## _wp15255

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---

### I. Introduction — link between banking crises and sovereign fiscal risk
- Historical observation: banking crises are often followed by sovereign debt crises (Reinhart and Rogoff, 2009).
- Recent examples and magnitude:
  - Gross fiscal cost of supporting troubled banks in Iceland and Ireland exceeded 40 percent of GDP.
  - EU guarantees on bank liabilities totaled 30 percent of 2011 EU GDP from Q1 2008 to Q3 2012; Ireland provided guarantees of about 250 percent of 2011 GDP.
  - U.S. Debt Guarantee Program in 2008 provided debt guarantees in excess of $600 billion.
- International experience (1970–2011): average fiscal cost of banking crises about 12 percent of GDP; for the top ten percentile the cost has been more than 30 percent of GDP (Laeven and Valencia, 2013).
- Motivation: need for a real-time, replicable index to track bank-related contingent liabilities that could transmit risk to the government balance sheet.

### II. Contingent liabilities — definitions and importance
- Definitions:
  - Contingent liabilities: obligations entered into by government commitments that materialize upon uncertain future events (IMF, 2001).
  - Explicit liabilities: created by law or contract.
  - Implicit liabilities: obligations reflecting public interest or special-interest pressures (Cebotari, 2008).
- Bank-related contingent liabilities include explicit guarantees (e.g., deposit insurance) and implicit guarantees (e.g., ad hoc guarantees on bank debt).
- Fiscal costs arise when guarantees are honored through recapitalization or resolution and are typically larger when banking crises accompany currency crashes (Hoggarth, Reis, Saporta, 2002).

### III. Conceptual model and key drivers
- Conceptual approach:
  - Treat liabilities of each bank as implicitly guaranteed by the government.
  - Treat the banking sector’s liabilities as a portfolio of government guarantees.
  - Calculate expected cost (EL) and unexpected cost (UL) of those guarantees using a portfolio credit risk approach.
- Key determinants of EL and UL:
  - Size of the banking sector (L).
  - Concentration / number of banks (N).
  - Diversification / distress correlation across banks (ρ).
  - Bank leverage and asset riskiness, which drive the bank probability of distress (pd).
- Empirical note: in most cases unexpected costs exceed expected costs.

### IV. Contingent liability for a single bank — components and costs
- Definitions used:
  - lit = total non-equity liabilities of bank i at time t, in percent of GDP.
  - pdit = probability that bank i falls into distress at time t (function of leverage and asset volatility).
  - pssit = probability of state support to bank i, conditional on the bank falling into distress.
  - α (unnamed in some sections) = average loss given government support per dollar of bank liability (losses from resolution or recapitalization).
- Costs:
  - Expected cost of the implicit public guarantee computed from lit, pdit, pssit, and α.
  - Unexpected cost measured as the standard deviation of potential losses.
- Practical implication: both expected and unexpected costs depend on bank size, leverage, and asset volatility.

### V. Aggregation: sector (N banks) under independence
- Aggregation properties:
  - EL for the sector equals the sum of individual expected costs.
  - UL for the sector declines with greater number of banks (diversification): UL falls roughly with 1/√N in symmetric cases.
- Simplified symmetric case:
  - EL unchanged by N.
  - UL decreases as N increases.

### VI. Aggregation when bank distress is correlated
- Effects of correlation ρ:
  - EL is unchanged by correlation.
  - UL increases with higher ρ because Var(A + B) includes Covar(A,B).
  - When ρ = 0, the correlated formulation reduces to the independence case.
- Implication: common exposures, balance-sheet linkages, or similar business models that raise ρ materially increase unexpected fiscal risk.

### VII. The Banking Sector Contingent Liability Index (BCLI) — definition and interpretation
- Purpose: summarize EL and UL into a single metric of fiscal risk from banking sector contingent liabilities, expressed in percent of GDP.
- Interpretive features:
  - Captures both expected and unexpected costs of implicit public guarantees.
  - Constructed to represent potential losses under an adverse scenario characterized as a two-standard deviation event.
  - When the banking sector is diversified and N is large and ρ is close to zero, the BCLI can be interpreted as the government’s “value-at-risk” at the 5 percent likelihood level.
- Comparative statics (from Table 1):
  - Size↑ (L ↑) → Expected Cost ↑, Unexpected Cost ↑, BCLI ↑
  - Concentration↑ (N ↓) → Expected Cost: No change, Unexpected Cost ↑, BCLI ↑
  - Diversification↑ (ρ ↓) → Expected Cost: No change, Unexpected Cost ↓, BCLI ↓
  - Bank leverage↑ (pd ↑) → Expected Cost ↑, Unexpected Cost ↑, BCLI ↑
  - Bank asset volatility↑ (pd ↑) → Expected Cost ↑, Unexpected Cost ↑, BCLI ↑

### VIII. Data inputs and parameter choices used for the BCLI
- Bank liabilities (L):
  - Use Moody’s “total adjusted liabilities” measure (all bank liabilities except equity, minority interest, and deferred taxes).
- Probability of distress (pd):
  - Use Moody’s Expected Default Frequency (EDF), an equity-market implied probability of distress based on leverage and asset volatility.
  - EDF applied over a 1 year horizon and used because it is available for a large sample of banks at high frequency.
- Probability of state support (pss):
  - Proxied using Fitch Support Ratings (Support Ratings (SRF) and Support Rating Floors (SRFs)).
  - When a bank lacks an assigned support rating, average support rating for other banks in the bank’s home country is used.
- Loss given state support (α):
  - α is assumed to be 20 percent loss per insured liability.
  - Justification: Laeven and Valencia (2010, 2013) find gross fiscal cost of bank bailouts historically in the order of 20 percent of bank assets for emerging and developing economies; depressed asset sale prices during widescale failures motivate the assumption.

### IX. Sample coverage and aggregation (scope and scale)
- BCLI constructed for 258 banks in 32 countries.
- Banks selected to capture at least half—and usually more than 80 percent—of the national banking system in each country (excluding foreign subsidiaries), measured by total assets.
- Sample includes all G-SIBs as of November 2014 except ING Bank.
- U.S. sample includes all banks that participated in the 2011–13 CCAR stress tests except Ally Financial (previously GMAC).
- Aggregate asset coverage (as of end-2014):
  - Advanced economies: 148 banks with total consolidated assets of around $65 trillion.
  - Emerging markets: 110 banks with total assets of around $20 trillion.

### X. Cross-country and time-pattern findings (2006–13)
- General patterns:
  - A general rise in bank-related contingent liabilities during the global financial crisis of 2008–09.
  - A noticeable second rise during the euro zone crisis of 2011–12, more pronounced in European countries.
- Major advanced economies:
  - Germany, France, and the U.K.: most pronounced BCLI rise after the global crisis; BCLI remained elevated as of end-2013 relative to pre-crisis levels.
  - U.S. and Japan: BCLI returned to pre-crisis levels to a large extent.
- Other euro area countries:
  - Most pronounced increases: Ireland at the time of the global financial crisis; Greece, Portugal, Austria, Italy, and Spain during 2011–12.
  - BCLI declined substantially after the euro zone crisis of 2011–12, but remains elevated compared to pre-crisis levels (except Ireland).
- Other European countries:
  - Biggest rises: Switzerland, followed by Denmark and Sweden.
  - Contingent liabilities declined substantially after 2011–12 but remain elevated compared to pre-crisis levels.
- Other advanced economies:
  - Most pronounced BCLI rise: Singapore.
  - BCLI remains elevated in Australia, Canada, and Korea driven by rising total bank liabilities (especially in Singapore) and high assessed likelihood of state support.
- Major emerging markets:
  - Most pronounced rises: China and more recently India; also rose in Brazil and Turkey but from relatively low levels.
  - In China, drivers include rising total bank liabilities, elevated probabilities of bank distress, and high perceived likelihood of state support due to high government ownership.
- Other emerging markets:
  - Largest BCLI rises: Malaysia and Thailand.
  - BCLI remained relatively low for Chile and Colombia.

### XI. Component behavior and empirical validation
- Aggregation method: country-group results aggregated as weighted averages based on banks’ total adjusted liabilities.
- Empirical validation with fiscal outcomes:
  - Countries with relatively high BCLIs experienced larger fiscal costs due to bank support measures during 2007–2011.
  - Figure 4 comparison: countries with BCLI score of 7 or above are identified as relatively high contingent liability risk (one-third of sample).
  - Among the eight countries with the largest fiscal costs, six were identified by the BCLI as having relatively high contingent liability risk.
  - Prior research (Arslanalp and Liao, 2014) finds changes in the BCLI have a statistically significant impact on sovereign CDS spreads for a panel of advanced and emerging market economies.

### XII. Bank-level and G-SIB applications
- Bank-by-bank marginal contributions:
  - BCLI can decompose the contribution of individual banks by removing each bank in turn and measuring the decline in the BCLI.
  - Example: In Australia, the four largest banks (Australia and New Zealand Banking Group; Commonwealth Bank of Australia; National Australia Bank; Westpac Banking Corporation) account for the bulk of contingent liability risk.
- G-SIB monitoring:
  - BCLI can monitor contingent liability related to groups of large global systemically important banks (G-SIBs).
  - Estimated contingent liability risk (in U.S. dollars) for 30 G-SIBs as of November 2014 (excluding ING Bank) rose starting late 2007, peaked in March 2009, and declined thereafter except for a 2011 uptick.
  - Aggregation across countries for G-SIBs expresses liabilities (l_it) in U.S. dollars rather than percent of home country GDP.
  - Decline in BCLI post-crisis attributed to deleveraging and de-risking of banks’ balance sheets (L and pd), reduced distress correlation among banks (ρ), and lower perceived state support (pss), partly tied to regulatory efforts (e.g., EU BRRD).

### XIII. Limitations of the BCLI
- Scope limitations:
  - BCLI measures only direct fiscal outlays committed to bank support operations; it does not measure all costs (direct and indirect) of bank crises.
  - BCLI provides upfront gross fiscal cost estimates, not net fiscal cost after asset recoveries.
- Wider economic costs excluded:
  - BCLI does not capture indirect costs from banking crises such as loss of output and loss of government revenues.
- Recovery and net cost uncertainty:
  - Example historical variation: U.S. authorities recovered more than the full cost of initial public support in 2008–09; U.K. recovered only about a quarter of the cost as of end-2014 (IMF, 2015).
  - Historically, the average recovery rate in banking crises has been around 25 percent of the gross fiscal cost, with large variance (Laeven and Valencia, 2013).
- Measurement error sensitivity:
  - Index sensitive to proxies used (notably probability levels); BCLI may overstate or understate true contingent liability.
  - Recommended usage: rank-ordering countries and monitoring trends; use empirical studies in first differences.
  - EDF measure: effective for rank ordering defaulters during the global financial crisis, though EDF levels were conservative before the crisis.

### XIV. Policy implications and recommended uses
- Empirical research tool:
  - BCLI can fill gaps in empirical studies on the relationship between contingent liabilities and sovereign risk (Arslanalp and Liao, 2014).
- Surveillance for public debt sustainability:
  - BCLI could be a surveillance tool to monitor risks to public debt sustainability; IMF survey of 117 countries (IMF, 2015) indicates measuring financial-sector risks to public debt is often inadequate prior to risk materialization.
- Monitoring regulatory reform effects:
  - BCLI can assess impact of regulatory reforms aimed at reducing implicit government support to banks.
  - Example: EU BRRD (effective January 2016) expected to reduce pss; Financial Stability Board’s TLAC rule (comes into force in 2019) expected to reduce α—both should reduce the BCLI.
- Extension to non-bank sectors:
  - Methodology allows extension to construct indices tracking contingent liability risks from corporates, including state-owned enterprises and quasi-sovereign entities.

*Source: IMF staff calculations and text from _wp15255 (Appendix and main text excerpts).*

### References .............................................................................................................

### _wp15255 - References .............................................................................................................

### I. Introduction — link between banking crises and sovereign fiscal risk
- Historical observation: banking crises are often followed by sovereign debt crises (Reinhart and Rogoff, 2009).
- Recent examples and magnitude:
  - Gross fiscal cost of supporting troubled banks in Iceland and Ireland exceeded 40 percent of GDP.
  - EU countries approved guarantees on bank liabilities totaling 30 percent of 2011 EU GDP from Q1 2008 to Q3 2012, with Ireland providing guarantees of about 250 percent of 2011 GDP.
  - U.S. Debt Guarantee Program in 2008 provided debt guarantees in excess of $600 billion.
- International experience (1970–2011): average fiscal cost of banking crises about 12 percent of GDP; for the top ten percentile the cost has been more than 30 percent of GDP (Laeven and Valencia, 2013).
- Motivation: need for a real-time, replicable index to track bank-related contingent liabilities that could transmit risk to the government balance sheet.

### II. Contingent liabilities, banking crises, and fiscal costs — definitions and importance
- Contingent liabilities: obligations entered into by government commitments that materialize upon uncertain future events (IMF, 2001).
  - Explicit liabilities: created by law or contract.
  - Implicit liabilities: obligations reflecting public interest or special-interest pressures (Cebotari, 2008).
- Bank-related contingent liabilities include explicit guarantees (e.g., deposit insurance) and implicit guarantees (e.g., ad hoc guarantees on bank debt).
- Fiscal costs arise when guarantees are honored through recapitalization or resolution; costs are typically larger when banking crises accompany currency crashes (Hoggarth, Reis, Saporta, 2002).

### III. Model of contingent liabilities — overview and drivers
- Conceptual approach:
  - Treat liabilities of each bank as implicitly guaranteed by the government.
  - Treat the banking sector’s liabilities as a portfolio of government guarantees.
  - Calculate expected cost (EL) and unexpected cost (UL) of those guarantees using a portfolio credit risk approach.
- Key determinants of EL and UL:
  - Size of the banking sector (L).
  - Concentration / number of banks (N).
  - Diversification / distress correlation across banks (ρ).
  - Bank leverage and asset riskiness, which drive the bank probability of distress (pd).
- Empirical note: in most cases unexpected costs exceed expected costs.

### IV. Contingent liability for a single bank — components
- Definitions (as presented):
  - lit = total non-equity liabilities of bank i at time t, in percent of GDP.
  - pdit = probability that bank i falls into distress at time t (function of leverage and asset volatility).
  - pssit = probability of state support to bank i, conditional on the bank falling into distress.
  - (unnamed) = average loss given government support per dollar of bank liability (losses from resolution or recapitalization).
- Costs:
  - Expected cost of the implicit public guarantee is computed from these components.
  - Unexpected cost is measured as the standard deviation of potential losses.
- Practical implication: both expected and unexpected costs depend on bank size, leverage, and asset volatility.

### V. Contingent liability for the banking sector (N banks) — independence case
- Aggregation under independence assumption (bank distress events independent):
  - EL for the sector equals the sum of individual expected costs (aggregation preserves expectation).
  - UL for the sector declines with greater number of banks (diversification effect): UL falls roughly with 1/√N in symmetric cases.
- Simplifications for a non-concentrated system (equal-size banks) and identical pd and pss show:
  - EL remains unchanged by N.
  - UL decreases as N increases (diversification reduces unexpected fiscal risk).

### VI. Contingent liability when bank distress is correlated
- When bank failures are correlated (correlation coefficient ρ):
  - EL is unchanged by correlation.
  - UL increases with higher ρ because Var(A+B) includes Covar(A,B).
  - When ρ = 0, the correlated formulation reduces to the independence case.
- Implication: common exposures, balance-sheet linkages, or similar business models that raise ρ materially increase unexpected fiscal risk.

### VII. The Banking Sector Contingent Liability Index (BCLI) — definition and interpretation
- Purpose: summarize EL and UL into a single metric of fiscal risk from banking sector contingent liabilities, expressed in percent of GDP.
- Interpretive features:
  - Captures both expected and unexpected costs of implicit public guarantees.
  - Constructed to represent potential losses under an adverse scenario characterized as a two-standard deviation event.
  - When the banking sector is diversified and N is large and ρ is close to zero, the BCLI can be interpreted as the government’s “value-at-risk” at the 5 percent likelihood level.
- Comparative statics (from Table 1):
  - Size↑ (L ↑) → Expected Cost ↑, Unexpected Cost ↑, BCLI ↑
  - Concentration↑ (N ↓) → Expected Cost: No change, Unexpected Cost ↑, BCLI ↑
  - Diversification↑ (ρ ↓) → Expected Cost: No change, Unexpected Cost ↓, BCLI ↓
  - Bank leverage↑ (pd ↑) → Expected Cost ↑, Unexpected Cost ↑, BCLI ↑
  - Bank asset volatility↑ (pd ↑) → Expected Cost ↑, Unexpected Cost ↑, BCLI ↑

### VIII. Illustration and data inputs used for the BCLI
- Bank liabilities (L):
  - Use Moody’s “total adjusted liabilities” measure (all bank liabilities except equity, minority interest, and deferred taxes).
- Probability of distress (pd):
  - Use Moody’s Expected Default Frequency (EDF), an equity-market implied probability of distress based on leverage and asset volatility.
  - EDF applied over a 1 year horizon and used because it is available for a large sample of banks at high frequency.

_Italic: Source — Content unit: _wp15255 - References ............................................................................................................._

### Appendix 1 provides further details on the construction of the EDF, including how it differs

### _wp15255 - Appendix 1 provides further details on the construction of the EDF, including how it differs

### Construction and key parameter definitions
- EDF (Expected Default Frequency)
  - For almost all banks in the sample, Moody’s provides the standard EDF measure.
  - For 22 banks that do not have publicly listed equity, Moody’s CDS-implied EDF is used; these banks are noted in Appendix Table 2.
- Distress Correlation (ρ)
  - ρ is measured as a 12-month rolling window correlation of pair-wise EDFs.
  - Higher correlation is expected where banks have more similar business models, raising joint distress likelihood.
- Probability of State Support Given Distress (pss)
  - pss is proxied using Fitch Support Ratings (Support Ratings (SRF) and Support Rating Floors (SRFs)).
  - When a bank lacks an assigned support rating, the average support rating for other banks in the bank’s home country is used.
- Loss Given State Support (α)
  - α is assumed to be 20 percent loss per insured liability (a relatively conservative assumption).
  - This assumption is informed by Laeven and Valencia (2010, 2013) findings that gross fiscal cost of bank bailouts historically has been in the order of 20 percent of bank assets for emerging and developing economies.
  - Motivating factors include depressed asset sale prices during widescale failures (Shleifer and Vishny 1992; Allen and Gale 1994).

### Sample coverage and aggregation
- Bank and country coverage
  - BCLI constructed for 258 banks in 32 countries.
  - Banks selected to capture at least half—and usually more than 80 percent—of the national banking system in each country (excluding foreign subsidiaries), measured by total assets.
  - Sample includes all G-SIBs as of November 2014 except ING Bank.
  - U.S. sample includes all banks that participated in the 2011–13 CCAR stress tests except Ally Financial (previously GMAC).
  - Sample spans 23 of 29 jurisdictions deemed to have systemically important financial sectors by the IMF as of end-2014.
- Aggregate asset coverage (as of end-2014)
  - Advanced economies: 148 banks with total consolidated assets of around $65 trillion.
  - Emerging markets: 110 banks with total assets of around $20 trillion.

### Cross-country and time-pattern findings (2006–13)
- General patterns
  - A general rise in bank-related contingent liabilities during the global financial crisis of 2008–09.
  - A noticeable second rise during the euro zone crisis of 2011–12, more pronounced in European countries.
- Major advanced economies
  - Most pronounced BCLI rise after the global crisis: Germany, France, and the U.K.; BCLI remained elevated as of end-2013 relative to pre-crisis levels due to total bank liabilities remaining high and perceived probabilities of state support being on the whole higher.
  - In contrast, the U.S., and to a large extent Japan, saw the BCLI return to pre-crisis levels.
- Other euro area countries
  - Most pronounced increases: Ireland at the time of the global financial crisis; Greece, Portugal, Austria, Italy, and Spain during 2011–12.
  - BCLI declined substantially after the euro zone crisis of 2011–12, but remains elevated compared to pre-crisis levels (except Ireland) because total bank liabilities remain above pre-crisis levels and bank distress probabilities remain relatively high in some cases.
  - Likelihood of state support is assessed to be lower partly due to reduced sovereign debt ratings affecting government ability to support the banking system.
- Other European countries
  - Biggest rises in BCLI: Switzerland, followed by Denmark and Sweden.
  - Contingent liabilities declined substantially after 2011–12 but remain elevated compared to pre-crisis levels despite significant declines in total bank liabilities in Switzerland.
- Other advanced economies
  - Most pronounced BCLI rise: Singapore.
  - BCLI remains elevated in Australia, Canada, and Korea driven by rising total bank liabilities (especially in Singapore) and high assessed likelihood of state support.
- Major emerging markets
  - Most pronounced rises: China and more recently India; also rose in Brazil and Turkey but from relatively low levels.
  - In China, drivers include rising total bank liabilities, elevated probabilities of bank distress, and high perceived likelihood of state support due to high government ownership.
- Other emerging markets
  - Largest BCLI rises: Malaysia and Thailand.
  - BCLI remained relatively low for Chile and Colombia, reflecting smaller banking systems and lower bank distress probabilities.

### Component behavior and illustrative results
- Country-group component aggregation
  - Figures aggregate country-group results as weighted averages based on banks’ total adjusted liabilities.
- Empirical validation with fiscal outcomes
  - Countries with relatively high BCLIs experienced larger fiscal costs due to bank support measures during 2007–2011.
  - Figure 4 compares largest fiscal costs associated with bank support measures during 2007–2011 from Laeven and Valencia (2013) with the BCLI maximum during 2007–11; countries with BCLI score of 7 or above are identified as relatively high contingent liability risk (one-third of sample).
  - Among the eight countries with the largest fiscal costs, six were identified by the BCLI as having relatively high contingent liability risk.
  - Prior research (Arslanalp and Liao, 2014) finds changes in the BCLI have a statistically significant impact on sovereign CDS spreads for a panel of advanced and emerging market economies.

### Bank-level and G-SIB applications
- Bank-by-bank marginal contributions
  - BCLI can decompose the contribution of individual banks to overall country contingent liability risk by removing each bank in turn and measuring the decline in the BCLI.
  - Example: In Australia, the four largest banks (Australia and New Zealand Banking Group; Commonwealth Bank of Australia; National Australia Bank; Westpac Banking Corporation) account for the bulk of contingent liability risk despite Australia’s overall BCLI being relatively low compared to other advanced economies.
- G-SIB monitoring
  - BCLI can monitor contingent liability related to groups of large global systemically important banks (G-SIBs).
  - Figure 6: estimated contingent liability risk (in U.S. dollars) for 30 G-SIBs as of November 2014, excluding ING Bank due to data unavailability.
  - These liabilities rose starting late 2007, peaked in March 2009, and declined thereafter except for a 2011 uptick during the euro area debt crisis.
  - To aggregate across countries for G-SIBs, liabilities (l_it) are expressed in U.S. dollars rather than percent of home country GDP.
  - Decline in BCLI post-crisis attributed to deleveraging and de-risking of banks’ balance sheets (L and pd), reduced distress correlation among banks (ρ), and lower perceived state support (pss), partly tied to regulatory efforts (e.g., EU BRRD).

### Limitations of the BCLI
- Scope limitations
  - BCLI measures only direct fiscal outlays committed to bank support operations; it does not measure all costs (direct and indirect) of bank crises.
  - BCLI provides upfront gross fiscal cost estimates, not net fiscal cost after asset recoveries.
- Wider economic costs excluded
  - BCLI does not capture indirect costs from banking crises such as loss of output and loss of government revenues, which can be substantially larger and contribute to rising public debt after a crisis.
- Recovery and net cost uncertainty
  - Example historical variation: U.S. authorities recovered more than the full cost of initial public support in 2008–09; U.K. recovered only about a quarter of the cost as of end-2014 (IMF, 2015).
  - Historically, the average recovery rate in banking crises has been around 25 percent of the gross fiscal cost, with large variance (Laeven and Valencia, 2013).
- Measurement error sensitivity
  - Index is sensitive to proxies used (notably probability levels). BCLI may overstate or understate true contingent liability.
  - Despite potential proxy errors, BCLI is useful for rank-ordering countries and monitoring trends; recommended usage includes empirical studies in first differences.
  - EDF measure: found effective for rank ordering defaulters during the global financial crisis, though EDF levels were conservative (somewhat higher than subsequently realized default rates) before the crisis.

### Policy implications and recommended uses
- Empirical research tool
  - BCLI can fill gaps in empirical studies on the relationship between contingent liabilities and sovereign risk (Arslanalp and Liao, 2014).
- Surveillance for public debt sustainability
  - BCLI could be a surveillance tool to monitor risks to public debt sustainability; IMF survey of 117 countries (IMF, 2015) indicates measuring financial-sector risks to public debt is often inadequate prior to risk materialization.
- Monitoring regulatory reform effects
  - BCLI can assess impact of regulatory reforms aimed at reducing implicit government support to banks.
  - Example: EU BRRD (effective January 2016) expected to reduce pss; Financial Stability Board’s TLAC rule (comes into force in 2019) expected to reduce α (loss given default) parameters—both should reduce the BCLI.
- Extension to non-bank sectors
  - Methodology generality allows extension to construct indices tracking contingent liability risks from corporates, including state-owned enterprises and quasi-sovereign entities—useful where corporate-sovereign nexus is strong.

*Source: IMF staff calculations and text from _wp15255 (Appendix and main text excerpts).*

### References

### _wp15255 - References

### Major References Cited
- Allen, F. and D. Gale, 1994, “Limited Market Participation and Volatility of Asset Prices,” American Economic Review 84, 933–955.
- Arslanalp, S. and Y. Liao, 2014, “Banking Sector Contingent Liabilities and Sovereign Risk,” Journal of Empirical Finance, Volume 29 (December).
- Acharya, V., I. Drechsler, and P. Schnabl, 2014, “A Pyrrhic Victory? Bank Bailouts and Sovereign Credit Risk,” Journal of Finance, 69(9), December 2014.
- Amaglobeli, D., N. End, M. Jarmuzek, and G. Palomba, 2015, “From Systemic Banking Crises to Fiscal Costs: Risk Factors,” IMF Working Paper 15/166 (Washington: IMF).
- Asonuma, T., S. Bakhache, and H. Hesse, 2015, “Is Banks’ Home Bias Good or Bad for Public Debt Sustainability,” IMF Working Paper 15/44 (Washington: IMF).
- Brandao-Marques, L., R. Correa, and H. Sapriza, 2013, “International Evidence on Government Support and Risk Taking in the Banking Sector” Federal Reserve International Finance Discussion Papers, Number 1086 (August).
- Cebotari, A., 2008, “Contingent Liabilities: Issues and Practice,” IMF Working Paper 08/245 October 2008 (Washington: International Monetary Fund).
- Claessens, S., and D. Klingebiel, 2002, “Measuring and Managing Government Contingent Liabilities in the Banking Sector,” in Government at Risk: Contingent Liabilities and Fiscal Risk, edited by H. Polackova Brixi and A. Schick (Washington: World Bank).
- Correa, R. and H. Sapriza, 2014, “Sovereign Debt Crises,” Federal Reserve International Finance Discussion Papers, Number 1104 (May).
- Duffie D., L. Saita, and K. Wang, 2007, “Multi-period Corporate Default Prediction with Stochastic Covariates,” Journal of Financial Economics, Vol. 83, No. 3, (March).
- Hull, J. C., 2000, Options, Futures, and Other Derivatives, 4th edition, Prentice Hall.
- International Monetary Fund, 2001, Government Finance Statistics Manual (Washington: International Monetary Fund).
- International Monetary Fund, 2014, “How Big Is the Implicit Subsidy For Banks Considered Too Big To Fail?” GFSR Chapter 3, April (Washington: International Monetary Fund).
- International Monetary Fund, 2015, “Banking to Sovereign Stress: Implications for Public Debt”, January (Washington: International Monetary Fund).
- Laeven L., and F. Valencia, 2010, “Resolution of Banking Crises: The Good, the Bad, and the Ugly,” IMF Working Paper No. 12/146 (June).
- Laeven L., and F. Valencia, 2013, “Systemic Banking Crises Database,” IMF Economic Review, vol. 61(2), pages 225-270, June.
- Merton, R.C., 1974, "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, 29(2): 449–470.
- Moody’s, 2012, “Public Firm Expected Default Frequency (EDF) Credit Measures: Methodology, Performance, and Model Extensions,” Capital Markets Research.
- Munves D. W., A. Smith, and D. T. Hamilton, 2010, “Banks and their EDF Measures Now and Through the Credit Crisis: Too High, Too Low, or Just About Right?” Moody’s Analytics, Capital Markets Research (December).
- Reinhart, C, M, and K. S. Rogoff, 2009, “This Time Is Different: Eight Centuries of Financial Folly,” Princeton University Press.
- Schich, S. and Y. Aydin, 2014, “Measurement and Analysis of Implicit Guarantees of Bank Debt: Key Findings from OECD Survey,” OECD Journal: Financial Market Trends.
- Shleifer, A., and R. Vishny, 1992, “Liquidation Values and Debt Capacity: A Market Equilibrium Approach,” Journal of Finance, Vol. 47, iss. 4, pp. 1343–1366.
- Ueda, K. and B. Weder di Mauro, 2013, “Quantifying Structural Subsidy Values for Systemically Important Financial Institutions,” Journal of Banking and Finance (37): 3830–3842.
- Additional technical and rating-methodology sources including Fitch Ratings (2013, 2014), FDIC (2003), and Moody’s KMV technical papers.

### Appendix 1. Moody’s Expected Default Frequency (EDF) — Key Points and Metrics
- Definition: EDF is a credit risk measure calculated by Moody’s to assess the probability that a firm will default over a specified period of time, typically one year.
- EDF model default criterion: a firm defaults when the market value of its assets falls below its liabilities payable (the default point).
- Three key determinants of EDF:
  - (i) current market value of the firm (market value of assets);
  - (ii) level of the firm’s obligations (default point);
  - (iii) asset volatility (vulnerability to large changes).
- Market value of assets estimation: derived from equity value, equity volatility, and liability structure using a Merton (1974) type model treating equity as a call option on assets.
- Default point estimation: firm specific and estimated from Moody’s research, observing each firm’s default point at the time of default.
- Asset volatility measure: standard deviation of the annual percentage change in the market value of the firm’s assets.
- EDF properties and distinctions:
  - EDFs are dynamic and forward-looking because they are based on equity markets.
  - EDFs are calibrated to actual default rates rather than assuming normality; example: under normality a distance to default of four implies near zero (0.003 percent) likelihood, whereas EDF empirical mapping indicates 0.4 percent probability of default (Moody’s, 2012).
  - Version information: The latest EDF measures, version 9.0, are calibrated with more than 10,700 defaults going back to 1973, including almost 4,000 defaults from outside North America.
  - EDFs reflect “actual” default probabilities, in contrast to “risk-neutral” probabilities from CDS or bond spreads.
  - EDFs are largely free of bailout-expectation effects that can depress CDS or bond-implied probabilities because EDFs are equity-based and government support typically excludes shareholders.
- Default event types considered in the EDF model (four broad types):
  - (i) missed payments;
  - (ii) bankruptcy, administration, receivership, or legal equivalent;
  - (iii) distressed debt restructuring;
  - (iv) government bailouts enacted to prevent a credit event.
- Empirical validation:
  - Bohn and others (2005) find EDF superior to credit ratings, z-scores, and simpler Merton models for U.S. 1996–2004.
  - Sellers and Arora (2004) report accuracy ratio for EDF of 0.83 vs. 0.73 for credit ratings (period referenced).
  - Duffie, Saita, and Wang (2007) find a more elaborate model only slightly outperforms EDF during 2000–04.
  - Munves, Smith, and Hamilton (2010) find EDF effective for financial institutions during the global financial crisis in rank ordering defaulters.
  - Harada, Ito, and Takahashi (2010) find distance to default (DD) generally reliable in predicting Japanese bank failures.
  - Crossen and Zhang (2011) find EDF predictive power in 2008–10 consistent with 2001–07 and often conservative pre-crisis.

### Appendix 2. Fitch’s Support Ratings — Framework and Mapping
- Purpose: Fitch Support Ratings (SRs) indicate Fitch’s view on the likelihood that a financial institution will receive extraordinary support to prevent default on senior obligations.
- Sources of extraordinary support: (i) parent/shareholders (institutional support) or (ii) national authorities (sovereign support).
- SR scale: five-point scale where 1 = extremely high probability of support, and 5 = support cannot be relied on.
- Support Rating Floors (SRFs): reflect likelihood of extraordinary support specifically from government authorities and are assigned on the “AAA” rating scale; “No Floor” indicates no reasonable expectation of sovereign support.
- SRF determination factors:
  - (i) sovereign’s ability to support;
  - (ii) sovereign’s propensity to support the banking sector;
  - (iii) sovereign’s propensity to support a specific financial institution.
- Global regulatory initiatives to reduce implicit government support are factored into SRs and SRFs.
- Mapping SRFs to Probabilities of State Support (pss):
  - An SRF of “AAA” maps to a pss of 1.00.
  - “No Floor” (NF) is mapped to a pss of 0.20 (based on Fitch guidance that No Floor reflects probability of support of less than 40 percent; the mapping uses the average between 0 and 40 percent).
  - A rating of “C” maps to a pss of 0.40.
  - All other SRF ratings are assigned a pss via linear mapping between these anchors.
- Explicit numeric SRF → PSS mappings shown in the Appendix Table:
  - AAA → 1.00
  - AA+ → 0.97
  - AA → 0.93
  - AA- → 0.90
  - A+ → 0.87
  - A → 0.83
  - A- → 0.80
  - BBB+ → 0.77
  - BBB → 0.73
  - BBB- → 0.70
  - BB+ → 0.67
  - BB → 0.63
  - BB- → 0.60
  - B+ → 0.57
  - B → 0.53
  - B- → 0.50
  - CCC → 0.47
  - CC → 0.43
  - C → 0.40
  - NF → 0.20

### Appendix 3. Sample of Banks — Coverage and Methodology
- Overall sample: 258 banks in 32 advanced and emerging market economies.
- Country group counts:
  - Advanced economies (20): Australia, Austria, Canada, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Japan, Korea, Norway, Portugal, Singapore, Spain, Sweden, Switzerland, the United Kingdom, and the United States.
  - Emerging market economies (12): Brazil, Chile, China, Colombia, India, Indonesia, Malaysia, Philippines, Russia, South Africa, Thailand, and Turkey.
- Sample construction:
  - In each country, the sample includes the largest banks (in descending order of size) so as to cover at least half—and usually more than 80 percent—of the national banking system (i.e., excluding foreign subsidiaries), as expressed in terms of total assets.
  - Asset size measurement: at the banking group level (consolidated basis) covering all subsidiaries and branches inside and outside the bank’s country of headquarters.
- Notes:
  - Example footnote: Bank Austria is not included in Austria’s sample because it is a subsidiary of UniCredit, which is headquartered in Italy; thus it appears in Italy’s sample.
  - Global systemically important banks (G-SIBs), as of end-2014, are indicated in the source tables (not reproduced here).
  - Banks without equity-implied EDF measures are indicated as such in the source tables (not reproduced here).

*Source: _wp15255 - References (PDF)._

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp15255.pdf_