## _wp13232

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---

### Purpose, scope, and uses
- Objective: identify "rules of thumb" for bank solvency (capital ratios) to serve as general guidelines for stress testing and to complement detailed country-specific analysis.
- Focus variables: credit losses, pre-impairment income, credit growth during crises, and the simulation of capital ratio evolution under stress.
- Evidence base: descriptive statistics and data from crises spanning the last 15 years and longer-sample evidence (Moody’s 1920–2012; Bankscope 1996–2011).
- Uses:
  - Design and calibration of tests for countries with limited data.
  - Importing behavioral relationships when local estimation is unreliable.
  - Robustness checks and rapid multiple-run sensitivity analysis.
  - Enhancing interpretability for senior managers and policy-makers.

### Main empirical findings and stylized facts
- Nonlinearity and severity:
  - Behavior of loss rates, income, credit growth, RWAs, and capital ratios is highly non-linear around crises; severe crises produce disproportionately large adverse effects.
  - Severe loss levels can be many times higher than in normal times.
- Income and buffers:
  - Pre-impairment income typically declines substantially in severe stress; income often remains positive on average but many banks face large negative tails.
  - Dividend-payout drops to zero under severe stress across country groups.
- Bank responses:
  - Common reactions include dividend suspension and deleveraging; deleveraging can restore solvency but may be macroeconomically costly.
- Cross-country differences:
  - EMs exhibit higher and more variable NPL and default rate peaks than ACs.
  - LIC evidence limited; functioning may differ due to commodity dependence and lower intermediation.

### Metrics, decompositions, and measurement implications
- Main solvency metric: risk-based capital ratio = bank’s capital / risk-weighted assets (RWA).
- Projection components:
  - Initial capital + projected retained net profit (depends on dividend payout assumptions).
  - Initial RWA + projected change in RWA (volume and risk-weight changes).
- Profit drivers:
  - Loan loss provisions/write-offs (PD × LGD or NPL-based provisioning), pre-impairment income (net interest, fees, trading, other income, operating expenses), dividend payouts, taxation.
- Complementary metric: unweighted leverage ratio (assets denominator).
- Regulatory measurement matter:
  - StA is less sensitive to shocks than IRB; IRB reflects deterioration and rebound more quickly if risk weights respond.
  - Consequence: a given risk-based capitalization may represent a smaller effective buffer for an IRB bank than for a StA bank.

### Crisis taxonomy and scenario percentiles
- Stress classification by percentiles of credit loss rates:
  - normal = median
  - moderate = 80th percentile
  - medium = 90th percentile
  - severe = 97.5th percentile
  - extreme = historical maximum (worst year in a century)
- Empirical frequency guidance:
  - Moderate or medium stress events in ACs: one-in-10 to one-in-15 years (moderate), one-in-20 years (medium) roughly.

### Credit loss rates by scenario and country group (percent of credit outstanding)
- Normal, median: AC 0.3, EM 1.0, LIC 1.4
- Normal, mean: AC 0.7, EM 1.9, LIC 2.4
- Moderate: AC 0.8, EM 2.2, LIC 3.1
- Medium: AC 1.1, EM 3.4, LIC 4.9
- Severe: AC 2.4, EM 7.4, LIC 13.4
- Extreme: AC 4.3, EM 14.0, LIC 33.8
- Sample coverage: No. of observations: AC 463, EM 1,457, LIC 698; No. of countries: AC 32, EM 104, LIC 52
- Cross-country pattern: losses higher in EMs by a factor of about three versus ACs; overlaps exist across groups.

### NPL and default-rate dynamics (selected stylized facts)
- NPL stock ratios:
  - Rise substantially and typically peak one year after crisis materialization.
  - Increase by about 10 percentage points from the typical level one year before in “average” crises, and almost 25 percentage points in severe crises.
  - Persistent: after three years the NPL ratio remains about the same as at crisis materialization.
- NPL flow (proxy for default rates):
  - Peak at about 10 percent in “average” crises, about 18 percent in severe crises, up from 3 percent in normal times.
  - Default rates tend to return to pre-crisis levels after three years (rough symmetry).

### Proxies and PD/LGD approximations
- PD proxy from NPL stocks uses PDt = α*(NPLt+1 - NPLt-1) with write-off speed parameter α:
  - Before crisis α = 0.5 (implying NPLs written off after ~2 years).
  - After peak α = 0.33 (implying write-off after ~3 years).
- LGD empirical patterns:
  - LGD–default correlation: 0.47 (pairwise).
  - LGDs fluctuate with cycle but less than default rates; LGDs typically double in severe/extreme stress while default rates increase many times over.
  - AC stress-level LGDs (percent) and default rates (percent) based on Moody’s:
    - Normal — Default rates: 0.7 — Projected LGD: 26
    - Moderate — 1.7 — 30
    - Medium — 2.9 — 34
    - Severe — 5.0 — 41
    - Extreme — 8.4 — 54
  - Historical average LGD: EMs ~59 percent; LICs ~62 percent (World Bank/Djankov et al. (2007) Doing Business data).
  - Practical approach for EMs/LICs: use long-term average LGD and add same absolute LGD increase as observed in ACs for a given stress intensity.
- Implied default rates (credit loss rate / LGD using Table 4 LGDs): Normal 1.3 percent, Moderate 2.7 percent, Medium 3.3 percent, Severe 5.7 percent, Extreme 8 percent.
- Using LGD = 60 percent for EMs/LICs yields implied default rates consistent with loss-rate PD approximations.

### Pre-impairment income behavior and tails
- Income normalized via ROC to account for leverage:
  - Median net pre-impairment ROC: LICs 25.0 percent; EMs 18.9 percent; ACs 11.9 percent.
- Under stress:
  - Median pre-impairment income remains on average positive but declines; behavior less symmetric than credit losses.
  - Tail outcomes:
    - Worst performing 25th percentile: under severe stress income becomes negative for at least a quarter of AC banks.
    - Worst performing 10th percentile: 10 percent of banks encounter ROCs below –20 percent at trough under severe stress.
- Components:
  - Net interest income: relatively stable.
  - Fees: relatively volatile for AC banks.
  - Trading income: mildly cyclical on average but can be highly negative in severe crises; for median small banks trading is unimportant, but large banks can face very large trading losses.
  - Operating expenses: median AC bank expenses become very volatile in severe crisis; median EM banks may reduce operating expenses during stress.

### Trading losses tail risk (Box 2)
- For median bank with trading operations, trading income is on average slightly positive under most stress conditions.
- Severe scenario magnitudes:
  - Worst performing decile (trading loss to capital): ~5 percent of capital loss.
  - Worst performing 1 percent: might lose ~a third of capital from trading losses alone.
- Historic note: a few large European banks lost more than one third of capital in one year due to trading losses during the recent global crisis.
- Trading income behaves close to a random walk with little serial correlation.

### Credit and asset growth under stress
- Nominal credit growth net of credit losses slows sharply under stress.
- Conditional patterns:
  - Deleveraging occurs in ACs only in severe crises; medium crises lead to ~three years of close-to-zero credit growth for ACs.
  - EM banks maintain fairly sizable credit growth under stress except in severe stress when credit growth becomes zero.
  - Asset growth mirrors credit growth affecting both RWA-based and leverage ratios.

### Satellite models and GDP-based sensitivities
- Satellite models link macro shocks (real GDP growth changes or cumulative deviations) to solvency variables via sensitivity parameters.
- Two GDP shock measures:
  - (i) change in real GDP growth at t=0 relative to t–4;
  - (ii) cumulative deviation of real GDP growth rates from trend from t–4 to t=0.
- Example sensitivities (illustrative calculations):
  - Cumulative-deviation example: cumulative deviation 5.9 percentage points (moderate AC) × sensitivity –0.1 ⇒ increase in median bank credit losses = –5.9×–0.1 = 0.59 percentage points.
  - Change-in-annual-growth rule (AC median credit loss sensitivity = –0.2):
    - Drop 2.4→0.0: –2.4×–0.2 = 0.48 percentage points.
    - Drop to –1.9 (medium): –4.3×–0.2 = 0.86 percentage points.
    - Drop to –5.0 (severe): –7.4×–0.4 = 2.96 percentage points.
- General patterns:
  - Sensitivities increase with stress; sensitivity of credit loss rates to GDP declines roughly same in moderate and medium but ≥2× under severe.
  - Tail (worst 10th percentile) coefficients are normally ≥2× median coefficients.
  - Credit growth shows a more linear relationship to GDP shocks.
- Absolute sensitivity example: 3.5 percentage points divided by a decrease in GDP growth levels of 6.4 percentage points ⇒ sensitivity ≈ 0.546875 (reported examples note 0.6 when excluding 1930s).

### Rules of thumb: GDP sensitivity parameters (Table 6-style specifications)
- Default rates sensitivity to GDP growth (point estimates):
  - Moderate: -0.4
  - Medium: -0.6
  - Severe: -0.8
- LGD sensitivity to GDP growth:
  - Moderate: -1.5
  - Medium: -2.5
  - Severe: -4.0
- Asset correlations (corporates) point estimate sensitivity: -2.7
- Note: For cumulative-deviation-based projections, parameters should be divided by two.

### Asset correlations and procyclicality
- Duellmann et al. (1997–2003): asset correlations ranged 4 percent–16 percent, mean 10.5 percent.
- Estimated GDP growth sensitivity of asset correlations: -2.7 (fall of GDP growth by 1 percentage point leads to increase of asset correlations by 2.7 percentage points).
- Implication: asset correlations may rise substantially with stress (example extrapolation toward ~30 percent from 10 percent under severe stress), with caveats on extrapolation.

### Worked illustrative banks and calibration inputs (selected figures)
- Example bank characteristics (US$ billions):
  - Assets: ACs 100.0 ; EMs 100.0
  - Customer loans: ACs 47.0 ; EMs 54.0
  - Other on-balance sheet assets subject to credit risk: ACs 46.0 ; EMs 39.0
  - Off-balance sheet assets subject to credit risk: ACs 21.0 ; EMs 24.0
  - Total regulatory capital: ACs 6.0 ; EMs 8.7
- StA RWAs (US$ billions): ACs 64.3 ; EMs 62.0
- StA capital ratio (percent): ACs 9.3 ; EMs 14.0
- Implied IRB RWAs (US$ billions): ACs 40.9 ; EMs 107.4
- Implied IRB capital ratio (percent): ACs 14.7 ; EMs 8.1
- Pre-impairment income (ROC, percent, long-term average): ACs 12.0 ; EMs 20.0
- Net income (US$ billions, long-term average): ACs 0.4 ; EMs 1.1
- ROC (percent, long-term average): ACs 6.7 ; EMs 9.3
- Assumptions: effective maturity 2.5 years; LGD normal set to 30 percent for corporate loans in AC example; scaling factors SMEs 1.5, retail 0.75; credit conversion factor for off-balance exposures 50 percent.

### Simulated RWA and leverage dynamics (selected tables)
- RWA StA — AC (Percent by t = –3 to t = 3):
  - Normal: 64 64 64 64 64 64 64
  - Moderate: 64 64 65 71 64 64 64
  - Medium: 64 65 73 79 64 64 64
  - Severe: 65 73 85 88 65 65 65
- RWA IRB — AC (Percent by t = –3 to t = 3):
  - Normal: 41 41 41 41 41 41 41
  - Moderate: 41 41 41 65 41 41 41
  - Medium: 41 41 67 87 66 42 42
  - Severe: 41 67 93 165 90 69 44
- RWA IRB — EC (Percent by t = –3 to t = 3):
  - Severe: 110 153 207 340 230 177 134
- Leverage effects:
  - AC severe stress: leverage ratio drops by 1.9 percentage points (from 5.0 to 3.1).
  - EC medium and severe: drops of 1.4 and 7.9 percentage points from initial 7.0.

### Earnings, contributions, and large negative outcomes
- Net income after loan losses becomes:
  - AC severe: –25 percent ROC at t=0 in simulations.
  - EC medium: –0.3 percent ROC; EC severe: –95 percent ROC (simulations show extreme negative outcomes and undefined later due to negative capital).
- Earnings decline contributions:
  - ACs: net interest income contributes 59 percent; net fees and commissions 21 percent; other income 20 percent.
  - ECs: net interest income contributes 74 percent; net fees and commissions 18 percent; other income 9 percent.

### Sensitivities of capital ratios to GDP growth changes (rules of thumb)
- AC bank:
  - StA: 1 percentage point drop in GDP growth ⇒ reduction in capitalization by 0.4 to 0.5 percentage points.
  - IRB: same 1 percentage point drop ⇒ about 1.6 to 2.3 percentage points reduction, depending on severity.
  - For cumulative deviation from GDP trend coefficients: divide by two.
- EM bank:
  - StA: 1 percentage point drop ⇒ about 0.5 to 1.2 percentage points per unit drop (preserved text).
  - IRB: 1 percentage point drop ⇒ 0.6 to 0.7 percentage points.
  - For cumulative deviation from GDP trend coefficients: divide by three.
- Note: IRB coefficient for EC banks relatively low because higher initial IRB risk weights reduce sensitivity of RWA to cyclical fluctuations.

### Required initial capital ratios to stay above 8 percent under stress (policy simulations)
- Average AC bank under IRB (PIT):
  - Severe stress: ~30 percent initial capital ratio to remain ≥8 percent at t=0.
  - Medium stress: ~17 percent initial capital ratio.
- Average AC bank under IRB (TTC):
  - Severe: 20 percent initial capital ratio.
  - Medium: 14 percent initial capital ratio.
- Average AC bank under StA:
  - Medium stress: 10 percent initial capital ratio.
  - Extreme stress: 12.5 percent initial capital ratio.
- EC bank under StA:
  - Medium shocks: 12 percent initial capital ratio.
  - Severe stress: ~22 percent initial capital ratio.
- Tail banks:
  - AC bank worst decile pre-impairment earnings: needs 22 percent capital ratio (IRB) to cope with medium stress.
  - EC bank worst decile (StA): needs 17 percent for medium stress and 25 percent for severe stress.

### Rules of thumb summary (selected entries, percents)
- AC bank (Normal / Medium stress / Severe stress):
  - Annual credit loss rate: 0.3 1.1 2.4
  - Pre-impairment ROC: 11.9 11.4 8.3
  - Credit growth rate: 7.2 1.3 -3.8
  - Asset correlation: 10.4 21.8 30.1
- EM bank (Normal / Medium stress / Severe stress):
  - Annual credit loss rate: 1.0 3.4 7.4
  - Pre-impairment ROC: 18.9 18.6 13.4
  - Credit growth rate: 18.9 3.2 -8.3

### Data sources, sample sizes, and data treatment
- Long-sample evidence: Moody’s default rates 1920–2012.
- Cross-country evidence: Bankscope sample 1996–2011; initial >16,000 banks; cleaned final data >10,000 banks from 169 countries.
- Cleaned Bankscope totals (final data):
  - AC: countries 32; banks 9,372; assets US$ trillions 68.8
  - EM: countries 90; banks 1,131; assets US$ trillions 10.4
  - LIC: countries 47; banks 206; assets US$ trillions 0.3
  - Total: countries 169; banks 10,709; assets US$ trillions 79.5
- Sample trimming: outliers removed (e.g., loss levels >60 percent), robustness checks (e.g., banks with ≥5 consecutive observations).
- Caveats: heterogeneity in NPL, capital, provisioning definitions; simulations assume no major managerial actions (capital raising, asset disposals) beyond retained earnings; focus on GDP-driven linkages and not on other macro factors in detail.

*Source: Appendix 1 and Sections II–IV excerpts from the supplied IMF working paper content (_wp13232).*

### Appendix 1. Data Summary ...............................................................................................

### Appendix 1. Data Summary

### Purpose and scope
- Objective: identify "rules of thumb" for bank solvency (capital ratios) to serve as general guidelines for stress testing and to complement detailed country-specific analysis.
- Focus variables: credit losses, pre-impairment income, credit growth during crises, and the simulation of capital ratio evolution under stress.
- Evidence base: descriptive statistics and data from various crises, with emphasis on crises during the last 15 years (including the Russian/Asian crisis, crises in transition countries in Central and Eastern Europe in the late 1990s, the burst of the internet bubble in the early 2000s, the global financial crisis, and country- and bank-specific crises).
- Distinction in analysis: advanced economies (ACs) versus emerging market economies (EMs); use of low income countries (LICs) evidence where available but noting limited data and structural differences.

### Uses of rules of thumb in stress testing
- Design and calibration of tests for countries with limited relevant experience or data.
- Importing behavioral relationships when local estimation is unreliable.
- Providing robustness checks and plausibility tests for more complex, model-based approaches.
- Rapid multiple-run analysis to assess sensitivity to nonlinearities and to quantify stability implications of prudential rules (e.g., minimum capital requirements).
- Enhancing interpretability and accessibility of stress-test frameworks for senior managers and policy-makers.

### Key questions addressed
- How much do credit losses usually increase in case of a moderate, medium and severe macroeconomic downturn and/or financial stress event (e.g., if cumulative real GDP growth turns out to be, say, 4 or 8 percentage points below potential (or average or previous years’) growth)?
- How do major factors affecting capital ratios—profitability, credit growth, and risk-weighted assets (RWA)—typically react under such circumstances?
- How does moderate, medium, or severe macro-financial stress translate into a decrease in bank capital, and consequently, how much capital do banks need to cope with different levels of stress?

### Desired properties of rules of thumb
- Coverage: encompass major factors contributing to banks’ solvency vulnerabilities.
- Applicability: wide but with clear criteria for inapplicability.
- Robustness: supported by a variety of evidence and not excessively model-dependent.
- Intuitiveness: useful for interpretation and decision-making.
- Simplicity: enhances applicability, robustness, and intuitiveness.

### Main empirical findings and stylized facts
- Nonlinearity: behavior of loss rates, income, credit growth, RWAs, and capital ratios is highly non-linear around crises; severe crises produce disproportionately large adverse effects.
- Credit losses: severe loss levels can be many times higher than in normal times.
- Income buffers: during severe stress, banks typically exhibit substantially lower pre-impairment income available to absorb losses.
- Bank responses: common reactions include dividend suspension and deleveraging; deleveraging can restore solvency but may be macroeconomically costly if it constrains credit supply.
- Cross-country differences: EMs and ACs display importantly different typical behavior—differences plausibly linked to larger cyclical fluctuations in EMs and structural factors such as effectiveness of loan workout mechanisms.
- LICs: evidence is limited; functioning may differ from ACs and EMs due to factors like commodity export dependence and lower bank intermediation.

### Measurement and methodological implications
- Regulatory capital measurement matters: risk-based capitalization measured under the standardized approach (StA) is less sensitive to shocks than under the Internal Ratings-Based approach (IRB).
  - Implication: StA may be slower to reveal emerging vulnerabilities; IRB reflects deterioration and rebound more quickly if IRB risk weights respond timely.
  - Consequence: a given level of risk-based capitalization in benign times may represent a smaller effective buffer for an IRB bank than for a StA bank.

### Analytical approach and structure
- Section II (of the source): explains main elements of the approach and evidence.
- Section III (of the source): proposes descriptive rules of thumb conditional on the evolution of credit losses, and illustrates their use in simulating capital ratio evolution under stress.
- Exclusions: effects of managerial actions (raising capital, asset disposals, balance sheet restructuring) and structural changes (exit of firms) are not analyzed, consistent with standard stress-testing methodology.

*Source: Appendix 1. Data Summary from the supplied IMF working paper content.*

### Section IV contains rules of thumb versions of satellite models that link the key drivers of

### _wp13232 - Section IV contains rules of thumb versions of satellite models that link the key drivers of

### Methodology and sources
- Main metric for bank solvency stress tests: risk-based capital ratio = bank’s capital divided by risk-weighted assets (RWA).
- Tests yield projections of capital ratios after stress over the relevant time horizon.
- Rules of thumb are derived from the literature on banking crises and statistical evidence from two datasets:
  - Long-sample evidence: default rates over a period of 90 years (1920–2012) for ACs (Moody’s 2013).
  - Cross-country evidence: Bankscope sample covering 1996–2011, initially >16,000 banks in 200 countries/jurisdictions; more than 13,000 in ACs (almost half in the United States), about 3,000 in EMs, and only 550 in LICs. After outlier removal and robustness checks the effective sample used for rules of thumb is more than 10,000 banks from almost 170 countries.

### Metrics and decompositions used for projections
- Risk-based capital ratio projection accounts for:
  - Initial capital and projected retained net profit (projected retained net profit is negative if net income is negative; otherwise depends on dividend payout assumptions).
  - Initial RWA and projected change in RWA.
- Main factors affecting net income relevant for solvency tests:
  - Loan loss provisions (and write-offs), which depend on probabilities of default (PDs) and loss given default (LGD), or on NPL categorization and provisioning rules.
  - Pre-impairment income: net interest income (including funding costs), commission and fee income, trading income, other operating income, and operating expenses.
  - Dividend payouts and taxation.
- RWA change depends on:
  - Volume: projected net growth in the balance sheet, especially loans.
  - Risk: changes in risk weights due to changes in the risk profile of assets, especially under IRB approaches.
- Complementary metric: unweighted leverage ratio; post-stress leverage ratio decomposed analogously to risk-based capital ratio but with assets (on- and off-balance sheet) in the denominator.
- Profitability metrics (ROC, ROA) are central: profitability is the first line of defense and determines ability to recover from capital losses.

### Data limitations and treatment
- Acknowledged heterogeneity in definitions (NPLs, capital, provisioning) across countries and banks.
- Robust techniques used to limit influence of data problems; outliers removed (e.g., very high loss levels above 100 percent due to off-balance sheet operations).
- For simplicity in many applications, assume shock effects pass through profit and loss rather than directly to capital.

### Typical banking crises and crisis severity taxonomy
- Historical and cross-sectional evidence show NPL ratios and default rates increase substantially during crises and typically peak with a lag.
- Classification of stress scenarios by percentiles of credit loss rates:
  - normal conditions = median of credit loss rates;
  - moderate stress = 80th percentile of credit loss rates;
  - medium stress = 90th percentile of credit loss rates;
  - severe stress = 97.5th percentile of credit loss rates;
  - extreme stress = historical maximum (typically the worst year in a century).
- Empirical frequency guidance (from percentiles and clustering):
  - Episodes of moderate or medium stress normally occur in ACs on a one-in-10 to one-in-15-years basis, and a one-in-20-years basis, respectively.

### Empirical patterns of NPLs, default rates, and credit losses
- NPL stock ratios:
  - Rise substantially during crises and typically peak one year after crisis materialization.
  - Increase by about 10 percentage points from the typical level one year before the crisis in “average” crises, and almost 25 percentage points in severe crises.
  - The stock is persistent: even after three years, NPL ratio is at about the same level as when the crisis materializes.
- NPL flow ratios as proxy for default rates:
  - Peak at about 10 percent in “average” crises, and at about 18 percent in severe crises, up from 3 percent in “normal” times.
  - Default rates tend to return to pre-crisis levels after three years (pattern roughly symmetric around the crisis), though stock reductions take longer.
- Cross-country patterns:
  - EMs exhibit higher and more variable NPL and default rate peaks than ACs.
  - Real GDP growth is much more variable in EMs than ACs.

### Proxies for credit loss rates (practical approximations)
- When PD and LGD data are unavailable, proxies based on NPL stocks and write-off assumptions are used.
- Proxy approximation for forward-looking PD from NPL stocks:
  - PDt = α*(NPLt+1 - NPLt-1) … (text provides a formula using α to reflect write-off speed).
  - Assumptions used in the study:
    - For years before the crisis, α = 0.5 (implying NPLs fully written off after about two years).
    - After the peak of NPLs, α = 0.33 (implying write-off after about three years).
  - These approximations are affected by country NPL definitions and shifts in impairment severity (provisioning rates).

### Historical evidence and interpretation
- Long-sample (Moody’s) default-rate peaks: five notable peaks over 1920–2012, with the highest during the Great Depression of the 1930s.
- Earlier history (pre-1900) shows even higher default-rate peaks, supporting the hypothesis that default rates are higher and more variable in EM-like economies.
- Applied classification to Moody’s long-term evidence:
  - One of the five crises classified as “moderate/medium”;
  - Two as “medium”;
  - The recent crisis (as of the study) as borderline between “medium” and “severe”;
  - The 1930s crisis as “severe/extreme.”
- Implication: rules of thumb and stress-test calibrations should distinguish by severity (normal, moderate, medium, severe, extreme) and by country type (ACs vs EMs vs LICs).

*Italic: Source: _wp13232 - Section IV contains rules of thumb versions of satellite models that link the key drivers of (PDF content provided).*

### 0.8 percent under moderate stress, 1.1 percent for medium stress, and 2.4 percent under

### _wp13232 - 0.8 percent under moderate stress, 1.1 percent for medium stress, and 2.4 percent under

### Credit loss rates by scenario and country group
- Reported median and mean credit loss rates (percent of credit outstanding) by scenario and country group:
  - Normal, median: AC 0.3, EM 1.0, LIC 1.4
  - Normal, mean: AC 0.7, EM 1.9, LIC 2.4
  - Moderate: AC 0.8, EM 2.2, LIC 3.1
  - Medium: AC 1.1, EM 3.4, LIC 4.9
  - Severe: AC 2.4, EM 7.4, LIC 13.4
  - Extreme: AC 4.3, EM 14.0, LIC 33.8
- Sample coverage:
  - No. of observations: AC 463, EM 1,457, LIC 698
  - No. of countries: AC 32, EM 104, LIC 52
- Cross-country patterns:
  - Across stress levels, losses are higher in EMs by a factor of about three compared to those in ACs.
  - Results overlap across country groups: some EM countries experienced lower median loss rates over 1996–2011 than some AC countries.
  - Historical maximum levels for country aggregates exceed 3 percent.

### Bank-level crisis dynamics and sampling
- Bank-by-bank methodology:
  - Maximum credit loss level for each bank was assigned to the respective level of severity.
  - Seven consecutive observations used per crisis episode: three before peak, peak year, three after.
  - Only one severity level (the maximum) per bank included to avoid multiple use of data points.
  - Banks with loss levels above 60 percent or with very low loss levels were excluded to avoid distortion.
  - Robustness check: sample restricted to banks with at least five consecutive observations during stress years (from –2 to 2); results qualitatively similar.
- Empirical pattern:
  - Credit loss rates peak sharply during one single year.
  - The credit loss rate pattern is symmetrical with respect to the crisis.

### Loss Given Default (LGD) behavior and linkage to default rates
- Empirical LGD evidence:
  - LGDs fluctuate with the business cycle.
  - Descriptive evidence for workout LGDs from Moody’s (1990–2012 loans series) used for ACs.
- Relationship between LGD and default rates:
  - Pairwise correlation between LGD and default rates: 0.47.
  - LGD rates tend to fluctuate proportionately less and are less cyclical than default rates.
  - LGDs typically double in case of a severe/extreme stress, whereas default rates increase many times over.
  - Because LGD variations have a linear impact on RWAs, their impact on bank solvency is considerable; in absolute terms LGDs greatly amplify stress under severe conditions.
- Table of stress levels for ACs (Percent):
  - Scenario — Default rates/1 — Projected LGD
    - Normal — 0.7 — 26
    - Moderate — 1.7 — 30
    - Medium — 2.9 — 34
    - Severe — 5.0 — 41
    - Extreme — 8.4 — 54
  - Note: Default rates based on Moody’s default rates shown in Figure 2.

- LGDs for EMs and LICs:
  - Historical average LGD rates: EMs about 59 percent, LICs about 62 percent (derived from World Bank/ Djankov et al. (2007) Doing Business data).
  - Practical stress-testing approach: use long-term average LGD in a country and add the same absolute increase as observed in ACs for a given stress intensity.

- Implied default rates from dividing credit loss rates by LGDs:
  - Using LGDs in Table 4, implied default rates are: Normal 1.3 percent, Moderate 2.7 percent, Medium 3.3 percent, Severe 5.7 percent, Extreme 8 percent.
  - Using an LGD of 60 percent for EMs and LICs yields implied default rates consistent with loss-rate-based PD approximations.

### Pre-impairment income dynamics under stress
- Definition and normalization:
  - Focus on net pre-impairment income (adjusted for operational expenses but not loan losses).
  - Income normalized via ROC (return on capital) rather than ROA to account for cross-country leverage differences.
- Median net pre-impairment ROC by country group (bank-by-bank Bankscope data):
  - LICs: 25.0 percent
  - EMs: 18.9 percent
  - ACs: 11.9 percent
- Conditional behavior under stress:
  - Pre-impairment income is affected in stress scenarios but on average remains positive, providing a buffer against credit losses.
  - Income behavior is less symmetric than credit losses: income often remains low for some years after the trough for AC banks, or drops significantly at the trough for EM banks.
- Tail outcomes:
  - For AC banks in the worst-performing percentiles:
    - Worst performing 25th percentile: income becomes negative under severe stress for at least a quarter of banks.
    - Worst performing 10th percentile: 10 percent of banks encounter ROCs below –20 percent at the trough under severe stress.
  - Similar patterns are observed for EM banks, although limited data restricts firm calibration for EMs and LICs.
- Dividend and tax behavior:
  - Dividend-payout drops to zero under severe stress for both AC banks and EM/LIC banks.
  - Tax payments are reduced reflecting lower net income.

### Income and expense component behavior and trading income risk
- Key pre-impairment income components:
  - (a) Net interest income — tends to be relatively stable as interest rate changes pass through when loans and deposits mature.
  - (b) Net fee and commission income — relatively volatile for AC banks across crises.
  - (c) Trading income — generally mildly correlated with the cycle but can become highly negative in severe crises.
  - (d) Other operating income.
  - (e) Operating expenses — median AC bank operating expenses become very volatile in a severe crisis; median EM banks reduce operating expenses at times of stress.
- Component-specific observations:
  - For AC banks, net commission and fee income is consistently relatively volatile.
  - For EM banks, changes in net income under stress are largely driven by net interest income due to foregone interest on credit losses and possible interest rate behavior during crises.
  - Trading income is relatively unimportant and stable for the median (small) bank, but trading losses can be large in severe crises ("Black Swan" events) and should be captured by stress tests for banks with meaningful trading operations.
- Cross-crisis volatility:
  - Standard deviations across crisis periods of median income and expense components measured as percent of capital show substantial variability across components and stress severities.

*Source: Authors, based on Bankscope data, Moody’s (2013), World Bank (Doing Business) and related analyses contained in the provided content.*

### Box 2. How Likely is it that Large Trading Losses Coincide with Large Credit Losses?

### Box 2. How Likely is it that Large Trading Losses Coincide with Large Credit Losses?

### Trading losses and tail risk
- For a median bank with some trading operations, trading income is, on average, slightly positive under most stress conditions.
- In severe scenarios (as defined by credit risk losses):
  - A bank at the worst performing decile (in terms of the ratio of trading income losses to capital) could lose about 5 percent of capital.
  - The worst performing 1 percent of banks might lose a third of capital.
- Trading activity is concentrated in larger banks; the worst performing 1 percent of banks could hold a substantial share of aggregate assets.
- Historical note: during the recent global crisis, a few large European banks lost within one year more than one third of their capital due to trading losses alone, while many smaller banks had insignificant trading losses.
- Trading income likely follows close to a random walk pattern with little serial correlation — a single very bad year of trading could be sufficient to bring down a large bank.

### Credit growth and asset growth under stress
- Nominal credit growth of banks’ customer loans net of credit losses tends to slow sharply under stress, even if it does not become negative.
- Conditional on stress (as measured by credit losses):
  - Deleveraging occurs only in case of severe crises in ACs, while medium intensity crises tend to end in three years of (close to) zero year-on-year credit growth for ACs.
  - Credit growth remains fairly sizable for EM banks under stress, except for severe stress, when credit growth becomes zero.
  - The pattern for LIC banks is less clear-cut owing to limited data.
- Asset growth behaves very similarly to credit growth and therefore affects both risk-weighted capital ratios and the unweighted leverage ratio via the denominator.

### Satellite models: approach and uses
- Satellite models project the impact of macro shocks (notably shocks to real GDP growth) on banks’ solvency variables (credit losses, income, credit growth).
- Methods used in the literature include time series analysis, linear and non-linear regression models (OLS, logistic, panel), and structural models.
- Satellite models are best suited to capturing exogenous macroeconomic shocks; they are less appropriate when shocks originate within the financial system (e.g., asset bubbles, large-scale malfeasance).
- Real GDP is the preferred explanatory variable for aggregate activity; for this study the average real GDP growth rate for 1980 to 2011 is used as a trend benchmark.
- Two measures of GDP shocks are used:
  - (i) changes in real GDP growth at t = 0 relative to t–4;
  - (ii) cumulative deviation of real GDP growth rates from trend from t–4 to t = 0.

### Rules of thumb and example calculations (Table 4 based approach)
- Rules link cumulative deviation or change in annual growth rates of real GDP to solvency variables via sensitivity parameters.
- Example using cumulative-deviation rule:
  - A cumulative deviation of 5.9 percentage points (moderate stress in an AC) multiplied by a sensitivity of –0.1 yields an increase in median bank credit losses of –5.9×–0.1 = 0.59 percentage points in the worst year.
- Examples using change-in-annual-growth-rate rule (AC median credit loss sensitivity = –0.2):
  - Drop from 2.4 percent (pre-crisis average) to 0.0 percent (moderate): –2.4×–0.2 = 0.48 percentage points increase in median AC bank credit losses.
  - Drop to –1.9 percent (medium stress): –4.3×–0.2 = 0.86 percentage points.
  - Drop to –5.0 percent (severe stress): –7.4×–0.4 = 2.96 percentage points.
- Path projections: apply the sensitivity to year-to-year changes in GDP growth along t = –3 to t = 0 to build trajectories of solvency parameters.
- For stress testing when the system is already under strain, choose which stress level (moderate/medium/severe) and which year (t–3 to t+3) reflects current situation, then apply corresponding sensitivities forward.

### Key tabulated benchmarks (as presented)
- Cumulative deviation of real GDP growth from t–4 to t=0 (typical base levels):
  - AC: 10.0
  - EM: 17.9
- Change in real GDP growth rate from t–4 to t=0 (typical base levels):
  - AC: 2.4
  - EM: 4.2
- General patterns from Table 4 and discussion:
  - Sensitivities generally increase with stress; sensitivity of credit loss rates to GDP declines is roughly the same in moderate and medium stress but at least twice as high under severe stress.
  - Sensitivities are much larger for the tail (worst performing 10th percentile) than for the median bank; coefficients for the worst performing 10th percentile are normally at least double, and sometimes many times, those of the median bank.
  - Not all relationships are highly nonlinear (credit growth shows a more linear relationship with GDP shocks).

### Credit quality link to GDP
- Large output falls can cause at least a one-for-one increase in default rates; Moody’s data over the covered period show that peaks of default rates coincided with sharp economic downturns.
- The absolute sensitivity of default rates to GDP growth is about 0.5 (as noted in the discussion of Moody’s and Table 5).

*Source: Box 2 text in the provided PDF content.*

### 3.5 percentage points divided by a decrease in GDP growth levels of 6.4 percentage

### _wp13232 - 3.5 percentage points divided by a decrease in GDP growth levels of 6.4 percentage

### Timing and magnitude of credit losses around macroeconomic crises
- The bulk of credit losses typically occur at the trough of the associated macroeconomic crisis; the year of lowest GDP growth coincides with the year when loss rates peak sharply.
- Default rates return to pre-crisis levels (long-term average of 1.1 percent) after three years in typical episodes.
- Exception: the 1930s Great Depression—losses remained elevated for several years after the trough in GDP growth and did not return to the long-term average until after 6 years.
- Observed lead/lag between GDP trajectory and credit loss trajectory:
  - 60 percent of cases: no lag between GDP and credit loss trajectories.
  - 20 percent of cases: GDP trajectory leads by one year.
  - 20 percent of cases: GDP trajectory lags by one year.
- Example sensitivities:
  - Absolute sensitivity including 1930s: 0.6 (= 3.1/4.8) when excluding 1930s observations; other example in text: 3.5 percentage points divided by a decrease in GDP growth levels of 6.4 percentage points.

### Rules of thumb for GDP growth sensitivity of credit risk parameters (Table 6)
- Default rates:
  - Moderate: -0.4
  - Medium: -0.6
  - Severe: -0.8
- LGDs:
  - Moderate: -1.5
  - Medium: -2.5
  - Severe: -4.0
- Asset correlations (corporates):
  - Point estimate: -2.7
- Note: For projections based on the cumulative deviation of GDP growth from trend, the parameters should be divided by two.

### LGD behavior and caveats
- Correlation between LGDs (Moody’s, 2013) and GDP real growth rates: -0.44.
- LGDs in normal times typically lie in the 30 to 60 percent range.
- Sensitivity of LGD rates to real GDP slowdown is usually moderate in ACs; sensitivity (in relative terms) is lower than that of PDs.
- In case of a bursting asset price bubble, especially a debt-financed real estate bubble, LGD rates should be expected to be exceptionally high; practical approach: use the severe-scenario LGD coefficient even when macroeconomic shock is moderate or medium.

### Income, retained earnings, and payout behavior under stress
- Median GDP sensitivities of pre-impairment income are relatively modest but highly non-linear in unfavorable circumstances, especially for poorly-performing banks.
- Expected levels of profit retention by banks under stress (Appendix Table 4 summary):
  - AC banks: pay-out about 35 percent in “normal” times and moderate stress; 20 percent under medium stress; 0 under severe stress.
  - EM banks: around 30 percent in normal times and moderate stress; 17 percent under medium stress; 0 under severe stress.
  - LIC banks: around 45 percent in normal times and moderate stress; 40 percent under medium stress; 0 under severe stress.
- Basel III reference: minimum regulatory rates for retention of income (“capital conservation”) (BCBS, 2011, para. 131).

### Credit growth and origins of crises
- For credit growth, AC banks exhibit similar GDP sensitivities across shock levels.
- Sensitivity in ECs tends to decrease with stress intensity; historical high credit growth in ECs during the last 15 year may influence this result.
- Crises provoked by external macroeconomic shocks are likely associated with relatively stable credit aggregates or only moderate slowdown.
- Crises provoked by bursting of credit-financed asset price bubbles or lending booms are likely followed by a more contractionary path for credit aggregates.

### Asset correlations: empirical behavior and implications
- Empirical evidence (Duellmann et al., 2008, 1997–2003 sample): asset correlations fluctuated from 4 percent to 16 percent, mean 10.5 percent.
- Estimated GDP growth sensitivity of asset correlations: -2.7 (i.e., a fall of GDP growth by 1 percentage points leads to an increase of asset correlations by 2.7 percentage points).
- Implication: estimated asset correlations can increase substantially with stress, potentially reaching about 30 percent from 10 percent under “normal” (TTC) conditions (caveat: extrapolation beyond 16 percent).
- Using point-in-time (PIT) correlations for stress testing can be appropriate but requires attention to potential double-counting once losses have materialized; alternative: fixed IRB correlations based on low PDs.

### Worked examples: illustrative banks (Table 7)
- Example bank characteristics (US$ billions):
  - Assets: ACs 100.0 ; EMs 100.0
  - Customer loans: ACs 47.0 ; EMs 54.0
  - Other on-balance sheet assets subject to credit risk: ACs 46.0 ; EMs 39.0
  - Assets not subject to credit risk: ACs 7.0 ; EMs 7.0
  - Off-balance sheet assets subject to credit risk: ACs 21.0 ; EMs 24.0
  - Total regulatory capital: ACs 6.0 ; EMs 8.7
  - Leverage ratio (capital/(on + off-balance assets)): ACs 5.0 ; EMs 7.1
- StA RWAs (US$ billions):
  - ACs: 64.3
  - EMs: 62.0
- StA capital ratio (percent):
  - ACs: 9.3
  - EMs: 14.0
- Implied IRB RWAs (US$ billions):
  - ACs: 40.9
  - EMs: 107.4
- Implied IRB capital ratio (percent):
  - ACs: 14.7
  - EMs: 8.1
- Pre-impairment income (ROC, percent, long-term average):
  - ACs: 12.0
  - EMs: 20.0
- Net income (US$ billions, long-term average):
  - ACs: 0.4
  - EMs: 1.1
- ROC (percent, long-term average):
  - ACs: 6.7
  - EMs: 9.3
- Notes on assumptions used in simulations:
  - Example AC bank: total on-balance sheet assets US$100 billion; customer loans US$47 billion; US$46 billion securities subject to credit risk; US$21 billion off-balance sheet assets subject to credit exposure; US$7 billion other assets not subject to credit risk; capital US$6.0 billion.
  - For StA: variable external ratings apply to 10 percent of assets subject to credit risk; RWAs for credit risk assumed to be 80 percent of total RWAs; risk-weights for non-loan assets subject to credit risk are one third of those applied to loans.
  - Effective maturity assumed to be 2.5 years; PDs and LGDs for corporate loans set as in Table 3 under normal conditions (LGD set to 30 percent). Scaling factors: SMEs 1.5, retail 0.75. Credit conversion factor for off-balance sheet exposures assumed 50 percent (i.e., US$21 billion ~= US$10.5 billion on-balance sheet equivalent).
  - For EM illustrative bank: same total assets, customer loans 54 percent, capital US$8.7 billion; elevated credit risk implies higher capital weights under IRB and lower IRB capital ratio relative to StA.

*Source: Authors' calculations and data excerpts as presented in the provided content.*

### 4.6 percent under “normal” conditions. Details of the worked example are available from the authors.

### _wp13232 - 4.6 percent under “normal” conditions. Details of the worked example are available from the authors.

### Impact of Stress on Capital Ratios and Capitalization (Advanced Countries (AC) and Emerging Countries (EC))
- For AC banks under the IRB, severe stress reduces capital levels to 3 percent, i.e., below the regulatory minimum of 8 percent.
- For AC banks under the IRB, medium stress reduces capital levels to about 7 percent from an initial level of 14.7 percent.
- Moderate stress for AC banks can be digested by banks (no exact numeric drop stated for moderate in this excerpt).
- Measured bank capitalization under the StA is generally affected less by stress than under the IRB, largely due to more substantial changes in RWAs under the IRB, especially under severe stress.
- Variations in RWAs based on PIT credit risk parameters (PD, LGD) are very sizable in the absence of mitigation through behavioral adjustments (e.g., re-balancing of assets toward highly-rated securities).

### Simulated Evolution of RWAs Relative to Total Assets During Stress Periods (Table 8)
- RWA StA — AC (Percent by t = –3 to t = 3)
  - Normal: 64 64 64 64 64 64 64
  - Moderate: 64 64 65 71 64 64 64
  - Medium: 64 65 73 79 64 64 64
  - Severe: 65 73 85 88 65 65 65
- RWA StA — EC (Percent by t = –3 to t = 3)
  - Normal: 63 63 63 63 63 63 63
  - Moderate: 63 63 64 69 63 63 63
  - Medium: 63 64 71 77 63 63 63
  - Severe: 64 71 80 87 64 64 64
- RWA IRB — AC (Percent by t = –3 to t = 3)
  - Normal: 41 41 41 41 41 41 41
  - Moderate: 41 41 41 65 41 41 41
  - Medium: 41 41 67 87 66 42 42
  - Severe: 41 67 93 165 90 69 44
- RWA IRB — EC (Percent by t = –3 to t = 3)
  - Normal: 108 109 109 110 110 110 111
  - Moderate: 108 109 111 148 111 111 112
  - Medium: 108 111 153 202 153 115 115
  - Severe: 110 153 207 340 230 177 134

### Leverage Ratio Effects
- Leverage ratio is affected if income becomes negative and will rise in the case of a credit contraction.
- Worked examples:
  - For ACs, severe stress leads to a drop of the leverage ratio by 1.9 percentage points (in the worst year), i.e., from 5 percent to 3.1 percent.
  - For EC banks, medium and severe stress result in drops of the leverage ratio by 1.4 and 7.9 percentage points, respectively, from an initial level of 7 percent.
- Conclusion: “Average” banks (as simulated) are, with the exception of EC banks under severe stress, in a solid position to maintain an adequate leverage ratio.

### Income, Net Income after Loan Losses, and Contributions to Earnings Decline
- Net income after loan losses becomes:
  - Negative under severe stress for the ACs: –25 percent ROC (AC severe at t=0 in Table 9).
  - Negative under medium (–0.3 percent ROC) and severe stress (–95 percent ROC) for the ECs.
- Contributions to decline in earnings (ACs vs ECs):
  - ACs: net interest income contributes 59 percent; net fees and commissions 21 percent; other income 20 percent (trading and fair value contributes half of this).
  - ECs: net interest income contributes 74 percent; net fees and commissions 18 percent; other income 9 percent.
- Simulated Evolution of Net Income during Stress Periods (Table 9 — Percent ROC by t = –3 to t = 3)
  - AC — Moderate: 7.0 6.9 6.5 3.0 6.6 6.1 6.2
  - AC — Medium: 7.0 6.4 2.1 -0.3 1.2 5.1 5.1
  - AC — Severe: 7.0 5.8 -2.4 -25.1 -6.1 -1.7 -0.4
  - EC — Moderate: 9.7 9.8 9.8 2.5 10.0 8.9 9.6
  - EC — Medium: 9.7 9.8 2.5 -5.8 -0.9 8.0 5.7
  - EC — Severe: 9.8 9.5 -5.5 -95.1 -290.5 ... 1/ ... 1/  (1/ Undefined due to negative capital.)

### Comparison to Historical Evidence and Stress Test Applications
- Predicted evolution of capitalization of an AC bank under severe stress based on the StA roughly matches the 25-th percentile of banks that experienced severe stress over the last 15 years; IRB-based prediction is close to the 10-th percentile of actual results.
- Rules of thumb applied to recent stress tests (EBA 2011; U.S. Federal Reserve Board 2012):
  - EBA (EU) scenario: cumulative deviation from baseline growth ~4 percentage points for 2011–2012.
    - IRB GDP change rule suggests a drop of capital ratios by 3 to 4 percentage points (2 percentage points drop in real GDP growth times sensitivity of 1.5-2 percentage points per unit of GDP).
    - Cumulative deviation rule suggests a drop of about 3.2 percentage points (4 percentage points drop times sensitivity ~0.8 percentage points per unit of GDP).
  - U.S. test: cumulative deviation during three years (2012–14) by 5 percentage points from baseline, including a dip by 6 percentage points within one year.
    - StA change rule suggests a drop by about 3.9 percentage points (6 percentage points drop times sensitivity of about 0.65 percentage points per unit of GDP).
    - Actual average drop during the dip year estimated around 4.3 percentage points.

### Rules of Thumb: Sensitivities of Capital Ratios to GDP Growth Changes
- For the AC bank:
  - A 1 percentage point drop in GDP growth leads to a reduction in capitalization by 0.4 to 0.5 percentage points for a StA bank.
  - The same 1 percentage point drop leads to about 1.6 to 2.3 percentage points for an IRB bank, depending on severity.
  - For cumulative deviation from GDP trend, coefficients should be divided by two.
- For the EM bank:
  - A 1 percentage point drop in GDP growth leads to about 0.5 to 1.2 (preserved text: "0.5 to 1.2 under the StA per unit drop of real GDP growth") under the StA.
  - The same drop leads to 0.6 to 0.7 percentage points under the IRB approach.
  - For cumulative deviation from GDP trend, coefficients should be divided by three.
  - Note: The IRB coefficient for EC banks is relatively low because EC banks exhibit higher initial risk weights than AC banks, reducing sensitivity of RWA to cyclical fluctuations.

### Through-The-Cycle (TTC) vs Point-in-Time (PIT) RWAs and Procyclicality
- PIT-based RWAs give earlier warning of strain, while TTC-based RWAs result in a slower decline in calculated capital ratios over the two years leading to a crisis, with a larger drop at the time of the crisis or thereafter.
- Policy trade-offs:
  - PIT can be pro-cyclical and amplify capital requirements in downturns, potentially provoking a credit crunch.
  - TTC (e.g., moving average over five years) can provide breathing space for banks to bolster capital, but may not reflect immediate survival risk under severe cyclical stress.
- Similar considerations apply to asset correlations.

### Required Initial Capital Ratios to Stay Above 8 Percent Under Stress (Policy Simulations)
- Average AC bank under IRB (PIT):
  - To remain at or above 8 percent at time t=0 under severe stress: around 30 percent initial capital ratio.
  - To remain at or above 8 percent under medium stress: about 17 percent initial capital ratio.
- Average AC bank under IRB (TTC):
  - Severe stress: 20 percent initial capital ratio.
  - Median (medium) scenario: 14 percent initial capital ratio.
- Average AC bank under StA:
  - To cope with medium stress without falling below regulatory floor: 10 percent initial capital ratio.
  - To cope with extreme stress: 12.5 percent initial capital ratio.
- EC bank under StA:
  - To cope easily with medium shocks: 12 percent initial capital ratio.
  - To cope with severe stress: around 22 percent initial capital ratio.
- Banks with volatile pre-impairment earnings require higher capital:
  - An AC bank from the worst decile of pre-impairment earnings would need a capital ratio of 22 percent using IRB to cope with medium stress.
  - An EC bank from the worst decile, using StA, would need 17 percent to deal easily with medium stress and 25 percent to cope with severe stress.

### Rules of Thumb Summary (Table 10 — Percent)
- AC bank (Normal / Medium stress / Severe stress)
  - Annual credit loss rate: 0.3 1.1 2.4
  - Pre-impairment ROC: 11.9 11.4 8.3
  - Credit growth rate: 7.2 1.3 -3.8
  - Asset correlation: 10.4 21.8 30.1
- EM bank (Normal / Medium stress / Severe stress)
  - Annual credit loss rate: 1.0 3.4 7.4
  - Pre-impairment ROC: 18.9 18.6 13.4
  - Credit growth rate: 18.9 3.2 -8.3

### Key Caveats and Limitations
- Simulations assume average bank behavior in credit growth, no substantial deleveraging beyond rules of thumb, no structural balance sheet changes (e.g., replacing higher risk weight assets), and neglect asset sales and capital raising beyond retained earnings—strong assumptions for multi-year periods but useful as benchmarks.
- Simulations use median risk parameters for banks that experienced severe stress; tail banks (below-average) can face much higher loss and income deterioration than median.
- The rules of thumb focus on GDP-driven macro-financial linkages and do not cover other macroeconomic risk factors in detail (e.g., interest movements, inflation shocks, exchange rate movements, sectoral concentration shocks).
- Regulatory approach (IRB vs StA) materially affects magnitude and timing of recognition of shocks; results relevant to discussions on RWA calibration and countercyclical capital buffers.

*Source: Authors (excerpt from document _wp13232).*

### APPENDIX 1. DATA SUMMARY

### APPENDIX 1. DATA SUMMARY

### Overview of Bankscope Data (Original Raw Data and Cleaned Final Data)
- Original Raw Data:
  - AC: Number of countries 33; Number of banks 13,271; Assets (US$ trillions) 120.4
  - EM: Number of countries 109; Number of banks 3,126; Assets (US$ trillions) 28.2
  - LIC: Number of countries 59; Number of banks 543; Assets (US$ trillions) 1.2
  - Total: Number of countries 201; Number of banks 16,940; Assets (US$ trillions) 149.9
- Cleaned, final data:
  - AC: Number of countries 32; Number of banks 9,372; Assets (US$ trillions) 68.8
  - EM: Number of countries 90; Number of banks 1,131; Assets (US$ trillions) 10.4
  - LIC: Number of countries 47; Number of banks 206; Assets (US$ trillions) 0.3
  - Total: Number of countries 169; Number of banks 10,709; Assets (US$ trillions) 79.5

### Raw Bankscope Sample Size by Year (Figure summary)
- Figure metric: Sample size (Number of banks) plotted over time with axis tick labels from 0 to 18,000 (number of banks).
- Page reference number: 57

### Top 10 Countries by Category for Cleaned Bankscope Data (counts and total assets)
- Advanced countries (Country (ISO code) — Number of banks — Total assets (US$ billion)):
  - US 5,930 11,447
  - DE 1,513 6,428
  - JP 497 10,030
  - IT 398 4,043
  - AT 194 967
  - CH 165 330
  - FR 137 10,190
  - ES 89 3,692
  - GB 78 9,026
  - DK 71 1,050
- Emerging market countries:
  - RU 96 773
  - BR 73 2,149
  - AR 49 118
  - IN 39 438
  - MY 30 496
  - UA 29 44
  - ID 28 78
  - DO 26 19
  - HR 25 57
  - TW 24 693
- Low income countries:
  - KE 19 12
  - NG 15 78
  - BD 13 28
  - TZ 11 2
  - ZM 9 3
  - ET 8 9
  - UG 8 1
  - AO 7 15
  - KH 6 2
  - YE 6 0

### Bankscope Data, by Stress Level (counts and assets)
- Number of banks by stress level:
  - AC: Total 9,372; Moderate stress 1,952; Medium stress 4,402; Severe/extreme stress 3,018
  - EM: Total 1,131; Moderate stress 305; Medium stress 491; Severe/extreme stress 335
  - LIC: Total 206; Moderate stress 65; Medium stress 77; Severe/extreme stress 64
- Assets in US$ billions by stress level:
  - AC: Total 68,767; Moderate stress 14,666; Medium stress 35,977; Severe/extreme stress 18,124
  - EM: Total 10,427; Moderate stress 2,734; Medium stress 5,102; Severe/extreme stress 2,592
  - LIC: Total 347; Moderate stress 129; Medium stress 80; Severe/extreme stress 138

### Evolution of Solvency Parameters around Crisis Dates (selected panels, years around crisis: -3 -2 -1 0 1 2 3)
- Credit loss rates/total customer loans (percent)
  - AC "Normal": 0.3 0.3 0.3 0.3 0.3 0.3 0.3
  - AC Moderate: 0.2 0.2 0.4 0.8 0.4 0.3 0.2
  - AC Medium: 0.3 0.4 0.7 1.5 0.7 0.5 0.5
  - AC Severe: 0.3 0.5 1.2 4.0 1.3 0.7 0.5
  - EM "Normal": 1.0 1.0 1.0 1.0 1.0 1.0 1.0
  - EM Moderate: 0.7 0.8 1.2 2.5 1.2 0.9 0.7
  - EM Medium: 1.1 1.3 2.3 5.2 2.0 1.2 0.9
  - EM Severe: 2.1 2.4 4.1 15.6 3.5 1.8 1.1
  - LIC "Normal": 1.4 1.4 1.4 1.4 1.4 1.4 1.4
  - LIC Moderate: 1.3 1.2 1.6 3.2 1.2 1.0 0.8
  - LIC Medium: 1.4 0.9 2.1 6.4 1.9 1.2 1.0
  - LIC Severe: 2.8 3.7 3.0 15.3 4.1 1.3 1.7
- Credit growth (adjusted for losses) (percent)
  - AC "Normal": 7.2 7.2 7.2 7.2 7.2 7.2 7.2
  - AC Moderate: 7.5 7.5 6.0 3.5 3.2 3.8 4.7
  - AC Medium: 7.0 6.3 4.2 1.3 1.2 2.5 4.0
  - AC Severe: 11.0 8.9 3.6 -3.8 -4.3 -0.3 2.6
  - EM "Normal": 22.7 22.7 22.7 22.7 22.7 22.7 22.7
  - EM Moderate: 19.8 21.8 19.3 11.8 14.4 18.3 22.7
  - EM Medium: 29.8 26.9 16.1 7.8 13.8 21.8 24.3
  - EM Severe: 23.8 20.1 11.6 1.3 15.5 24.9 23.6
  - LIC "Normal": 20.5 20.5 20.5 20.5 20.5 20.5 20.5
  - LIC Moderate: 13.3 30.0 36.2 22.0 21.8 28.8 21.4
  - LIC Medium: 31.7 17.1 23.9 12.3 14.9 26.2 23.4
  - LIC Severe: 19.8 20.5 24.5 13.0 15.5 30.3 20.7
- Pre-impairment income/capital (percent)
  - AC "Normal": 11.9 11.9 11.9 11.9 11.9 11.9 11.9
  - AC Moderate: 13.9 13.8 13.2 13.5 13.1 12.5 12.6
  - AC Medium: 14.2 13.4 12.7 12.5 11.4 11.2 11.2
  - AC Severe: 14.4 12.9 10.5 8.0 8.3 8.9 9.8
  - EM "Normal": 18.9 18.9 18.9 18.9 18.9 18.9 18.9
  - EM Moderate: 22.1 21.8 21.0 24.2 22.0 20.7 21.4
  - EM Medium: 22.9 21.1 23.0 23.7 18.6 18.7 16.2
  - EM Severe: 17.6 21.9 23.2 26.2 14.4 13.4 17.9
  - LIC "Normal": 25.0 25.0 25.0 25.0 25.0 25.0 25.0
  - LIC Moderate: 10.2 13.2 18.7 24.7 30.2 32.8 36.3
  - LIC Medium: 63.5 47.6 30.4 30.0 22.3 23.7 21.5
  - LIC Severe: 15.4 16.5 11.8 41.1 29.2 15.5 25.1
- Dividend pay-out/net income (percent)
  - AC "Normal": 33.7 33.7 33.7 33.7 33.7 33.7 33.7
  - AC Moderate: 41.6 42.9 40.0 34.9 34.0 33.3 38.5
  - AC Medium: 37.4 37.1 35.1 20.0 22.5 27.9 25.0
  - AC Severe: 23.9 23.2 0.0 0.0 0.0 3.6 17.0
  - EM "Normal": 28.8 28.8 28.8 28.8 28.8 28.8 28.8
  - EM Moderate: 26.8 34.7 25.8 31.3 27.5 21.6 28.1
  - EM Medium: 21.3 22.3 22.6 17.1 25.3 24.8 25.5
  - EM Severe: 24.4 22.4 21.3 0.0 11.7 23.7 23.7
  - LIC "Normal": 44.3 44.3 44.3 44.3 44.3 44.3 44.3
  - LIC Moderate: 37.6 46.9 41.2 44.9 37.2 49.4 53.5
  - LIC Medium: 46.4 48.4 32.6 40.8 47.2 52.3 39.2
  - LIC Severe: 44.8 33.3 37.1 0.0 42.9 35.0 38.5
- Tax payments/pre-tax net income (percent)
  - AC "Normal": 28.2 28.2 28.2 28.2 28.2 28.2 28.2
  - AC Moderate: 28.0 27.2 26.1 25.2 26.2 27.2 28.4
  - AC Medium: 30.5 29.3 28.4 23.4 27.1 29.4 32.3
  - AC Severe: 30.2 29.3 26.7 15.7 18.9 24.3 26.6
  - EM "Normal": 20.6 20.6 20.6 20.6 20.6 20.6 20.6
  - EM Moderate: 23.1 21.9 22.0 22.2 21.7 22.1 22.9
  - EM Medium: 20.6 21.5 20.0 17.9 18.7 18.1 21.0
  - EM Severe: 19.6 21.0 18.6 9.9 12.5 14.7 17.8
  - LIC "Normal": 27.0 27.0 27.0 27.0 27.0 27.0 27.0
  - LIC Moderate: 27.9 33.0 33.4 31.3 33.6 31.5 31.3
  - LIC Medium: 29.0 30.6 30.1 27.8 30.4 30.8 29.9
  - LIC Severe: 33.0 32.9 32.5 23.7 20.9 28.2 27.0

### Components of Pre-impairment Income and Expenses (Percent of capital; medians)
- Advanced Countries (years around crisis: -3 -2 -1 0 1 2 3)
  - Normal conditions:
    - Net pre-impairment income: 13.1 13.1 13.1 13.1 13.1 13.1 13.1
    - Net interest income: 32.8 32.8 32.8 32.8 32.8 32.8 32.8
    - Fees: 1.8 1.8 1.8 1.8 1.8 1.8 1.8
    - Other operating income: 4.8 4.8 4.8 4.8 4.8 4.8 4.8
    - Operating expenses: -26.6 -26.6 -26.6 -26.6 -26.6 -26.6 -26.6
  - Moderate stress:
    - Net pre-impairment income: 13.9 13.8 13.2 13.5 13.1 12.5 12.6
    - Net interest income: 33.7 33.2 32.9 32.9 32.4 31.9 32.5
    - Fees: 5.1 5.1 2.0 0.7 0.5 0.7 1.6
    - Other operating income: 5.2 4.9 4.7 4.7 4.5 4.7 4.8
    - Operating expenses: -26.4 -26.1 -26.0 -26.0 -26.1 -26.0 -25.2
  - Medium stress:
    - Net pre-impairment income: 14.2 13.4 12.7 12.5 11.4 11.2 11.2
    - Net interest income: 34.1 33.8 33.2 33.1 32.3 31.8 32.1
    - Fees: 5.1 5.3 1.2 0.4 0.4 0.8 3.3
    - Other operating income: 5.4 5.3 5.0 4.6 4.3 4.1 4.3
    - Operating expenses: -27.2 -27.5 -27.6 -27.5 -27.4 -27.4 -27.7
  - Severe stress:
    - Net pre-impairment income: 14.4 12.9 10.5 8.0 8.3 8.9 9.8
    - Net interest income: 34.7 33.7 32.5 35.6 34.1 32.5 32.7
    - Fees: 4.4 4.6 0.6 0.2 0.1 0.2 0.8
    - Other operating income: 5.0 4.6 4.5 5.6 5.5 4.9 5.2
    - Operating expenses: -26.8 -27.2 -29.0 -35.1 -32.7 -31.0 -29.6
- Emerging Market Countries (years around crisis: -3 -2 -1 0 1 2 3)
  - Normal conditions:
    - Net pre-impairment income: 19.6 19.6 19.6 19.6 19.6 19.6 19.6
    - Net interest income: 30.3 30.3 30.3 30.3 30.3 30.3 30.3
    - Fees: 7.3 7.3 7.3 7.3 7.3 7.3 7.3
    - Other operating income: 10.4 10.4 10.4 10.4 10.4 10.4 10.4
    - Operating expenses: -24.7 -24.7 -24.7 -24.7 -24.7 -24.7 -24.7
  - Moderate stress:
    - Net pre-impairment income: 22.1 21.8 21.0 24.2 22.0 20.7 21.4
    - Net interest income: 30.5 29.1 30.4 31.7 32.1 32.3 33.2
    - Fees: 8.3 6.7 6.8 6.4 6.7 6.4 5.8
    - Other operating income: 11.9 9.1 8.5 9.3 9.7 10.4 9.0
    - Operating expenses: -27.6 -25.5 -23.4 -22.2 -22.1 -24.2 -22.7
  - Medium stress:
    - Net pre-impairment income: 22.9 21.1 23.0 23.7 18.6 18.7 16.2
    - Net interest income: 31.5 30.9 34.4 32.5 28.8 27.8 26.8
    - Fees: 9.8 8.8 8.0 7.9 8.1 8.2 8.5
    - Other operating income: 12.9 11.6 10.5 10.2 10.7 10.9 10.7
    - Operating expenses: -27.7 -26.5 -25.8 -24.9 -25.4 -23.0 -23.6
  - Severe stress:
    - Net pre-impairment income: 17.6 21.9 23.2 26.2 14.4 13.4 17.9
    - Net interest income: 28.7 34.3 37.1 32.9 24.2 27.4 27.6
    - Fees: 8.9 7.8 6.9 8.0 6.9 6.4 7.3
    - Other operating income: 11.5 11.7 11.6 12.2 10.2 10.5 9.4
    - Operating expenses: -33.1 -30.6 -32.4 -33.7 -26.9 -25.3 -23.1

### Asset Correlations (Figures)
- Appendix Figure 2: Asset Correlations (Percent). Source: Authors, based on Duellmann et al. (2008).
- Appendix Figure 3: Asset Correlations and GDP Growth Rates (Percent)
  - Time axis samples Jan. 97 to Jan. 03; plotted asset correlation (percent) with Real GDP growth.
  - Summary statistics shown on figure:
    - Min: 4.3
    - Mean: 10.5
    - Median: 11.2
    - Max: 16.2
  - Fitted relation on figure: Asset corr. = -2.66RGDP gr.+ 16.76
  - R² = 0.44

*Source: Authors, based on Bankscope data.*

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