Contagion in the interbank market: Funding versus regulatory constraints

Journal of Financial Stability 18 (2015) 1–18

Contents lists available at ScienceDirect

Journal of Financial Stability journal homepage: www.elsevier.com/locate/jfstabil

Contagion in the interbank market: Funding versus regulatory constraints夽 Oana-Maria Georgescu a,b,∗ a b

Deutsche Bundesbank, Wilhelm-Epstein-Straße 14, 60431 Frankfurt am Main, Germany Goethe University Frankfurt, Grüneburgplatz 1, 60323 Frankfurt am Main, Germany

a r t i c l e

i n f o

Article history: Received 5 February 2014 Received in revised form 6 June 2014 Accepted 12 February 2015 Available online 25 February 2015 Keywords: Contagion Mark-to-market accounting Funding constraints

a b s t r a c t The contagion potential of mark-to-market accounting rules interacting with regulatory constraints is compared to that of funding constraints in a network of banks. The fair value accounting rules were amended at the height of the crisis to break the vicious link between allegedly irrational market prices and regulatory constraints. Anecdotal evidence from the recent crisis suggests that funding constraints posed more serious problems to banks than regulatory constraints. Simulation results show that, for low equity and high levels of short-term debt relative to liquid asset holdings, the contagion potential arising due to funding constraints is higher than the one due to accounting induced regulatory constraints. Allowing balance sheet valuation to affect the expectations about future insolvency, and implicitly, the roll-over decision of short-term creditors, can mitigate or amplify systemic risk depending on which contagion channel is dominating. These results could be interesting for a regulator wishing to achieve a trade-off between transparency, the main goal of fair value accounting, and financial stability. © 2015 Elsevier B.V. All rights reserved.

1. Introduction This paper compares the contagion potential of mark-to-market accounting rules interacting with regulatory constraints to that of funding constraints in a network of banks during a crisis. Markto-market valuation has been criticized for fuelling the balance sheet contagion channel during the 2007–2008 financial crisis. Critics blame the accounting regime for creating a mechanical link between the decrease in asset prices, accounting losses and the resulting asset fire sales needed to satisfy regulatory constraints (see for example Merrill et al., 2012; Allen and Carletti, 2008; Wallison, 2008; Forbes, 2009). The latter, the argument goes, will create additional downward pressure on prices, leading to further write-downs and regulatory constraints of banks holding the

夽 I want to thank Cristian Badarinza for support and useful discussions, as well as Ben Craig, Co-Pierre Georg, Josef Hollmayr, Julia Körding, Jan Krahnen, Christian Laux, Joseph Schroth, the anonymous referee and numerous seminar participants. I am grateful to the Frankfurt Institute for Risk Management for Financial Support. The views expressed in this paper do not reflect the position of the affiliated institutions. All remaining errors are my own. ∗ Correspondence to: Deutsche Bundesbank, Wilhelm-Epstein-Straße 14, 60431 Frankfurt am Main, Germany. Tel.: +49 (0)69 9566 5152. E-mail address: [email protected] http://dx.doi.org/10.1016/j.jfs.2015.02.003 1572-3089/© 2015 Elsevier B.V. All rights reserved.

same asset and applying mark-to-market valuation, reinforcing the above mentioned spiral. Anecdotal evidence from the 2007 to 2008 crisis shows that illiquidity, and not regulatory insolvency due to large fair value losses lead to the demise of systemically important banks. Banks like Bear Stearns, Lehman Brothers, Fortis and Northern Rock experienced a silent run on their wholesale funds, although their regulatory capital ratios were adequate.1 These funding constraints eventually spread to other banks in the system, potentially generating a negative feedback between funding constraints and asset fire sales. This type of contagion was potentially more serious than the one described by the asset fire sale – regulatory constraints channel, as frequently argued in the debate on the procyclical character of fair value accounting. The theoretical literature on contagion due to funding constraints focuses on the combination of the decrease in the collateral value and the resulting increase in roll-over risk. In Gai et al. (2011), a shock to repo haircuts deteriorating the liquidity condition of all banks funded through repos leads to liquidity hoarding that eventually spreads to all banks in the system. In Brunnermeier and Pedersen (2009) the drop in asset prices causes margin calls and

1

See Shin (2009) for a detailed account on the run on Northern Rock.

2

O.-M. Georgescu / Journal of Financial Stability 18 (2015) 1–18

asset fire sales, depressing prices even further. Gai et al. (2011) also considers the interaction of various network properties with these liquidity constraints, but they exclude asset fire sales as a source of liquidity. Overall these papers do not consider the negative feedback between regulatory constraints, the reporting regime and the resulting assets fire sales. This paper considers both contagion channels in isolation and simultaneously. Their effect is not simply additive, since they are allowed to interact. In particular, liquidity risk interacts with future solvency risk, similar to Gauthier et al. (2010). The difference to their setting is that solvency risk arises due to the combination of regulatory constraints, mark-to-market accounting and asset fire sales. Regulatory constraints are deteriorated due to the negative feedback between falling prices and asset fire sales. Depending on which contagion channel dominates, the mutual reinforcement of the two channels is mitigated in the presence of unsecured debt. The roll-over decision on unsecured debt depends on the markto-market balance sheet value. Asset fire sales needed to satisfy regulatory constraints deteriorate the balance sheet value, possibly affecting the roll-over decision on unsecured debt. If the creditor considers that the default probability in the next period is too high, he will cut the unsecured credit line and ask for collateral, basing his roll-over decision on the value of the collateral. The creditor will update her roll-over decision conditional on the market value of the collateral, forcing banks to engage in fire sales, thus amplifying funding constraints. The paper has four main findings. First, across a wide range of possible network structures, contagion risk increases with the degree of maturity transformation and decreases with the size of the liquidity buffer of banks in the network. In addition, the relationship between interconnectedness and system stability depends on the size of the initial shock to asset values. It seems that the funding constraints and the regulatory constraints channel have different thresholds for the size of the initial shock beyond which more interconnections amplify contagion. Second, at low levels of capital and high short-term debt relative to liquid asset holdings, the contagion potential is higher due to funding than due to accounting induced regulatory constraints; in contrast, when equity is high, funding constraints dominate regulatory constraints irrespective of the level of the liquidity buffer and the interbank short-term debt. Third, activating both contagion channels in the absence of unsecured debt leads to a mutual reinforcement of the two channels. Fourth, allowing the two contagion channels to interact through the relevance of accounting information for the roll-over decision on unsecured debt can mitigate or amplify systemic risk depending on which channel is dominating. The intuition for these findings is that market discipline acts as a complementary tool to regulatory constraints. Low capitalized banks are sanctioned by the regulator through regulatory constraints. Even when banks are adequately capitalized from a regulatory perspective, the constraint imposed by creditors can be stricter than the one imposed by the regulator. Both the regulatory constraint and the roll-over decisions are relaxed by a higher liquidity buffer and a lower level of interbank short-term debt, albeit at a different rate. The dominance of one of the two channels is explained by the different sensitivity to these variables. The initial level of net worth plays a larger role for the regulatory constraints channel, implying that increasing capital is more effective in reducing solvency risk than liquidity risk. Intuitively, the latter is more sensitive to the degree of maturity transformation and the value of posted collateral. Thus, funding constraints are related to market valuation, can lead to contagion, and exist independently of the accounting regime. When the secured funding constraint is more binding than the regulatory constraint, allowing the two channels to interact can mitigate systemic risk. This is because

allowing accounting information to affect the funding decision of short-term creditors enables the access to unsecured debt, making asset fire sales due to funding constraints less likely. Fair value accounting rules were relaxed at the height of the crisis after intense pressure from politicians and banks, allegedly in order to level the playing field with US banks and to enhance financial stability. The results show that the vulnerable balance sheet structure of banks poses a larger threat to financial stability than the balance sheet valuation per se. This source of vulnerability may be better addressed through adequate regulatory tools, like the NSFR and the LCR ratio,2 rather than by changing the accounting regime. These results could be interesting for a regulator wishing to achieve a trade-off between transparency, the main goal of fair value accounting, and financial stability. The rest of the paper is organized as follows: Section 2 outlines the related literature, Sections 3–5 present the model and the extensions, Section 6 describes the data used to calibrate the model, Section 7 discusses the results and Section 8 concludes. 2. Related literature This paper contributes to two strands of literature. The first is the literature on mark-to-market contagion arising due to the interplay between the accounting regime and regulatory constraints. The second strand of literature relates to the contagion due to funding constraints. The reference setup on contagion due to the interplay between accounting and regulatory constraints belongs to Cifuentes et al. (2005). Contagion arises due to direct interbank links, common assets and asset fire sales depressing the value of the common assets in a network of banks facing regulatory constraints. In this setting, a higher liquidity buffer and capitalization mitigates contagion. Gauthier et al. (2012) use this setting to derive implications for macro-prudential capital requirements. Nier et al. (2007) study how the relationship between network connectivity and system fragility changes in the presence of asset fire sales driven by the default of one bank in the system. In the absence of liquidity effects due to asset fire sales, the relation between network connectivity and system stability is hump-shaped. Introducing asset fire sales outweighs the shock absorbing capacity of increased connectivity. This effect is particularly pronounced at low levels of net worth of the banks in the system. Allen and Carletti (2008) show how the mark-to-market accounting regime can play a key role in the contagion between the banking and insurance sector. The net asset value of banks turns negative because they hold the same asset as the insurance sector. Market frictions lead to liquidity pricing in bad states of the world, unrelated to the fundamental value of the asset. The funding constraints of these banks are not an issue for banks in Allen and Carletti (2008). It could be that banks pledge the same asset whose price is subject to liquidity pricing as collateral. These banks could face funding constraints before the regulatory constraints become an issue. This aspect is modeled in this paper in a network setting. The literature on contagion due to funding constraints does not consider the negative feedback between regulatory constraints and the accounting regime. The link between market liquidity and funding constraints is analyzed by Brunnermeier and Pedersen (2009). Margins increase as prices drop, as they are a function of asset price volatility. Arbitrageurs must finance the haircut on their investments with their own capital and they will be forced to sell assets in order to satisfy margin calls, depressing prices even further. This leads to higher margins

2 NSFR and LCR are the Net Stable Funding Ratio and the Liquidity Coverage Ratio as defined under Basel III.

O.-M. Georgescu / Journal of Financial Stability 18 (2015) 1–18

and tougher funding constraints. Similar results are obtained by Gorton and Metrick (2011), who document empirically the relation between increased counterparty risk and the haircuts charged on the repo market for collateralized lending. The assumption that financial institutions use fire sales to raise liquidity in a crisis is also supported by Allen and Carletti (2008), Adrian and Shin (2010) and Diamond and Rajan (2011). Adrian and Shin (2010) provide empirical evidence on the balance sheet adjustments undertaken by financial intermediaries to accommodate a shock in asset prices. The procyclicality of leverage affects aggregate liquidity and has important asset prices consequences. Diamond and Rajan (2011) study the conditions under which banks undertake fire sales to accommodate a liquidity shock. They show that fire sales of some banks in the system lead to a decrease in price that makes further asset sales unattractive for the rest of the banks, since they would fail even by doing so. Instead, these banks prefer to maximize the value of their assets conditional on survival and will wait for better times, thus curbing the downward spiral in asset prices. Numerous empirical papers on bank networks analyze contagion through direct interbank links and credit losses, either based on actual or estimated interbank exposures (see Upper, 2011 for a more comprehensive overview). In general, these papers find that the contagion potential due to direct interbank links is low (see Furfine, 2003 for the US, Wells, 2002 for the UK, Mistrulli, 2011 for the Italian, Lublóy, 2005 for the Hungarian and Sheldon and Maurer, 1998/Müller, 2006 for the Swiss market). In contrast, Upper (2004) finds that in the absence of safety mechanisms like the institutional guarantees for saving banks and Landesbanken, the German interbank market is highly susceptible to contagion after the failure of one bank. Memmel et al. (2012) analyze the resilience of the German interbank market to an exogenous shock using bilateral data at different points in time and conclude that the assumption of a constant loss-given-default rate tends to underestimate contagion risk. Most of the simulations using actual interbank data show that entropy maximization techniques do not yield a satisfactory approximation of the actual interbank market (see for example Mistrulli, 2011; Van Lelyveld and Liedorp, 2006). Some simulations also consider the effect of liquidity hoarding (Furfine, 2003; Müller, 2006). Furfine (2003) uses payment flow data from the Federal Reserve’s large-value transfer system to simulate contagion due to counterparty failures and liquidity hoarding. The effect of counterparty failures is contained, with total assets of defaulting banks accounting for less than 1% of system-wide assets. He finds that the illiquidity of the largest lender has a greater potential for contagion than the failure of that institution. Müller (2006) analyzes the contagion in the Swiss interbank market using actual bilateral data on credit lines. A shock to the network affects banks due to the default of debtor banks, because they fail to repay their debt and but also due to the default of lender banks, since they cut credit lines. In his setting, a high capital buffer does not supplement a low liquidity buffer. In this paper, domino effects due to the failure of a counterparty do play a role but they are of secondary importance. The focus is rather the effect of contagion due to a combination of asset commonality, funding and regulatory constraints and the resulting fire sales. Several papers use simulated data to analyze the spillover of funding risk and contagion in a bank network. Gai et al. (2011) model funding liquidity risk in a network of banks, showing how system fragility depends on liquid asset holdings, the structure of the interbank network and the size of the haircut on the bank’s assets. Liquidity effects and contagion via funding constraints amplify systemic risk through the decrease in the value of collateral used in repo transactions. Gai et al. (2011) exclude fire sales as a source of liquidity that can be obtained to satisfy margin constraints, arguing that liquidity hoarding is the main channel

3

through which funding constraints are transmitted through the network. Elliott et al. (2014) analyze the probability and the extent of contagion depending on network integration and diversification. They distinguish between these two properties in a simulation setting and find non-monotonic effects, with the middle-ranges identified as the most dangerous. Gauthier et al. (2010) use a twoperiod model to study the interaction between solvency risk and liquidity risk in a network of banks. They find that higher capital reduces solvency risk but not liquidity risk and that higher liquid asset holdings can, to some extent, compensate for the higher systemic risk implied by large levels of short-term debt. Morris and Shin (2009) discuss the regulatory implications of liquidity risk in an interconnected financial system and conclude that imposing higher liquidity requirements and introducing a simple measure for leverage should enhance financial stability. Brunnermeier (2009) discusses the liquidity spiral at the core the 2007–2009 crisis and show how runs on financial institutions can have network effects when the institutions are borrowers and lenders at the same time. The contagion mechanism via funding constraints is similar in the setup of this paper. The literature on the relation between funding risk, collateral value and contagion emphasizes the critical role of information during stress times. Anand et al. (2012) study the effect of debt maturity and news arrival on systemic bank failure in a network of banks. They show that when the cost of coordination failure faced by a bank’s creditors is high, they are highly sensitive to the arrival of bad news and changes in the asset liability ratio of the debtor bank, precipitating a bank run. Interbank linkages lead to the propagation of this shock to the rest of the system. The negative effects that imprecise information can have on the efficiency of wholesale funding are modeled by Huang and Ratnovski (2011). The disciplining effects of short-term wholesale funds are diminished in the presence of a noisy public signal on the bank’s project quality because the imprecise signal increases monitoring costs, resulting in inefficient liquidations. Acharya et al. (2011) analyze the market freeze in the market for short-term secured borrowing market in a theoretical setting. Their main result is that the debt capacity of an asset depends on the rate at which information on the asset arrives relative to the frequency at which debt has to be rolled over. The debt capacity is always lower than its fundamental value, and it reaches extremely low values when debt has to be rolled over frequently. In the setting of this paper, the relevance of information for the funding constraints of banks is modeled by letting the rollover decision on unsecured debt depend on the accounting balance sheet value. The precision and frequency of information arrival is not the focus here. The idea is that in the absence of accounting information the unsecured lending market freezes and is crowded out by the secured funding market. This can amplify systemic risk due to the margin spiral described by Brunnermeier and Pedersen (2009). 3. The model The two contagion channels rely on a similar mechanism, because both channels are reinforced by the negative feedback loop between asset fire sales and prices. However, while the first channel leads to balance sheet contagion due to the link between mark-tomarket valuation and regulatory constraints, the second channel arises irrespective of the accounting regime due to a combination of an increase in roll-over risk, asset fire sales and higher haircuts charged for collateralized lending. Although avoiding a fragile balance sheet structure could avoid the funding constraints of these banks, their balance sheet structure is not determined endogenously within the setting of this paper. The intuition is that banks

4

O.-M. Georgescu / Journal of Financial Stability 18 (2015) 1–18

Table 1 Stylized balance sheet.

to satisfy (1). Rewriting (1), each bank will first sell the amount ti of the liquid asset ci according to:

Liquid assets, ci Interbank claims, xic Illiquid assets, ei Fixed assets, fi

Interbank debt, xi ST debt (world), di Deposits, Di Equity, Ei

 ti = min ci , max

will always choose a vulnerable balance sheet structure if the probability of a run is sufficiently low, as shown by Chang and Velasco (2000). Each of the two channels are activated in isolation to establish under which conditions one of the two channels dominates. In a second step, the two channels are allowed to interact and the results are compared to the setting where they exist independently. The benchmark setting is provided by Cifuentes et al. (2005). Assumptions regarding the capital buffer, the liquidity ratio, the interbank linkages and price elasticity are needed. Similar to Cifuentes et al. (2005), a network of N banks is assumed, where each bank holds an amount ei of the illiquid asset, an amount ci of the liqN uid asset and interbank claims x  of bank i from bank j, with j=1 j ij ij the weight of bank’s i claim in bank’s j total liabilities. For sim-

N

x  is referred to as xic . The total amount of interbank plicity j=1 j ij assets in the system matches the total amount of interbank liabilities. In line with Gai et al. (2011), liquid assets are assumed to be assets that can be sold without a price discount and can be pledged without a haircut for collateralized borrowing. Illiquid assets can only be sold at a discount during the crisis, and the amount of borrowing that can be obtained using the illiquid asset as collateral is limited by a haircut. The rest of the assets on the bank’s balance sheet are fixed assets fi , for example loans, that cannot be sold to satisfy regulatory constraints or pledged as collateral to obtain short-term funds. Table 1 below displays a stylized balance sheet. di is the short-term debt to the outside world, Di are the longterm liabilities of bank i to outside creditors, for example depositors and xi interbank short-term debt. Interbank claims are assumed to be short-term. Thus, the source of vulnerability comes from the short-term nature of the liability, but also from the type of funds used. 3.1. Balance sheet contagion: accounting induced regulatory constraints Banks not able to satisfy the capital constraint will sell ti units of the liquid asset and si units of the illiquid asset for cash, for which there is no capital requirement, thus reducing the denominator. All banks have to satisfy the following capital constraint: ci + p1 ei + xic + fi − xi − di − Di (ci − ti ) + p1 (ei − si ) + xic + fi

≥ r∗

(1)

With p1 the equilibrium market price of the illiquid asset at time t = 1. The short-selling restriction implies: si ∈ [0, ei ] and ti ∈ [0, ci ]. The equilibrium price p1 of the illiquid assets is given by the market clearing condition which can be rewritten as3 :



p1 = exp

N 

−˛



si

(2)

−

 0, ci + p1 ei + xic + fi

ci + xic + p1 ei + fi − xi − di − Di



r

(3)

The sale of the liquid asset for cash decreases the denominator in Eq. (1) because cash does not carry a risk weight. If the capital requirement is still not satisfied, the bank will sell the amount si of the illiquid asset: si = min [ei , max (0, ei −

1 [c + p1 ei + xic rp1 i

+ fi − xi − di − Di − r(ci + xic + fi − ti )])]

(4)

The equation above implies that there is always a buyer for the illiquid asset ei . Assuming for simplicity that deposits yield a return RD and that the price p2 of ei will return to its fundamental value of 1 at period 2, the investment in ei will clearly be preferred to the investment in deposits as long as: RD <

1 −1 p1

Assuming RD = 3%, it can easily be verified that the condition above will be satisfied for a value of si ≥ 0.05 * ei (implying a value for p1 < 0.96).4 A bank cannot sell more than ci of the liquid asset and ei of the illiquid asset. It will sell 0 if the capital requirement is satisfied. At the new price, derived from Eq. (2), some banks will have negative equity. Banks with negative equity are declared insolvent. Their assets are distributed proportionally among creditors, according to their seniority. Depositors and outside short-term creditors have the highest seniority, followed by interbank creditors.5 After outside claims Di and di are paid off, the remaining assets are distributed proportionally to creditor banks. Thus, actual payments xi∗ are below required payments xi . The payment vector respects the limited liability of banks. Two main algorithms are used in the literature in order to determine the payment vector: the sequential default algorithm proposed by Furfine (2003) and the fictitious default algorithm proposed by Eisenberg and Noe (2001). The sequential default algorithm assumes that banks default sequentially after an initial shock and ignores any feedback effects between the defaulting banks and the previously solvent banks. Thus, the losses on the interbank claims from banks failing in the previous rounds are constant. Most papers use the sequential default algorithm, since it is easier to implement (see for example Amundsen and Arndt, 2005; Blåvarg and Nimander, 2002; Degryse and Nguyen, 2007; Elsinger et al., 2006). Similar to Cifuentes et al. (2005), Elsinger et al. (2006) and Müller (2006), this paper uses the fictitious default algorithm proposed by Eisenberg and Noe (2001) for determining the payment vector, as it has the advantage that it addresses the problem of

i=1

After an initial shock to the asset values of a bank in the system, each bank determines the amounts ti and si it needs to sell in order

3 To ease the interpretation of results, the price elasticity ˛ is chosen such that when all assets e in the system are sold the price drops to 0.5. Thus,

˛ = ln(0.5)/

N

i=1

ei in (2).

4 Economically there is a fundamental difference between investors in assets like structured products or repos (ei ) that engage in active portfolio management, and unsophisticated depositors. Structured products and repos are assets that can be reposted as collateral to obtain liquidity, whereas deposits cannot be used for this purpose. For this reason the former would most likely prefer to invest in ei . 5 Depositors typically enjoy a higher seniority because of deposit insurance. The higher seniority of short-term debt to the outside world is meant to emphasize the endogenous fragility resulting from bilateral interbank claims.

O.-M. Georgescu / Journal of Financial Stability 18 (2015) 1–18

higher order feedback effects. The payment vector is the solution of a fixed point problem, with the payment vector of banks defaulting in the first round being continuously updated as higher order defaults occur. The Eisenberg and Noe (2001) algorithm is structured as follows: 1 After an initial shock, the available payments are computed for each bank, assuming that all other banks are solvent. If all the liabilities in the system can be satisfied, the algorithm terminates. 2 If some banks default, even though all other banks are solvent, the available payments are computed again for all the banks in the system, assuming that only first order defaults occur. If only first order default occur, the algorithm terminates. 3 This procedure is repeated for a maximum of n times, until no more nth order defaults occur in the system. It should be noted that these iterations are only a computation tool, in fact contagion occurs instantaneously. xi∗ = max(min(xi , ci + p1 ei + xic + fi − di − Di ), 0)

(5)

If ci + p1 ei + xic + fi − di − Di < 0, there are no interbank payments and xi = xi∗ = 0. Following Eisenberg and Noe (2001), the 

payment vector X* is obtained from the mapping x ∗ → FF x∗ (x∗ ): 

FF x∗ (x∗ ) = (x∗ )

T ij





(x∗ )x∗ + [I − (x∗ )]x + c + p1 e + f

+ [I − (x∗ )]x

(6)

where D(x* ) is the set of defaulting banks under x* and (x* ) an NxN diagonal matrix, with (x∗ )ij = 1 if i = j and i ∈ D(x* ) and 0 otherwise. Multiplying other matrices with (x* ) converts the corresponding entries corresponding to nondefaulting nodes to 0. The first term in Eq. (6) returns the node values for banks defaulting under x* , assuming that nondefaulting nodes, (I − (x* )), pay x, the required payments, and defaulting nodes, (x* ), pay  x∗ . The last term returns the node values for banks not defaulting under x* , assuming that all nondefaulting banks pay the required amount x. The fixed point x* is determined such that the differ ence FF x∗ (x∗ ) − FF x∗ (x∗ ) is minimized. A numerical example of the clearing vector is provided in Appendix. Balance sheets are again evaluated using the new vector of payments. Some banks will have to sell illiquid assets, leading to a new price p. The process results in the equilibrium vector (X* , S* , P* ) of payments, sales and price of the illiquid asset. The relation between the new vector of payments and the price is shown in Fig. 1. There is no formal expression for the equilibrium price, but its properties can be characterized. The equilibrium price is defined in conjunction with the equilibrium vector of sales and payments (X* , S* , P* ). When only regulatory constraints are active, the equilibrium price is the price for which: (i) the market clearing condition in Eq. (2) is satisfied. (ii) after selling the minimum quantity of assets si as defined in Eq. (4), all non-defaulting banks satisfy regulatory constraints. (iii) for all banks, the vector of payments is defined as in Eq. (5). 3.2. Contagion due to funding constraints The contagion mechanism described above focused on the asset side of the balance sheet and assumed that banks only face regulatory constraints. During the recent financial crisis, many banks

5

faced funding constraints on the interbank market before regulatory constraints became apparent.6 The same balance sheet structure and price function are assumed as in Eqs. (1) and (2), respectively. However, the funding constraint depends on the value of assets placed as collateral (ci and ei ) and the level of short-term debt. Creditors form expectations on asset price volatility and apply a haircut to the value of the illiquid asset ei used as collateral. They will roll-over short term debt if their value-at-risk constraint is satisfied. The margin/haircut m1 is derived similar to Brunnermeier and Pedersen (2009):  = Pr

 −p ≥ m  2 1 I1

(7)

where p2 is the change in the price of the illiquid assets from t = 1 to t = 2, I1 is the information set at t = 1 and m1 is the margin required by the creditor using as collateral an asset worth p1 . The derivation of the margin is based on the following important assumptions: the change in the fundamental value evolves according to a random process, the price of the illiquid asset is the best proxy for its fundamental value and creditors set their margin such that the value-at-risk constraint is satisfied. The expectations of the creditors on the asset prices in Eq. (7) need not match the market clearing condition and the resulting price process in Eq. (2). Creditor banks do not know the amount of assets that other banks sell and have no information on the price function in Eq. (2). They form expectations on the price process taking the current price as given. They assume that there is a deviation from the fundamental value, , which may be due to liquidity pricing or due to a change in the fundamental value of the asset ei . In the absence of other information, they assume that the price process is random.7 The detailed derivation of the margin, in line with Brunnermeier and Pedersen (2009) is presented in Appendix. The required margin is given by: ¯ m1 = ¯ + |p 1|

(8)

A sufficient condition for the margin requirement to be satisfied is: ci + (p1 − m1 )ei > xi + di

(9)

The amount of short-term debt a creditor is willing to extend depends on the value of the collateral, the illiquid asset ei , less a haircut. Short-term debt is the sum of interbank debt and shortterm debt to the outside world, as in Eq. (9). Whenever the value of the collateral does not satisfy the margin requirement, the bank will try to pledge ti units of its liquid asset and if that is not enough use the cash proceeds from the sale of si units of illiquid assets to compensate for the decrease in the collateral value. If the bank cannot satisfy the margin call the creditor will refuse to roll-over the existing debt and the bank is declared insolvent. Similar to Gai et al. (2011), the underlying assumption is that the central bank does not accept collateral at better terms than the market. Moreover, there is no depositor inflow or outflow and the bank cannot raise fresh equity. Unlike Gai et al. (2011), who distinguish between unsecured interbank borrowing and collateralized lending, at this stage

6 When the interbank market dried out, banks with a high reliance on short-term debt found it more and more difficult to renew their commitment. The Belgian bank Dexia for example had to pledge 4 times more cash collateral in 2008 than in 2007, from D 6.2bn in 2007 to D 26.4bn in 2008, while funds obtained from other bank decreased by D 64 bn in the same period. Dexia Annual Report 2008, pp. 138, 154. 7 See Jarrow, 2013 for an intuitive derivation of regulatory capital requirements from the regulator’s value-at-risk constraint and a discussion on the analogy between this approach and the haircut charged by creditors for collateralized lending.

6

O.-M. Georgescu / Journal of Financial Stability 18 (2015) 1–18

shock to asset value

yes

conditional on accounting balance sheet value: rollover unsecured debt? ** yes

no

yes satisfy regulatory constraint? *

no roll-over secured debt? (satisfy funding constraint?)***

no sfund= 0

sfund > 0

sreg > 0

sreg = 0

s = max(sfund, sreg)

determine new price

evaluate balance sheet (run Eisenberg/Noe algorithm)

* Equation (1) ** Equation (16) *** Equation (9)

determine vector of payments and default matrix Fig. 1. Interplay between funding and regulatory constraints.

all short-term lending, including interbank lending, is assumed to be collateralized. The experience of the 2007–2008 crisis has shown that this is the preferred form of lending during a financial turmoil. In the next section this assumption will be relaxed and unsecured interbank lending will be allowed up to a certain level of bank specific credit risk. Each bank not satisfying the margin constraint will have to sell ti units of the liquid asset; if that is not enough, implying that ci = ti , the bank will sell si units of the illiquid asset: ti + p1 si + (ei − si )(p1 − m1 ) > xi + di

(10)

Rewriting (10), si becomes: si =

xi + di − ei (p1 − m1 ) − ti m1

value-at-risk condition in Eq. (7) is evaluated with the new equilibrium price. The process stops when there is no unsatisfied margin call (or default). The payment and the resulting default matrix is estimated as in Eq. (5) resulting in the equilibrium vector of payments, sales and price of the illiquid asset. The equilibrium vector (X* , S* , P* ) is defined similar as for the regulatory constraints channel, where condition (i) requires that the equilibrium price satisfies the market clearing condition in Eq. (2) and in addition that the margin is derived according to expression Eq. (8). Condition (ii) requires that the minimum quantity of assets to be sold is defined as in Eq. (11). 3.3. Funding and regulatory constraints

(11)

All banks forced to sell the illiquid asset will simultaneously determine the amount si of the illiquid asset thrown on the market and the new equilibrium price is determined as in Eq. (2). The

For both contagion channels the endogenous amplification of the initial shock is achieved via the asset fire sales spiral. The relevant variable in order to compare the potential for contagion for the mark-to-market versus illiquidity contagion channel is the quantity of assets sold on the market in order to satisfy regulatory constraints, sreg,i and funding constraints, sfund,i . If sreg,i < sfund,i in

O.-M. Georgescu / Journal of Financial Stability 18 (2015) 1–18

Eqs. (4) and (11) we have:

ei − <

ci + preg ei + xic + fi − Di − xi − di − r(xic + fi ) r ∗ preg

xi + di − ei (pfund − m1 ) − ci m1

(12)

It is assumed for simplicity that ti = ci , since si becomes positive only when the liquid assets have been sold. preg and pfund refer to the price for the regulatory constraints and funding contagion channel respectively. Denoting equity E = ci + preg ei + xic + fi − Di − xi − di , Eq. (12) can be rewritten as: m1 [rpreg ei − Ei + r(xic + fi )] < rpreg [xi + di − ei (pfund − m1 ) − ci ] (13) Or alternatively: m1 (r(xic + fi ) − Ei ) < rpreg (xi + di − ei pfund − ci )

(14)

Since the left-hand side is decreasing in Ei , the higher the capital buffer, the more likely it becomes that funding constraints dominate regulatory constraints. The right-hand side falls in the level of short-term debt relative to liquid and illiquid assets. If shortterm debt exceeds assets that can be pledged as collateral, the bank is illiquid. The larger the level of short-term debt, the more likely it is that the quantity of illiquid assets sold in order to satisfy margin requirements exceeds the quantity needed to satisfy regulatory constraints. In addition, the downward price spiral should be steeper in the latter case since the illiquid asset is evaluated at the market price less the margin, which is increasing in asset price volatility. While regulatory constraints are worsened only by the decrease in asset prices in the case of the mark-to-market contagion channel, funding constraints are worsened both by the decrease in asset prices and the simultaneous increase in margins in the case of the contagion channel due to funding constraints. In line with Gai et al. (2011) and Mistrulli (2011), netting of interbank claims is not allowed. This is because in case of default bilateral netting is not feasible. The liabilities of the defaulting bank are pooled and the claims are satisfied according to seniority. The economic rationale for allowing banks to net bilateral claims is that in periods of high financial distress, banks will engage in liquidity hoarding: a bank facing funding constraints will first cut credit lines to other banks to whom it owes money before looking for other sources of cash. Liquidity hoarding is captured here by letting the size of the haircut increase endogenously as a function of asset price volatility. As an extension, Section 5 explicitly models liquidity hoarding. When both funding and regulatory constraints are active, every bank has to satisfy the funding constraint in Eq. (9) and the regulatory constraint Eq. (1). The required quantities of assets to be sold, sreg,i and sfund,i , are determined as in Eqs. (4) and (11) respectively. The final quantity of assets to be sold by each bank is determined as si = max(sreg,i , sfund,i ). In equilibrium, condition (i) requires that the equilibrium price satisfies the market clearing condition in Eq. (2) and in addition that the margin is derived according to expression Eq. (8). Condition (ii) requires that the minimum quantity of assets to be sold by each bank is determined as si = max(sreg,i , sfund,i ). 4. Extension: unsecured debt The assumption so far was that secured short-term debt is the only type of short-term debt available. This assumption is relaxed

7

and short-term credit lines are initially considered to be unsecured. The creditor’s decision to roll-over unsecured debt depends on the accounting balance sheet value, since mark-to-market losses reported in the balance sheet represent additional information that can be used by creditors to assess the future solvency of the reporting bank, affecting its current liquidity position. After observing the price of the illiquid asset, the creditor evaluates the expected value of the bank’s mark-to-market balance sheet and decides whether to renew the unsecured credit line or ask for collateral to insure himself against the default of the debtor bank. If he extends the unsecured credit line, he will earn a return R on his claim xi + di with probability 1 − and receive (xi∗ + di ) with probability where is the default probability. If he does not roll over, he will receive xi + di with probability one. If the roll-over decision is negative, the creditor will ask for collateral and change his decision rule for the rollover decision like in Eq. (10). The creditor will roll over the unsecured credit line if the expected value of the debt repayment in the next period is greater than the value of the principal he would receive today with certainty. (1 − )(1 + R)(xi + di ) + (xi∗ + di ) > (xi + di )

(15)

The roll-over decision for the unsecured credit line is satisfied if: R(xi + di ) − ((xi + di )(1 + R) − (xi∗ + di )) > 0

(16)

The survival probability becomes:



1 − = P 2 <



1 ( + |p1 |)ei

∗ ci + p1 ei + (xc,i − xi∗ )(1 + R) + fi − di − Di



(17)

Given that 2 is i.i.d. with cumulative distribution function N: 1− =N



1 [ci ( + |p1 |)ei



∗ + p1 ei + (xc,i − xi∗ )(1 + R) + fi − di − Di ]

(18)

The lower the expected default probability and the higher the interest rate earned next period, the less likely it is that the unsecured credit line will be cut-off and replaced by a collateralized line. The seniority structure is defined as in the previous sections. In case of default the interbank short-term creditors are junior to all the other creditors. After di and Di are paid off, the remaining assets are distributed proportionally among creditor banks. The expected probability P that the net asset value is positive the next period is computed as: ∗ P(ci + p2 ei + xc,i (1 + R) + fi − xi∗ (1 + R) − di − Di > 0)

(19)

Where p2 is the next period’s price. Assuming the price at period 2 evolves according to: p2 = p1 + p2 = p1 + 2 2

(20)

Considering that  2 evolves as in: 2 =  + |p1 |

(21)

Fig. 1 explains the interaction between accounting information, funding and regulatory constraints in the model. At each iteration, banks have to satisfy two constraints. The regulatory capital condition is evaluated as in Eq. (1). The unsecured credit line is extended if the roll-over decision in Eq. (16) is satisfied. If the unsecured credit line is not extended, banks will have to pledge

8

O.-M. Georgescu / Journal of Financial Stability 18 (2015) 1–18

collateral to renew their short-term credit line and satisfy the collateral requirement as in Eq. (9). The amount sreg of illiquid assets needed to satisfy the regulatory constraint is compared with the amount sfund needed to satisfy the collateral requirement. The final amount of illiquid assets thrown on the market is s = max(sreg , sfund ). In this setting, the interaction between solvency (captured by the regulatory constraint) and liquidity (captured by the funding constraint) is affected by the accounting balance sheet value through the roll-over decision on unsecured debt. The new equilibrium price is determined and bank balance sheets are evaluated. The Eisenberg/NOE algorithm insures that the new vector of payments together with the default matrix are jointly determined. The process stops when all non-defaulting banks satisfy the regulatory and the funding constraint.

As pointed out by Upper (2011), simulations of the type described in this paper lack any behavioral foundations. Given that bank behavior is endogenous to the crisis scenario constructed within the simulation and that the domino effects are likely to be overstated, it seems difficult to integrate the simulation results in the regulators’ toolkit (when designing a stress test for example). This section relaxes the assumption that banks automatically engage in asset fire sales when they cannot satisfy funding or regulatory constraints. When a bank cannot satisfy either of these constraints, it determines a quantity si,test of assets that has to be sold as explained in the previous sections. However, instead of selling the assets, the bank will withdraw this amount proportionally from its debtor banks. Its interbank assets xic will decrease by this amount. All banks in the system simultaneously do this adjustment resulting in a new interbank matrix. Allowing banks to withdraw their interbank lines entirely would lead the collapse of the interbank market. This is not supported by empirical evidence on the lending behavior of banks during the crisis: Afonso et al. (2011) show that counterparty risk played a more important role than precautionary liquidity hoarding after the collapse of Lehman brothers. Bad banks receive less funds and at a higher interest rate, but the transaction volume was remarkably stable during that period. Another recent study on the European interbank market using TARGET2 data shows that after the Lehman bankruptcy the transaction volume on the interbank market diminished by around 30%. In addition, the maturity structure of the interbank market changed, with the volume of loans with a short maturity experiencing a sharp increase (see Georg et al., 2013). In line with empirical evidence, liquidity hoarding is allowed up to a share  of the initial interbank assets. In the simulations, the level of liquidity hoarding, , is set to 30%. The new interbank liability matrix becomes: (22)

where  is the weight of bank’s j liability in banks’ i total claims. A liquidity demand matrix is determined, where each column represents the amount of liquidity that a bank withdraws from other banks. The sum over the columns represents the demand for liquidity hoarding for each bank.

demandbank =

n  j=1

Lij

Bank

ci

ei

xic

fi

xi

sti

Di

capi

Ei

Bank 1 Bank 2 Bank 3 Bank 4 Bank 5 Bank 6 Bank 7 Bank 8 Bank 9 Bank 10 Mean

4 13 12 3 8 2 7 4 7 7 7

65 83 35 82 51 37 53 19 50 64 54

10 7 9 8 7 7 8 9 9 10 8

28 1 48 12 35 60 37 71 39 28 36

6 9 8 9 5 11 1 8 10 6 8

31 51 24 15 30 68 45 33 77 40 30

69 40 68 80 61 22 46 56 15 60 51

9 8 8 11 8 9 10 9 8 11 9

2 3 4 2 4 2 3 6 4 2 3

The sum over rows shows the amount of funds that each bank has to raise in other to satisfy the liquidity hoarding demand of other banks.

5. Extension: liquidity hoarding

Lij,new = max(Lij − si,test ∗ ij , (1 − ) ∗ Lij )

Table 2 Calibration.

(23)

demandother =

n 

L ij

(24)

j=1

The amount of liquid assets will increase by a bank’s own liquidity demand and decrease by the liquidity demand of other banks. The upper bound on the increase in liquid assets is a factor 1 + . The assumption is that the liquid assets of liquidity hoarding banks increase relative to the level of liquidity hoarding in the system. The reason for this additional restriction is that, given that liquid assets represent only a fraction of interbank liabilities (and implicitly interbank assets), allowing c to increase by the absolute value of demandbank − demandother could lead to a disproportionate increase in liquid assets for low levels of liquidity hoarding demand by other banks. In addition, the nonnegativity restriction insures that banks cannot short-sell liquid assets to satisfy the liquidity demand of other banks. ci = max(0, min(ci + demandbank − demandother , (1 + ) ∗ ci )) (25)

6. Calibration The data used for the initial calibration is obtained from the Annual Reports and Bankscope for the 10 largest European banks at the end of 2008. Table 2 shows the balance sheet data used to calibrate the simulations. All items are expressed in percent of total assets. Liquid assets are defined as cash, cash equivalents and funds eligible for central bank funding. Illiquid assets are defined as total assets valued at fair value plus reverse repo assets. All fair value assets are considered illiquid assets: even though the structured portfolio is only a share of total fair value assets, sharp price falls were also affecting corporate bonds and stock prices and thus the terms of collateralized lending after Lehman bankruptcy. After the third quarter 2008, lenders were reluctant to accept corporate bonds as collateral at a reasonable haircut due to high counterparty risk concerns, leading to the drying up of the repo market. The interbank assets vector is the transposed interbank liabilities vector, such that the sum of interbank assets in the system equals the sum of interbank liabilities. The assumption is that all interbank debt and receivables relate to the N banks in the network. The difference between interbank assets obtained through this transposition and the amounts obtained from the balance sheet of banks is added to short-term debt to the outside creditors, to compensate

O.-M. Georgescu / Journal of Financial Stability 18 (2015) 1–18

for the overstatement of interbank assets.8 The rest of the assets on the balance sheet are defined as fixed assets, fi , and refer to loans and other assets that cannot be pledged as collateral to obtain short-term funds. This residual category was introduced in order to ensure that the calibration is consistent with actual balance sheet data. Short-term debt is assumed to be the sum of debt toward banks in the system and the level of short-term debt to the outside creditors. Short-term debt toward the outside creditors is the sum of liabilities with less than 3 months maturity and repos. Interbank liabilities are obtained from the balance sheet. Table 2 shows that interbank assets and liabilities represent a small portion of the bank’s balance sheet, around 8% of total assets. To generate the interbank connections matrix, a maximum number of interconnections Nmax is assumed for each bank. To determine the column vector of interbank connections for each bank, Nmax elements are randomly chosen from the column vector formed by the N banks in the network, after excluding the bank in question. The procedure is repeated N times to fill N columns, where N is the number of banks in the system. An adjacency matrix I of dimension NxN is obtained with zero entries for position ij meaning that bank i has no connection to bank j. The number of interconnections is assumed to be equal for all banks and has the value of 7 for the first two simulations. The simulations were structured as follows:

9

3 For the simulations concerning the network connectivity, the interbank liability matrix is defined as follows: Lij =

Li Nmax

To see the sensitivity of the results to the network connectivity, Nmax is varied between 3 and 9 (Fig. 3(a)–(d)). The rest of the balance sheet items were calibrated as in Table 2. The volatility parameters  and  were set similarly to Brunnermeier and Pedersen (2009) at 0.1 and 0.3 respectively. The value for the regulatory capital ratio is 4% for the simulations calibrated with high equity (capi in Table 2) and 1.5% for the simulations calibrated with low equity (Ei in Table 2).9 For the simulations in part 1 and 3, a high equity is obtained by adding the difference between regulatory capital capi and equity Ei to the fixed assets fi . Given that a risk-weighted measure of assets could not be replicated in this setting, the fact that risk weights matter for the denominator is captured by the zero risk weight for cash; cash is therefore excluded from the denominator of the regulatory capital ratio.

ci = (capi + Di + xi + di − xic − fi ) ∗

To start the simulations, a shock is applied to the illiquid assets of one bank in the system. The simulations run after applying a shock to each of the banks in the system. The size of the shock is set to 10% of the value of illiquid assets. To see whether the results change when a random rather than a deterministic shock is applied to asset values, the simulations were repeated with a random initial shock. The graphs show the average number of defaults over n * p * q iterations, where n is the number of iterations over the network structure, p is the number of iterations over the parameter varied, for example liquidity ratio, and q is the number of iterations over the identity of the bank to which the shock is applied. In the simulations below, n is set to 500, and p, q = 10.

Illiquid assets are defined as:

7. Results

ei = (capi + Di + xi + di − xic − fi ) ∗ (1 − )

This section analyze how systemic risk is endogenously amplified or mitigated when different sources of vulnerability of the financial system, like the level of liquid asset holdings, the degree of maturity transformation and the structure of the interbank network interact with regulatory and funding constraints. Let denote the liquidity ratio, the ratio of liquid assets over illiquid assets and  the ratio of liquid assets to interbank short-term debt. The results in the 4 panels of Fig. 2 were produced in different simulations runs, with the initial parameters calibrated as described in the previous section.

1 For the simulations concerning the liquidity ratio, the vector of interbank liabilities, Li is obtained from balance sheet data (column 6 in Table 2). The liabilities to individual banks are split homogenous across the banks in the network. For these simulations, liquid assets are defined as follows:

The ratio of liquid assets over illiquid assets, , is varied between 0 and 1 (Fig. 2(a) and (b)); capi refers to the regulatory Tier 1 capital ratio (high equity) in Fig. 2(a) and the equity ratio (low equity) in Fig. 2(b). 2 For the simulations concerning the level of interbank debt, the interbank liabilities matrix is obtained by multiplying each element of the adjacency matrix I with a constant ω and a random number, rand, to obtain some heterogeneity across banks. This number is uniformly distributed between 0 and 1. Lij = Iij ∗ rand ∗ ω To see how the results change with the level of interbank debt, the constant ω is varied in the simulations between 5 and 50, which is equivalent to a variation of the ratio of liquid assets to interbank short-term debt, , between 0 and 1.5 (Fig. 2(c) and (d)).

8 Balance sheet interbank assets are smaller since the banks in the sample are net borrowers. This adjustment was not necessary for graphs 2(c), 2(d), 4 (b), 5(c), 5(d), 6(c) and 6(d), where the level of interbank short-term debt is varied for the simulations. The simulations in Fig. 3 were run without this adjustment, since doing so would render the system too unstable. All banks in the system default and there is no sensitivity to the parameters of interest.

7.1. Funding versus regulatory constraints Fig. 2(a) and (b) display the results for different levels of the equity and liquidity buffer when the level of short-term debt is kept constant, corresponding to an average value for  of 0.8. A higher level of liquid assets implies that both the regulatory and the funding constraint are less binding. Intuitively, the number of defaults decreases with the liquidity ratio for both contagion channels. Fig. 2(c) and (d) display the results for different levels of equity when is kept fixed while the interbank short-term debt is varied between 5 and 50. Table 2 shows that the average liquidity ratio for the 10 banks considered in the simulation is 0.14. The number of defaults for both contagion channel decreases steadily as  increases from 0.1 to 1.5. Similar to the results obtained for the

9

1.5% is the lowest value of equity of the banks in the sample.

10

O.-M. Georgescu / Journal of Financial Stability 18 (2015) 1–18

Fig. 2. Contagion: regulatory versus funding constraints. (For interpretation of the references to color in this text, the reader is referred to the web version of the article.)

liquidity buffer, the dominance of one of the two contagion channels depends on the initial level of equity. For high levels of equity and a liquidity ratio smaller than 0.45, the regulatory constraints channel dominates the funding constraints channel (Fig. 2(a)). For low levels of equity the regulatory constraints channel dominates irrespective of the level of the liquidity buffer (Fig. 2(b)). For high levels of equity, the funding constraints channel dominates the regulatory constraints channel irrespective of the level of interbank short-term debt (Fig. 2(c)). For low levels of equity, contagion due to funding constraints dominates contagion due to regulatory constraints up to a value of  of around 0.4. When the level of short-term debt is high and the funding constraint is nearly binding, the haircut imposed by the creditor on the collateral value will trigger a steeper downward pricing spiral compared to the case where the collateral is evaluated at the market price, as is the case for the regulatory ratio. The initial shock leads to a higher quantity of assets sold, larger funding constraints due to the low collateral value and a higher number of defaults. For  larger than 0.4, regulatory constraints dominate funding constraints in terms of the number of defaults. Eq. (13) provides some intuition on the results in Fig. 2. For high equity, the left hand side will be negative, and the amount of assets sold in order to satisfy regulatory constraints, sreg , is lower than the amount sold to satisfy funding constraints, sfund . As can be seen in Fig. 2(a) and (c), when equity is high, funding constraints tend to dominate regulatory constraints. Clearly the dominance of one of the two channels also depends on other parameters, like the liquidity buffer and the level of interbank short-term debt.

From Eqs. (4) and (11) it can be seen that both sreg and sfund decrease in the level of liquid assets c and increase in the level of interbank short-term debt x, but at a different rate. Differentiating sreg and sfund with respect to c we obtain10 :

     ∂sreg   ∂sfund  1 1  −   ∂c   ∂c  = r ∗ preg − m

¯ From Eq. (8), m = ¯ + |p fund |, implying m = 2.32 + 0.69| pfund |.11 It can easily be verified that the above expression is positive for all p ∈ [0.5 ; 1], implying that sreg decreases in c at a faster rate than sfund . This is also confirmed by the simulation results in Fig. 2(a) and (b): the slope of the black continuous line (regulatory constraints) is steeper than the slope of the dotted line (funding constraints). In the same vein, differentiating sreg and sfund with respect to x we obtain:

     ∂sreg   ∂sfund  1 1  −   ∂x   ∂x  = r ∗ preg − m

The expression above is positive for all p ∈ [0.5 ; 1], again implying that sreg increases in x at a faster rate than sfund . This is only confirmed in Fig. 2(c) for a very high level of short-term debt and high initial equity levels. For lower levels of short-term debt, the slope of the black continuous line (regulatory constraints) is only

10

Assuming ci = ti , otherwise there is no need to sell ei implying that si = 0. Considering the definitions of ¯ and ¯ from the margin derivation section in Appendix and values  = 0.1,  = 0.3 and p ∈ [0.5 ; 1] as in Section 6. 11

O.-M. Georgescu / Journal of Financial Stability 18 (2015) 1–18

marginally higher than the slope the dotted line (funding constraints), while in Fig. 2(d) the slope appears broadly similar. Thus, other factors must be at play, unrelated to the level of sreg and sfund . As will be seen in Table 3, from a network perspective, the level of interbank short-term debt also represents node strength. Table 3 shows that unlike the results for the liquidity ratio in Fig. 2(a), driven mostly by the asset fire sale channel, the results in Fig. 2(d) are driven to a large extent by the number of interconnections, particularly at intermediary and high levels of interbank debt. Thus, increasing the level of interbank debt increases the contagion potential of direct interbank links. Keeping s constant, the contagion potential due to a more dense network is similar for both contagion channels. This explains why the sensitivity to the variation of interbank short-term debt is broadly similar for the two channels. The results so far suggest that market discipline acts as a complementary tool to regulatory constraints. Low capitalized banks are sanctioned by the regulator through regulatory constraints. Even when banks are adequately capitalized from a regulatory perspective, the constraint imposed by creditors can be stricter than the one imposed by the regulator. This result is similar to Gordy and Howells (2006) who find that the procyclicality of Basel II capital requirements depends on the extent to which the capital requirements imposed by the market are more binding. The regulator could therefore not enhance financial stability by decreasing the level of required capital. It could do this by tailoring capital requirements such that they match real-world funding constraints, for example by applying mark-to-market only for assets which are funding short-term liabilities, in the spirit of the ‘mark-to-funding’ approach proposed by Brunnermeier et al. (2009). The introduction of the Net Stable Funding (NSFR) ratio within the Basel III framework has a similar objective. The next section discusses how the interaction between the two channels can amplify or mitigate systemic risk. 7.2. Interaction Depending on which of the two contagion channels dominates, allowing the two channels to interact in the presence of unsecured debt can mitigate or deteriorate financial stability. The effect of activating both contagion channels is not simply additive, as the two channels can reinforce each other. The black and gray dashed lines in Fig. 2 plot the average number of defaults when both regulatory and funding constraints are relevant. The difference between the two lines is the existence of unsecured debt for the funding constraints channel.12 Adding unsecured debt to the funding constraint renders balance sheet information relevant for the interaction between the two channels. As explained in the previous section, balance sheet information can influence the roll-over decision on unsecured bank debt as in Eqs. (15) and (16). Letting the roll-over decision on unsecured short-term debt depend on accounting information, through the expected balance sheet value, implies that some banks will no longer receive uncollateralized loans. These banks will face a funding constraint that only depends on the value of collateral less a haircut and the level of short-term debt. The funding constraint on secured debt in Eq. (10) only becomes relevant if the roll-over decision on unsecured debt is not satisfied. Depending on whether the funding or the regulatory contagion channel dominates, the more binding constraint may be relaxed or reinforced by the interaction. Looking at Fig. 2(a), (c) and (d) (when

12 See Fig. B.9 in Appendix for a comparison between the contagion potential of funding constraints with and without unsecured debt.

11

 < 0.4), it seems that when funding constraints dominate regulatory constraints, the fact that banks have access to unsecured debt conditional on the value of their accounting balance sheet mitigates the mutual reinforcement of the two contagion channels. Funding constrained banks relying heavily on short-term debt financed by a collateral with a low market value will get access to funding by disclosing balance sheet information. They will not have to sell assets to satisfy the roll-over decision on secured debt (sfund = 0 in Fig. 1). The upper bound on the supply of illiquid assets thrown on the market is the one needed to satisfy regulatory constraints. In the opposite case, when regulatory constraints dominate funding constraints, access to unsecured debt no longer mitigates funding constraints (see Fig. 2(b) and (d) for  > 0.4). In Fig. 2(d), activating both contagion channels in the presence of unsecured debt leads to a slightly higher number of defaults when the regulatory constraints channel is dominating ( > 0.4). Even though funding constraints are less of a problem, they can become binding if asset fire sales needed to satisfy regulatory constraints push down the price of the illiquid assets low enough such that the funding constraint on secured debt is no longer satisfied. More assets are thrown on the market relative to the case when the two contagion channels are activated separately, as the two channels reinforce each other. Activating both channels without allowing for unsecured debt, i.e. without allowing balance sheet information to matter for the roll-over decision on unsecured debt, amplifies systemic risk irrespective of which constraint is more binding (gray dashed line in Fig. 2). Asset fire sales needed to satisfy one of the two constraints lead to a price decrease that makes the other constraint binding too, reinforcing the spiral. In particular, when the level of short-term debt is high, and contagion due to funding constraints dominates contagion due to accounting induced regulatory constraints, the supply of illiquid assets that is thrown on the market in order to satisfy regulatory constraints only is smaller than the one needed to satisfy funding constraints only (sreg < sfund in Fig. 1). The drop in price induced by fire sales necessary to satisfy funding constraints will also deteriorate regulatory constraints, leading to more fire sales. Eqs. (9) and (16) show that the roll-over conditions on secured and unsecured debt, Rolls and Rollu , are decreasing in x, however at a different rate:

     ∂Rolls   ∂Rollu   −   ∂x   ∂x  = 1 − (1 + R) The expression above is positive for all R < 1. This implies that as x becomes larger, the presence of unsecured funding makes asset fire sales due to funding constraints less likely. This is confirmed by the black dashed line in Fig. 2(d) for  < 0.45 (when funding constraints dominate regulatory constraints). Thus, the interaction between the two channels in the presence of unsecured debt can mitigate systemic risk. Similarly, Eqs. (9) and (16) show that the probabilities that the roll-over condition on secured and unsecured debt, Rolls and Rollu are satisfied, are increasing in c, with the difference in sensitivities given by:

     ∂Rolls   ∂Rollu  (xi + di )(1 + R)N  ( )  −   ∂c   ∂c  = 1 − ( + p)ei The sign of the expression above is ambiguous. If N ( ) < 0, the expression is positive only if xi + di < 0.1 * ei . It is however unlikely that the sum of deposits and interbank debt is less than one tenth

12

O.-M. Georgescu / Journal of Financial Stability 18 (2015) 1–18

Table 3 Contagion: asset fire sales versus bilateral exposures. Comparison of the average number of defaults when each of the two contagion channels are activated (first two columns) to the average number of defaults due when the asset fire sales channel is shut down (third column). The simulation results in the first two columns correspond to the simulation results displayed in Fig. 2(a) and (d). Liquid assets/interbank ST debt 1.5 1.3 1.0 0.8 0.5 0.3 Liquidity ratio 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Regulatory constraints fire sales: yes

Funding constraints fire sales: yes

Regulatory &Funding constraints fire sales: no

8.60 8.80 9.10 9.30 9.75 9.85

8.04 8.60 9.05 9.24 9.75 9.90

0.47 2.25 3.96 5.02 5.72 6.16

10 10 8.45 0 0 0 0

10 10 9.3 7.99 4.20 1.01 0

1.00 0.57 0 0 0 0 0

of illiquid assets.13 For all positive values of the probability density function N ( ) the expression above is positive. From Fig. 2(a) it seems that, for the present calibration, this condition is met. This means that the unsecured roll-over condition is improved faster than the roll-over condition on secured debt when the liquidity buffer is improved. Again, the presence of unsecured debt makes asset fire sales due to funding constraints less likely. The above effects only play a role when funding constraints dominate regulatory constraints, since the final amount of assets thrown on the market, s, is computed as s = max(sfund , sreg ) (see Fig. 1). When sreg > sfund , access to unsecured funding can no longer diminish the amount of assets thrown on the market. On the contrary, the unsecured roll-over condition may be deteriorated by asset fire sales needed to satisfy regulatory constraints, leading to the activation of the secured roll-over decision in Eq. (9) and additional fire sales. Hence, the interaction can amplify systemic risk. To see whether the results change when a random rather than a deterministic shock is applied to asset values, the simulations in Fig. 2 were re-run with a random initial shock. The results are qualitatively unchanged (see Fig. B.6 in Appendix). 7.3. Network structure From a network perspective, the level of interbank short-term debt also represents the node strength. The simulation results shown in Fig. 2(c) and (d) also inform on the relation between the node strength and contagion. From Fig. 2 it seems that the higher the node strength, the higher the contagion potential. Table 3 below shows the average number of defaults when the asset fire channel is shut down. Since the only difference between the regulatory and the funding constraints channel in terms of the number of defaults is the expression for s, the quantity of assets to be sold, the results are identical for the regulatory and the funding constraints channel when the asset fire sales channel is shut down. From Table 3 it is

13 With a 99% probability, the probability density function of the standard normal distribution takes values between −3 and 3. Considering the largest value for

p = 0.5,

xi +di ei

is multiplied with a factor ∈[8.9 ; 10] and ∈[−8.9 ; −10].

easy to see that the asset fire sales channel dominates the contagion channel. Thus, the results in Fig. 2(a) and (d) are driven mainly by the asset fire sale spiral due to funding or regulatory constraints, and less so by a specific network property (i.e. node strength). This is consistent with other simulation results in the literature finding that the interbank exposures are of secondary importance for the propagation of systemic risk (see Upper, 2004; Furfine, 2003; Georg, 2013; Glasserman and Young, 2013). Instead, common portfolios have been identified as the main drivers of contagion (see Caccioli et al., 2013; Corsi et al., 2013). The results in the literature concerning the relationship between system fragility and interconnectedness are mixed. Allen and Gale (2000) and Freixas et al. (2000) argue that a more dense network enhances system resilience because the impact of a negative shock is distributed across more institutions in the system.14 On the other hand, Vivier-Lirimont (2006) and Battiston et al. (2012) find that more interconnections in the system are destabilizing. Reconciling both views, Ladley (2013) concludes that the relevance of the number of interconnections in the system depends on the size of the initial system wide shock. In response to large initial shocks, more interbank lending relationships amplify systemic risk, while the opposite effect is observed for smaller initial shocks. Fig. 3(a) shows that systemic increases with the number of interconnections for both contagion channels. The reason for this may be that the initial shock is deteriorating balance sheets to an extent that the effect of indirect links via asset fire sales and contagion due to counterparty defaults dominates the risk sharing potential of an increase in connectivity. Another explanation could be the finding of Nier et al. (2007) on the relationship between network connectivity, system fragility and the initial level of net worth of the banks in the system: at low levels of net worth, increasing connectivity amplifies contagion. Indeed, repeating the simulations with a higher initial level of equity leads to a negative relation between network connectivity and defaults, suggesting that asset fire sales may be dominating the shock absorption capacity of increased connectivity only at low levels of equity (see Fig. 3(b)).15 To see whether the size of the initial shock affects the results in Fig. 3(a), the simulations are repeated for different shock values. For a lower initial shock value (5% of illiquid assets ei ), increasing connectivity mitigates contagion only for the funding constraints channel, but not for the regulatory constraints channel (Fig. 3(c)). The reason for the decoupling in the sensitivity to the degree of interconnectedness of the two channels is not clear. It seems that the two contagion channels have different thresholds beyond which the size of the shock is low enough such that risk sharing due to more interconnections outweighs the effect of asset fire sales and domino effects due to more interconnections. For a large initial shock (30% of illiquid assets ei ), increasing connectivity does not matter since all banks in the system default (Fig. 3(d)). This is line with Caccioli et al. (2013) and Nier et al. (2007) who find that if the value of the common asset of the banks in the network has dropped low enough such that balance sheets are significantly deteriorated, interbank exposures no longer drive contagion. Simulations using actual interbank data show that random graph networks fail to capture the hub and spoke nature of real

14 The result in Allen and Gale (2000) refers to complete markets. A complete market is one in which each bank lends to all other banks. Thus, the direction of the links matter when assessing the degree of market completeness. In the setting of this paper, two banks that are interconnected are automatically both lenders and borrowers. Thus, more interconnections imply that the interbank liability matrix approaches the complete market structure. 15 Higher equity was obtained by adjusting fixed assets fi with the difference between regulatory capital and equity, (capitali − Ei ), as explained in Section 6. The average equity of the banks in our simulation is 3.13%.

O.-M. Georgescu / Journal of Financial Stability 18 (2015) 1–18

13

Fig. 3. Contagion and connectivity.

world networks (see for example Mistrulli, 2011; Van Lelyveld and Liedorp, 2006). In reality banks form preferential links, i.e. highly interconnected banks have a higher probability of forming links to other banks than do low connected banks. The simulations comparing the two network structures conclude that random graphs tend to overestimate contagion risk relative to scale-free networks in the case of random shocks, while targeted shocks are more destabilizing for scale-free networks than for random networks. To see how the results change when a scale-free network is assumed rather than a random graph, the network structure was generated accounting for the tendency of highly connected banks to form preferential links similar to Barabási and Albert (1999).16 Fig. B.5 in Appendix shows that the results in Fig. 2(a) and (c) do not qualitatively change when a scale-free network is assumed instead of the random network. Fig. B.5(a) and (c) show the results when the 10% shock to asset values is applied sequentially to each bank in the network, similar to Fig. 2(a) and (c). Fig. B.5(b) and (d) show the results when a targeted shock is applied to the most interconnected bank. In the case of the funding constraints channel, the system is more fragile for both types of shocks, while for the regulatory constraints channel only the combination of a low liquidity ratio and a targeted shock leads to a more unstable system compared to the same scenario for the random network. Overall, the results are broadly similar for the two types of networks. The reason could be that the banking system contains too

16 The algorithm starts with a random adjacency matrix consisting of four banks and extends this initial seed to form a network of 10 banks. The probability that a bank i forms a link with another bank depends on the number of degrees of that

bank and is expressed as: plink = ki /

n

j=1

n

j=1

kj , where ki is the degree of bank i and

kj the sum of the degrees of all banks in the system.

few banks, such that the difference between the degree of peripheral banks and the degree of money center banks is too small. Given that the asset fire sale spiral as described above is only likely to affect systemically relevant banks that are highly connected to each other and that are market makers for the price of the illiquid asset (structured products for example), this issue is deemed to be of secondary importance for the simulation results discussed above. The simulation results in Fig. 3 change when a random shock is applied to asset values (see Fig. B.7 in Appendix). This is intuitive since, as explained in Section 6, the algorithm in Fig. 1 is run when the shock is sequentially applied to each bank in the system for different values of the number of interconnections. This implies that at each step a new realization of the random variable can lead to a high or a low shock to asset values. As can be seen in Fig. 2, the size of the shock matters for the relationship between interconnectedness and systemic risk. This effect is “washed out” when the shock is modeled as a sequential realization of a random variable. 7.4. Liquidity hoarding Introducing liquidity hoarding does not substantially mitigate the contagion potential for the regulatory constraints and the funding constraint channel. Fig. 4 shows that now regulatory constraints dominate funding constraints irrespective of the level of the liquidity ratio and of the share of liquid assets relative to short-term interbank debt.17 Allowing banks to engage in liquidity hoarding leads to a less dense network of bilateral exposures. At the same time the

17 In Fig. 4, the label ‘Funding and Regulatory Constraints’ refers to the case when the two channels are allowed to interact via the unsecured credit line.

14

O.-M. Georgescu / Journal of Financial Stability 18 (2015) 1–18

Fig. 4. Contagion with liquidity hoarding.

liquidity buffer is improved. Funding constraints are relaxed more than regulatory constraints, such that the latter constraints are always dominating. Consistent with the results without liquidity hoarding, when the regulatory constraints channel is dominating the funding constraints channel, letting the funding constraint interact with the regulatory constraint through the roll-over decision on unsecured debt cannot mitigate the mutual reinforcement of the two channels. Varying the magnitude of , the level of liquidity hoarding does not qualitatively change the results. These results show that in the absence of liquidity hoarding, funding constraints could have been a more serious concern than regulatory constraints. The presence of liquidity hoarding makes regulatory constraints more binding. The reason for why this could not be observed during the crisis could be that funding constraints always precede insolvency (in this case regulatory insolvency). Government capital injections presumably made the regulatory constraints-asset-fire-sales spiral unlikely. Moreover, liquidity hoarding was modeled in a very simplistic way. One drawback to the approach is that the liquidity demand of hoarding banks does not continuously adjust to the liquidity demand of other creditor banks in an iterative procedure similar to the one used to determine the payments vector. The second drawback of the approach is that counterparty credit risk is not captured, although at a later stage the roll-over decision on unsecured debt does take into account the fact that during a crisis, bad banks receive funds under stricter credit terms than good banks. The idea of this extension was to show that liquidity hoarding matters and can prevent fire sales. This aspect is generally ignored in network models simulating contagion due to asset fire sales. A more accurate representation of the liquidity hoarding behavior of banks in a network and its relevance for the decision to engage in asset fire sales could be an interesting path for future research. 8. Conclusion This paper compares the contagion potential of accounting induced regulatory constraints to that of funding constraints in a network of banks during a crisis. The trigger for this paper was anecdotal evidence from the recent crisis suggesting that funding constraints were a more serious problem for banks than regulatory constraints. The results show that whether one of the two contagion channels dominates depends on the capital buffer, the liquidity buffer and the level of interbank short-term debt. At low capital levels and high short-term debt relative to liquid asset holdings, the contagion potential due to funding constraints is higher than the one

due to accounting induced regulatory constraints. In contrast, when capital buffers are high, funding constraints dominate regulatory constraints irrespective of the level of interbank short-term debt and the liquidity buffer. In addition, the relationship between system stability and connectivity depends on the size of the initial shock. The simulation results imply that the two contagion channels have different thresholds beyond which the size of the shock is large enough such that risk sharing due to more interconnections is outweighed by the effect of asset fire sales and domino effects due to more interconnections. The results suggest that market discipline can act as a complementary tool to regulatory constraints. Poorly capitalized banks are sanctioned by the regulator through the regulatory constraint. Even when banks are adequately capitalized from a regulatory perspective, creditors can impose stricter constraints on banks than the regulator. Asset fire sales could be the undesirable side effects of these constraints. Allowing for liquidity hoarding can mitigate the asset fire sales spiral and render the accounting regulatory constraints more binding than the funding constraint. When the two contagion channels are allowed to interact, the presence of unsecured debt can mitigate the mutual reinforcement of the two channels depending on which contagion channel dominates. When funding constraints dominate regulatory constraints, allowing balance sheet valuation to affect the expectations about future insolvency and implicitly, the roll-over decision on unsecured debt, mitigates systemic risk relative to the case when the roll-over decision only depends on the market value of the collateral. Thus, accounting information has a stabilizing effect because it enables access to unsecured funding.18 The fair value accounting rules were amended at the height of the crisis to break the vicious link between allegedly irrational market prices and regulatory constraints. The results contribute to the ongoing debate about the role of fair value accounting during the crisis and could be interesting for a regulator wishing to achieve a trade-off between transparency, the main goal of fair value accounting, and financial stability. This paper suggests that the interplay between illiquidity and solvency can lead to bank failure independent of the way the assets are valued on the balance sheet. Beyond the mechanical link that exists between accounting and regulatory constraints, balance 18 The difference between accounting values and market values is twofold. First, accounting balance sheet values are less volatile due to the larger weight of fixed assets. Second, accounting values relevant for the unsecured debt decision refer to all assets and liabilities on the balance sheet, whereas market information relevant for the secured debt roll-over decision only refers to the value of collateral and the level of short-term debt.

O.-M. Georgescu / Journal of Financial Stability 18 (2015) 1–18

sheet valuation per se is not a problem, but rather the vulnerable funding structure of banks during a crisis. This source of vulnerability may be better addressed through adequate regulatory tools, like the NSFR or the LCR ratio, rather than via ad-hoc amendments to the accounting regime. One possible policy implication would be to adapt the balance sheet information relevant for regulatory requirements to reflect real world funding constraints, for example by applying mark-market only for banks with a high level of maturity transformation, in the spirit of the mark-to-funding rules proposed by Brunnermeier et al. (2009). Possible extensions of this paper could explore further how the incentives of banks to gamble for resurrection affect the decision to engage in fire sales (see for example Diamond and Rajan (2011)) and how the degree of imprecision of accounting information affects the relationship between illiquidity and solvency. Appendix A. Margin derivation In the setting of Brunnermeier and Pedersen (2009), there are two types of creditors: informed financiers and uninformed financiers. Informed financiers have the information set F = [z, v0 , v1 , p0 , p1 , 1 ]. In the setting of this paper, z is the initial exogenous wealth shock applied to banks, decreasing their stock of illiquid assets ei . This shock need not originate form asset prices. 1 can be interpreted as the demand shock resulting from the market clearing condition in Eq. (2). Uninformed financiers only observe prices, that is F = [p0 , p1 ]. Creditors assume that the fundamental value v of the illiquid asset evolves according to:

v2 = v1 + v2 = v1 + 2 2

(A.1)

where all 2 follow a standard normal distribution with the cumulative distribution function  and the volatility has dynamics: 2 =  + |v1 |

(A.2)

with ,  ≥0. Denoting the illiquidity of the asset t as the departure from the fundamental value in period t: t = pt − vt

(A.3)

and using the assumption as in Brunnermeier and Pedersen (2009) that in the next period prices return to their fundamental value, that is p2 = v2 , we can express −p2 in Eq. (7) as: −p2 = −(p2 − p1 ) = −(v2 − (1 + v1 )) = −v2 + 1

(A.4)

The above decomposition is interesting for the informed creditors because it allows them to distinguish between price variations that are due to variations in the fundamental value of the asset and temporary deviations from the fundamental value that are due to illiquidity (i.e. liquidity pricing as in Eq. (2)). For an informed creditor it makes sense to accept assets as collateral for which the deviation from the fundamental value is only temporary, such that he can engage in speculative trading.  in Eq. (7) becomes:  = Pr(−v2 + 1 ≥ m1 )

(A.5)

Replacing v2 with  2 2 from Eq. (A.1):



 = Pr(−2 2 + 1 ≥ m1 ) = Pr − 2 ≥

m1 − 1 2

 (A.6)

15

Solving (A.7) for m1 and denoting ¯ = −1 (1 − ) and ¯ = −1 (1 − ), the required margin m1 is given by: ¯ v1 | + 1 m1 = ¯ + |

(A.8)

Assuming as in Brunnermeier and Pedersen (2009) that creditors have no information about the fundamental value v of the illiquid assets e, m1 becomes:19 ¯ m1 = ¯ + |p 1|

(A.9)

Eq. (2) implies that p1 = 1 whenever s = 0. To insure consistency with Eq. (2), the fundamental value is assumed to be 1. When the shock leads to a value of s = 0, p1 = v1 = 1. Appendix B. Numerical example payment and clearing vector B.1. Payment vector Consider the following numerical example in Fig. B.8.20 Assume a banking system formed of four banks, with ai total assets available to pay the interbank debt excluding interbank receivables, xi,j the interbank debt of bank i toward bank j and ij the weight of xi,j in bank’s i total liabilities. According to the clearing vector x* = (0.20 ; 0.95 ; 020 ; 0.60), bank’s 1 payment is 0.20. Since 12 = 1, this payment goes to bank 2 in its entirety. Bank 1 does not lend to other banks in the system, therefore it can only cover the required payment from its assets ai of 0.2. In the case of bank 1, actual payments x* of 0.2 are below required payments xi of 1. Bank’s 2 payment is 0.95, which is less than the required payments xi of 1.2. Since 23 = 1, this payment goes to bank 3. Bank 3 is lending to both bank 4 and bank 2. The payment from bank 2 is 0.95. Bank 4 will pay 0.15 = 0.25 * 0.60 to bank 3. The net asset value of bank 3 is 1 = 0.95 + 0.15 + 0.1 − 0.2. Bank 2 receives a payment of 0.75 * 0.6 = 0.6, less than its required payment of 0.8. B.2. Clearing vector Consider the following numerical example for a clearing vector, where  is the matrix of liabilities weights:

⎛

0

⎜ ⎜0 ⎜ 1 ⎝ 16

=⎜

0

15 16 0

1 16 15 16

0

0

3 4

1 4

0 1 16 15 16

⎞ ⎟ ⎟ ⎟ ⎟ ⎠

 x=

1,

6 1 4 , , 5 5 5



 a=

m −   1 1 2

(A.7)

 .

0

0  Assuming full repayment, for the trial solution x =

6 1 4 the default set is D0 = {1, 4}. Assuming that only , , 5 5 5 bank 1 and 4 default, balance sheets are   reevaluated leading to a 1 6 1 3 new clearing vector x1 = and a new set of defaulted , , , 5 5 5 5 1 banks D = {1, 2, 4}. The next iteration assumes  that only banks  1 19 1 3 1, 2 and 4 default. The new clearing vector x2 = , , , 5 20 5 5 leads to the same default set D2 = {1, 2, 4}, which terminates the algorithm. Figs. B.5–B.9 1,

Combining Eqs. (7), (A.1), (A.2) yields: =1−

1 3 1 2 , , , 5 10 10 5

19 20

The margin here is an absolute and not a relative value. Example from Eisenberg and Noe (2001).

16

O.-M. Georgescu / Journal of Financial Stability 18 (2015) 1–18

Fig. B.5. Contagion: regulatory versus funding constraints (scale-free network).

Fig. B.6. Regulatory versus funding constraints (random shock).

O.-M. Georgescu / Journal of Financial Stability 18 (2015) 1–18

Fig. B.7. Contagion and connectivity (random shock).

Fig. B.8. Numerical example payment vector.

Fig. B.9. Funding constraints.

References Acharya, V., Gale, D., Yorulmazer, T., 2011. Rollover risk and market freezes. J. Financ. 66 (4), 1177–1209. Adrian, T., Shin, H., 2010. Liquidity and leverage. J. Financ. Intermed. 19 (3), 418–437. Afonso, G., Kovnera, A., Schoar, A., 2011. Stressed, not frozen: the federal funds market in the financial crisis. J. Financ. 66 (4), 1109–1139. Allen, F., Carletti, E., 2008. Mark-to-market accounting and liquidity pricing. J. Account. Econ. 45 (2), 358–378. Allen, F., Gale, D., 2000. Financial contagion. J. Polit. Econ. 108 (1), 1–33. Amundsen, E., Arndt, H., 2005. Contagion risk in the Danish interbank market. In: Danisch Central Bank Working Paper., pp. 2005–2025.

17

Anand, K., Gai, P., Marsili, M., 2012. Rollover risk, network structure and systemic financial crises. J. Econ. Dyn. Control 36 (8), 1088–1100. Barabási, A.-L., Albert, R., 1999. Emergence of scaling in random networks. Science 286 (5439), 509–512. Battiston, S., Delli Gatti, D., Gallegati, M., Greenwald, B., Stiglitz, J.E., 2012. Liaisons dangerousness: increasing connectivity, risk sharing, and systemic risk. J. Econ. Dyn. Control 36 (8), 1121–1141. Blåvarg, M., Nimander, P., 2002. Interbank exposures and systemic risk. Economic Review, vol. 2. Sveriges Riksbank. Brunnermeier, M., 2009. Deciphering the liquidity and credit crunch 2007-08., pp. 77–100. Brunnermeier, M., Crocket, A., Goodhart, C., Persaud, A., Shin, H., 2009. The Fundamental Principles of Financial Regulation. Geneva Reports on the World Economy. Brunnermeier, M., Pedersen, L., 2009. Market liquidity and funding liquidity. Rev. Financ. Stud. 22 (6), 2201–2238. Caccioli, F., Farmer, J., Foti, N., Rockmore, D., 2013. How interbank lending amplifies overlapping portfolio contagion: a case study of the Austrian banking network. In: Santa Fe Institute Working Paper. Chang, R., Velasco, A., 2000. Banks, debt maturity and financial crises. J. Int. Econ. 51 (1), 169–194. Cifuentes, R., Ferrucci, G., Shin, H., 2005. Liquidity risk and contagion. J. Eur. Econ. Assoc. 3 (2–3), 556–566. Corsi, F., Marmi, S., Lillo, F., 2013. When micro prudence increases macro risk: the destabilizing effects of financial innovation, leverage, and diversification. Lever. Diversif. Degryse, H., Nguyen, G., 2007. Interbank exposures: an empirical examination of contagion risk in the Belgian banking system. Int. J. Cent. Bank. 3 (2), 123–171. Diamond, D., Rajan, R., 2011. Fear of fire sales, illiquidity seeking, and credit freezes. Q. J. Econ. 126 (2), 557–591. Eisenberg, N., Noe, T., 2001. Systemic risk in financial systems. Manag. Sci. 47 (2), 236–249. Elliott, M., Golub, B., Jackson, M.O., 2014. Financial networks and contagion. Am. Econ. Rev. 104 (10), 3115–3153. Elsinger, H., Lehar, A., Summer, M., 2006. Risk assessment for banking systems. Manag. Sci. 52 (9), 1301–1314. Forbes, S., 2009. End mark-to-market. http://www.forbes.com/2009/03/20/steveforbes-mark-to-market-intelligent-investing-market.html Freixas, X., Parigi, B.M., Rochet, J.-C., 2000. Systemic risk, interbank relations, and liquidity provision by the central bank. J. Money Credit Bank. 32 (3), 611–638. Furfine, C., 2003. Interbank exposures: quantifying the risk of contagion. J. Money Credit Bank. 35 (1), 111–128. Gai, P., Haldane, A., Kapadia, S., 2011. Complexity, concentration and contagion. J. Monet. Econ. 58 (5), 453–470. Gauthier, C., He, Z., Souissi, M., 2010. Understanding systemic risk: the trade-offs between capital, short-term funding and liquid asset holdings. In: Bank of Canada Working Paper. Gauthier, C., Lehar, A., Souissi, M., 2012. Macroprudential regulation and systemic capital requirements. J. Financ. Int. 21 (4), 594–618. Georg, C., 2013. The effect of the interbank network structure on contagion and common shocks. J. Bank. Financ. 37 (7). Georg, C., Abbassi, P., Gabrieli, S., 2013. A network view on money market freeze. In: Banque de France Discussion Paper. Glasserman, P., Young, P., 2013. How likely is contagion in financial networks? In: Discussion Paper No. 642, University of Oxford. Gordy, M., Howells, B., 2006. Procyclicality in Basel II: can we treat the disease without killing the patient? J. Financ. Intermed. 15 (3), 395–417. Gorton, G., Metrick, A., 2011. Securitized banking and the run on repo. J. Financ. Econ. 104 (3), 425–451. Huang, R., Ratnovski, L., 2011. The dark side of bank wholesale funding. J. Financ. Intermed. 20 (2), 248–263. Jarrow, R., 2013. A leverage ratio rule for capital adequacy. J. Bank. Financ. 37 (3), 973–976. Ladley, D., 2013. Contagion and risk-sharing on the interbank market. J. Econ. Dyn. Control 37 (7), 1384–1400. Lublóy, Á., 2005. Domino effect in the Hungarian interbank market. Hung. Econ. Rev. 52 (4), 377–401. Memmel, C., Sachs, A., Stein, I., 2012. Contagion in the interbank market with stochastic loss given default. Int. J. Cent. Bank. 8 (3), 177–206. Merrill, B., Nadauld, D., Stulz, R.M., Sherlund, S., 2012. Did capital requirements and fair value accounting spark fire sales in distressed mortgage-backed securities? In: Working Paper No. 18270, National Bureau of Economic Research. Mistrulli, P., 2011. Assessing financial contagion in the interbank market: maximum entropy versus observed interbank lending patterns. J. Bank. Financ. 35 (5), 1114–1127. Morris, S., Shin, H., 2009. Illiquidity component of credit risk. In: Princeton University Working Paper. Müller, J., 2006. Interbank credit lines as a channel of contagion. J. Financ. Serv. Res. 29 (1), 37–60. Nier, E., Yang, J., Yorulmazer, T., Alentorn, A., 2007. Network models and financial stability. J. Econ. Dyn. Control 31 (6), 2033–2060. Sheldon, G., Maurer, M., 1998. Interbank lending and systemic risk: an empirical analysis for Switzerland. Swiss J. Econ. Stat. 134 (4), 685–704.

18

O.-M. Georgescu / Journal of Financial Stability 18 (2015) 1–18

Shin, H., 2009. Reflections on Northern Rock: the bank run that heralded the global financial crisis. J. Econ. Perspect. 23 (1), 101–120. Upper, C., 2011. Simulation methods to assess the danger of contagion in interbank markets. J. Financ. Stab. 7 (3), 111–125. Upper, C.A.W., 2004. Estimating bilateral exposures in the German interbank market: Is there a danger of contagion? Eur. Econ. Rev. 48 (4), 827–849.

Van Lelyveld, I., Liedorp, F., 2006. Interbank contagion in the Dutch banking sector: a sensitivity analysis. Int. J. Cent. Bank. 2 (2), 99–133. Vivier-Lirimont, S., 2006. Contagion in interbank debt networks. In: Working Paper. Wallison, P.J., 2008 July. Fair Value Accounting: A Critique. American Enterprise Institute for Public Policy Research Outlook Series. Wells, S., 2002. UK interbank exposures: systemic risk implications. Financ. Stab. Rev. 13 (12), 175–182.