## _wp14103

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---

### Major themes and objectives
- Focus: design of stress tests that capture spillover effects and demonstrate potential impact via a case study.
- Approach: an amended version of the indirect approach to stress testing that explicitly incorporates spillover effects into macroeconomic scenarios through a quasi-feedback (sensitivity) loop.
- Scope: spillover effects originating from the recent sovereign debt crisis (Euro area periphery), applied to a sample of 154 large international banks from the “S-25” country sample.

### Methodology and scenario design
- Two-step (indirect) framework:
  - Step 1: estimate economic and financial variables conditional on a macroeconomic scenario.
  - Step 2: translate trajectories of these variables into bank solvency and liquidity measures using “satellite” or “auxiliary” models (commonly (panel) regression models).
- Alternative or supplementary methods:
  - Structural econometric models, Vector autoregressive methods, Pure statistical approaches, Direct approach (projects solvency/liquidity parameters without explicit links to economic/financial variables).
- Iterative/quasi-feedback enhancement:
  - Establish macro scenario (initially not informed by spillovers).
  - Estimate marginal increase of stress due to spillovers by translating sovereign spread spillovers into reduced output paths.
  - Optionally iterate by feeding bank-level impacts back into macro models.
- Techniques to capture spillovers:
  - Panel regressions for average effects (Advanced Markets and Emerging Markets).
  - GARCH models (Dynamic Conditional Correlation, DCC) for point-in-time country-specific co-movements.
  - Controls: VIX, high yield spreads, and country-specific macro factors (trade openness, M2/GDP, reserves/GDP, inflation, GDP growth, current account, public debt and deficits to GDP).

### Empirical findings on drivers and heterogeneity of spillovers
- Drivers:
  - Increasing sovereign risk in the Euro periphery is a major driving force.
  - Risk aversion (VIX and high yield spreads) rises during stress and exhibits non-linear patterns.
  - Country-specific macroeconomic factors matter but less so and do not change much under stress.
- Panel regression results (35-country sample):
  - For 2006–2012:
    - A one percentage point change in Euro periphery sovereign spreads (GIIPS and GIP) → 0.2–0.3 percentage point change in sovereign spreads for the 35 sample countries.
    - A one percentage point change in high-yield spreads → around 0.6 percentage point change in sovereign spreads.
    - Transmission from Italy and Spain to the sample countries is more pronounced than from the GIPs.
  - For 2008–2012 (crisis-only):
    - Coefficients higher than 2006–2012.
    - A one percent shock to Euro periphery spreads → 0.5 percentage point increase in sample risk premium if shock originates in the GIPs; 1 percentage point increase if it originates in Italy and Spain.
    - Global risk aversion shocks translate almost one-to-one into spreads.
- DCC GARCH (daily 2007–end August 2012) — implied correlations with GIIPS:
  - European: Austria, Belgium, France, Netherlands up to 0.7–0.8 during stress; UK 0–0.2; Switzerland up to 0.4; Scandinavia lower than continental peers.
  - Non-European AMs: Australia and Canada up to 0.2; Hong Kong, Japan, Singapore up to 0.3, one jump to 0.4.
  - EMs: China subdued; Turkey up to 0.6 (highest among EM sample).
  - Flight-to-quality since 2009: average GIIPS rates negative correlation with German Bunds and U.S. Treasuries, lows at -0.6 (Germany) and -0.4 (US).

### Sample, data coverage, and mapping to bank-level parameters
- Bank sample:
  - 154 large banks, 26 countries: Austria, Australia, Belgium, Brazil, Canada, Switzerland, China, Germany, Denmark, Finland, France, UK, HK, India, Japan, Korea, Luxembourg, Mexico, Netherlands, Norway, Poland, Russia, Sweden, Singapore, Turkey, USA.
  - Captures $84 trillion of bank assets, about 50 percent of assets held by banks worldwide.
  - Captures $39 trillion non-bank deposits.
  - Captures around $7 trillion of government securities held by banks.
- Bank-level parameters simulated:
  - Solvency: Credit Losses, Security P/L impact, Pre-impairment income; Tier 1 capital ratio hurdle = 6 percent.
  - Liquidity: Haircuts (Market Liquidity), Outflow of funding.
- Solvency simulation horizon: Tier 1 capital ratios simulated by end-2014 based on 2-year horizon (2013–2014) GDP trajectories with and without spillovers.
- Liquidity approach: implied cash-flow approach (bank-run scenarios) covering demand/term deposits, short-term wholesale funding, derivatives’ funding, long-term funding; assets include cash, government/trading/investment securities, loans and advances, reverse repos/cash collateral.

### Spillover scenarios and GDP impacts (scenario definitions)
- Baseline macro scenario: April 2012 WEO baseline for 2013–14 (Scenario 1).
- Three GIIPS spread shock sizes applied to Scenario 1 (scenarios 2.x):
  - 100 basis points (scenario 2a)
  - 200 basis points (scenario 2b)
  - 300 basis points (scenario 2c)
- Distinction by stress-period methodology:
  - Periods of substantial financial stress: panel 2008–12 and GARCH 2010–12.
  - Periods of less significant stress: panel 2006–12 and GARCH 2008–12.
- Six spillover scenarios in total: 2a/1, 2a/2, 2b/1, 2b/2, 2c/1, 2c/2.
- Example GDP impacts (Austria stylized, GDP Elasticity = 3.5 over 2013–2014):
  - Scenario 2a/1: GDP 2013 = 1.4 percent; 2014 = 1.8 percent (drop = 0.45 percentage points from baseline 1.8/2.2).
  - Scenario 2a/2: GDP 2013 = 0.9 percent; 2014 = 1.3 percent (impact about twice).
  - Scenario 2b: growth drops by 1.7 percentage points (per year).
  - Scenario 2c: growth drops by 2.6 percentage points (per year).
  - Appendix IV exact Austria impacts (impacts on spreads for 100/200/300 bps): average = 24.4/48.8/73.2; peak = 49.8/99.6/149.4 (values preserved as presented).

### Stylized solvency results and non-linearities (Appendix IV)
- Stylized baseline bank assumptions:
  - Loan impairment rates baseline = 0.5 percent.
  - Pre-impairment return on capital = 10 percent in 2012.
- Loan impairment rates (Percent of credit exposure) across scenarios (exact values preserved):
  - Baseline: 2012 = 0.5; 2013 = 0.4; 2014 = 0.4
  - 2a/1: 2012 = 0.5; 2013 = 0.45; 2014 = 0.4
  - 2b/1: 2012 = 0.5; 2013 = 0.5; 2014 = 0.45
  - 2c/1: 2012 = 0.5; 2013 = 0.55; 2014 = 0.5
  - 2a/2: 2012 = 0.5; 2013 = 0.5; 2014 = 0.45
  - 2b/2: 2012 = 0.5; 2013 = 0.7; 2014 = 0.6
  - 2c/2: 2012 = 0.5; 2013 = 0.9; 2014 = 0.8
- Pre-impairment income (Percent of total capital) across scenarios:
  - Baseline: 2012 = 10; 2013 = 10.3; 2014 = 10.5
  - 2a/1: 2012 = 10; 2013 = 10.15; 2014 = 10.3
  - 2b/1: 2012 = 10; 2013 = 10; 2014 = 10.1
  - 2c/1: 2012 = 10; 2013 = 9.8; 2014 = 10
  - 2a/2: 2012 = 10; 2013 = 10; 2014 = 10.1
  - 2b/2: 2012 = 10; 2013 = 9.7; 2014 = 9.8
  - 2c/2: 2012 = 10; 2013 = 9.2; 2014 = 9.5
- RWAs (Indexed) and Capital (exact values preserved):
  - RWAs indexed (Baseline → 2012/2013/2014 = 100/90/90; 2c/2 = 100/140/132, etc.).
  - Capital (Baseline → 2012/2013/2014 = 10/10.58/11.21; 2c/2 = 10/10.47/10.99, etc.).
- Capital ratio (= Capital/RWA, Percent) outcomes (exact values preserved):
  - Baseline: 2012 = 10.0; 2013 = 11.8; 2014 = 12.5
  - 2a/1: 2012 = 10.0; 2013 = 11.1; 2014 = 12.5
  - 2b/1: 2012 = 10.0; 2013 = 10.6; 2014 = 11.7
  - 2c/1: 2012 = 10.0; 2013 = 10.0; 2014 = 11.1
  - 2a/2: 2012 = 10.0; 2013 = 10.6; 2014 = 11.7
  - 2b/2: 2012 = 10.0; 2013 = 8.8; 2014 = 9.9
  - 2c/2: 2012 = 10.0; 2013 = 7.5; 2014 = 8.3
- Key solvency finding:
  - Large international banks can absorb the baseline plus some spillover stress, but additional Euro-area periphery stress produces highly non-linear increases in capital needs driven by satellite-model non-linearities and kick-in effects when banks fall below the 6 percent Tier 1 hurdle.

### Stylized liquidity results and non-linearities (Appendix V and Appendix III)
- Benchmark stress severity table (selected exact parameters preserved):
  - Severity (x times Lehman/1): 0.25 0.5 1 2
  - Customer deposits (Term): 2.5 percent; 5 percent; 10 percent; 20 percent
  - Customer deposits (Demand): 5 percent; 10 percent; 20 percent; 40 percent
  - Short-term (secured): 5 percent; 10 percent; 20 percent; 40 percent
  - Short-term (unsecured): 25 Percent; 50 Percent; 100 Percent; 100 Percent
  - Haircut for Trading Assets/3: 3 Percent; 6 Percent; 30 Percent; 100 Percent
  - Haircut for other securities: 10 Percent; 30 Percent; 75 Percent; 100 Percent
  - Percent of liquid assets encumbered/4: 10 Percent (or actual figure); 20 Percent (or actual figure plus 10 ppt); 30 Percent (or actual figures plus 20 ppt); 40 Percent (or actual figures plus 30 ppt)
- Liquidity test method: implied cash-flow approach; GDP-based funding shocks linked to Lehman-period fund outflows; worst-case “Lehman Brothers type” severe scenario used as benchmark.
- Stylized Austria bank, scenario 2c/2 (exact values preserved):
  - For scenario 2c/2 measured against Tier 1 capital (entire bank sample): maximum liquidity shortfall = 20 percent.
  - Measured against total assets:
    - Scenario 2c/2: 0.3 percent.
    - Scenario 2b/2: 1 percent.
  - Example asset fire-sale availability (Portion; Haircut Scenario 2c/2; Available assets):
    - Cash and cash-like: Portion = 4; Haircut Scenario 2c/2 = 0; Available = 4.0
    - Government securities: Portion = 6; Haircut Scenario 2c/2 = 3; Available = 5.8
    - Trading securities: Portion = 5; Haircut Scenario 2c/2 = 20; Available = 4.0
    - Other securities: Portion = 15; Haircut Scenario 2c/2 = 49; Available = 7.7
  - Example liabilities required funding (Portion; Outflow Scenario 2c/2; Required funding):
    - Customer Term deposits: Portion = 30; Outflow Scenario 2c/2 = 6.5; Required funding = 2
    - Customer Demand deposits: Portion = 20; Outflow Scenario 2c/2 = 20; Required funding = 2.6
    - Unsecured short-term wholesale funding: Portion = 10; Outflow Scenario 2c/2 = 65; Required funding = 6.5
    - Contingent liabilities: Portion = 20; Outflow Scenario 2c/2 = 6.5; Required funding = 1.3
  - Stylized example outcome: bank generates inflow = 21.5 units of assets versus required level = 13.7 units and remains liquid under the stylized parameters.
- Note: no explicit modeling of central bank LOLR response; in reality central banks would provide large liquidity support to solvent banks subject to appropriate haircuts.

### Implications for stress testing practice and recommendations
- Scenario design:
  - Design of stress scenarios is crucial and highly sensitive for stress-test outcomes.
  - Explicitly incorporating spillover effects produces a richer story and better captures non-linear macro-financial interactions than the pure direct approach.
- Modeling recommendations:
  - Use market data to capture point-in-time and dynamic time-series effects, while acknowledging market prices may reflect factors beyond underlying vulnerabilities.
  - Combine panel and DCC GARCH approaches to capture both average and granular/country-specific spillover dynamics.
  - Foster close cooperation between macroeconomic forecasting staff and financial stability/stress-testing teams to run iterative approaches that feed bank-level outcomes back to macro models.
  - Run a range of scenarios of varying severity, including reverse stress tests, due to inherent uncertainty and limited precision.
- Role of integrated stress tests:
  - Stress tests that capture spillovers can help identify potential systemic vulnerabilities ex ante and should incorporate bank behavioral responses and market liquidity dynamics.

*Source: _wp14103 (IMF working paper content as provided).*

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

### _wp14103 - References

### Major themes and objectives
- Focus: design of stress tests that capture spillover effects and demonstrate potential impact via a case study.
- Approach: an amended version of the indirect approach to stress testing that explicitly incorporates spillover effects into macroeconomic scenarios through a quasi-feedback (sensitivity) loop.
- Scope: spillover effects originating from the recent sovereign debt crisis (Euro area periphery), applied to a sample of 154 large international banks from the “S-25” country sample.

### Methodology and scenario design
- Two-step (indirect) framework:
  - Step 1: estimate economic and financial variables conditional on a macroeconomic scenario.
  - Step 2: translate trajectories of these variables into bank solvency and liquidity measures using “satellite” or “auxiliary” models (commonly (panel) regression models).
- Alternative approaches noted:
  - Structural econometric models.
  - Vector autoregressive methods.
  - Pure statistical approaches.
  - Direct approach: projects solvency and liquidity parameters without explicit links to economic/financial variables (less suitable for capturing non-linear macro-financial factors).
- Iterative/quasi-feedback enhancement:
  - Establish a macroeconomic scenario (initially not explicitly informed by spillovers).
  - Estimate marginal increase of stress due to spillovers by translating sovereign spread spillovers into reduced output paths.
  - Optionally iterate by feeding bank-level impacts back into the structural model until equilibrium is reached.
- Data and techniques used to capture spillovers:
  - Panel regressions to estimate an “average” impact of sovereign debt spillovers for Advanced Markets (AM) and Emerging Markets (EM).
  - GARCH models (Dynamic Conditional Correlation) to obtain more granular, point-in-time country-specific co-movements between peripheral European GIIPS sovereign debt spreads and spreads in banks’ home countries (S-25 sample).
  - Control variables included market sentiment measures (VIX, high yield spreads) and country-specific macroeconomic factors.

### Key empirical findings
- Drivers of spillovers:
  - Increasing sovereign risk in the Euro periphery was a major driving force behind spillover effects.
  - Risk aversion, measured through changes in the VIX and high yield spreads, increases during periods of financial stress and exhibits a non-linear pattern.
  - Country-specific macroeconomic factors matter but to a lesser degree; their impact does not appear to change significantly under periods of stress.
- GARCH model results:
  - Significant cross-country differences in spillovers.
  - Higher spillover impacts for most core Euro area countries (especially during peak crisis periods) than for Scandinavian countries, Switzerland, the UK, and most non-European countries.
  - Presence of a flight-to-quality: negative co-movement of GIIPS spreads with German Bunds and U.S. Treasuries.
- Bank-level simulation outcomes:
  - Integrated solvency and liquidity stress tests applied to 154 large international banks (S-25 countries) reveal that spillover effects have a highly non-linear impact on bank soundness in both liquidity and solvency dimensions.
  - The magnitude of impacts observed could serve as a benchmark, while acknowledging future spillover channels may differ in direction and magnitude.

### Implications for stress testing practice
- Importance of scenario design:
  - The design of stress scenarios is highly crucial and sensitive with respect to stress test outcomes.
  - Explicitly incorporating spillover effects produces a richer story and better captures non-linear macro-financial interactions than the pure direct approach.
- Recommendations for improved modeling of contagion and spillovers:
  - Use market data to capture point-in-time and dynamic time-series effects, while recognizing market prices may reflect factors beyond underlying vulnerabilities.
  - Combine panel and GARCH approaches to capture both average and granular/country-specific spillover dynamics.
  - Foster close cooperation between macroeconomic forecasting staff and financial stability/stress-testing teams to run iterative approaches that feed bank-level outcomes back to macro models.
- Role of stress tests:
  - Stress tests that capture spillovers can help identify potential systemic vulnerabilities ex ante, addressing a role stress tests have not always fulfilled historically.

### Data, figures, and appendices referenced
- Tables and sample periods:
  - I.1. Spread Panel Regressions, 2006Q1–2012Q2 (Quarterly data)
  - I.2. Spread Panel Regressions, 2008Q1–2012Q2 (Quarterly data)
  - I.3. Main Explanatory Variables
- Figures (selection):
  - Stylised Design of Stress Tests (Figure 1)
  - Estimated GARCH Correlations GIIPS with European Countries (Figure 1)
  - Estimated GARCH Correlations GIIPS with Non-European Countries (Figure 2)
  - Estimated GARCH Correlations GIIPS with EM Countries and Korea (Figure 3)
  - Estimated GARCH Correlations GIIPS with Germany and the U.S. (Figure 4)
  - Overview of the concept to simulate stress at the bank level (Figure 5)
  - Outcome of solvency tests (Figure 6)
  - Outcome of liquidity tests (Figure 7)
- Appendixes include:
  - Outcome of Panel Regressions Assessing Spillover Risks (I)
  - Outline of the DCC GARCH Method (II)
  - Benchmark Stress Scenarios (III)
  - Illustrative Example for the Solvency Test (IV)
  - Illustrative Example for Liquidity (V)

*Source: _wp14103 - References (IMF).*

### Section III provides a brief overview of the stress testing framework used to simulate the

### _wp14103 - Section III provides a brief overview of the stress testing framework used to simulate the

### II. FINANCIAL SPILLOVERS FROM THE EURO PERIPHERY TO THE REST OF THE WORLD — Overview
- Objective: establish benchmark parameters to simulate spillover effects at the bank level and inform bank-level stress tests.
- Sample: 35 countries.
- Key identified drivers of sovereign spread spillovers:
  - (i) a stress spillover catalyst – in this study AM sovereign debt yields (Euro periphery sovereign spreads);
  - (ii) risk aversion in global markets (measured by high yield spreads and the VIX);
  - (iii) country-specific macroeconomic risk factors (trade openness, liquidity proxied by M2 to GDP and reserves to GDP, inflation rates, GDP growth, current account, public debt and deficits to GDP).

### A. Panel approach — methods and main quantitative findings
- Methodology:
  - Random effects panel regressions of sovereign spreads for the 35 sample countries on three sets of peripheral spreads: (i) average GIIPS; (ii) GIP (Greece, Ireland, Portugal); (iii) IT-ES (Italy and Spain).
  - Risk aversion proxied by high yield spreads (difference between yields to maturity of Moody’s Aaa and Baa1 U.S. corporate bonds) and the VIX (implied volatility for S&P 500 index options).
  - Control variables: trade openness, liquidity (M2 to GDP and reserves to GDP), inflation, GDP growth, current account, public debt and deficits to GDP.
  - Two quarterly sample periods: (i) 2006–2012 and (ii) 2008–2012.
- Key empirical findings (from Tables I.1 and I.2 as reported):
  - All three factors—peripheral sovereign risk, global risk aversion, and country-specific factors—are important to explain sovereign spread movements.
  - For 2006–2012:
    - A one percentage point change in Euro periphery sovereign spreads (GIIPS and GIP) translates into a 0.2–0.3 percentage point change in sovereign spreads for the 35 sample countries.
    - A one percentage point change in high-yield spreads translates into around 0.6 percentage point change in sovereign spreads.
    - Transmission from Italy and Spain to the sample countries is more pronounced than from the GIPs.
    - Domestic liquidity availability and trade openness can contribute to spillovers depending on specification.
  - For 2008–2012 (crisis-only period):
    - Coefficients for the three drivers (European periphery shocks, global risk aversion, slope of the US yield curve) are higher than for 2006–2012.
    - A one percent shock to Euro periphery spreads translates into a 0.5 percentage point increase in the risk premium of the sample if the shock originates in the GIPs and a one percentage point increase if it originates in Italy and Spain.
    - Global risk aversion shocks translate almost one-to-one into spreads during the crisis period.
- Interpretations:
  - Size of the originating peripheral country matters for spillover magnitude.
  - Joint movements of global risk aversion and peripheral spreads exacerbate transmission during stress.

### B. DCC GARCH approach — daily co-movements and heterogeneity
- Methodology:
  - Multivariate DCC GARCH (Engle 2002) estimated in first differences to allow time-varying correlations and heteroskedasticity.
  - Sample period: daily data from 2007 to end August 2012.
  - GIIPS spreads included as a conditioning variable, as is the VIX.
  - Sovereign spreads measured to German Bunds for European AMs, to 10-year U.S. Treasuries for non-European AMs, EMBI Global spread for EMs, and HSBC Asian U.S. Dollar spread for Asian countries.
- Key empirical findings (implied DCC correlations):
  - European countries:
    - Austria, Belgium, France, Netherlands: implied correlations with GIIPS up to 0.7–0.8 during systemic stress episodes.
    - UK: implied correlation oscillates between 0 and 0.2.
    - Switzerland: model-implied correlation reaches a maximum of 0.4.
    - Scandinavian countries (Denmark, Norway, Sweden, Finland) exhibit lower co-movement with GIIPS than continental peers.
  - Non-European AMs:
    - Australia and Canada: implied correlations up to 0.2.
    - Hong Kong, Japan, Singapore: implied correlations up to 0.3 with one jump to 0.4.
  - EMs:
    - China: subdued co-movement compared to Brazil, Mexico, Russia, and Turkey.
    - Turkey: highest implied correlation among EM sample with GIIPS during stress up to 0.6.
  - Safe-haven behavior since 2009:
    - Average GIIPS interest rates show negative correlation with German Bund and U.S. Treasury rates since 2009, with lows at -0.4 (US) and -0.6 (Germany), indicating flight to safety.

### III. LIQUIDITY AND SOLVENCY STRESS TESTING — framework and scenario design
- Framework basis:
  - Uses recently developed IMF liquidity stress testing framework (Schmieder et al. 2012) integrated with solvency stress testing (Schmieder, Puhr and Hasan 2011).
  - Designed to run integrated solvency and liquidity stress tests that incorporate spillover effects and feedback loops.
- Emphasis and recommendations:
  - Focus on scenario design: build integrated scenarios for solvency and liquidity that take account of spillovers and bank reaction behaviors.
  - Recommend running a range of scenarios of varying severity, including reverse stress tests, due to inherent uncertainty and limited precision.
- Box 1 highlights — integrating bank reactions and modeling approaches:
  - Banks’ defensive reactions include use of capital and retained earnings, generating liquid assets via collateralized market funding or central bank facilities, fire sales, deleveraging, debt-to-equity conversions, issuance of convertible bonds, and RWA optimization.
  - Integrating bank reactions requires coherent modeling of solvency and liquidity shocks because reactions affect both capital and liquidity.
  - Recent analytical approaches:
    - Van den End (2008) and Wong & Hui (2009) empirical frameworks.
    - Barnhill & Schumacher (2011) general empirical model.
    - Schmieder et al. (2012) Excel-based liquidity framework linked to solvency.
    - RAMSI (Aikman et al., 2009) models liquidity conditional on capitalization.
    - ARNIE (OeNB, 2013) as an applied integrated framework.
  - For liquidity stress test principles and EBA assessment, see BCBS (2013) and Hardy and Hesse (2013) referenced.

### Liquidity Stress Testing Approach — implementation details
- Method: implied cash-flow approach to simulate bank-run type scenarios.
- Liability breakdown:
  - demand and term deposits;
  - short-term wholesale funding (including bank and secured funding);
  - derivatives’ funding;
  - long-term funding such as senior debt or subordinated debt.
- Asset coverage:
  - cash;
  - government, trading and investment securities (available-for-sale and held-to-maturity);
  - loans and advances to banks and reverse repos and cash collateral;
  - inclusion of loan-level collateral use (e.g., covered bonds) as a crude portion of total assets given European periphery banks’ increased collateral use.

### Solvency Stress Testing Approach — implementation details
- Approach: simplified solvency test using rules of thumb from Hardy and Schmieder (2013).
- Simulations:
  - Credit losses, banks’ pre-impairment income, and trajectories of Risk-Weighted Assets (RWAs) over a 2-year horizon based on GDP trajectories with and without spillover effects.
- Capital shortfall measurement:
  - Against a tier 1 capital ratio (Tier 1 capital/Risk-weighted Assets) of 6 percent; banks below 6 percent are considered undercapitalized.

### IV. Integration of spillover analysis with stress testing — purpose and next steps
- Integrated approach: use the empirical spillover estimates (panel and DCC GARCH) to inform scenario calibration for bank-level integrated solvency-liquidity stress tests, capturing feedback loops and bank reactions.
- Scenario design guidance:
  - Leverage the range of spillover magnitudes observed across methods and periods (average panel estimates and time-varying DCC GARCH correlations) to construct scenarios of varying severity.
  - Incorporate bank behavioral responses and market liquidity dynamics as part of scenario mechanisms.
- Suggested analytical practice:
  - Run multiple scenarios including reverse stress tests.
  - Use the integrated Excel-based frameworks referenced to operationalize solvency-liquidity interactions given data limitations.

*Source: IMF working paper content as provided.*

### 1. Scenario design: We use the GDP trajectories of a specific macroeconomic

### _wp14103 - 1. Scenario design: We use the GDP trajectories of a specific macroeconomic

### Scenario design
- Use the GDP trajectories of a specific macroeconomic scenario: the WEO baseline scenario for 2013–14 as of April 2012, and add the spillover stress component.
- Scenario 1: The April 2012 WEO baseline scenario for 2013–14 (Scenario 1).

### Spillover analysis
- The outcome of the spillover analysis, measured through a widening of sovereign spreads, worsens the macroeconomic scenario and is used as a sensitivity analysis.
- The translation of the spillover effects into the revised macroeconomic trajectories is based on recent IMF work.
- The IMF Spillover analysis employs Panel/GARCH methods.

### Soundness of banks: translation to bank-level stress parameters
- The scenario is translated into bank level stress parameters to simulate both banks’ solvency and liquidity positions.
- Solvency translation draws on work by Hardy and Schmieder (2013).
- Liquidity translation draws on work by Schmieder, Hesse, and others (2012).
- The evidence referenced is based on a comprehensive set of data from 16,000 banks during the last 15 years (as available).
- The specific choice of scenario intensity is meant for illustration only—through a similar level as used for the European stress tests conducted in 2010 and 2011, for example.

### Sample and coverage
- Bank-level data source: Bankscope (from end-June 2012) for large Systematically Important Banks (SIBs).
- Sample size and coverage:
  - 154 large banks
  - 26 countries: Austria, Australia, Belgium, Brazil, Canada, Switzerland, China, Germany, Denmark, Finland, France, UK, HK, India, Japan, Korea, Luxembourg, Mexico, Netherlands, Norway, Poland, Russia, Sweden, Singapore, Turkey, and the USA.
  - Captures $84 trillion of bank assets (i.e., about 50 percent of the assets held by banks worldwide).
  - Captures $39 trillion non-bank deposits.
  - Captures around $7 trillion of government securities held by banks.
- The sample comprises almost the full EBA sample for the European banks (except for the banks in the GIIPS countries) and includes the largest banks in the non-European countries.

### Simulation framework and mapped bank-level parameters
- Bank solvency parameters simulated:
  - Credit Losses
  - Security P/L impact
  - Pre-impairment income
- Bank liquidity parameters simulated:
  - Haircuts (Market Liquidity)
  - Outflow of funding
- Overall soundness of bank translated into bank-level stress scenario:
  - Solvency: Hardy/Schmieder
  - Liquidity: Schmieder/Hesse/at al

### Spillover scenarios and specifications
- Three spillover scenarios conditional on Scenario 1 (referred to as scenarios 2.x) adjust Scenario 1 for increases of GIIPS spreads by:
  - 100 basis points (scenario 2a)
  - 200 basis points (scenario 2b)
  - 300 basis points (scenario 2c)
- Distinction by stress-period methodology:
  - Periods of substantial financial stress: panel regression for 2008–12 and the GARCH model for 2010–12.
  - Periods of less significant stress: panel regression for 2006–12 and the GARCH model for 2008–12.
- Total of six spillover scenarios: 2a/1, 2a/2, 2b/1, 2b/2, 2c/1, 2c/2.

### Solvency and liquidity simulation horizons and examples
- For banks’ solvency, Tier 1 capital ratios are simulated by end-2014, based on the evolution of the main solvency dimensions (banks’ income and losses).
- For liquidity, determine the impact of a worst-case idiosyncratic shock to the bank’s liquidity profile on top of the impact on liquidity resulting from the macroeconomic/spillover scenarios.
- Illustrative examples are provided in Appendix IV (solvency) and V (liquidity).

### Impact on bank solvency — example using IMF Spillover Report
- Use outcome of the 2012 IMF Spillover Report, which simulates the impact of a 300bp increase in peripheral countries’ spreads (including a lower yield increase for core countries) on European countries’ GDP paths based on the IMF G-35 model (drawing upon Vitek and Bayoumi, 2011).
- Appendix IV illustrative example for a stylized Austrian bank:
  - A 100 basis point shock of GIIPS spreads (scenario 2a) would result in an increase of Austrian spreads by:
    - 24 basis points for less significant spillover stress (scenario 2a/1)
    - 50 basis points for more substantial spillover stress (scenario 2a/2)
  - Measured relative to the April 2012 WEO baseline scenario for Austria, suggesting real GDP growth rates of 1.8 percent (2013) and 2.2 percent (2014), spillover analysis carried out at the IMF (2012) would predict a drop of real GDP growth by about

*Source: _wp14103 - 1. Scenario design: We use the GDP trajectories of a specific macroeconomic*

### 0.45 percentage points for scenario 2a/1 (less significant spillover stress), whereby the

### _wp14103 - 0.45 percentage points for scenario 2a/1 (less significant spillover stress), whereby the

### Scenario definitions and GDP impacts
- Scenario 2a/1 (less significant spillover stress): GDP trajectory becomes 1.4 percent (2013) and 1.8 percent (2014).
- Scenario 2a/2 (more significant spillover): impact about twice (0.9 percentage points), whereby the GDP trajectory is 0.9 percent (2013) and 1.3 percent (2014).
- Scenario 2b (200 basis point shock): growth drops by 1.7 percentage points (per year).
- Scenario 2c (300 basis point shock): growth drops by 2.6 percentage points (per year).
- Note: the 0.45 percentage points referenced applies to scenario 2a/1 (less significant spillover stress).

### Solvency stress test — methodology and stylized bank outcomes
- Satellite models by Hardy and Schmieder (2013) are used to determine banks’ loan impairment levels and pre-impairment income for 2013 and 2014.
- Stylized bank baseline assumptions:
  - Loss impairment rates of 0.5 percent.
  - Pre-impairment return on capital of 10 percent in 2012.
- Under baseline and mild spillover conditions:
  - Loan impairment rates simulated to decrease slightly.
  - Pre-impairment income follows a similar pattern (decrease under stress).
- Under increasing spillover stress:
  - Loan impairment rates and pre-impairment income increase non-linearly.
- Capital simulation inputs:
  - Simulated capital, Risk-weighted assets (RWAs), and capital ratio.
  - RWAs simulated based on Schmieder and others (2011), assuming point-in-time credit risk parameters.
- Stylized bank capital ratio outcome:
  - Decrease to 7.5 percent under the most severe scenario.
  - This is above the hurdle rate in terms of Tier 1 capital to pass the stress test (6 percent).

### Solvency test sample outcome and non-linearity drivers
- Sample: solvency stress test applied to 154 banks (presented in Figure 6).
- Key finding:
  - Large international banks are able to digest the baseline scenario plus some level of spillover stress.
  - Additional stress in the Euro area periphery has a highly non-linear impact on potential capital needs.
- Two drivers of non-linearity:
  1. Non-linearity in the satellite models for loan impairment rates and pre-impairment income.
  2. Kick-in effect of capital needs for banks that fall below the hurdle rate.

### Liquidity stress test — methodology
- Tests simulate impact on:
  - Market liquidity (ability to fire sale assets).
  - Funding liquidity (potential outflow of funding).
- Assumption: the bank is affected by the shock in its home country (all assets based in the home country).
- Empirical linkage:
  - Based on Schmieder, Hesse and others (2012).
  - GDP trajectories implied by changes of sovereign spreads are linked to funding shocks experienced by the most affected banks during the Lehman crisis.
  - Simulate highly adverse idiosyncratic liquidity shocks conditional upon macroeconomic conditions.
- Worst-case benchmark:
  - “Lehman Brothers type” scenario = “severe stress scenario” in Appendix III.
  - For the stylized example in Appendix V, stress level is at 0.65 (benchmark funding stress parameters for the “severe stress scenario” are multiplied by 0.65).
- Funding cushion:
  - Funding available under the ECB’s Long Term Refinancing Operations (LTROs) inferred from country-level data and used as a cushion.

### Liquidity test outcomes and magnitudes
- Baseline scenario: all banks have sufficient liquidity.
- Adding spillover stress triggers a non-linear increase of liquidity needs; more substantial spillover stress makes the increase highly non-linear.
- Measured against Tier 1 capital (entire bank sample):
  - Scenario 2c/2 (300bp spread shock, significant spillover stress): maximum liquidity shortfall of 20 percent.
  - Scenario 2b/2 (200bp spread shock): liquidity shortfall close to 6 percent.
- Measured against total assets:
  - Scenario 2c/2: 0.3 percent.
  - Scenario 2b/2: 1 percent.
- Note: no explicit modeling of central bank Lender of Last Resort (LOLR) response; in reality central banks would provide large liquidity support to solvent banks subject to an appropriate haircut.

### Conclusions and implications for stress-testing
- Spillover effects observed for sovereign debt markets have a highly non-linear impact on bank soundness (liquidity and solvency).
- Design of stress scenarios is crucial and very sensitive to stress-test outcomes.
- The approach provides a menu for future analyses of potential spillovers.
- Sensitivity analysis and reverse stress tests are important complements.

### Appendix — panel regressions and explanatory variables (selected points)
- Panel regressions cover 2006Q1–2012Q2 and 2008Q1–2012Q2 (dependent variable: Sovereign Spreads of 35 sample countries; quarterly data).
- Selected regression diagnostics:
  - R-squared (within) reported between 0.70 and 0.93 across specifications.
  - Observations reported (e.g., 415, 435, 454 for 2006Q1–2012Q2; 321, 357, 341 for 2008Q1–2012Q2).
- Main explanatory variables described:
  - Sovereign Risk:
    - GIIPS spread: Average of Euro periphery sovereign spreads to German Bunds.
    - GIP spread: Average of Greece, Ireland and Portugal sovereign spreads to German Bunds.
    - Italy/Spain spread (IS spread): Average of Italy and Spain sovereign spreads to German Bunds.
  - Risk aversion:
    - High-yield spread: Difference between yields to maturity of AAA rated and BAA rated corporate US bond.
    - VIX: Implied volatility of S&P 500 index options.
  - Macroeconomic environment:
    - Openness: Sum of imports and exports to GDP ratio.
    - M2/GDP: Broad money to GDP ratio.

*Source: Authors*

### APPENDIX II. OUTLINE OF THE DCC GARCH METHOD

### _wp14103 - APPENDIX II. OUTLINE OF THE DCC GARCH METHOD

### DCC estimation procedure (three-stage)
- The DCC model is estimated in a three-stage procedure using an n x 1 vector of asset returns r_t with mean zero and time-varying covariance H_t:
  - Stage 1: Fit univariate GARCH models separately for each asset (five variables in the specification). The diagonal matrix D_t comprises the standard deviations implied by these univariate GARCH estimations; the i-th element is h_it.
  - Stage 2: Obtain intercept parameters from the transformed asset returns (residuals ε_t).
  - Stage 3: Estimate the coefficients governing the dynamics of the conditional correlations.

### Model equations and components (as presented)
- The DCC model is characterized by:
  - H_t = D_t R_t D_t  (Equation form summarized in text)
  - R_t is the time-varying correlation matrix, a function of Q_t (the covariance matrix).
  - S is the unconditional correlation matrix of the residuals ε_t of the asset returns r_t.
  - In Q_t dynamics: ι is a vector of ones; A and B are square, symmetric matrices; ∘ is the Hadamard product.
  - λ_i is a weight parameter (contributions of 2_{t-1}D declining over time as described); κ_i is associated with squared lagged asset returns.
- References for methodological framework cited in text: Engle (2002); Frank, Gonzalez-Hermosillo and Hesse (2008); Frank and Hesse (2009).

### Benchmark stress scenarios (Appendix III): selected scenario parameters
- Scenario severity and shocks (table entries preserved as presented):
  - Severity (x times Lehman/1): 0.25 0.5 1 2
- Customer deposits (Term): 2.5 percent; 5 percent; 10 percent; 20 percent
- Customer deposits (Demand): 5 percent; 10 percent; 20 percent; 40 percent
- Short-term (secured): 5 percent; 10 percent; 20 percent; 40 percent
- Short-term (unsecured): 25 Percent; 50 Percent; 100 Percent; 100 Percent
- Contingent liabilities: 0 Percent need funding; 5 Percent need funding; 10 Percent need funding; 20 Percent need funding
- Haircut for Cash: 0 Percent; 0 Percent; 0 Percent; 0 Percent
- Haircut for Government Securities/2: 1 Percent; 2 Percent; 5 Percent; 10 Percent
- Haircut for Trading Assets/3: 3 Percent; 6 Percent; 30 Percent; 100 Percent
  - Proxies, specific assets for trading assets:
    - Moderate: Equities: 3; Bonds: 3
    - Medium: Equities: 4-6; Bonds: 3-8
    - Severe: Equity: 10-15; Bonds (only LCR eligible ones): 5-10
    - Very Severe: Not liquid
- Haircut for other securities: 10 Percent; 30 Percent; 75 Percent; 100 Percent
  - Proxies, specific assets for other securities:
    - Moderate: Equities: 10; Bonds: 10
    - Medium: Equities: 25; Bonds: 20 (some not liquid)
    - Severe: Equity: 30; Bonds (only LCR eligible ones): 20-30
    - Very Severe: Not liquid
- Percent of liquid assets encumbered/4: 10 Percent (or actual figure); 20 Percent (or actual figure plus 10 ppt); 30 Percent (or actual figures plus 20 ppt); 40 Percent (or actual figures plus 30 ppt)
- Notes preserved:
  - 3/ A haircut of 100 Percent means that the asset is illiquid, i.e., the market has closed.
  - 4/ The figures account for a downgrade of the bank, which triggers margin calls, and higher collateral requirements for generally. Please note that the unencumbered portion applies to a gradually narrower definition of liquid assets.
  - 1/ The Lehman type scenario description as presented in the source.
  - 2/ Haircut dependence on government debt features as presented.

### Illustrative solvency example (Appendix IV) — Austria stylized bank: key steps and exact values
- Step 1.1: Spillover impact in sovereign debt markets observed for Austria (increase of GIIPS sovereign debt spreads by...)
  - Impact on Austria, average for 2006-2012 and peak spillover stress (2008-2012) for scenarios:
    - 100 bps (2a): Impact average = 24.4 (=24*1.017); Impact peak = 49.8 (=49*1.017)
    - 200 bps (2b): Impact average = 48.8; Impact peak = 99.6
    - 300 bps (2c): Impact average = 73.2; Impact peak = 149.4
  - Source notes preserved regarding Table I.1 and Table I.2 specifications and GARCH analysis multipliers.
- Step 1.2: GDP trajectory for Austria, adjusted for spillovers
  - GDP Elasticity of widening of spreads for Austria estimated for two year period from 2013-2014: 3.5 (based on IMF, 2012)
  - Trajectory based on evidence for 2006-2012 (less significant spillovers)
    - Baseline (1): 2012 = 0.9; 2013 = 1.8; 2014 = 2.2; Cumulative deviation (2013-14) = 2.2
    - (2a/1): 2012 = 0.9; 2013 = 1.4 (=1.8-0.5*3.5*0.244); 2014 = 1.8 (=2.2-0.5*3.5*0.244); Cumulative = 1.3
    - (2b/1): 2012 = 0.9; 2013 = 0.9 (=1.8-0.5*3.5*0.488); 2014 = 1.3 (=2.2-0.5*3.5*0.488); Cumulative = 0.4
    - (2c/1): 2012 = 0.9; 2013 = 0.5 (=1.8-0.5*3.5*0.732); 2014 = 0.9 (=2.2-0.5*3.5*0.732); Cumulative = -0.4
  - Trajectory based on evidence for 2008-2012 (more significant spillovers)
    - Baseline (1): 2012 = 0.9; 2013 = 1.8; 2014 = 2.2; Cumulative = 2.2
    - (2a/2): 2012 = 0.9; 2013 = 0.9 (=1.8-0.5*3.5*0.498); 2014 = 1.3 (=2.2-0.5*3.5*0.498); Cumulative = 0.4
    - (2b/2): 2012 = 0.9; 2013 = 0.1 (=1.8-0.5*3.5*0.996); 2014 = 0.5 (=2.2-0.5*3.5*0.996); Cumulative = -1.2
    - (2c/2): 2012 = 0.9; 2013 = -0.8 (=1.8-0.5*3.5*1.494); 2014 = -0.4 (=2.2-0.5*3.5*1.494); Cumulative = -3
  - Note preserved: The GDP elasticities of sovereign debt spreads vary between 0.5 (e.g. Brazil) and 3.5.
- Step 2: Simulation of impact at the bank level (stylized bank) — change of key solvency parameters (exact table values)
  - Loan impairment rates (Percent of credit exposure)
    - Baseline: 2012 = 0.5; 2013 = 0.4; 2014 = 0.4
    - 2a/1: 2012 = 0.5; 2013 = 0.45; 2014 = 0.4
    - 2b/1: 2012 = 0.5; 2013 = 0.5; 2014 = 0.45
    - 2c/1: 2012 = 0.5; 2013 = 0.55; 2014 = 0.5
    - 2a/2: 2012 = 0.5; 2013 = 0.5; 2014 = 0.45
    - 2b/2: 2012 = 0.5; 2013 = 0.7; 2014 = 0.6
    - 2c/2: 2012 = 0.5; 2013 = 0.9; 2014 = 0.8
  - Pre-impairment income (Percent of total capital)
    - Baseline: 2012 = 10; 2013 = 10.3; 2014 = 10.5
    - 2a/1: 2012 = 10; 2013 = 10.15; 2014 = 10.3
    - 2b/1: 2012 = 10; 2013 = 10; 2014 = 10.1
    - 2c/1: 2012 = 10; 2013 = 9.8; 2014 = 10
    - 2a/2: 2012 = 10; 2013 = 10; 2014 = 10.1
    - 2b/2: 2012 = 10; 2013 = 9.7; 2014 = 9.8
    - 2c/2: 2012 = 10; 2013 = 9.2; 2014 = 9.5
  - Evolution of Risk-weighted Assets (RWAs) and Capital (indexed / percent)
    - RWAs (Indexed)
      - Baseline: 2012 = 100; 2013 = 90; 2014 = 90
      - 2a/1: 2012 = 100; 2013 = 95; 2014 = 90
      - 2b/1: 2012 = 100; 2013 = 100; 2014 = 95
      - 2c/1: 2012 = 100; 2013 = 105; 2014 = 100
      - 2a/2: 2012 = 100; 2013 = 100; 2014 = 95
      - 2b/2: 2012 = 100; 2013 = 120; 2014 = 111
      - 2c/2: 2012 = 100; 2013 = 140; 2014 = 132
    - Capital
      - Baseline: 2012 = 10; 2013 = 10.58; 2014 = 11.21
      - 2a/1: 2012 = 10; 2013 = 10.57; 2014 = 11.18
      - 2b/1: 2012 = 10; 2013 = 10.56; 2014 = 11.15
      - 2c/1: 2012 = 10; 2013 = 10.54; 2014 = 11.12
      - 2a/2: 2012 = 10; 2013 = 10.56; 2014 = 11.15
      - 2b/2: 2012 = 10; 2013 = 10.52; 2014 = 11.08
      - 2c/2: 2012 = 10; 2013 = 10.47; 2014 = 10.99
    - Note preserved: RWA elasticity to credit losses assumed to be 0.5 (for simplification).
  - Evolution of the Bank’s Capital Ratio (= Capital/RWA, Percent)
    - Baseline: 2012 = 10.0; 2013 = 11.8; 2014 = 12.5
    - 2a/1: 2012 = 10.0; 2013 = 11.1; 2014 = 12.5
    - 2b/1: 2012 = 10.0; 2013 = 10.6; 2014 = 11.7
    - 2c/1: 2012 = 10.0; 2013 = 10.0; 2014 = 11.1
    - 2a/2: 2012 = 10.0; 2013 = 10.6; 2014 = 11.7
    - 2b/2: 2012 = 10.0; 2013 = 8.8; 2014 = 9.9
    - 2c/2: 2012 = 10.0; 2013 = 7.5; 2014 = 8.3

### Illustrative liquidity example (Appendix V) — Austria stylized bank: key steps and exact values
- Step 1: GDP trajectories for Austria are the same as Appendix IV (solvency). For scenario 2c/2 the cumulative deviation from baseline is 5.2 percentage points. For the liquidity severity, stress parameters for the severe scenario in Appendix III are multiplied by factor 0.65 (=5.2/8).
- Step 2: Simulation at bank level (stylized bank, scenario 2c/2)
  - The stress factor reduces haircuts and outflows of the benchmark scenario; in the example the bank generates an inflow of 21.5 units of assets versus required level of 13.7 units and remains liquid.
  - Assets (portion of total; Haircut, Percent (Appendix 3); Haircut Scenario 2c/2; Available assets (fire sales))
    - Cash and cash-like: Portion = 4; Haircut, Percent = 0; Haircut Scenario 2c/2 = 0; Available assets (fire sales) = 4.0
    - Government securities: Portion = 6; Haircut, Percent = 5; Haircut Scenario 2c/2 = 3; Available assets (fire sales) = 5.8
    - Trading securities: Portion = 5; Haircut, Percent = 30; Haircut Scenario 2c/2 = 20; Available assets (fire sales) = 4.0
    - Other securities: Portion = 15; Haircut, Percent = 75; Haircut Scenario 2c/2 = 49; Available assets (fire sales) = 7.7
    - Loans: Portion = 60; Haircut, Percent = NA; Haircut Scenario 2c/2 = NA
    - Other: Portion = 10; Haircut, Percent = NA; Haircut Scenario 2c/2 = NA
  - Liabilities (portion of total; Outflow, Percent (Appendix 3); Outflow Scenario 2c/2; Required funding)
    - Customer Term deposits: Portion = 30; Outflow, Percent = 10; Outflow Scenario 2c/2 = 6.5; Required funding = 2
    - Customer Demand deposits: Portion = 20; Outflow, Percent = 20; Outflow Scenario 2c/2 = 20; Required funding = 2.6
    - Secured short-term wholesale funding: Portion = 10; Outflow, Percent = 20; Outflow Scenario 2c/2 = 13; Required funding = 1.3
    - Unsecured short-term wholesale funding: Portion = 10; Outflow, Percent = 100; Outflow Scenario 2c/2 = 65; Required funding = 6.5
    - Long-term funding: Portion = 20; Outflow, Percent = 0; Outflow Scenario 2c/2 = 0; Required funding = 0
    - Equity based funding: Portion = 10; Outflow, Percent = 0; Outflow Scenario 2c/2 = 0; Required funding = 0
    - Contingent liabilities: Portion = 20; Outflow, Percent = 10; Outflow Scenario 2c/2 = 6.5; Required funding = 1.3
  - Notes preserved:
    - Portions aligned to the average composition of OECD banks’ balance sheets (see Schmieder and others (2012), p. 38).
    - The LTRO allocation method and Bankscope source for balance sheet items as described in the text.

*Source: _wp14103 - APPENDIX II. OUTLINE OF THE DCC GARCH METHOD*

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