## 1. Indicator Approach to Systemic Importance

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---

### Executive summary
- Australia’s four largest banks can be considered domestically systemic.
- The top four institutions hold assets close to 200 percent of GDP.
- The top four institutions account for almost 80 percent of resident assets.
- Authorities deploy a multi-pronged approach: risk-based supervision, recovery and resolution planning, and conservative risk weights and definitions of loss-absorbent capital.
- Market-based methodologies using the expected default frequency (EDFTM) or implied funding cost advantage can gauge Higher Loss Absorbency (HLA) requirements.
- Application of these methods to Australian banks provides a range of HLA estimates and a transparent framework for discussion and selection.

### Defining domestic systemic importance
- Dominant criteria and observations:
  - Banks dominate Australia’s financial system; the four largest banking groups are far larger than the rest.
  - Size alone is not sufficient; global systemic importance (G-SIB) indicators include interconnectedness, substitutability/infrastructure, complexity, and cross-jurisdictional activity.
  - None of the Australian banks were identified as G-SIBs.
  - The BCBS framework for Domestic Systemically Important Banks (D-SIBs) emphasizes principle-based national discretion and complementarity with the G-SIB approach.
- Applying indicators (size, interconnectedness, non-substitutability, complexity) to Australia:
  - All indicator variants consistently identify the same four banks as D-SIBs.
  - Some smaller banks may be regionally important but are generally replaceable by the larger banks’ activities.
  - Braemer and Gischer (2012) adapt the G-SIB indicator approach to D-SIBs and find similar rankings; removing weaker non-substitutability indicators only slightly modifies relative systemic importance.
- Qualitative considerations:
  - Non-substitutability, interconnectedness, and complexity are judgmental and may require non-public information and qualitative inputs for finer differentiation.
  - Support ratings (Fitch uplift, Moody’s uplift) broadly confirm indicator-based assessments but allow limited differentiation and are only available for a subset of institutions.

### Indicators and methodological mapping
- Indicator translation examples (mapping G-SIB indicators to D-SIB measures):
  - Size: Total exposures as defined for use in the Basel III leverage ratio → Total resident assets.
  - Interconnectedness: Intra-financial system assets/liabilities and wholesale funding ratios → Loans to financial corporations; Deposits from financial corporations; Investment securities; Wholesale funding; Loan deposit ratio; Intra-group exposures.
  - Non-substitutability: Assets under custody; Payments cleared and settled; Values of underwritten transactions → Loans to households; Loans to non-financial corporations; Loans to the general government; Loans to community service and non-profit organizations.
  - Complexity: OTC derivatives notional value; Level 3 assets; Held for trading and available for sale → Trading book, trading securities, plus qualitative information.
  - Cross-jurisdictional activity: Cross-jurisdictional claims/liabilities → not included or replaced by domestic sentiment measures in D-SIB mapping.

### Empirical depiction for Australia
- IMF staff calculations and Braemer-Gischer results both show the same four banks as clearly systemically important.
- Figures referenced in the source emphasize the concentration of assets and relative systemic importance.
- Key takeaway:
  - There is little doubt, across indicator specifications and qualitative considerations, that the same four large Australian banks are D-SIBs for the domestic economy.

### Systemic importance and Higher Loss Absorbency (HLA)
- On a comparable basis, total Tier 1 capital of Australia’s major banks is about average among a peer group of 47 universal and commercial banks (from 16 countries) after adjusting Australian data upward for APRA’s conservative risk weights.
- Most countries that have identified strategies for systemic institutions incorporate HLA into their approach.
- Examples of cross-country HLA or related measures (as presented):
  - Switzerland: 19 percent of RWA total capital for two very large Swiss G-SIBs, of which up to 9 percent can be contingent capital (cocos) by 2016.
  - Austria: Adoption of Basel III by January 2013; additional 3 percent by 2016.
  - Canada: No HLA, but accelerated implementation of the CET1 standard of 7 percent: January 2013; additional reporting requirements.
  - Korea: Additional capital for D-SIBs likely.
  - Singapore: 2 percent additional by 2015.
  - Sweden: Accelerated adoption of Basel III; plus 3 percent by 2013 and 5 percent by 2015; Sweden’s systemic banks carry much higher capital levels than peers.
  - United Kingdom (proposal): 3 percent additional to Basel III and up to 17 percent of RWA loss absorbency for the largest institutions and ring-fenced entities; proposed ring-fencing of retail deposit taking.
  - United States: Supplementary Tier 1 of 3 percent of RWA for complex institutions; separation of proprietary trading and leverage ratios.

### Capital, insolvency risk, and funding cost — conceptual framing
- The desired HLA level depends on taxpayer risk tolerance:
  - Higher loss-absorbent capital relative to RWA reduces insolvency probability and potential need for public support.
  - Countries like Sweden, Switzerland, and the United Kingdom choose very high capital to minimize taxpayer exposure.
  - Alternatively, perception of credible public support lowers a bank’s funding cost; the implicit subsidy can be internalized by requiring additional private capital.
- Two practical approaches to internalize systemic risk:
  1. Define an acceptable level of dislocation from a bank failure and require systemic banks to have a lower probability of failure than non-systemics to equalize expected impact.
  2. Estimate the funding cost advantage (implicit subsidy) of perceived public support and compute additional capital required to offset that advantage.

### Use of EDF and empirical implementation
- EDFTM (Moody’s KMV) is used to gauge desired capital levels; it is based on Black-Scholes-Merton contingent claims analysis (see Annex 1).
- EDF definition and properties:
  - EDF is the estimated probability that a company will default within a given time horizon—default meaning failure to make a scheduled payment.
  - EDF depends on firm asset value, asset volatility, and a distress barrier from book value of liabilities.
  - The EDF methodology is proprietary, built on a large real-world database, and has documented empirical performance.
- Empirical sample and variables:
  - Daily data from June 22, 2011 through June 25, 2012 from Moody’s CreditEdge were used.
  - The EDF used is the one-year ahead default frequency (likelihood of missed payment within the next 12 months).
- Relationship findings:
  - Relationship between market capitalization and EDF (pooled sample) fits a power function with R2 = 0.81.
  - Removing outlying episodes improves pooled fit to R2 = 0.88.
  - Bank-specific EDF vs. market capitalization R2 ranges:
    - Full sample: 0.33 to 0.53.
    - With outliers removed: 0.53 to 0.71.
  - Relationship between CDS spreads and market capitalization is less robust:
    - Pooling data does not yield meaningful results for CDS spreads.
    - Individual-bank CDS vs. market capitalization fits show R2 in the range 0.39 to 0.45 after removing outliers.
- Interpretation and caveats:
  - The EDF–market capitalization relationship is highly non-linear; a power function produced a robust pooled fit.
  - Bank-specific estimations are less robust and vary with sample period and outlier treatment.
  - CDS spreads are more volatile and reflect market-wide risk appetite shifts unrelated to individual institutions; panel methods with fixed effects could improve robustness.
  - These findings indicate the need for careful interpretation, further robustness testing, or more comprehensive model specifications.

### Empirical application: implications for HLA estimation
- Two quantitative ways to translate market-based measures into HLA:
  - Use EDF-based models to compute additional capital required to lower the probability of default for systemic banks to an acceptable, lower level relative to non-systemic peers.
  - Use implied funding cost advantage (from market prices) to estimate the size of the implicit subsidy and compute the additional capital that would offset that subsidy.
- The application to Australian banks yields a range of HLA estimates and provides a transparent framework to discuss and select specific HLA levels.

### The link between market capitalization and expected default frequency
- Capital from EDF and survival probabilities:
  - The link between market capitalization and expected default frequency (EDF) is used to compute the capital required to meet targeted default frequencies.
  - Desired probability of survival can be set in absolute or relative terms; the exercise uses:
    - 99.9
    - 99.95
  - The first (99.9) is consistent with the threshold chosen for the capital requirements under the Basel agreements (from Basel II onward).
  - An illustrative relative approach: assume the impact of systemic failure is ten times that of a non-systemic bank and require that the probability of failure of the systemic bank be no more than one-tenth of that of a non-systemic institution. Based on the estimated one-year ahead EDF of a small, representative non-systemic Australian financial institution, this implies a desirable survival probability of 99.937 (which falls between 99.9 and 99.95).
- Relation between market capitalization and regulatory capital:
  - Market capitalization and total Tier 1 capital ratios are very similar for the large Australian banks when the supervisor’s view of risk weights coincides closely with the market’s view and Tier 1 capital is perceived to be of high quality.
  - End-2011 reported metrics:
    - Reported total Tier 1 capital averaged 10.1 percent of RWA
    - Ratio of market capitalization to the market value of assets averaged 9.4 percent
  - The ratio between these two was used to compute the total Tier 1 equivalent of market capitalization.
- HLA requirement estimates (pooled sample):
  - Reflecting the non-linear relationship between market capitalization and EDFs, capital requirements rise as the desired probability of meeting all payments increases.
  - Based on market data between June 2011-June 2012, accounting data of end-2011, and the pooled sample:
    - All but one of the large four banks pass or nearly pass the lower hurdle (i.e., 99.9).
    - For the most stringent case (99.95), none of the banks would meet the requirement; additional HLA in terms of Tier 1 capital required ranges from 1.4 percent to 5.2 percent of RWA.
    - For the middle-case, HLA requirements would range from 0.6 percent to 4.3 percent of RWA.
- HLA requirement estimates (bank-specific / allowing heterogeneity):
  - Allowing the relationship between market capitalization and EDFs to vary across systemic institutions yields qualitatively similar results but a narrower range of supplementary capital requirements:
    - Most stringent case (99.95): additional Tier 1 HLA between 0.6 percent and 2.5 percent of RWA.
    - Middle case, using the relative comparator: one bank’s additional requirement is 0.2 percent; the other three have additional capital in the range of 1.5 to 2.0 percent of RWA.

### Compensating the funding cost advantage of systemic institutions
- Systemic institutions enjoy a funding-cost advantage because investors assume government support, leading to acceptance of a lower yield versus non-systemic banks.
- Options to offset the advantage:
  - Charge systemic banks a fee to offset implicit support.
  - Require systemic banks to hold more capital until the systemic advantage vanishes.
- Estimation requires:
  1. An estimate of the funding cost advantage for each institution.
  2. An estimate of the relationship between funding costs and capitalization.
  3. An estimate or assumption about the impact of higher capital requirements on market structure.
- Using rating-agency-based measures of implicit support (Ueda and Weder di Mauro (2012)):
  - Estimated wholesale funding cost advantages for Australian banks:
    - Four large banks: about 80 basis points prior to the global financial crisis (GFC) and 120 basis points in 2009 (during the GFC).
    - Two sets of regional banks: 60 and 40 basis points before the GFC, and 70 and 50 basis points during the GFC.
  - Compared to international peers, the estimated wholesale funding advantage for Australian banks was about average before the GFC and somewhat above average at the time of the crisis.
- Because the funding advantage is relative, charging a fee equal to the full difference would be unduly severe. Absent a detailed market-share study, the analysis uses a scalar parameter of 0.7 (meaning 70 percent of the fee needs to be imposed to offset market dominance of the four large banks).
- Resulting HLA estimates (evaluated near the observed sample average level of capitalization):
  - At end-2011 average level of capitalization (10.1 percent of RWA), to offset 80 basis points of funding advantage: additional capital required in the range of 1.2 percent to 1.6 percent of RWA.
  - To offset 120 basis points: additional capital required in the range of 1.8 percent to 2.4 percent of RWA.
- A drawback: the level of required HLA varies inversely and in a non-linear way with the actual level of market capitalization; prudent evaluation is near observed sample averages.

### Concluding remarks and policy implications
- By any metric, Australia’s four largest banks appear to be of systemic importance in a domestic context; similarities in business models and common exposures imply shocks are likely to affect them similarly.
- International consensus: systemic risks require heightened attention; the approach to G-SIBs is being extended to D-SIBs with flexibility to adapt to national circumstances.
- Essential elements of the approach to domestic systemic banks:
  - Heightened supervision
  - Strong recovery and resolution planning
  - Higher loss absorbency (HLA) for systemic institutions
- Two potential methods to determine HLA explored:
  - Target an expected default probability (set a desirable survival probability): more robust, requires only setting the desired EDF and modeling its behavior, and can allow institution-specific characteristics.
  - Offset the funding advantage enjoyed by systemic institutions: requires more steps, a judgment about the impact of HLA on market structure, and differentiation is limited to rating-agency measures of implicit public support.
- Both methods allow variation over time and states of the world and permit adjustments based on supervisory judgment.

### Annex 1. Contingent Claims Analysis — overview
- Contingent claims analysis (CCA) generalizes option pricing theory pioneered by Black-Scholes (1973) and Merton (1973).
- CCA constructs risk-adjusted balance sheets and is based on three principles:
  - (i) the values of liabilities (equity and debt) are derived from assets;
  - (ii) liabilities have different priority (i.e., senior and junior claims); and,
  - (iii) assets follow a stochastic process.
- Assets (present value of income flows, proceeds from asset sales, etc.) are stochastic and over a horizon period may be above or below promised payments on debt, which constitute a default barrier. Default occurs when assets decline below the barrier.

### Annex 1. Model structure, calibration, and KMV adaptation
- Model structure and option interpretation:
  - Total market value of assets, A, at time t equals the sum of its equity market value, E, and its risky debt, D.
  - Asset value is stochastic and may fall below the present value of promised payments on debt, the default barrier, B. Default occurs when A < B.
  - Equity value is the value of an implicit call option on the assets, with an exercise price equal to the default barrier.
  - The expected loss to bank creditors can be calculated as the value of an implicit put option, P, on the assets with an exercise price equal to B.
  - The model assumes the implicit options are European and sets the time until expiry, T, equal to the time horizon of interest, usually between one and five years.
- Key formulas and decompositions (presented in source text; algebra reproduced as in source):
  - The expected loss decomposition into risk-neutral default probability (RNDP), loss given default (LGD), and the value of the default-free value of debt (B) is presented in the source.
  - The spread can be written as a function of RNDP and LGD as shown in the source: 1 ln1sRNDPLGD T
  - Yield and spread definitions in the source: yT DBe ; s = y – r ; and related algebraic manipulations presented exactly in the source.
- Calibration and implementation:
  - Calibration uses balance sheet information and forward-looking information from equity markets to imply asset values and volatilities.
  - In the traditional Merton (1974) model, calibration requires inputs including E, equity volatility, and the distress barrier, to solve for implied asset value A and implied asset volatility A .
  - Once asset value and asset volatility are known, expected losses to bank creditors can be calculated using asset value, asset volatility, default barrier, time horizon, and discount rate r to calculate the implicit put option, E P.
- KMV adaptation and EDFs:
  - KMV adapted Merton’s CCA approach to estimate Expected Default Frequencies (EDFTM); the exact methodology is confidential.
  - EDF calculation uses an iterative procedure to solve for implied asset volatility (Bohn and Crosby, 2003): uses an initial guess of volatility to determine asset value and de-lever equity returns, then iterates until convergence.
  - KMV uses equity return volatility, equity values, distress barrier from book value of liabilities, and time horizon to compute a distance-to-distress, which is mapped to actual default probabilities (EDFs) using a database of detailed real world default events.
  - Robustness checks show the model to be quite accurate and it is a leading indicator for default.

*Source: IMF staff paper section "1. Indicator Approach to Systemic Importance" and Annex 1 from the supplied PDF content unit.*

### 1. Indicator Approach to Systemic Importance .........................................................................7

### 1. Indicator Approach to Systemic Importance

### Executive summary
- Australia’s four largest banks can be considered domestically systemic.
- The top four institutions hold assets close to 200 percent of GDP.
- The top four institutions account for almost 80 percent of resident assets.
- Authorities deploy a multi-pronged approach: risk-based supervision, recovery and resolution planning, and conservative risk weights and definitions of loss-absorbent capital.
- Market-based methodologies using the expected default frequency (EDFTM) or implied funding cost advantage can gauge Higher Loss Absorbency (HLA) requirements.
- Application of these methods to Australian banks provides a range of HLA estimates and a transparent framework for discussion and selection.

### Defining domestic systemic importance
- Dominant criteria and observations:
  - Banks dominate Australia’s financial system; the four largest banking groups are far larger than the rest.
  - Size alone is not sufficient; global systemic importance (G-SIB) indicators include interconnectedness, substitutability/infrastructure, complexity, and cross-jurisdictional activity.
  - None of the Australian banks were identified as G-SIBs.
  - The BCBS framework for Domestic Systemically Important Banks (D-SIBs) emphasizes principle-based national discretion and complementarity with the G-SIB approach.
- Applying indicators (size, interconnectedness, non-substitutability, complexity) to Australia:
  - All indicator variants consistently identify the same four banks as D-SIBs.
  - Some smaller banks may be regionally important but are generally replaceable by the larger banks’ activities.
  - Braemer and Gischer (2012) adapt the G-SIB indicator approach to D-SIBs and find similar rankings; removing weaker non-substitutability indicators only slightly modifies relative systemic importance.
- Qualitative considerations:
  - Non-substitutability, interconnectedness, and complexity are judgmental and may require non-public information and qualitative inputs for finer differentiation.
  - Support ratings (Fitch uplift, Moody’s uplift) broadly confirm indicator-based assessments but allow limited differentiation and are only available for a subset of institutions.

### Indicators and methodological mapping (from the source table)
- Indicator translation examples:
  - Size: Total exposures as defined for use in the Basel III leverage ratio → Total resident assets.
  - Interconnectedness: Intra-financial system assets/liabilities and wholesale funding ratios → Loans to financial corporations; Deposits from financial corporations; Investment securities; Wholesale funding; Loan deposit ratio; Intra-group exposures.
  - Non-substitutability: Assets under custody; Payments cleared and settled; Values of underwritten transactions → Loans to households; Loans to non-financial corporations; Loans to the general government; Loans to community service and non-profit organizations.
  - Complexity: OTC derivatives notional value; Level 3 assets; Held for trading and available for sale → Trading book, trading securities, plus qualitative information.
  - Cross-jurisdictional activity: Cross-jurisdictional claims/liabilities → not included or replaced by domestic sentiment measures in D-SIB mapping.

### Empirical depiction for Australia
- IMF staff calculations and Braemer-Gischer results both show the same four banks as clearly systemically important.
- Figure-based findings in the source emphasize the concentration of assets and relative systemic importance (figures referenced in text).

### Key takeaway
- There is little doubt, across indicator specifications and qualitative considerations, that the same four large Australian banks are D-SIBs for the domestic economy.

---

### Systemic importance and Higher Loss Absorbency (HLA)

- On a comparable basis, total Tier 1 capital of Australia’s major banks is about average among a peer group of 47 universal and commercial banks (from 16 countries) after adjusting Australian data upward for APRA’s conservative risk weights.
- Most countries that have identified strategies for systemic institutions incorporate HLA into their approach.
- Examples of cross-country HLA or related measures (as presented):
  - Switzerland: 19 percent of RWA total capital for two very large Swiss G-SIBs, of which up to 9 percent can be contingent capital (cocos) by 2016.
  - Austria: Adoption of Basel III by January 2013; additional 3 percent by 2016.
  - Canada: No HLA, but accelerated implementation of the CET1 standard of 7 percent: January 2013; additional reporting requirements.
  - Korea: Additional capital for D-SIBs likely.
  - Singapore: 2 percent additional by 2015.
  - Sweden: Accelerated adoption of Basel III; plus 3 percent by 2013 and 5 percent by 2015; Sweden’s systemic banks carry much higher capital levels than peers.
  - United Kingdom (proposal): 3 percent additional to Basel III and up to 17 percent of RWA loss absorbency for the largest institutions and ring-fenced entities; proposed ring-fencing of retail deposit taking.
  - United States: Supplementary Tier 1 of 3 percent of RWA for complex institutions; separation of proprietary trading and leverage ratios.

---

### Capital, insolvency risk, and funding cost — conceptual framing
- The desired HLA level depends on taxpayer risk tolerance:
  - Higher loss-absorbent capital relative to RWA reduces insolvency probability and potential need for public support.
  - Countries like Sweden, Switzerland, and the United Kingdom choose very high capital to minimize taxpayer exposure.
  - Alternatively, perception of credible public support lowers a bank’s funding cost; the implicit subsidy can be internalized by requiring additional private capital.
- Two practical approaches to internalize systemic risk:
  1. Define an acceptable level of dislocation from a bank failure and require systemic banks to have a lower probability of failure than non-systemics to equalize expected impact.
  2. Estimate the funding cost advantage (implicit subsidy) of perceived public support and compute additional capital required to offset that advantage.

---

### Use of EDF (Expected Default Frequency) and empirical implementation
- EDFTM (Moody’s KMV) is used to gauge desired capital levels; it is based on Black-Scholes-Merton contingent claims analysis (see Annex 1).
- EDF definition and properties:
  - EDF is the estimated probability that a company will default within a given time horizon—default meaning failure to make a scheduled payment.
  - EDF depends on firm asset value, asset volatility, and a distress barrier from book value of liabilities.
  - The EDF methodology is proprietary, built on a large real-world database, and has documented empirical performance.
- Empirical sample and variables:
  - Daily data from June 22, 2011 through June 25, 2012 from Moody’s CreditEdge were used.
  - The EDF used is the one-year ahead default frequency (likelihood of missed payment within the next 12 months).
- Relationship findings:
  - Relationship between market capitalization and EDF (pooled sample) fits a power function with R2 = 0.81.
  - Removing outlying episodes improves pooled fit to R2 = 0.88.
  - Bank-specific EDF vs. market capitalization R2 ranges:
    - Full sample: 0.33 to 0.53.
    - With outliers removed: 0.53 to 0.71.
  - Relationship between CDS spreads and market capitalization is less robust:
    - Pooling data does not yield meaningful results for CDS spreads.
    - Individual-bank CDS vs. market capitalization fits show R2 in the range 0.39 to 0.45 after removing outliers.
- Interpretation and caveats:
  - The EDF–market capitalization relationship is highly non-linear; a power function produced a robust pooled fit.
  - Bank-specific estimations are less robust and vary with sample period and outlier treatment.
  - CDS spreads are more volatile and reflect market-wide risk appetite shifts unrelated to individual institutions; panel methods with fixed effects could improve robustness.
  - These findings indicate the need for careful interpretation, further robustness testing, or more comprehensive model specifications.

---

### Empirical application: implications for HLA estimation (summary of approach and findings)
- Two quantitative ways to translate market-based measures into HLA:
  - Use EDF-based models to compute additional capital required to lower the probability of default for systemic banks to an acceptable, lower level relative to non-systemic peers.
  - Use implied funding cost advantage (from market prices) to estimate the size of the implicit subsidy and compute the additional capital that would offset that subsidy.
- The application to Australian banks yields a range of HLA estimates and provides a transparent framework to discuss and select specific HLA levels.

---

*Source: IMF staff paper section "1. Indicator Approach to Systemic Importance" from the supplied PDF content.*

### 17.      The link between market capitalization and expected default frequency can be

### _cr12311 - 17.      The link between market capitalization and expected default frequency can be

### Capital from EDF and survival probabilities
- The link between market capitalization and expected default frequency (EDF) is used to compute the capital required to meet targeted default frequencies.
- Desired probability of survival can be set in absolute or relative terms; the exercise uses:
  - 99.9
  - 99.95
- The first (99.9) is consistent with the threshold chosen for the capital requirements under the Basel agreements (from Basel II onward).
- An illustrative relative approach: assume the impact of systemic failure is ten times that of a non-systemic bank and require that the probability of failure of the systemic bank be no more than one-tenth of that of a non-systemic institution. Based on the estimated one-year ahead EDF of a small, representative non-systemic Australian financial institution, this implies a desirable survival probability of 99.937 (which falls between 99.9 and 99.95).

### Relation between market capitalization and regulatory capital
- Market capitalization and total Tier 1 capital ratios are very similar for the large Australian banks when the supervisor’s view of risk weights coincides closely with the market’s view and Tier 1 capital is perceived to be of high quality.
- End-2011 reported metrics:
  - Reported total Tier 1 capital averaged 10.1 percent of RWA
  - Ratio of market capitalization to the market value of assets averaged 9.4 percent
- The ratio between these two was used to compute the total Tier 1 equivalent of market capitalization.

### HLA requirement estimates (pooled sample)
- Reflecting the non-linear relationship between market capitalization and EDFs, capital requirements rise as the desired probability of meeting all payments increases.
- Based on market data between June 2011-June 2012, accounting data of end-2011, and the pooled sample:
  - All but one of the large four banks pass or nearly pass the lower hurdle (i.e., 99.9).
  - For the most stringent case (99.95), none of the banks would meet the requirement; additional HLA in terms of Tier 1 capital required ranges from 1.4 percent to 5.2 percent of RWA.
  - For the middle-case, HLA requirements would range from 0.6 percent to 4.3 percent of RWA.

### HLA requirement estimates (bank-specific / allowing heterogeneity)
- Allowing the relationship between market capitalization and EDFs to vary across systemic institutions yields qualitatively similar results but a narrower range of supplementary capital requirements:
  - Most stringent case (99.95): additional Tier 1 HLA between 0.6 percent and 2.5 percent of RWA.
  - Middle case, using the relative comparator: one bank’s additional requirement is 0.2 percent; the other three have additional capital in the range of 1.5 to 2.0 percent of RWA.

### Compensating the funding cost advantage of systemic institutions
- Systemic institutions enjoy a funding-cost advantage because investors assume government support, leading to acceptance of a lower yield versus non-systemic banks.
- Options to offset the advantage:
  - Charge systemic banks a fee to offset implicit support.
  - Require systemic banks to hold more capital until the systemic advantage vanishes.
- Estimation requires:
  1. An estimate of the funding cost advantage for each institution.
  2. An estimate of the relationship between funding costs and capitalization.
  3. An estimate or assumption about the impact of higher capital requirements on market structure.
- Using rating-agency-based measures of implicit support (Ueda and Weder di Mauro (2012)):
  - Estimated wholesale funding cost advantages for Australian banks:
    - Four large banks: about 80 basis points prior to the global financial crisis (GFC) and 120 basis points in 2009 (during the GFC).
    - Two sets of regional banks: 60 and 40 basis points before the GFC, and 70 and 50 basis points during the GFC.
  - Compared to international peers, the estimated wholesale funding advantage for Australian banks was about average before the GFC and somewhat above average at the time of the crisis.
- Because the funding advantage is relative, charging a fee equal to the full difference would be unduly severe. Absent a detailed market-share study, the analysis uses a scalar parameter of 0.7 (meaning 70 percent of the fee needs to be imposed to offset market dominance of the four large banks).
- Resulting HLA estimates (evaluated near the observed sample average level of capitalization):
  - At end-2011 average level of capitalization (10.1 percent of RWA), to offset 80 basis points of funding advantage: additional capital required in the range of 1.2 percent to 1.6 percent of RWA.
  - To offset 120 basis points: additional capital required in the range of 1.8 percent to 2.4 percent of RWA.
- A drawback: the level of required HLA varies inversely and in a non-linear way with the actual level of market capitalization; prudent evaluation is near observed sample averages.

### Concluding remarks and policy implications
- By any metric, Australia’s four largest banks appear to be of systemic importance in a domestic context; similarities in business models and common exposures imply shocks are likely to affect them similarly.
- International consensus: systemic risks require heightened attention; the approach to G-SIBs is being extended to D-SIBs with flexibility to adapt to national circumstances.
- Essential elements of the approach to domestic systemic banks:
  - Heightened supervision
  - Strong recovery and resolution planning
  - Higher loss absorbency (HLA) for systemic institutions
- Two potential methods to determine HLA explored:
  - Target an expected default probability (set a desirable survival probability): more robust, requires only setting the desired EDF and modeling its behavior, and can allow institution-specific characteristics.
  - Offset the funding advantage enjoyed by systemic institutions: requires more steps, a judgment about the impact of HLA on market structure, and differentiation is limited to rating-agency measures of implicit public support.
- Both methods allow variation over time and states of the world and permit adjustments based on supervisory judgment.

*Source: IMF staff calculations.*

### Annex 1. Contingent Claims Analysis

### Annex 1. Contingent Claims Analysis

### Overview and core principles
- Contingent claims analysis (CCA) generalizes option pricing theory pioneered by Black-Scholes (1973) and Merton (1973).
- CCA is used to construct risk-adjusted balance sheets and is based on three principles:
  - (i) the values of liabilities (equity and debt) are derived from assets;
  - (ii) liabilities have different priority (i.e., senior and junior claims); and,
  - (iii) assets follow a stochastic process.
- Assets (present value of income flows, proceeds from asset sales, etc.) are stochastic and over a horizon period may be above or below promised payments on debt, which constitute a default barrier. Default occurs when assets decline below the barrier.

### Model structure and option interpretation
- The CCA model assumes total market value of assets, A, at time t equals the sum of its equity market value, E, and its risky debt, D.
- Asset value is stochastic and may fall below the present value of promised payments on debt, the default barrier, B. Default occurs when A < B.
- Equity value is the value of an implicit call option on the assets, with an exercise price equal to the default barrier.
- The expected loss to bank creditors can be calculated as the value of an implicit put option, P, on the assets with an exercise price equal to B.
- In its basic concept, the model assumes the implicit options are European and sets the time until expiry, T, equal to the time horizon of interest, usually between one and five years.

### Key formulas and decompositions (as presented)
- Equity value, E, can be computed as the value of a call option.
- The formula for the implicit put option is presented in the source text.
- The expected loss to bank creditors (implicit put option, P) formula can be rearranged and decomposed into:
  - (i) risk-neutral default probability (RNDP),
  - (ii) loss given default (LGD),
  - (iii) the value of the default-free value of debt (B).
- The source presents the decomposition in the form:
  - 1 2 2 1 rT E rT RNDP LGD P Nd A Be NdBe Nd ,
- The spread can be written as a function of RNDP and LGD as shown in the source:
  - 1 ln1sRNDPLGD T
- The yield to maturity on the risky debt, y, is defined by:
  - yT DBe
- The credit spread is defined as s = y – r (r is the risk-free rate of interest), thus:
  - yTsTrT D B eee
- The source further manipulates algebra to express the credit spread in alternative forms, including expressions such as:
  - 1 EE rT sT rTrTrT BPPD BBB e e eee
  - 1 1 E rT s P TBe

(Note: formulas and algebraic expressions are reproduced exactly as they appear in the source text.)

### Calibration and implementation
- Several widely-used techniques calibrate CCA models using a combination of balance sheet information and forward-looking information from equity markets.
- The market value of assets of corporations and financial institutions cannot be observed directly but can be implied using financial asset prices.
- From observed prices and volatilities of market-traded securities, one can estimate implied values and volatilities of underlying assets.
- In the traditional Merton (1974) model, calibration requires knowledge about:
  - value of equity, E,
  - volatility of equity, (denoted in source as E ),
  - the distress barrier,
  - as inputs into equations 0 1 2 ()() rT EANdBeNd and 1 () EA EANd to calculate the two unknowns, implied asset value A and implied asset volatility A .
- Once asset value and asset volatility are known, expected losses to bank creditors can be calculated using asset value, asset volatility, default barrier, time horizon, and discount rate r to calculate the implicit put option, E P.

### KMV adaptation and EDFs
- In the 1990s, KMV adapted Merton’s CCA approach to estimate Expected Default Frequencies (EDFTM). The exact methodology is confidential.
- EDF calculation uses an iterative procedure to solve for implied asset volatility (Bohn and Crosby, 2003):
  - Uses an initial guess of volatility to determine asset value and de-lever equity returns.
  - Volatility of asset returns feeds into the next iteration of asset values and returns until convergence.
- The KMV approach uses equity return volatility, equity values, distress barrier from book value of liabilities, and time horizon to compute a distance-to-distress.
- Distance-to-distress is mapped to actual default probabilities (EDFs) using a database of detailed real world default events.
- Robustness checks show the model to be quite accurate and it is a leading indicator for default (see, e.g., Korablev and Qu, 2009).

*Source: Annex 1. Contingent Claims Analysis (from the supplied IMF content unit)*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/scr/2012/_cr12311.pdf_