theory predicts as these interactions should only emerge once banks become funding constraint. Therefore this analysis strongly supports the theoretical insights by Brunnermeier and Petersen (2007).

Figure 3: Interactions between funding liquidity risk and market liquidity

18 Similar results emerge when undertaking the same analysis with LRP_1 and the spread between the marginal and policy rate. Interestingly, the R-squared is highest for LRP (.76) and lowest for LRP_1 (.26) whilst the regression with the spread between the marginal and policy rate has an explanatory power of .66 (R-squareds are given for the regression using the full sample).

22

-3-2

-10

1E

CB

mar

ket l

iqui

dity

inde

x

0 .1 .2 .3LRP

Normal TurmoilFitted values

Note: Normal indicates the period from June 2005 until 7 August 2007. Turmoil is the remaining period until December 2007. Fitted values are based on the regression using the whole sample.

Table 2: Regression results of market liquidity index on LRP

Coefficient Standard Error P-value R-squaredFull sampleLRP -9.47 0.51 0.00 0.73constant 1.03 0.05 0.00

NormalLRP -0.08 0.50 0.87 0.00constant 0.46 0.03 0.00

TurmoilLRP -6.30 2.36 0.02 0.30constant 0.32 0.41 0.44 Normal indicates the period from June 2005 until 7 August 2007. Turmoil is the remaining period until December 2007.

7 Conclusion In this paper we propose definitions of funding liquidity and funding liquidity risk and present a simple, yet intuitive measure of funding liquidity risk, based on information from the liquidity providing operations of the central bank. We define funding

23

liquidity as the ability to settle obligations with immediacy. However, given the importance of central bank money in modern settlement and payment systems, we use a more operational definition of liquidity as the ability to satisfy the demand for central bank money with immediacy. Accordingly, funding liquidity risk is driven by the possibility that over a specific horizon the bank will become unable to settle obligations (with central bank money) with immediacy. We show that funding liquidity risk has two components: future (random) in- and outflows of money and future (random) prices of obtaining funding liquidity from different sources. We then discuss how higher funding liquidity risk can in turn lead to higher bids during OMOs conducted by the central bank.

Using information from a data set of 135 MROs conducted by the ECB from June 2005 to December 2007, we construct two measures of funding liquidity risk, which aim to take into account the (normalised) information of both the price and the quantity of the liquidity demanded. Unsurprisingly, we find that the resulting measures record spikes after August 2007, indicating the presence of increased funding liquidity risk as would have been expected. We also find that our measures bear resemblances with market liquidity and have properties such as low levels, persistence and occasional spikes, which market practitioners using confidential information have identified. Finally we are able to find evidence that there is indeed an inverse relationship between funding liquidity risk and market liquidity risk.

Our analysis is certainly only a starting point in using bidding data to assess funding liquidity risk. It would certainly be interesting to implement our measure for different jurisdictions, such as the United States. There the provision of central bank money is significantly different. Daily OMOs are only conducted with a narrow set of broker dealers, who rely on settlement banks to settle all their transactions (hence they generally settle in commercial bank money). More in line with the auctions described above which should are the newly introduced Term Auction Facility.19 Here banks can bid directly for central bank money with the maturity of one month. Even though the auction is conducted as a single-price auction format it should be possible to use bids as a measure for funding liquidity risk based on our approach. Another important issue is that bids can be affected by variables such as year end effects of differences in collateral values which are not associated with funding liquidity risk. In a follow-up paper by Drehmann, Eisenschmied, Linzert and Nikolaou (2008) we use econometric techniques to filer out these effects. Preliminary results indicate this to be a promising approach.

19 For further details see http://www.federalreserve.gov/monetarypolicy/taf.htm.

24

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Diamond, D and Dybvig, P (1983), “Bank runs, deposit insurance, and liquidity,” Journal of Political Economy, Vol. 91, pages 401-19 Diamond, D. W. and Rajan, R. G. (2005). "Liquidity shortages and banking crises'', Journal of Finance, Vol. 60 (2), 615-647. Drehmann, M., J. Elliot and S. Kapadia (2007), “Funding Liquidity Risk: Potential Triggers and Systemic Implications,” mimeo, Bank of England Drehmann, M, J. Eisenschmidt, T. Linzert and K. Nikolaou (2008), “Measuring Funding Liquidity risk”, mimeo ECB (2004), The use of central bank money for settling securities transactions ECB (2007), Financial Stability Review, December ECB (2008), Financial Stability Review, June Flannery, M. J. (1996). "Financial Crises, Pament System Problems, and Discount Window Lending'', Journal of Money, Credit and Banking, Vol. 28 (4), 804-24. Furfine, C. (2002), "The Interbank Market during a Crisis'', European Economic Review, Vol. 46 (4-5), 809-20. Goldstein I. and A. Pauzner (2005), “Demand Deposit Contracts and the Probability of Bank Runs,” Journal of Finance, 60, 1293-1328.

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Annex 1: Funding liquidity and funding liquidity risk as a flow concept

A1: Funding liquidity

In this Annex we provide a more granular view of the key components of funding liquidity. Taking the narrower perspective we have argued that funding liquidity can be defined as the ability to satisfy the demand for central bank money with immediacy. A bank is able to satisfy the demand for central bank money, and hence is liquid, as long as at each point in time outflows are smaller or equal to inflows and the stock of central bank money (M) held by the bank. This lead to the stock flow constraint discussed in the text:

Outflowst ≤ Inflowst + Stock of Moneyt (1)

Table A1: Components and sources of in- and outflows of money

Outflow Inflow

Depositors ( )DdueDdueDnew AIAL ++ ( )DnewDdueDdue ALIL ++

Interbank ( )IBdueIBdueIBnew AIAL ++ ( )IBnewIBdueIBdue ALIL ++

Asset market soldA boughtA

Off-balance sheet items outOB inOB

Central Bank ( )otheroutMROdueMROdue CBCBICB ++ ( )otherinMROnew CBCB + Where:

• L/A are liabilities and assets of the bank;20 • LI/AI/CBI are interest payments paid or received by the bank; • IB/D stands for interbank and other depositors (or borrowers); • due stands for assets and liabilities which are contractually due in the period; • new stands for assets and liabilities newly issued; new can also include liabilities or assets

which are rolled over; • OB are off-balance sheet items which can contribute to out- or inflows; • Assets can also be sold/bought on the secondary market; • CBMRO are central bank balances obtained from the weekly main refinancing operations; • CBother are in- and outflows of central bank balances obtained directly from the central bank

but not in the weekly refinancing operations, for example by accessing the marginal lending or deposit facility or participating in fine tuning operations.21

20 These include assets and liabilities in both the banking and trading book. 21 In the Eurosystem reserves are also remunerated which constitute are part of otherinCB .

29

Note: Liquidity will also be determined by other cash flows which can be inflows such as fees and commissions or new equity capital, or outflows such as costs or dividend payments.

Table A1 provides an overview of key components of in- and outflows and attributes them to the five main funding sources. Note that in order to keep sub-indices to a minimum, t was dropped in Table A1. The reader should keep in mind that time plays an important role for funding liquidity. For liquidity risk management purposes, banks also have to distinguish between different currencies the bank is active in. The stock flow constraint has to hold in each currency but as long as foreign exchange markets are functioning, (funding) liquidity can be transferred. We therefore ignore currency differences in our analysis. The analysis of the stock flow constraint and its components gets also more complicated if the banking system is tiered and some small banks use corresponded banks to participate in the settle and payment system or the central bank auctions. Even though tiering is not uncommon in banking systems, we do not take account of this in our discussion below, but instead focus on the main systemically important banks which also participate in the auctions.

The first source of inflows and outflows is driven by behaviour of depositors. A bank receives an inflow of money if borrowers pay back their loan and/or interest (Adue+AIdue) or by receiving new deposits (Lnew). Similarly, outflows can be a result of depositors withdrawing money (Ldue), the bank paying interest (LIdue) or the bank issuing new loans (Anew). Note that not all withdrawals of depositors have to necessarily lead to a change in central bank balances. A large bank can settle a lot of transactions on its own book. If for example consumer A pays company Y and both have an account at the same bank this transaction gets settled in the bank’s own money. If however company Y has an account with another bank, the transfer between the banks is ultimately settled in central bank money. Even though it may be the case that, depending on the settlement system, only net transfers between both banks at the end of the day are settled in central bank money (CPSS, 2003)

The second source is different from the first one only insofar as we distinguish between interbank markets and other depositors/borrowers. Distinguishing is important because the behaviour of interbank markets and other depositors is significantly different. The latter are generally very sluggish to react and do not monitor banks very well. This was exemplified by the run on Northern Rock in 2007 after it had to ask the Bank of England for an emergency loan as it was frozen out of interbank markets. Only once this was granted did retail depositors realise that Northern Rock was vulnerable and started the run, which then was self-perpetuating until all deposits were guaranteed. A further difference between depositors and the interbank market is that all transfers between large banks are settled in central bank

30

money. In the euro area these transfers take place in TARGET222 which is a real time gross settlement system (RTGS), i.e. payments are settled continuously and in gross rather than net amounts.

Whether in- and outflows are secured or not does not matter for the flow analysis. Therefore, repo transactions are also contained in the interbank flows. However, depending on the legal structure, repos can also be asset sales/purchases with a binding agreement to reverse the trade in the future. Asset sales/purchases are the third component in the stock flow constraint. For the conceptual analysis it is not important to distinguish asset sales/purchases from the trading book from those of the banking book. However, practically they differ as equity and bonds held in the trading book can often be traded on organised exchanges in relatively liquid markets (in the sense of market liquidity).23 Whilst assets held in the banking book are sold and purchased for example via securitisation programmes “over the counter”. This requires more time and effort and markets tend to be less liquid, especially during times of stress as could be observed recently (ECB, 2007). Practically, asset sales from the trading and banking book also differ how they are settled. Whilst many over the counter transactions are settled in the payment system and hence involve central money, the interaction of central bank money and securities settlement systems is more complex. A survey by the ECB (2004) highlights the range of practices in the euro area. Settlement can be effectively real time as in Crest in the UK or there can be settlement cycles such as the overnight cycle use by Monte Titoli (Italy) where central bank money is only involved to settle net amounts. Nonetheless, central bank money to achieve finality in the settlement of at least net-transfers always plays an important role.

The fourth source is cash in- and outflows from off-balance sheet activities. An important part of liquidity demands from off balance sheet items (OBout) are committed credit lines to companies or off-balance sheet vehicles such as conduits (see IIF, 2007, BIS, 2006). Essentially, are drawn credit line is a new obligation for the bank. In that sense they could be included in Lnew. However, for expositional purposes we present them in a separate group as they proved to be a key transmission channel from liquidity problems in the structured credit to the interbank market during the recent turmoil (see ECB, 2007). In addition, margin calls, which are also part of OBout, can have a significant impact on cash flows. However, as part of their contingency preparation, banks themselves generally have contingent liquidity lines with other banks (OBin). 22 TARGET2 became operational in November 2007 and replaced the previous TARGET system. 23 Depending on the settlement system, securities settlement generally involves central bank money, especially in the euro area (see ECB, 2004) again indicating the crucial role for central bank money in the economy.

31

The last source of the stock flow constraint is for our empirical analysis the most important one as banks can obtain new central bank money from the central bank directly. These are also important from a system perspective as all transactions discussed so far do not change the amount of central bank money but represent a transfer from A to B. Only direct interactions can change the aggregate amount of central bank money in the economy.

Given our empirical measure we distinguish MROs and other interactions with the central bank. MROs are based on repo-arrangements and have a maturity of one

week. Hence, new borrowing ( MROinCB ) can only be obtained against collateral but the

transaction is reversed at the end of the maturity. At this point the bank faces an outflow of central bank money, which also includes interest payments

( MROdueMROdue CBICB + ). In- and outflows of central bank money (

otherinCB or

otheroutCB ) are

also generated when banks access the marginal lending or deposit facility (also referred to as the discount window) or if banks participate in fine tuning operations or long term refinancing operations. In the Eurosystem reserves are also remunerated which constitutes another type of inflows of central bank money. In an extreme case, the central bank may also act as a lender of last resort and provide a struggling bank with an emergency loan as the Bank of England has done for Northern Rock. This is

also captured by otherinCB .24

A.2 Funding liquidity risk

In the main text we define funding liquidity risk as driven by the possibility that over a specific horizon the bank will become unable to settle obligations with central bank money with immediacy. We argue there that it is has two main components: random in- and outflows and random prices of obtaining liquidity from different sources.

This becomes apparent by looking at the net liquidity demand (NLD). This is constructed by reworking the stock flow constraint, namely we take the difference between all outflows (Outflows) and contractual inflows, including inflows from off-balance see items (Inflowsdue) net of the stock of money.

( )

otherin

MROnewsold

IBnew

Dnew

tdue

CBCBALL

MInflowsOutflowsNLD

++++≤

−−= (2)

24 Banks’ direct access to central bank money differs significantly across jurisdictions as has been shown in the short discussion in Section 7 about differences in the US and Europe. Collateral accepted is also different for different countries. In many countries such as the US accessing the marginal facilities is also associated with a stigma and may have reputational repercussions for the bank. Stigma is the euro area is less pronounced.

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As discussed in the main text ex-ante inflows and outflows are uncertain. Contractual obligations (assets and liabilities due) and their maturities are known, even though defaulting counterparties can lead to some randomness. Other components, such as

the inflow of new retail deposits (part of DnewL ), are relatively easy to predict under

most circumstances as a large part of customer deposits are constantly rolled over. As already mentioned, off-balance sheet items (OBout) or the re-investment behaviour of

large and sophisticated investors (part of DnewL ) as well as other banks (IBnewL ) are more

difficult to predict. As seen during the sub-prime turmoil, these components can induce large swings in cash flows. Also note that outflows are partly endogenously determined. Under severe stress the bank may decide to cut back on new lending (Anew) or reduce asset purchases (Abought).

We have also briefly touched on random prices from obtaining liquidity from different sources in the main text. Equation 2 highlights the different funding sources. and the choice of the funding source will be determined by the prices. Given a large branch network, commercial banks rely heavily on deposits from other depositors and

the interbank market ( DnewL and IBnewL ). Whilst consumer deposits receive a low

remuneration pD which is often below the risk free rate (e.g. see Corvoisier, S and Gropp, R, 2002), interbank interest rates (pIB) can be volatile. However, customer deposits are sluggish to react and it takes time for a bank to increase its customer funding base. Hence, liquidity shocks in the short run cannot be smoothed out from this source in contrast to interbank funding. Asset sales can be another key source of funding, especially for investment banks. From a funding liquidity risk management perspective the price of Asold (pA) is not only determined by the fundamental value of the asset but also by the (market) liquidity of market the asset is sold in.25 It is well known that (market) liquidity is not constant (see e.g. Amihud, 2002). Furthermore, the majority of banks’ assets are illiquid in the sense that they cannot be sold with immediacy without suffering a large discount. This is essentially the underlying reason why a solvent bank can become illiquid.26

Finally, looking at central bank channel for liquidity, prices for obtaining central bank liquidity directly also differ. As was explained in the main text the price pMRO for 25 Please note that Asold is used in a very broad sense as banks do not only sell (and buy) items in the trading book such as equities, bonds or more complex products. More generally, they also sell assets from the banking book, e.g. via outright sales or securitization programs. 26 In a world with perfect information and perfect capital markets, a solvent bank can always satisfy the demand for money with immediacy by selling assets at their fair value in a fully liquid market (in the sense of market liquidity). Hence, liquidity risk is zero for the bank in this hypothetical world.

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MROnewCB is determined by the bank’s bid during the weekly refinancing operation and

the bids of other banks. Prices CBotherp for otherinCB can also be determined by bids

submitted during open market operations (e.g. for a long term refinancing operation) or for accessing the marginal facilities. The latter are non-stochastic as central banks generally charge a fixed term spread above the policy rate, equalling a 100bp in case of the Eurosystem. This spread effectively constitutes an upper bound to prices for short term liquidity.

The notation used for Equation 2 is flexible enough to capture bank runs or a lack of collateral: getting rationed out the interbank market or becoming the target of a

depositor run would for example mean that ∞→IBD pp / . Similarly, when the bank

runs out of collateral ∞→CBMRO pp / as a bank cannot obtain any funding from the

central bank without collateral, as discussed above.

Taken together the stock flow constraint highlights that funding liquidity risk from the perspective of an individual bank is driven by stochastic in- and outflows as well as by stochastic prices for liquidity, which in turn are the key determinants in deciding which funding source banks want to access. Hence, liquidity risk over a one week horizon (and before the bank takes part in the weekly refinancing operations) is determined by the joint distribution of prices and volumes F.

∫ ∫ ++++= ),..,(),..,(.. otherinDotherinDotherinCBotherMROnewMROsoldAIBnewIBDnewD CBpdCBpfCBpCBpApLpLpF (3)

Putting it differently, F characterises the distribution of possible total costs the bank could have to pay over the next week to be able to satisfy the demand for money in all possible circumstances. In line with credit or market risk, a possible liquidity risk measure would then be the tail of the distribution, e.g. measured by VaR at the 99th percentile (see McNeil, et al. 2006). Ideally, we would therefore want to measure this distribution directly. But it is characterised by an endogenous choice on the part of the bank which funding source it wants to access. More importantly, most components are unobservable and neither their current level nor their distributional properties are known.

A.3 The theoretical literature and the stock flow constraint

The reader may be interested to know that the theoretical literature can be reformulated into the stock flow constraint. Starting with the seminal work by

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Diamond and Dybvig (1983),27 in their model, depositors who want to consume early (period 1) or late (period 2) cannot be distinguished by the bank, and deposits of both

are contractually due ( DdueL ) in the early period. Cash (M1) held by banks is used to

payout early depositors in period 1. If there is no crisis, late depositors roll over their

deposits ( DnewL ) so that total cash inflows equal cash outflows. But if late depositors do

not roll over their deposits – that is if there is a bank run – the bank is forced to sell assets to satisfy all cash outflows (Asold). As the bank is only able to realise heavily discounted prices for their assets (i.e. markets for the banks’ assets are illiquid) not enough cash can be raised. Therefore, the stock flow constraint is not satisfied and the bank fails.28 In this sense the market liquidity of the assets held determines funding liquidity risk.

The stock flow constraint can also capture the downward spiral of funding and market liquidity risk (see for example Brunnermeier and Pedersen, 2007). Assume a severe drop in asset prices which induces higher margin calls (part of OBout).29 In a situation where the bank (or in these models the broker) cannot attract new deposits or raise liquidity with the central bank (i.e. Lnew=CBnew=M=0), higher margin calls can only be satisfied by selling assets (Asold), which lowers asset prices further because of a lack of market liquidity. In turn this raises margin calls, leading to increased funding liquidity demands and so forth.

Kashyap et al. (2002) argue that banks can reduce liquidity risk by offering demandable deposits and credit lines to customers as long as both are not too strongly correlated. Gatev and Strahan (2006) strengthen the argument by showing that banks receive deposit inflows in times of stress when committed credit lines are withdrawn. The rational for this is a flight to quality as banks have access to emergency liquidity from the central bank and depositors are sheltered from bank failures by the deposit insurance scheme.30 In our notation, their argument is about the joint distribution of

the volume of new deposits ( DnewL ) and the draw down of committed credit lines (part

of OBout).

Even though the stock flow constraint is bank specific, the key sources also drive system wide liquidity risk. Allen and Gale (2004, 2005) analyse for example liquidity in a general equilibrium set-up. As markets are incomplete, aggregate shocks cannot

27 A similar argument applies for models, where bank runs on individual banks are driven by adverse information (e.g. see Chari and Jagannathan, 1988, or Goldstein and Pauzner, 2005). 28 All other components of the stock flow constraint are not captured by the model. 29 In these models, Net Income, Assets(new/bought), and Liabilities(due) are all zero. The model also considers only borrowing and lending to other depositors D. 30 Pennachi (2006) shows that the negative correlation between deposit inflows and draw down of committed credit lines cannot be observed prior to the introduction of deposit insurance.

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be hedged. Hence, a system wide high demand for funding liquidity ( DdueL high and DnewL low) can only be satisfied by banks by selling assets (Asold). However, the market

is characterised by a ‘cash in the market’ constraint and thus prices pA are lower than justified by fundamentals (i.e. market illiquidity crystallises). Similarly, literature on contagion via direct exposures in the interbank market (LIB/AIB) (see Upper, 2007 for a survey) and /or via lower asset price interacting with marked-to-market accounting can also be viewed though the stock flow constraint (see e.g. Cifuentes et al, 2005, or Shin, 2008).

Reminiscent of the credit turmoil in 2008, Flannery (1996) analyses liquidity provision in the interbank market. In contrast to the analysis by Goodfriend and King (1988), where the interbank market always distributes the aggregate liquidity through the system, interbank markets in Flannery’s model can break down because of a “lemons problem”. In his model, banks are uncertain about the fundamentals of loan applicants in the interbank market as well as their own ability to evaluate these credits. In the spirit of Akerlof, the lemons problem will increase the price from borrowing in the interbank market (i.e. pIB) or, if significant, lead to a break down of the interbank market (i.e. pIB →∞). Flannery also highlights the role of the central bank as he shows that in crises it can be welfare enhancing for the central bank to provide liquidity below the market price (i.e. pCB

36

Annex 2: Additional Figures

Figure A1: Interest rates in the euro area

0.1

.2.3

spre

ad

22.

53

3.5

44.

5