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A Guide to IMF Stress Testing
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Chapter 15. Balance Sheet Network Analysis of Too-Connected-to-Fail Risk in Global and Domestic Banking Systems

Author(s):
Li Ong
Published Date:
December 2014
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Author(s)
Jorge A. Chan-LauThis chapter was previously published as IMF Working Paper No. 10/107 (Chan-Lau, 2010a). It has benefited from comments from Santiago Acosta, Jorge Canales-Krijlenko, Martin Cerisola, Teresa Daban, Mercedes Garcfa-Escribano, Franka Liedorp, Robert Rennhack, Rafael Romeu, Rodrigo Valdés, Hanne van Voorden, and Mercedes Vera-Martfn and from seminar participants at the IMF.

The 2008–9 financial crisis highlighted the importance of evaluating vulnerabilities owing to interconnectedness, or too-connected-to-fail risk, among financial institutions for country monitoring, financial surveillance, investment analysis, and risk management purposes. This chapter illustrates the use of balance sheet–based network analysis to evaluate interconnectedness risk, under extreme adverse scenarios, in banking systems in mature and emerging market countries, and between individual banks in Chile, an advanced emerging market economy.

Method Summary

Method Summary
OverviewThis technique is used to assess the impact of credit and liquidity shocks on the balance sheets of a group of interconnected institutions.
ApplicationThe method is appropriate for assessing how idiosyncratic shocks affecting one institution or group of institutions are propagated through the financial system.
Nature of approachSimulation-based.
Data requirements
  • Individual firm data on claims against and liabilities to other firms active in the financial system.
  • Users are required to make assumptions on market-level parameters (e.g., haircuts, funding rollover levels).
Strengths
  • The model enables the ranking of firms by the systemic risk they pose to the system and their vulnerability to other firms’ failures.
  • The model specification is flexible.
Weaknesses
  • Assumptions are required on the different parameters of the model.
  • The data may be very difficult to obtain and aggregation issues may compromise the results.
ToolExcel and MATLAB programs are available from the author upon request.

1. Too-Connected-to-Fail Risk

The recent financial crisis experienced in 2008—09 has raised concerns on the adverse consequences associated with externalities inherent in the financial system. One particular concern associated with the increased pace of globalization and financial integration is interconnectedness risk, or the too-connected-to-fail (TCTF) problem. The TCTF problem, in turn, brings up issues on how best to regulate TCTF institutions and how to ensure they fall within the perimeter of regulation.

A rather simplistic characterization of the TCTF problem is that the failure of one institution could lead to successive rounds of failures of other institutions in the system. The failure cascade is prompted by interinstitution exposure from the existence of direct and indirect linkages between the institutions in the system. The direct linkages arise, for instance, from balance sheet claims that expose one institution to the default of other institutions or from the reliance on credit lines that can be withdrawn abruptly without enough advance notice. The source of indirect linkages could be through derivatives contracts and securities with market values linked to the failure of an otherwise unrelated institution.1

Prudential regulation and systemic risk surveillance, therefore, call for the development of methods useful for assessing TCTF risk as emphasized recently by the IMF, the Bank for International Settlements (BIS), and the Financial Stability Board (FSB) (IMF/BIS/FSB, 2009a, 2009b). One such method, balance sheet–based network analysis, offers a practical way to analyze risks arising from linkages associated to direct exposures related to the balance sheet of financial institutions. The method is suitable for the type of data typically available to financial supervisors in most jurisdictions and the type of cross-country banking data available from institutions such as the BIS. When secondary market prices are available, network analysis complements assessments based on market-based methods.

This chapter first illustrates the use of balance sheet–based network analysis to evaluate interconnected risk from direct exposures across banking systems in advanced and emerging market economy countries. The analysis, based on BIS crosscountry bank claim data for reporting jurisdictions, suggests that the main sources of risk in the global banking system are shocks that could impair the solvency of banks based in the United States and the United Kingdom. Among BIS reporting jurisdictions in Latin America, it appears that the banking system in Brazil is the most resilient to global shocks whereas the banking system in Chile may be more exposed to funding risk from Spanish banks.

The chapter then turns to the analysis of bank exposures within a jurisdiction, specifically Chile, and takes advantage of bank-specific disaggregated data on claims vis-à-vis domestic banks, foreign banks, and other nonbank financial institutions publicly reported by the supervisory agency. The country-specific analysis highlights that the main sources of domestic risk in the Chilean banking system are shocks that affect banks’ claims on households and domestic corporations publicly reported by the supervisory agency. To a lesser extent, the banking system is exposed to shocks affecting banks domiciled in Spain and the United States. On the basis of balance sheet data, no bank operating in Chile appears to be a TCTF institution. The results suggest that, from a financial stability perspective, the focus is better placed on linkages with foreign banks and the creditworthiness of claims on the nonbank financial sector.

Before proceeding to describe the method and results, it is worth bearing in mind that the TCTF problem is not necessarily related to the problems of too-big-so-fail (TBTF) or too-many-to-fail (TMTF). An institution considered to be TBTF is not necessarily TCTF. For instance, in a banking system where retail deposits are the main funding source, interbank exposures are negligible, and there is deposit insurance, any bank with a large share of deposits could be TBTF owing to the costs associated with deposit insurance in case the bank defaults. The failure of such a bank, however, may not have a direct negative impact on other banks. Moreover, stronger banks may benefit from a flight to quality from depositors. In contrast, the business and operational framework under which banks operate may be such that the failure of a relatively small institution may put all institutions in the system at risk. An example in point is the distress experienced by the payment and settlement system following the liquidation of Herstatt Bank in 1974.

The TMTF problem is associated with the simultaneous failure of a large number of institutions owing to herd behavior (Acharya and Yorulmazer, 2007). The herd behavior is prompted by the observation that an individual institution, unless deemed TBTF, may be allowed to fail by the supervisory agency. It is in their best interest, therefore, for small institutions to coordinate their behavior such that, under adverse circumstances, a large number of them fail simultaneously. The TMTF problem, therefore, is different from the TCTF problem because the failure of one institution does not cause other institutions’ failures.

2. Balance Sheet-Based Network Analysis

A financial or banking system can be visualized as a network of institutions (or vertices) linked to each other through directed edges (or arcs). In graph theory, the combination of a set of vertices and a set of arcs constitutes a directed graph or digraph. Figure 15.1 depicts the digraph of a stylized banking system, consisting of seven banks that are represented by the vertices numbered from 1 to 7. Claims on a bank are represented by inbound arcs to the respective vertex. For instance, Bank 7 has claims on Banks 4 and 6.

Figure 15.1A Digraph Representation of a Banking System

Source: Author.

The mapping of a financial system into a digraph is useful from a supervisory and financial stability perspective. The digraph provides a simple visualization of the different linkages across institutions that, for instance, could help guide the design of the perimeter of regulation. Once the mapping has been established, different analytical tools can be brought in to analyze the stability of the financial system. This chapter describes a simple set of tools, balance sheet–based network analysis, which builds on simple balance sheet accounting identities and simulations to analyze different types of shocks affecting the banking system. A more sophisticated set of tools, graph theory–based models, are described in some detail in the Appendix.2

Balance sheet—based network analysis models rely on financial statements data to construct the matrix of cross-claims across institutions and use simulation to analyze how shocks affecting one institution are propagated through the banking system. Among others, balance sheet—based models include those of Sheldon and Maurer (1998), Furfine (2003), Upper and Worms (2004), Wells (2004), Elsinger, Lehar, and Summer (2006), and, more recently, Aikman and others (2009) and Chan-Lau and others (2009). Though definitely more rudimentary than network models based on graph theory, balance sheet—based models are relatively easy to implement, and the results have a clear economic interpretation, which facilitates communication with senior decision makers.3

A. The basic accounting identity

Balance sheet—based models start from the observation of the equality between the asset side and the liability side of the balance sheet of a bank or financial institution (Figure 15.2). On the asset side of the balance sheet, the bank records its claims on other financial institutions, corporations, and households, such as loans, receivables, equity shares, and debt securities. On the liability side, the bank records what it owes to its shareholders, that is, the bank’s equity, and to different creditors, including depositors, plus other items, which together with the bank’s equity constitutes the bank capital.4

Figure 15.2A Simplified Bank Balance Sheet

Source: Author.

The bank’s capital is the first cushion against declines in the value of the assets of the bank. If the decline in asset value exceeds the value of the bank’s capital, the bank defaults as its capital disappears.5 The default of the bank ripples through the banking system as the bank defaults on its liabilities or through the forced withdrawing of the funding it has extended to other banks in the system. Losses from claims on the defaulted banks erode the capital of the surviving banks. In addition, funding withdrawals, if not fully replaced, could force fire sale of assets at depressed values and reduce the asset and equity value of the selling bank while forcing mark-to-market losses in other banks.

Balance sheet–based network analysis models can accommodate a number of different shocks, namely, credit shocks, funding shocks, risk-transfer shocks, and different combinations of the aforementioned shocks. The next paragraphs offer a diagrammatic explanation of the concepts underlying the framework presented in Chan-Lau and others (2009). Readers interested in the full details of the methodology, including the equations, should refer to this paper.

B. Credit shocks

Credit shocks are associated with losses on the asset side of the balance sheet.6 Claims on other banks are recorded as an asset. When other banks default, the value of the claim is reduced because it is unlikely that the creditor bank recovers the claim’s full value, or in other words, the loss given default is strictly positive, or equivalently, the recovery ratio is less than 100 percent. In consequence, the capital of the bank declines (Figure 15.3).

Figure 15.3Credit Shock

Source: Author.

The bank defaults if the losses exceed the value of its capital:

A simple simulation can determine whether the default of a bank can trigger a cascade of failures. After setting the default of a specific bank, equation (15.1) is used to see whether losses to other banks could trigger their default. If another bank defaults, its defaulted claims are taken away from the capital of the surviving banks, and again, it is necessary to check whether another bank defaults as a consequence of the new default. The previous step is repeated until no other bank defaults. When only credit shocks are analyzed, it is assumed that other banks can replace funding from defaulted banks without major difficulties.

C. Funding shocks

Funding shocks are associated with the sudden withdrawal of funding and constitute a liability shock. Because assets need to be supported by liabilities, a sudden shortfall in funding sources leads to a reduction of the balance sheet of the bank if it cannot find alternative funding sources. Under normal market conditions, the amount of assets the bank needs to sell is equal to the loss of funding and the bank capital is not affected (Figure 15.4). Furthermore, the leverage of the bank declines, lowering the probability that it may become insolvent.

Figure 15.4Funding Shock under Normal Market Conditions

Source: Author.

The bank, however, may be forced to liquidate assets at below face values under fire sale conditions, especially if the market is undergoing a liquidity shortage, the assets are very illiquid, or if the bank holds large positions in certain assets. In the last case, if other banks and market participants know that the affected bank needs to liquidate certain assets, they may collude to mark these assets down in order to take advantage of the bank’s distress.7 In this case, the bank may need to liquidate assets in excess of the funding withdrawn from the bank. These losses are reflected in capital losses (Figure 15.5).

Figure 15.5Funding Shock under Stressed Market Conditions

Source: Author.

For some banks, funding losses could exceed their capital and cause their default. In this case, the initial funding shock leads to both subsequent credit and funding shocks as other banks default. The following inequalsty determines when a bank defaults:

As in the pure credit shock case, simulations can be used to determine how resilient the system is to funding shocks affecting the system banks.

D. Risk transfer shocks and off-balance-sheet exposures

Risk transfer shocks are associated with losses from off-balance-sheet (OBS) exposures. Analyzing these losses in a balance sheet framework requires additional information related to the size of the OBS exposure and the provisions held against it by the bank. Once this information is obtained, the analysis of a risk transfer shock can be analyzed in an extended balance sheet framework (Figure 15.6).

Figure 15.6Risk Transfer Shock

Source: Author.

Note: OBS = off-balance-sheet.

When the bank experiences losses in its OBS exposure, it first uses its OBS provisions as a buffer. When the loss exceeds the provisions, the bank suffers capital losses, and if the capital losses are large enough, the bank defaults:

It goes without saying that a bank default owing to an OBS exposure shock could trigger subsequent credit and funding shocks in the banking system and lead to the failure of other banks. As in the case of credit shocks and funding shocks, simple simulations can be used to analyze the impact of OBS losses on the banking system.

3. Balance Sheet-Based Network Analysis in Practice

This section illustrates the use of balance sheet–based network analysis in the assessment of TCTF or interconnectedness risk in the global banking system and in the domestic banking system in Chile, an advanced emerging market economy closely integrated into the financial system.8

Only credit shocks, funding shocks, and simultaneous credit and funding shocks are considered in the analysis. The following assumptions are used to calculate the results: (1) the loss given default in the credit shock scenario is set equal to 70 percent; and (2) in the case of funding shocks, only 40 percent of the funding can be replaced, forcing the sale of assets at fire sale prices 50 percent below book value.

Risk transfer shocks are not considered in the analysis of the global banking system because the aggregate data approximate only roughly the interbank exposure across countries. Furthermore, up to date there are no publicly available data sources on risk transfers at the individual institution level. Given the data limitations, it may not be proper to add another layer of approximations to try to infer risk transfer between banks. In the analysis of the Chilean domestic banking system, credit risk transfers between institutions are negligible.

One important caveat in interpreting the results is that in all the calculations, it is assumed that either a bank or banking system fails, which is a very low-probability event under the current environment, or that a sudden withdrawal of funding takes place, which is also a low-probability event. Therefore, the results should be interpreted as those corresponding to very extreme adverse scenarios.

A. TCTF risk analysis in mature and emerging market countries’ banking systems

The analysis of TCTF risk from the perspective of the global banking system relies on the availability of data on crosscountry claims across different bank jurisdictions. Currently, the BIS is the only institution that compiles cross-border banking statistics. In particular, consolidated banking statistics, constructed using central bank reports in 42 countries, comprise a country’s aggregate banking system financial claims on the rest of the world.9 These statistics have been widely used to assess the risk of exposures of lenders’ national banking systems to other countries, but there is wide consensus that it is necessary to improve data collection on interbank exposures (FSB and IMF, 2009).

Consolidated banking statistics are reported on an immediate borrower and an ultimate borrower basis. Figures reported on an immediate borrower basis correspond to contractual claims by the head office of a bank and all its branches and are assigned to the home country of the head office. Because banks have access to risk transfer or risk mitigation instruments and techniques, cross-country claims could actually differ from contractual claims. Figures reported on an ultimate borrowing basis account for the impact of risk transfers on contractual claims.

In principle, the difference between claims on an immediate borrower basis and ultimate borrower basis can be used to infer the risk transfer exposures. The analysis here refrains from performing such inference because the aggregate data are only an approximation to interbank exposures as they include, in addition to claims on banks, claims on nonbank financial institutions, nonfinancial institutions, and households. Under these circumstances, it was not considered appropriate to add another layer of approximation by inferring risk transfer exposures.10

Balance sheet–based network analysis was used to evaluate TCTF risk in banking systems with BIS consolidated claims data on an immediate borrower basis for 20 countries in the first and third quarters of 2009.11 The country sample includes emerging market countries: Brazil, Chile, and Mexico; and mature market countries: Austria, Belgium, Canada, Denmark, France, Germany, Greece, Ireland, Italy, Japan, the Netherlands, Portugal, Spain, Sweden, Switzerland, the United Kingdom, and the United States. Data on total capital in the banking system in the countries analyzed were obtained from different sources, including the European Central Bank statistics and different issues of banking system supplements published by Moody’s Investor Services.

Table 15.1 shows what banking systems may be at risk because of shocks affecting banks headquartered in other countries. For the purpose of the analysis, it is assumed that a banking system fails if losses from the shocks exceed the aggregate capital in the system because aggregated data do not allow identifying specific banks that may fail as a consequence of the shock. Imposing the above banking system failure condition is akin to assuming that claims and liabilities of failed banks are taken over by the surviving banks in the country. The results are complemented by Table 15.2, which shows capital losses in national banking systems because of shocks to other jurisdictions.

Table 15.1Global Banking System: Number of Potential Failures
Panel A: First Quarter, 2009
Type of Shock, and Orginating Banking System
CreditFundingCredit and Funding
Banking system failure inUKUnited StatesSpainDenmarkFranceGermanyNetharlandsSpainUKUnited States
AustriaYesYes
BelgiumYesYesYesYesYesYesYes
Brazil
CanadaYesYesYes
ChileYesYesYesYes
DenmarkYesYesYesYesYes
FranceYesYesYesYes
GermanyYesYesYesYes
GreeceYesYes
IrelandYesYesYesYesYes
ItalyYesYes
JapanYesYesYes
MexicoYesYes
NetherlandsYesYesYesYesYesYes
PortugalYesYesYes
SpainYesYesYes
SwedenYesYesYesYesYesYes
SwitzerlandYesYesYesYes
UKYesYes
United StatesYes
Total, excluding originating country8131125111818
Sources: Author; Bank for International Settlements (BIS); European Central Bank; and Moody’s Investors Services.Note: The table shows potential banking system failures induced by shocks originating in banking systems in other countries. The calculations use BIS cross-border claims data on an immediate borrower basis.
Panel B: Third Quarter 2009
Type of Shock, and Orginating Banking System
CreditFundingCredit and Funding
Banking system failure inDenmarkUKUnited StatesSpainDenmarkFranceGermanySpainUKUnited States
AustriaYesYesYesYes
BelgiumYesYesYesYesYesYes
Brazil
CanadaYesYesYesYes
ChileYesYesYesYesYes
DenmarkYesYesYesYesYes
FranceYesYesYesYesYes
GermanyYesYesYesYes
GreeceYesYesYes
IrelandYesYesYesYesYes
ItalyYesYesYesYes
JapanYesYesYesYes
MexicoYesYesYes
NetherlandsYesYesYesYesYesYesYes
PortugalYesYesYesYesYes
SpainYesYesYesYesYes
SwedenYesYesYesYesYesYesYes
SwitzerlandYesYesYesYesYes
UKYesYesYes
United StatesYesYesYes
Total, excluding originating country110151121811818
Sources: Author; Bank for International Settlements (BIS); European Central Bank; and Moody’s Investors Services.Note: The table shows potential banking system failures induced by shocks originating in banking systems in other countries. The calculations use BIS cross-border claims data on an immediate borrower basis.
Sources: Author; Bank for International Settlements (BIS); European Central Bank; and Moody’s Investors Services.Note: The table shows potential banking system failures induced by shocks originating in banking systems in other countries. The calculations use BIS cross-border claims data on an immediate borrower basis.
Table 15.2Global Banking System: Potential Capital Losses(in percent)
Panel A: First Quarter, 2009
Capital losses inAustriaBelgiumBrazilCanadaChileDenmarkFranceGermanyGreeceIrelandItalyJapanMexicoNetharlandsPortugalSpainSwedenSwitzerlandUKUnited States
Austria301032675343720131519100100
Belgium6180910010055840100100739412100100
Brazil1011155001202121035858
Canada041021826021120120115100100
Chile0150122330034114010011100100
Denmark15010241000192401215865100100
France31823058888512813642229100100
Germany16816116775264114138633912100100
Greece340001524155301231128100100
Ireland52006011651005311503672145100100
Italy205010154822730151813100100
Japan1214022528034180315100100
Mexico0000002117001512010004100100
Netherlands89061931310010072045207768519100100
Portugal2670024572722710226916100100
Spain152018240510510223181612100100
Sweden25120100311001745016178100100
Switzerland7871101076922481144229285100100
UK2738055077122813220221310100
United States1632114486718545720110327100
Sources: Author; Bank for International Settlements (BIS); European Central Bank; and Moody’s Investors Services.Note: The table shows capital losses induced by shocks affecting other countries as percent of banking system total capital. The calculations use BIS cross-border claims data on an immediate borrower basis.
Panel B: Third Quarter, 2009
Credit and funding shock originated in:
Capital losses inAustriaBelgiumBrazilCanadaChileDenmarkFranceGermanyGreeceIrelandItalyJapanMexicoNetharlandsPortugalSpainSwedenSwitzerlandUKUnited States
Austria50104301004741201727210100100
Belgium91601010010076446110100843312100100
Brazil11031776000303228037676
Canada1300220100071130130115100100
Chile011701221000023113010011100100
Denmark15010251000193401114988100100
France3183306100810562913742439100100
Germany181015116856274416141635913100100
Greece4500015610065501361136100100
Ireland62109012711005331703992246100100
Italy2150102571001740152913100100
Japan12250327100145180326100100
Mexico0000011710000159010004100100
Netherlands88772331210010062146205972620100100
Portugal2780035410012281020277825100100
Spain2526092441000512223191912100100
Sweden24130100341001747116178100100
Switzerland99811014771003191355232295100100
UK27590657100124816222223311100
United States16523155510019650722111324100
Sources: Author; Bank for International Settlements (BIS); European Central Bank; and Moody’s Investors Services.Note: The table shows capital losses induced by shocks affecting other countries as percent of banking system total capital. The calculations use BIS cross-border claims data on an immediate borrower basis.
Sources: Author; Bank for International Settlements (BIS); European Central Bank; and Moody’s Investors Services.Note: The table shows capital losses induced by shocks affecting other countries as percent of banking system total capital. The calculations use BIS cross-border claims data on an immediate borrower basis.

In general, if shocks originate in the banking systems in the United Kingdom and the United States, they may have had the potential to cause failures in the banking systems in most countries during 2009. By this standard, banks headquartered in the United Kingdom and the United States could be TCTF from a global perspective. Similarly, systemic risk from shocks originating in the banking system in Germany appears to have increased twofold in the six-month period from March 2009 to September 2009.

In Europe, shocks that originate in the French banking system could potentially have a large impact on banking systems in Belgium and the Netherlands. It is also apparent that Swedish banks could be exposed to negative shocks to Danish banks. Among the Latin American countries analyzed, the banking system in Chile is the most exposed to funding risks from Spanish banks. Interestingly, the Brazilian banking system appears robust enough to withstand the ripple effect from adverse shocks affecting major banking systems.

Some simple measures can be used to assess the vulnerability of a national banking system to external shocks and the risk it poses to the banking systems in other countries. For instance, the average capital loss experienced by a national banking system because of shocks in other countries is a measure of TCTF vulnerability. Similarly, the average losses that shocks in a national banking system induce in other countries is a measure of TCTF risk. These measures are reported in Table 15.3 for simultaneous credit and funding shocks. Banks headquartered in Austria, for instance, lose on average 23 percent of their capital because of shocks in other banking systems. Conversely, shocks to banks headquartered in Austria induce average capital losses of around 5 percent in other countries.

Table 15.3Global Banking System: Too-Connected-to-Fail Risk (TCTF) and Vulnerability Measures
First Quarter 2009Third Quarter 2009
TCTFTCTFTCTFTCTF
VulnerabilityRiskVulnerabilityRisk
Austria204235
Beligum37103811
Brazil83154
Canada155195
Chile201241
Denmark24102510
France26462749
Germany27662899
Greece194234
Ireland28122913
Italy21162318
Japan15121914
Mexico192232
Netherlands39233924
Portugal253284
Spain21292530
Sweden267268
Switzerland2993110
UK19982199
United States20982399
Sources: Author; Bank of International Settlements (BIS); European Central Bank; and Moody’s Investors Service.Note: The table shows TCTF vulnerability and risk measures due to joint credit and funding shocks. The TCTF vulnerability measure is the average capital loss suffered by the banking system in the country listed in the column due to shocks affecting banking systems in other countries. The TCTF risk measure is the average capital loss induced by the failure of the banking system listed in the first column on other banking systems.
Sources: Author; Bank of International Settlements (BIS); European Central Bank; and Moody’s Investors Service.Note: The table shows TCTF vulnerability and risk measures due to joint credit and funding shocks. The TCTF vulnerability measure is the average capital loss suffered by the banking system in the country listed in the column due to shocks affecting banking systems in other countries. The TCTF risk measure is the average capital loss induced by the failure of the banking system listed in the first column on other banking systems.

From a TCTF perspective, the most vulnerable banking systems are those of Belgium, the Netherlands, and Switzerland, while the riskiest are those based in Germany, the United Kingdom, and the United States. Both TCTF risks and vulnerabilities increased during 2009. From a financial stability perspective, note that the continuous updating of a matrix of TCTF risks and vulnerabilities such as the one presented in Table 15.3 could be a useful input for financial surveillance and the setup of a dynamic risk scoring system.

Finally, by recalling the digraph representation of a financial system network in Figure 15.1, it is clear that the absence of direct exposure between two banking systems does not preclude their simultaneous failure if both are connected to a banking system that fails. For instance, in Figure 15.1, the failure of Bank 1 could prompt the failure of Bank 4 if the failure of the former induces the failure of Bank 3. Therefore, the failure of one banking system can trigger a default cycle. Take, for instance, the hypothetical default cycle triggered by a credit shock originating in the banking system in the United Kingdom (Table 15.1, first column). In a first round, the banking systems of Ireland, the Netherlands, and Switzerland are affected. In a second round, the banking systems of Belgium and Germany are affected; in a third round, the banking system in France fails, and the cumulative impact affects the banking system in Denmark in the last round.

B. Chile: TCTF risk analysis in an advanced emerging market economy

This section uses balance sheet–based network analysis to evaluate the TCTF risk in Chile, an advanced emerging market economy. Data on claims and liabilities of individual banks vis-à-vis the central bank, foreign banks, and the corporate, nonbank financial, and household sectors are available from the Monthly Report on Financial Institutions published by the Banking Supervisory Agency/Superintendencia de Bancos e Instituciones Financieras with a one- to two-month lag.12

The monthly report covers 20 domestic banks and foreign bank subsidiaries and 5 foreign bank branches. For each supervised financial institution, the report states the total amount the institution owes to other banks in the system but not to specific institutions. Similarly, the report states the total claims the institution has on other banks in the system but does not disaggregate claims by individual banks.

In the absence of more detailed interbank exposure data, the matrix of interbank exposures was constructed by assuming that the amount a bank owes in the system is divided equally among all banks reported as having claims on other banks. The above shortcut is analogous to assuming that banks attempt to diversify their interbank exposure as much as possible. This is not the only possible way to construct the matrix of interbank exposures. One alternative is to assign the amount owed by the bank proportionally to the size of the claimant banks. Another alternative is the use of entropy techniques, as done, for instance, by Sheldon and Maurer (1998) and Wells (2004).

Similarly, there is no publicly available detailed information on assets and liabilities vis-à-vis individual foreign banks or specific foreign banking systems. In the analysis presented here, foreign banks are modeled as a single sector. The assumption of a single foreign banking sector errs on the conservative side as it implies that all foreign banks will be simultaneously affected by the same shocks. For instance, a funding shock implies that all foreign banks withdraw funding to banks operating in Chile at the same time.

In addition to domestic and foreign banks, the banking system network was augmented to include the Central Bank of Chile/Banco Central de Chile (BCCH), the nonbank financial institutions sector, the corporate sector, and the household sector. The BCCH is included because it has been an important provider of liquidity and financing to the banking sector in the aftermath of the 2008—09 global financial crisis. The inclusion of the central bank in the network is relatively straightforward because there are bank-specific data on the claims and liabilities it holds vis-à-vis domestic banks.

The importance of nonbank financial institutions, especially pension funds and mutual funds, has increased in the wholesale funding market. In the case of nonbank financial institutions, the monthly report provides data on the deposits they held on individual banks, but there are no data on what they may owe to banks. So, in the analysis, nonbank financial institutions appear only as creditors to the banking system.

Corporations account for a substantial share of bank claims. Claims on corporates are constructed using data on corporate loans and receivables. In the analysis, the corporate sector appears only as a debtor because there are no data on corporates’ claims on the banking system. Finally, households play a large role on the funding side, through deposits, as well as on the asset side, as borrowers. Data on household deposits and consumer loans are used to include the household sector in the network.

Tables 15.4 and 15.5 report the results of the analysis in January, July, and December 2009. Table 15.4 reports the number of potential defaults and Table 15.5 the average capital losses.

Table 15.4Chile: Potential Number of Induced Defaults
Type of Shock
Number of bank failuresCredit ShockFunding ShockCredit and Funding Shock
when shock comes fromJan. 2009Jul. 2009Dec. 2009Jan. 2009Jul. 2009Dec. 2009Jan. 2009Jul. 2009Dec. 2009
Bank 1000000000
Bank 2000000000
Bank 3000000000
Bank 4000000000
Bank 5000000000
Bank 6000000000
Bank 7000000000
Bank 8000000000
Bank 9000000000
Bank 10000000000
Bank 11000000000
Bank 12000000000
Bank 13000000000
Bank 14000000000
Bank 15000000000
Bank 16000000000
Bank 17000000000
Bank 18000000000
Bank 19000000000
Bank 20000000000
Bank 21000000000
Bank 22000000000
Bank 23000000000
Bank 24000000000
Bank 25000000000
Central bank000000000
Foreign banks000111111
Nonbank financial institutions000214214
Corporates171614N/AN/AN/A171614
Households141212171716171716
Sources: Author; and Banking Supervisory Agency/Superintendencia de Bancos e Instituciones Financieras (SBIF).Note: The table shows the number of induced bank defaults due to credit shocks, funding shocks, and the joint realization of credit and funding shocks.
Sources: Author; and Banking Supervisory Agency/Superintendencia de Bancos e Instituciones Financieras (SBIF).Note: The table shows the number of induced bank defaults due to credit shocks, funding shocks, and the joint realization of credit and funding shocks.
Table 15.5Chile: Average Capital Losses(in percent)
Type of Shock
Average bank capital lossesCredit ShockFunding ShockCredit and Funding Shock
when shock comes fromJan.2009Jul. 2009Dec. 2009Jan. 2009Jul. 2009Dec. 2009Jan. 2009Jul. 2009Dec. 2009
Bank 10.01.10.00.00.00.00.01.10.0
Bank 24.40.00.10.00.00.04.40.00.1
Bank 37.41.70.60.00.00.07.41.70.7
Bank 40.33.15.70.20.00.00.53.16.9
Bank 510.21.00.80.00.10.110.21.11.1
Bank 63.20.00.00.00.00.03.20.00.0
Bank 70.00.00.00.20.10.10.20.10.1
Bank 80.20.00.00.20.10.00.40.10.0
Bank 90.00.20.00.20.00.00.20.20.0
Bank 100.30.00.50.20.10.10.50.10.7
Bank 110.00.00.00.00.10.00.00.10.0
Bank 120.00.00.00.20.10.10.20.10.1
Bank 130.50.00.00.00.00.00.50.00.0
Bank 140.00.00.00.00.10.00.00.10.0
Bank 150.51.00.50.20.00.00.71.00.6
Bank 160.02.80.00.00.10.10.02.90.1
Bank 172.65.80.00.20.00.02.85.80.0
Bank 181.00.40.10.20.10.11.20.50.2
Bank 192.40.60.00.00.10.12.40.70.1
Bank 200.30.10.00.20.10.10.50.20.1
Bank 210.00.00.00.20.10.10.20.10.1
Bank 220.00.00.00.00.00.00.00.00.0
Bank 230.00.10.00.20.10.00.20.20.0
Bank 240.00.00.00.20.10.00.20.10.0
Bank 250.00.00.00.20.10.10.20.10.1
Central bankn.a.n.a.n.a.2.93.93.55.07.04.7
Foreign banks7.83.05.317.313.416.825.116.422.2
Nonbank financial institutions0.00.00.043.141.743.743.141.743.7
Corporates82.176.675.8N/AN/AN/A83.177.076.1
Households68.064.558.586.585.985.486.585.985.5
Sources: Author; and SBIF.Note: The table shows the average bank capital losses suffered due to credit shocks, funding shocks, and the joint realization of credit and funding shocks as percent of the institution’s total capital.
Sources: Author; and SBIF.Note: The table shows the average bank capital losses suffered due to credit shocks, funding shocks, and the joint realization of credit and funding shocks as percent of the institution’s total capital.

Domestic interbank exposure is relatively unimportant as the default of a single bank would not lead to further defaults (Table 15.4). The average capital losses reported in Table 15.5 provide further support while pointing toward a reduction of interbank exposures during 2009. For instance, in January 2009, the hypothetical default of Bank 5 and Bank 3 would have triggered average capital losses of 10.2 percent and 7.4 percent, respectively, but in December 2009, these losses declined to 1.1 percent and 0.7 percent, respectively. Against this trend, risks from Bank 4 appear to have trended upward. Average capital losses induced by its hypothetical default have increased to 6.9 percent from 0.3 percent. The hypothetical capital losses are mainly concentrated on Bank 12 (35 percent), Bank 21 (54 percent), and Bank 25 (47 percent).

A close examination of the results in Table 15.4 and 15.5 suggests that domestic banks were reducing their claim exposure to the corporate and household sectors during 2009. The number of banks that could default following a negative credit shock from the systemwide collapse of the corporate sector declined to 14 from 17 at the beginning of the year, while average capital losses declined to 76 percent from 82 percent. Similarly, average capital losses following defaults on household loans fell to 59 percent from 68 percent.

Domestic banks increased their reliance on wholesale funding from nonbank financial institutions in 2009. In December 2009, a hypothetical sudden withdrawal of nonbank financial deposits could lead to problems in four banks (Bank 16, Bank 17, Bank 18, and Bank 20) up from two in January 2009 (Bank 18 and Bank 20).

Another important funding source during 2009 was the central bank. On average, capital losses would be approximately 3 percent if central bank funding were not available. These losses, however, are heavily concentrated in a handful of institutions. As of December 2009, the institutions more affected by reduced funding from the central bank are Bank 4 (32 percent capital loss), Bank 11 (24 percent), and Bank 13 (22 percent).

Table 15.6 reports TCTF risk and vulnerability measures for Chilean financial institutions. Overall, in 2009, TCTF vulnerability was higher for foreign bank branches owing to their large interbank exposures relative to their capital. TCTF risk related to Bank 5 and Bank 17 declined during the year, but it increased substantially for Bank 4.

Table 15.6Chile: Too-Connected-to-Fail Risk (TCTF) and Vulnerability Measures
TCTF VulnerabilityTCTF Risk
JanuaryJulyDecemberJanuaryJulyDecember
200920092009200920092009
Bank 10.00.10.00.01.10.0
Bank 20.20.00.04.40.00.1
Bank 30.30.10.07.41.70.7
Bank 40.10.10.20.53.16.9
Bank 50.20.10.110.21.11.1
Bank 60.80.00.03.20.00.0
Bank 71.30.60.70.20.10.1
Bank 81.20.50.00.40.10.0
Bank 93.80.10.00.20.20.0
Bank 100.40.20.20.50.10.7
Bank 110.04.70.00.00.10.0
Bank 124.31.92.20.20.10.1
Bank 130.40.00.00.50.00.0
Bank 140.01.30.00.00.10.0
Bank 153.50.50.40.71.00.6
Bank 160.00.10.00.02.90.1
Bank 170.20.10.02.85.80.0
Bank 180.70.30.31.20.50.2
Bank 190.40.40.42.40.70.1
Bank 200.20.10.10.50.20.1
Bank 216.52.93.30.20.10.1
Bank 220.00.00.00.00.00.0
Bank 235.12.30.00.20.20.0
Bank 240.60.30.00.20.10.0
Bank 256.02.62.90.20.10.1
Sources: Author; and SBIF.Note: The table shows TCTF vulnerability and risk measures due to simultaneous credit and funding shocks. For the banks listed in the first column, the TCTF vulnerability is measured as the average capital loss the bank suffers from shocks to other banks in the system. The TCTF risk is measured as the average capital loss the bank induces on other banks in the system.
Sources: Author; and SBIF.Note: The table shows TCTF vulnerability and risk measures due to simultaneous credit and funding shocks. For the banks listed in the first column, the TCTF vulnerability is measured as the average capital loss the bank suffers from shocks to other banks in the system. The TCTF risk is measured as the average capital loss the bank induces on other banks in the system.

Finally, Table 15.7 reports excess capital losses in the banking system, as percent of total aggregate capital, owing to shocks originating in banks operating in Chile. Excess capital losses measure the capital losses in the system excluding the losses of the bank that triggered the shocks. This measure is a TCTF risk measure closely related to the concepts of incremental contribution to risk introduced in Chan-Lau (2009) and of marginal contribution to risk introduced by Tarashev, Borio, and Tsatsaronis (2009).

Table 15.7Banking System Excess Capital Loss(in percent)
Type of Shock
Banking system excess capitalCredit ShockFunding ShockCredit and Funding Shock
loss due to shocks fromJan. 2009Jul. 2009Dec. 2009Jan.2009Jul. 2009Dec. 2009Jan. 2009Jul. 2009Dec. 2009
Bank 10.00.10.00.00.00.00.00.10.0
Bank 20.70.00.10.00.00.00.70.00.1
Bank 31.20.20.70.00.00.01.20.20.7
Bank 40.10.56.90.20.00.00.20.56.9
Bank 51.80.21.00.00.10.11.80.21.1
Bank 60.50.00.00.00.00.00.50.00.0
Bank 70.00.00.00.20.10.10.20.10.1
Bank 80.00.00.00.20.10.00.20.10.0
Bank 90.00.00.00.20.00.00.20.00.0
Bank 100.00.00.70.20.10.10.20.10.7
Bank 110.00.00.00.00.10.00.00.10.0
Bank 120.00.00.00.20.10.10.20.10.1
Bank 130.10.00.00.00.00.00.10.00.0
Bank 140.00.00.00.00.10.00.00.10.0
Bank 150.10.10.60.20.00.00.20.10.6
Bank 160.00.40.00.00.10.10.00.50.1
Bank 170.40.90.00.20.00.00.60.90.0
Bank 180.10.00.10.20.10.10.30.10.2
Bank 190.40.10.00.00.10.10.40.10.1
Bank 200.00.00.00.20.10.10.20.10.1
Bank 210.00.00.00.20.10.10.20.10.1
Bank 220.00.00.00.00.00.00.00.00.0
Bank 230.00.00.00.20.10.00.20.10.0
Bank 240.00.00.00.20.10.00.20.10.0
Bank 250.00.00.00.20.10.10.20.10.1
Sources: Author; and SBIF.Note: The table shows banking system excess capital losses, in percent of capital in the banking system, induced by the failure of one bank. Excess capital losses are the total banking losses excluding the losses from the bank that triggered subsequent shocks in the system.
Sources: Author; and SBIF.Note: The table shows banking system excess capital losses, in percent of capital in the banking system, induced by the failure of one bank. Excess capital losses are the total banking losses excluding the losses from the bank that triggered subsequent shocks in the system.

In January 2009, Bank 3 accounted for 6.7 percent of the total capital in the banking system. In the hypothetical case that a credit shock affecting Bank 3 realizes, the banking system may suffer a capital loss of 7.9 percent, of which 6.7 percent corresponds to the capital of Bank 3 capital and an excess capital loss of 1.2 percent from banks with exposure to Bank 3. Hence, it can be stated that the TCTF risk posed by Bank 3 is equivalent to 1.2 percent of the banking system capital. As of December 2009, excess capital losses were relatively small and at most equal to 1½ percent for shocks from Bank 4. The overall analysis indicates that TCTF risk in the domestic banking system in Chile is relatively small.

4. Conclusion

Interconnectedness risk and the externalities associated with too-connected-to-fail institutions were a major amplifying and transmission mechanism during the 2008—09 global financial crisis. In response, there have been renewed efforts to understand and measure interconnectedness and TCTF risk and to ensure that the risk is properly addressed, as advanced in the current proposals for reforming the regulatory and supervisory framework as suggested by the Basel Committee on Banking Supervision (2009) and by Brunnermeier and others (2009). For instance, recent proposals on capital charges on interconnectedness risk are described in Adrian and Brunnermeier (2008); Tarashev, Borio, and Tsatsaronis (2009); Chan-Lau (2010c); and Gauthier, Lehar, and Souissi (2010).

This chapter has illustrated the use of a simple methodology, balance sheet–based network analysis, to capture inter-connectedness and TCTF risk in domestic and international banking systems using publicly available data sources under extreme adverse scenarios. In contrast to graph theory–based network analysis, there is no complex mathematics involved in the analysis but just simple balance sheet accounting identities. In consequence, balance sheet–based network analysis can be easily implemented whenever balance sheet data are available.

In the case of the global banking system, the analysis relies on data on cross-country claims compiled by the BIS. The results point out that shocks affecting the solvency of banks based in the United Kingdom and the United States, and, to a lesser extent, in Germany, could be the main sources of risk to banking systems worldwide. The results, however, should be interpreted with caution because of the high level of aggregation of the data.

In the case of Chile, detailed data at the bank level on claims and liabilities vis-à-vis other banks in the system, foreign banks, and nonbank financial institutions are available from the banking supervisory agency. The results suggest that TCTF risk is low and that, from a financial stability perspective, financial surveillance is better focused on the linkages of domestic banks with foreign banks and nonbank financial institutions.

Finally, although there are advantages to the use of balance sheet data and accounting identities, there are also some disadvantages related to the reliability of accounting data, as these are subject to manipulation, and the reporting lags, which may render the analysis irrelevant, especially if interbank exposures are changing rapidly.13 Some of the disadvantages can be addressed by complementing network analysis with market-based measures, which use information from security prices and common economic factors to assess TCTF risk. Examples of recent work in this direction are Adrian and Brunnermeier (2008), Chan-Lau (2009), and Chan-Lau (2013), among others.14

Appendix. Graph Theory–Based Network Models

Graph theory is the natural analytical framework for analyzing the properties of a financial system once it has been mapped into a digraph. In particular, it is possible to classify the different banks (vertices) into clusters and to evaluate how the system changes after the removal of a set of banks (vertices) and their respective linkages (arcs). In the latter case, the use of random graph theory makes it possible to add randomness either to the number of banks (vertices) in the system (digraph) or to the existence of linkages (arcs) between them. Random graph theory can, in principle, accommodate the observation that the number of participants in a connected financial system as well as the nature of their cross-linkages change over time.

Graph theory has been used extensively to analyze payment and settlement systems, as in Soramaki and others (2007); Bech, Chapman, and Garrat (2008); and Embree and Roberts (2009), among others. The focus of the analysis has been mostly on the topological properties of the system. Some of the topological properties include size, or the number of institutions in the system, connectivity, or the relative number of existing linkages to the maximum number of linkages, and the clustering coefficient, or the probability that two institutions “close” to a third one are also “close” to each other.

The insights gained from the application of graph theory to payment and settlement systems are difficult to translate to more complex systems, such as the interbank market, a domestic banking system, or the global financial system. The difficulty arises from the relative complexity that characterizes cross-claims across financial institutions, which stand in sharp contrast with the homogeneity of the transactions undertaken in the payment and settlement systems. Notwithstanding this difficulty, there have been some recent advances in extending graph theory to the analysis of complex banking systems in stylized models. Hattori and Suda (2009) use BIS banking data to analyze the topological properties of cross-border banking networks and their implications for banking stability. Nier and others (2007) use Erndos-Renyi graphs to explore how the different topological properties of a banking system affect the propagation of defaults. Gai and Kapadia (2010) use the small-world model of Watts (2002) to analyze contagion in a stylized network using numerical simulations.

Calibrating graph theory–based models with real data remains a major challenge for bringing these models to an operational level suitable for surveillance and supervisory purposes. As an alternative, applied research in policymaking institutions has opted for a simpler approach based on balance sheet data, which is described in the main text.

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1See Chan-Lau (2010b) and references therein.
2It is important to distinguish between the usage of the term network analysis in economics and social sciences and the usage in other disciplines. In economics and social sciences, network analysis refers to the analysis of the properties of systems that can be mapped into graphs using graph theory and combinatorics, for example, Bollobas (1998) and Durrett (2007). In other disciplines, network analysis focuses on optimizing flows between different nodes (or vertices), a problem closely related to optimization theory, for example, Ahuja, Magnanti, and Orlin (1993). For an early application of the latter type of techniques to financial systems, see Nagurney and Siokos (1997).
3An alternative approach not described here is the use of agent-based computational modeling, as in Markose and others (2010).
4The bank capital is equal to the sum of Tier 1 capital and Tier 2 capital. Tier 1 capital includes permanent shareholders’ equity plus disclosed reserves, including retained earnings less goodwill. Tier 2 capital includes general provisions and loan loss reserves, revaluation reserves, hybrid capital instruments, subordinated term debt, and undisclosed reserves less investments in unconsolidated financial subsidiaries and in the capital of other financial institutions.
5It can be argued, however, that the relevant event from a supervisory perspective is not the default of the bank per se but rather the event when the bank’s capital falls below the regulatory minimum level. The analysis using the tools in this chapter, in this case, could be easily extended by assuming that a bank “default” occurs when capital is less than the regulatory capital rather than when capital vanishes. The simplest way to incorporate this situation into the analysis is by reducing the amount of capital in the bank by the minimum regulatory capital and keeping the original definition of default intact.
6This is the case considered in Sheldon and Maurer (1998), Furfine (2003), and Wells (2004).
7See Hagan (2009) for a vivid narrative of the problems related to fire sale of assets and the markdown of positions faced by Bear Stearns in 2008.
8All calculations in this section were performed using Excel-Visual Basic for Applications programs based on Chan-Lau (2013).
9The consolidated banking statistics are available at http://www.bis.org/statistics/consstats.htm. See BIS (2008) for a detailed guide to the statistics and several issues of the BIS Quarterly Review.
10Readers interested in how to approximate risk transfers should refer to Chan-Lau and others (2009).
11The choice of consolidated banking statistics presumes that profits, as well as losses, are consolidated and ultimately borne by the head office of the bank. However, if foreign banks operate mainly as subsidiaries in host jurisdictions, the subsidiaries are required to operate as stand-alone institutions and to hold their own capital. In many instances, domestic supervisors would demand that foreign subsidiaries are ring-fenced, so that the head office or a related subsidiary in another country cannot have recourse to its capital. Under such circumstances, it could be argued that the analysis should be based on the BIS locational banking statistics. These statistics report claims and liabilities of bank offices in the countries in which they operate. Locational banking statistics are available at http://www.bis.org/statistics/bankstats.htm.
13Even sophisticated financial institutions may have problems collecting accounting data on a timely basis. According to Paul Friedman, COO of fixed income at Bear Stearns in 2008: “We go through the cash position, and there’s lot of questions as to how accurate it is…. The firm was not really set up—most firms are not—to do real-time cash accounting” (as quoted in Cohan, 2009).
14One caveat about using security prices, however, is that prices may not fully reflect the fundamental value of the banks and/or their true default risk: prices may be capturing the effects of factors like liquidity and technical supply-and-demand drivers, such as regulatory changes, that affect the decisions of market participants.

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