## How to do a Meaningful Stress Test as a non-IRB Bank?

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---

### Introduction: purpose, design principles, and scope
- Purpose of stress tests:
  - Risk management, financial stability analysis, and crisis management (illustrated by SCAP and European banking sector stress tests).
- Three key conditions for effective stress tests:
  - Scenarios: plausible but severe assumptions on level and duration of adverse shocks.
  - Risk sensitivity: translate changes in risk parameters into economic measures of solvency (beyond statutory measures).
  - Communication: results must be easy to communicate to decision makers and market participants.
- Features of the presented framework:
  - Integrates adverse-shock assumptions to run “severe yet plausible” scenarios.
  - Translates key risk parameter responses into an economic assessment of solvency.
  - Excel-based, flexible for hundreds of banks and up to five-year simulations.
  - Applicable to Basel II IRB banks and to Standardized Approach/Basel I banks via a quasi-IRB (QIRB) approach.
- Applications and planned extensions:
  - Applied in Germany, Chile, Oman; ECB used a modified version for benchmarking.
  - Planned modules for liquidity, contagion risk, Islamic banking, and regulatory updates.

### Methodology: structure, metric, and drivers
- Core stress-test metric:
  - Capitalization (t+1) = [Capital (t) + Net income (t+1)]/RWAs (t+1)
  - Notes:
    - Negative net income under stress reduces capital; positive net income increases capital subject to taxation and retention.
    - RWAs under StA/Basel I: reduce pre-stress RWAs by exposure lost due to stress and account for credit growth.
    - RWAs under IRB/QIRB: adjust for change in unexpected losses (portfolio quality), credit losses, and credit growth.
- Income modeling (key elements):
  - Net interest income, net fee and commission income, trading and investment income, other operating income.
  - Net operating income including impairments is benchmark; retained portion after tax adds to capital.
- Credit losses and impairments:
  - Expected loss under stress computed as PD × LGD or as change in credit losses/impairments under stress.
  - Dynamic provisioning not included in standard version but can be extended.
- Credit risk scope:
  - Includes all assets subject to default risk, including counterparty credit risk.
  - Market risk of liquid assets simulated separately through income.

### PD–LGD relationship and LGD calibration under stress
- Empirical basis:
  - Positive PD–LGD relationship evidenced in literature (Altman et al. 2003; Moody’s 2009; S&P 2010).
- Downturn LGD formulations:
  - U.S. Federal Reserve downturn formula: Downturn-LGD = 0.08 + 0.92*Long-term average LGD
  - Framework calibration used: LGD (under stress) = 0.4022 + 2.1535*PD
- Practical calibration notes:
  - Intercept of equation can be modified for country-specific LGD levels.
  - World Bank DoingBusiness data proposed as fallback if bank/country data unavailable.
  - LGD capped at 100 percent.
- Illustrative numeric point retained from source:
  - “70.8 percent, i.e., an increase of LGDs by 7.7 percentage points in absolute terms.”

### Risk-Weighted Assets (RWAs): framework overview and non-linearity
- Objective:
  - Compute RWAs for credit risk in economic terms and determine changes under stress.
- Model foundation:
  - Uses the one-factor model underlying the IRB approach to translate PDs, correlations, maturities, and name concentration into RWAs.
- Options for baseline RWA level:
  - (a) economic RWAs (IRB);
  - (b) QIRB-adjusted Basel I/StA RWAs (scaling factor);
  - (c) Basel I/StA RWAs.
- Key transmission channels:
  - (a) increase in expected losses (ELs) can hit capital via net income;
  - (b) increase in riskiness of performing loans raises RWAs (unexpected losses).
- Non-linear RWA response:
  - Corporate IRB formula used (as printed in source):
    - [LGD × N[(1 – R)^-0.5 × G(PD) + (R / (1 – R))^0.5 × G(0.999)] – PD x LGD] × (1 – 1.5 × b)^-1 × (1 + (M – 2.5) × b)    (4)
  - RWA elasticity examples from source (preserve numeric values exactly):
    - For low pre-stress PDs, RWA elasticity = 0.6 (an increase of PDs by 1 percent yields an increase of RWAs by 0.6 percent).
    - For PDs of 5 percent, elasticity ≈ 0.35.
    - For PDs of 10 percent, elasticity ≈ 0.2.
  - Polynomial fit used in framework to capture non-linearity:
    - Change of RWA = 0.006 - 0.050 Change in PD + 0.120 Change in PD^2    (5)
- Implementation detail:
  - Incremental increase of RWAs calculated based on average PD between pre-stress and stress levels (assumes gradual increase during the year).
  - Exposure subject to default assumed risk-weighted at 2.5 times average risk weight (example: average risk weight 80 percent → default exposure RW = 200 percent) — verify and change if applicable.

### Asset correlations and RWAs
- Objective:
  - Assess RWA elasticity to increases in asset correlations, holding PDs and LGDs constant.
- Key findings and table excerpts (LGDs assumed constant at 45 percent):
  - Table 3: Incremental Effect for an increase of asset correlations by 1 percent on RWAs
    - Level of PD (Percent) — Corporate — SME — Retail
    - 0.5 — 1.44 — 1.37 — 1.22
    - 1.0 — 1.24 — 1.19 — 1.07
    - 2.0 — 1.03 — 0.99 — 0.89
    - 4.0 — 0.83 — 0.81 — 0.73
    - 10.0 — 0.62 — 0.62 — 0.57
  - Empirical robustness (Mager and Schmieder (2009)):
    - RWA elasticity for a 1 percent increase in correlations:
      - small banks: 0.45
      - medium-sized banks: 0.7
      - large German banks: 1.25
- Framework default assumption:
  - Linear relationship between asset correlations and RWAs (stress testers can modify).

### Scaling factor for QIRB (rescaling StA/Basel I RWAs to IRB proxy)
- Rationale:
  - StA/Basel I RWAs can underestimate economic risk; rescaling to a QIRB proxy provides risk-sensitive starting point.
- Conceptual scaling factor expression from source:
  - SF = RWAs_QIRB / RWAs_StA = RWAs_IRB_MCorrLGDPDEADRWAs / RWAs_StA    (6)
    - (“Corr” = global asset correlations; M = effective Maturity; IRB asset class weights denote corporate/bank/public, SME and retail portions.)
- Practical notes:
  - If uncomfortable with scaling factor, testers may use reported RWAs (scaling factor = 1) as starting point.
  - Precondition: use meaningful credit risk parameters to calculate QIRB RWAs.
- Illustrative observations:
  - Example bank: scaling factor 1.34 (QIRB RWAs $13.4 billion vs. StA RWAs $10 billion).
  - In emerging markets low-income countries, LGDs typically higher at 60-80 percent → scaling factor tends to be above 1 except in very benign years.

### Name concentration and granularity (Pillar 2) adjustment
- Problem:
  - Basel II IRB assumes perfectly granular portfolios; name concentration can significantly increase capital needs.
- Remedy:
  - Approximate granularity adjustment using Gordy and Lütkebohmert (2007) to translate name concentration into additional RWAs (in percent).
- Granularity adjustment fragment preserved verbatim from source (retain original textual/formula fragment as presented):
  - 0.02*HHI*100RWA = 599.1*(1*HHI + (1 - PD/0.4%))*0.1*?  (original printed expression: 0.1))*1)-PD/0.4%((1*HHI)*599.120.02(*100RWA)    (7)
- Example outcomes from source:
  - If HHI = 0.01 → Pillar 2 add-on ≈ 15 percent of RWAs for credit risk (all else equal).
  - If PD changes from calibration level 0.4 percent to 0.8 percent → Pillar 2 add-on becomes 16.5 percent.
  - Granularity adjustment increases by 10 percent in relative terms for an increase of PDs by 0.4 percentage points.
  - Synthetic examples (Mager and Schmieder (2009)):
    - Small bank: HHI ≈ 0.02; average PD = 2 percent → granularity adjustment = 40 percent.
    - Medium-sized bank: HHI ≈ 0.005; PD = 1.2 percent → granularity adjustment = 10 percent.

### Basel III — simulation features and assumptions
- Simulation key elements (BCBS 2010a):
  - (i) An increase of RWAs.
  - (ii) Phase-out of eligible capital from 2013 (Total Capital, Tier 1) and 2014 (Common/Core Tier 1).
  - (iii) Changes in minimum capital ratios over time.
- Application of QIS 6 outcomes:
  - Banks with equity less than USD 3 billion classified as Group 2 banks.
  - Behavioral adjustment example: 50 percent mitigation of expected RWA increases.
    - Group 1 banks: RWAs increase 23 percent on average → 50 percent behavioral adjustment → increase 11.5 percent.
    - Group 2 banks: increase 50 percent of 4 percent → 2 percent.
- QIS 6 phase-out findings (as reported):
  - Tier 1 capital: phase-out 30.2 percent (Group 2 banks: 14.1 percent).
  - Total capital: phase-out 26.8 percent (16.6 percent).
  - Basel III schedule simulated a gradual phase-out by 10 percent of the current capital from 2013 on.
  - For core tier 1 capital, phase-out rate 20 percent beginning 2014.
  - Phase-out ratio cited: 41.3 percent (24.7 percent).
- Income retention/pay-out behavior:
  - Basel III applied via uniform pay-out ratios or bank-specific behavior; maximum pay-out ratios (minimum retention rates) pre-defined under BCBS 2010a, para. 129f.

### Framework design, execution steps, and data requirements
- Modular Excel design:
  - Kernel plus extendable modules; guided user interface with help menus and drop-downs.
  - Modules correspond to workbook tabs; dashed boxes indicate modules for follow-up releases.
- Three execution steps:
  - Step 1: define scenario, configure framework, enter input data.
  - Step 2: link macro-scenario to financial risks (use satellite models or rules of thumb).
  - Step 3: execute stress test and review outputs.
- Scenario definition and parameterization:
  - Framework allows reverse stress tests and uniform scenario testing (example cited: “stress level of, say 3 percent”).
  - Parameter tabs list explicit relationships to be specified:
    - i. PDs ↔ LGDs
    - ii. PDs ↔ RWAs
    - iii. Asset Correlations ↔ RWAs
    - iv. Rescaling StA → QIRB RWAs
- Input data sets:
  - Minimum set: about 30 inputs (minimum precision, retains core functionalities).
  - Extended set: includes bank-specific credit risk parameters (EADs, PDs, LGDs) by sector.
  - Maximum set: about 600 inputs (for first-tier international bank benchmarks).
  - Mixed-data-sample capability: uses most granular information available per bank.
- Satellite models:
  - Not embedded; Input_Satellite tab allows uploading linking equations (up to five explanatory variables per equation; up to four scenarios).
  - Guidance and illustrative models provided in Appendix II; caution advised before using illustrative models.

### Box 1 — Practical guidance for non-IRB banks and stylized numerical example
- Preconditions and proxies for credit risk parameters:
  - First best: forward-looking PDs and LGDs estimated under IRB.
  - Second best: use NPL inflows or translate NPL stocks into flows or use credit impairment flows.
  - Third best: NPL stocks.
  - Fourth best: country or peer-country data as proxies.
  - LGDs: bank/sector-level first best; country-level LGDs meaningful proxy; Doing Business database useful fallback.
- Translating statutory capital to economic capital:
  - Calculate quasi-IRB RWAs using implied PDs and LGDs and sector composition; scaling factor example 1.34.
  - Add granularity surcharge for borrower concentration.
- Scenario design parameters (nine stress-test parameter groups, Table 4):
  - Credit Risk: PDs, Change in Ratings, LGD, Credit Losses, Asset Correlations, Largest Exposures, Credit Growth.
  - Market Risk: FX rate, interest rate, asset prices, Change in RWAs.
  - Operational Risk: Increase in RWAs for operational risk.
  - Pillar 2 RWAs: Increase in RWAs for Pillar 2.
  - Change in Income: NII, fee/commission income, other operating income.
  - Basel III: simulate RWA increases, capital phase-out, minimum capitalization schedules.
- Stylized numerical example (single bank, single period, credit risk focus) — preserve exact figures:
  - Bank baseline:
    - Total assets: $10 billion
    - Credit portfolio: $5.7 billion
    - Total regulatory capital: $1.3 billion
    - Expected loss: $0.1 billion (EAD: 5.7 billion; PD: 2.4 percent; LGD: 71.8 percent)
    - Total RWAs (StA, incl. market & operational risk): $10 billion
    - QIRB RWAs: $13.4 billion
    - Scaling factor (QIRB/StA): 1.34
  - Two stress scenarios:
    - Both: PDs increase by 100 percent (from 2.4 to 4.7 percent).
    - Scenario 1: LGDs unchanged at 71.8 percent; correlations unchanged at 15.7.
    - Scenario 2: LGDs increase to 76.8 percent (+7.2 percent); correlations increase to 18.8 (+20 percent); concentration risk added equal to 4.0 percent of total credit RWAs.
  - Key outcomes (preserve exact CAR results as reported):
    - If StA RWAs used and RWAs adjusted only for losses/credit growth:
      - Pre-stress RWAs: 10; CAR pre-stress: 13.0 percent
      - Scenario 1 CAR after stress: 13.5 percent
      - Scenario 2 CAR after stress: 13.4 percent
    - If StA RWAs adjusted to reflect economic change in riskiness:
      - Pre-stress CAR: 13.0 percent
      - Scenario 1 CAR after stress: 9.5 percent
      - Scenario 2 CAR after stress: 7.6 percent
    - If QIRB RWAs used (pre-stress CAR shown as 9.6 percent):
      - Scenario 1 CAR after stress: 5.9 percent
      - Scenario 2 CAR after stress: 4.0 percent
  - Interpretation:
    - Economic RWAs (QIRB or StA adjusted) produce substantially lower CARs under stress than leaving RWAs unchanged; net income in these stylized scenarios remains positive.

### Key policy-relevant findings and recommendations
- Adjust RWAs for increased riskiness of credit exposure to avoid false sense of security; particularly important for emerging economies and low income countries.
- Improve data quality on credit risk to enable forward-looking PDs and better LGD estimates — a critical precondition for meaningful stress testing.
- Apply granularity/name-concentration adjustments, especially for medium-sized and smaller banks.
- Use simplified “rules of thumb” cautiously; stress testers must assess plausibility of macro-financial linkages and scenario severity and adapt to country-specific circumstances.
- The Excel-based framework enables flexible stress tests, comparison of StA-type and economic (IRB-like) tests, and supports policy makers, senior bank managers, and market participants.

*Source: _wp1183 — “How to do a Meaningful Stress Test as a non-IRB Bank?” (content unit as supplied).*

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

### _wp1183 - References .............................................................................................................

### Tables
- 1. Financial Risk Drivers ...........................................................................................................7
- 2. Income Under Stress ............................................................................................................10
- 3. Incremental Impact of an Increase of Asset Correlations on RWAs ...................................16
- 4. Assumptions for Risk Parameters ........................................................................................29
- 5. Other Assumptions...............................................................................................................30
- 6. Numerical example—Stress Test Assumptions ...................................................................33
- 7. Stylized Numerical example—Outcome .............................................................................34

### Figures
- 1. Link Between LGD and PD, Illustrative Example for Hungary ..........................................13
- 2. Incremental Impact of an Increase of PDs on RWAs ..........................................................15
- 3. Illustrative Example for the Scaling Factor (Advanced Economy) .....................................17
- 5. Overview of the Basel III Phase-in Agreements ..................................................................20
- 6. The Modular Design of the Stress Testing Framework .......................................................21
- 7. Stress Testing Framework—Conceptual overview .............................................................23
- 8. Screenshot of Bank Specific Results ...................................................................................32

### Box
- (No box entries listed in the supplied content)

*Source: _wp1183 - References .............................................................................................................*

### 1. How to do a Meaningful Stress Test as a non-IRB Bank? ..................................................27

### 1. How to do a Meaningful Stress Test as a non-IRB Bank?

### Introduction: purpose, design principles, and scope
- Purpose of stress tests:
  - Risk management, financial stability analysis, and crisis management.
  - Role illustrated by the US Supervisory Capital Assessment Program (SCAP) and European banking sector stress tests.
- Three key conditions for effective stress tests:
  - Scenarios: assumptions about level and duration of adverse shocks should be plausible but severe enough.
  - Risk sensitivity: frameworks must translate changes in risk parameters into economic measures of solvency (in addition to statutory/regulatory measures).
  - Communication: results should be easy to communicate to decision makers and market participants.
- Features of the presented framework (a "new generation" balance sheet framework):
  - Integrates assumptions about adverse shocks to enable running “severe yet plausible” scenarios.
  - Translates key risk parameter responses into an economic assessment of solvency.
  - Excel-based and easy to use.
  - Flexible to handle hundreds of banks and simulations up to five years with different levels of input data.
- Conceptual orientation:
  - Seeks to enrich balance-sheet based tests with portfolio model elements and is geared toward Basel II/III.
  - Main contribution: an economic assessment of solvency under stress via a more refined approach to the impact on Risk-Weighted Assets (RWAs).
  - Applicable to banks using Basel II IRB approaches and banks using Basel II Standardized Approach (StA) or Basel I through a quasi-Internal Rating Based (QIRB) approach.
- Applications and uptake:
  - Applied in countries including Germany, Chile, and Oman as part of IMF surveillance.
  - ECB has used a modified version for financial stability benchmarking.
  - Results used to indicate approaches to determine countercyclical capital buffers.
- Planned extensions:
  - Future modules aimed at liquidity and contagion risk (including a module for Islamic banking).
  - Updates to reflect regulatory developments and best practices.

*Source: Authors (from provided content).*

### Related literature and positioning relative to other frameworks
- Predominant approach in recent macro stress testing: structural (balance-sheet based) rather than general equilibrium or asset price-based.
- Two noteworthy frameworks referenced:
  - RAMSI (Risk Assessment Model for Systemic Institutions) by the Bank of England:
    - Structural macroeconomic model drives yield curve and PDs.
    - Income via a risk-neutral asset pricing model; reinvestment rules update balance sheets.
    - Funding liquidity risk introduced via a threshold model; contagion via Eisenberg and Noe network model.
  - SRM (Systemic Risk Monitor) by the Austrian Central Bank:
    - Bank-by-bank balance sheet approach integrating a network model with credit and market risk.
    - Models macro- and micro-risk factors individually, then interdependence via a grouped t-copula.
- Comparison points:
  - Many frameworks are more sophisticated in embedding linking equations (satellite models) inside the tool; the presented framework keeps satellite models external but allows their output to be uploaded and used via drop-down menus.
  - The tool closes the gap by providing rules of thumb for credit risk (Hardy and Schmieder (2011)), enabling macro stress testing without calibrating satellite models—subject to careful application to avoid misleading results.
- Unique contribution of the presented framework:
  - Multifaceted calculation of changing RWAs under stress, allowing stress of the denominator of capitalization ratios (Total Capital, Tier 1, Common/Core Tier 1) without requiring fully-fledged portfolio models.

*Source: Authors (from provided content).*

### Methodology: structure, metric, and drivers
- Framework guide: Table 1 "Financial Risk Drivers" (overview):
  - Income: includes Operating income and Provisions for credit losses (according to stress scenario).
  - Credit losses: fundamentals EAD, PDs, and LGDs; the relationship between PDs and LGDs.
  - RWAs: relationship between PDs and RWAs; relationship between Asset Correlations and RWAs; factors to rescale credit-risk related RWAs based on the StA into QIRB RWAs; relationship between name concentration and RWAs.
- Stress test metric: Capitalization under stress
  - Objective: determine whether post-stress capitalization is sufficient to (a) stay above regulatory minima; (b) meet market expectations; or (c) safeguard against additional idiosyncratic shock.
  - Capitalization (t+1) formula:
    - Capitalization (t+1) = [Capital (t) + Net income (t+1)]/RWAs (t+1)
  - Notes:
    - If net income is negative under stress, capital takes a hit; otherwise capital increases subject to taxation and earnings retention rate.
    - For Basel I/Basel II StA frameworks: RWAs under stress are determined by reducing pre-stress RWAs by exposure lost due to stress while accounting for credit growth.
    - For IRB (and QIRB): RWAs adjusted to reflect the change in unexpected losses (portfolio quality) under stress, plus credit losses and credit growth.
    - Framework allows adjustment of RWAs for market and operational risks, and other Pillar 1 and Pillar 2 risks under stress.
- Income modeling (Section B)
  - Rationale: income is the first line of defense; simulate total income and/or specific components guided by satellite models where possible.
  - Key income elements modeled:
    - Net interest income (treated separately; usually most important).
    - Net fee and commission income (treated separately).
    - Trading and investment income (can be expert- or satellite-model based; mark-to-market gains/losses from interest rate and FX shocks can be simulated if bank-specific data available).
    - Other operating income (simulated based on expert judgment; nonrecurring income omitted by default).
  - Treatment of post-shock income:
    - Reported operating income net of impairments serves as a benchmark for subsequent years.
    - If net income after stress is positive, retained portion (after tax) is added to capital; otherwise losses are deducted.
    - Rules for payout/retention could be bank-specific (e.g., in line with Basel III maximum pay-out rules) but are not part of the standard version.
  - Table 2 summary (Income Under Stress):
    - Net Operating Income including impairments modeled as sum of net interest income, net fee and commission income, and other operating income (including expenses).
    - Change in net operating income vs. reporting year: stress testers define changes in net interest income (expert or model based); account for foregone interest due to losses and additional interest income from credit growth; changes in net fee/commission and other operating income accounted for.
    - Impairments for credit losses exceeding reporting year: outcome of credit risk stress test.
    - Changes in trading and investment income including mark-to-market gains/losses: based on expert judgment or satellite models; simulate shocks affecting interest rates in the banking book and/or FX rates.
    - Change in other income: simulated based on expert judgment.
- Impairments for credit losses:
  - Expected loss under stress computed as product of PDs and LGDs or as change in credit losses/impairments under stress.
  - Dynamic provisioning not included in standard version but can be extended.
- Trading and investment income:
  - Treated separately; evolution can be expert-based or model-based.
  - Tool allows simulating mark-to-market gains/losses of specific asset classes (sovereign debt, etc.) and losses from market shocks.
  - Important to avoid double-counting.
- Credit losses (Section C): key innovation
  - Based on Basel II/III notion using PDs, LGDs, EADs, maturities, and asset correlations.
  - Tool provides:
    - Determination of credit losses (informing numerator of capital adequacy).
    - Determination of RWAs for credit risk under stress (denominator).
  - Credit risk analyses include all assets subject to default risk, including counterparty credit risk.
  - Market risk of liquid assets is simulated separately through income.

### PD-LGD relationship and LGD calibration under stress
- Empirical basis:
  - Evidence of a positive relationship between PDs and LGDs for bonds and loans (e.g., Altman et al. 2003; Moody’s 2009; S&P 2010; Appendix III).
- Downturn LGD formulations provided:
  - U.S. Federal Reserve formula for downturn LGD:
    - Downturn-LGD = 0.08 + 0.92*Long-term average LGD
  - Adjusted, non-linear calibration used in the framework:
    - LGD (under stress) = 0.4022 + 2.1535*PD
  - Practical calibration notes:
    - Intercept of equation (3) can be modified to match country-specific LGD levels (legal frameworks influence LGDs).
    - If bank-specific or country-specific data unavailable, World Bank DoingBusiness data (Djankov et al. (2007)) is proposed as a fallback for calibration.
    - Example application (illustrative): Hungary calibration referenced (PD (NPLs) in 2007 ≈ 2 percent; World Bank LGD 62.1 percent), showing how recalibration would proceed and how an increase in PDs to 6 percent would yield a higher LGD (explicit numerical result truncated in provided content).

*Source: Authors (from provided content).*

*This overlay is based solely on the supplied content from the specified chapter.*

### 70.8 percent, i.e., an increase of LGDs by 7.7 percentage points in absolute terms.

### _wp1183 - 70.8 percent, i.e., an increase of LGDs by 7.7 percentage points in absolute terms.

### LGD–PD mapping (illustrative example for Hungary)
- Sequence of PD-LGD mapping functions:
  - Bright triangles: empirical relationship found by Moody’s.
  - Dark rectangles: empirical relationship adjusted for economic downturn conditions (using (2)).
  - Upper grey rectangles: LGD level for Hungary derived through a modification of (3).
- Specific numeric points and rules:
  - “70.8 percent, i.e., an increase of LGDs by 7.7 percentage points in absolute terms.”
  - Downturn LGDs defined in para. 468 of the Basel II framework (BCBS, 2006).
  - LGD is capped at 100 percent.
  - Long-term averages should include periods of stress; Basel II foresees banks use a period of at least seven years to qualify for the AIRB.

_Source: Authors._

### Risk-Weighted Assets (RWAs) — framework overview
- Purpose:
  - Compute RWAs for credit risk in economic terms to determine level and compute changes under stress.
- Model:
  - Uses the one-factor-model underlying the IRB approach to determine changes of RWAs conditional on changes in PDs, correlations, and name concentration.
- Options for baseline RWA level:
  - (a) economic RWAs (IRB, economic capital requirements);
  - (b) QIRB-adjusted Basel I/StA RWAs (scaling factor);
  - (c) RWAs based on Basel I/StA.
- Relationship:
  - LGDs exhibit a linear relationship with RWAs (no model needed for LGD→RWA mapping).

### PDs and RWAs — stress transmission and non-linearity
- Two channels by which credit risk stress affects solvency:
  - (a) increase in expected losses (ELs) can hit capital if net income becomes negative;
  - (b) increase in riskiness of performing loans (unexpected losses) raises RWAs.
- Non-linear effect:
  - Calculation of ELs is linear; calculation of RWAs is non-linear due to correlations.
- Implementation:
  - The framework uses the Basel II formula to translate increases in PDs into stressed RWAs.
  - If LGDs and correlations are held constant, incremental increases of PDs produce larger changes in RWAs when pre-stress PDs are lower; incremental effect decreases with the level of PDs.
  - For link between PD changes and RWA changes, the corporate IRB formula is used, fixing correlations at the level of the lowest PDs.

- Corporate IRB formula (BCBS 2006, para. 272) used in framework:
  - [LGD × N[(1 – R)^-0.5 × G(PD) + (R / (1 – R))^0.5 × G(0.999)] – PD x LGD] × (1 – 1.5 × b)^-1 × (1 + (M – 2.5) × b)    (4)
    - N(.) is the cumulative distribution function for a standard normal random variable.
    - G is the inverse of N(.).
    - R denotes the IRB asset correlations.
    - b is the maturity adjustment.
    - M is the effective maturity.
- RWA elasticity of PDs (examples given):
  - For low levels of pre-stress PDs, RWA elasticity = 0.6 (an increase of PDs by 1 percent yields an increase of RWAs by 0.6 percent).
  - For PDs of 5 percent, elasticity ≈ 0.35.
  - For PDs of 10 percent, elasticity ≈ 0.2.
- Polynomial fit used to capture non-linearity:
  - Change of RWA = 0.006 - 0.050 Change in PD + 0.120 Change in PD^2    (5)
- Calculation detail:
  - Incremental increase of RWAs is calculated based on the average PD between pre-stress and stress PD levels (assumes gradual increase during the year).
- Adjustment for defaulted exposure:
  - Exposure subject to default assumed to exhibit risk weights equal to 2.5 times the average risk weight (example: bank with average risk weight 80 percent → exposure subject to default risk-weighted at 200 percent prior to default). This assumption should be verified and changed if applicable.

### Incremental impact of PD increases on RWAs (illustration)
- Figure 2 (descriptive):
  - Shows incremental impact on RWAs per 1% change of PD across PD levels from 0% to 20%.
  - Observed pattern: incremental impact declines as PD increases (non-linear relationship captured by polynomial fit).

### Asset correlations and RWAs
- Objective:
  - Assess RWA elasticity of asset correlations (impact of increase in asset correlations on RWAs while holding PDs and LGDs constant).
- Key findings:
  - Impact based on IRB formula (4) depends on asset class and pre-stress PD level.
  - For corporate IRB formula, effect is more than linear (PD elasticity above 1) for PDs lower than 2 percent.
- Empirical robustness check:
  - Mager and Schmieder (2009) stress tests of synthetic German portfolios find RWA elasticity for a 1 percent increase in correlations:
    - small banks: 0.45
    - medium-sized banks: 0.7
    - large German banks: 1.25
  - Framework default: linear relationship between asset correlations and RWAs (stress testers can modify).
- Table 3: Incremental Effect for an increase of asset correlations by 1 percent on RWAs (LGDs assumed constant at 45 percent)
  - Level of PD (Percent) — Corporate — SME — Retail
  - 0.5 — 1.44 — 1.37 — 1.22
  - 1.0 — 1.24 — 1.19 — 1.07
  - 2.0 — 1.03 — 0.99 — 0.89
  - 4.0 — 0.83 — 0.81 — 0.73
  - 10.0 — 0.62 — 0.62 — 0.57

_Source: Authors._

### Scaling factor for QIRB (rescaling StA/Basel I RWAs to IRB proxy)
- Rationale:
  - Use of a risk-sensitive measure is essential for stress testing; StA/Basel I RWAs can underestimate economic risk.
  - Framework allows using QIRB RWAs as a starting point for RWAs rather than Basel I/StA.
- Mechanism:
  - (a) Rescale banks’ RWAs for credit risk that use the StA (or Basel I) into a proxy for IRB RWAs.
  - (b) Simulate scenarios based on the IRB.
- Scaling factor formula (conceptual expression provided):
  - SF = RWAs_QIRB / RWAs_StA = RWAs_IRB_MCorrLGDPDEADRWAs / RWAs_StA  (6)
    - Where “Corr” is the “global” asset correlations, M is the effective Maturity, and IRB asset class weights denote portions of exposure that are corporate/bank/public, SME and retail, respectively.
- Practical notes:
  - If stress testers are uncomfortable with the scaling factor determined in the tool, reported RWAs (assuming a scaling factor of 1) can be used as a starting point.
  - A key precondition to calculate QIRB RWAs is to use meaningful credit risk parameters; for non-IRB banks, other second/third/fourth best solutions are discussed elsewhere in the source.
- Illustrative example (hypothetical bank):
  - Under StA: capital requirements assumed at 8 percent of total exposure and do not fluctuate over time.
  - Under IRB: capital requirements determined using Moody’s default rates observed during last decade for their rated universe and an LGD of 40 percent (realistic TTC benchmark for advanced countries).
  - Observation: IRB capital requirements fluctuate significantly and are lower during most years (e.g., during 2003 to 2008).
  - Scaling factor (crosses, Right-hand scale in Figure 3) compares relative level of capital requirements between StA and IRB over time; scaling factor adjusts level of StA RWA to IRB capital requirement level.
  - Note: For emerging markets and low income countries, LGDs typically higher at 60-80 percent, leading scaling factor to be above 1 except in very benign years with very low PDs.

### Name concentration and RWAs (granularity adjustment / Pillar 2)
- Problem:
  - Basel II IRB minimum capital requirements assume perfectly granular portfolios and do not account for name concentration; this can underestimate capital needs, particularly for small banks.
- Remedy in framework:
  - Include capital charges for name concentration via Pillar 2 supervisory scrutiny, using approximation from Gordy and Luetkebomert (2007) to translate name concentration into additional RWAs (in percent).
- Granularity adjustment approximation (formula provided):
  - 0.02*HHI*100RWA = 599.1*(1*HHI + (1 - PD/0.4%))*0.1*?  (original printed expression: 0.1))*1)-PD/0.4%((1*HHI)*599.120.02(*100RWA)  — retain exact textual/formula fragment as presented in source.    (7)
  - Example outcomes (as reported):
    - If HHI = 0.01, Pillar 2 add-on ≈ 15 percent of RWAs for credit risk (all else equal).
    - If PD changes from calibration level 0.4 percent to 0.8 percent, Pillar 2 add-on becomes 16.5 percent.
    - Granularity adjustment increases by 10 percent in relative terms for an increase of PDs by 0.4 percentage points.
- Illustrative synthetic portfolio examples (based on Mager and Schmieder (2009)):
  - Small bank: HHI ≈ 0.02; average PD = 2 percent → granularity adjustment = 40 percent.
  - Medium-sized bank: HHI ≈ 0.005; PD = 1.2 percent → granularity adjustment = 10 percent.
  - Large bank: HHI ≈ 0.0006; PD = (text truncated in source).

_Source: Authors._

### 0.8 ercent) about 3 percent.

### _wp1183 - 0.8 ercent) about 3 percent.

### E. Basel III — simulation features and assumptions
- Simulation includes three key elements (see BCBS 2010a):
  - (i) An increase of RWAs.
  - (ii) The phase-out of eligible capital from 2013 (Total Capital, Tier 1) and 2014 (Common/Core Tier 1).
  - (iii) Changes in the minimum capital ratios over time.
- Changes in the first two elements are simulated based on the outcome of the QIS 6, and applied to banks according to their size (banks with equity less than USD 3 billion are classified as Group 2 banks).
- Behavioral adjustment example:
  - If one assumes that there is a behavioral adjustment by 50 percent, banks are assumed to mitigate 50 percent of the expected increase of RWAs.
  - With RWAs for Group 1 banks increasing by 23 percent on average, a 50 percent behavioral adjustment yields an increase of 11.5 percent.
  - For Group 2 banks, the increase is 50 percent of 4 percent, i.e., 2 percent.
- Phase-out of capital eligibility (QIS 6 findings):
  - Tier 1 capital: phase-out amounts to 30.2 percent (Group 2 banks: 14.1 percent).
  - Total capital: phase-out amounts to 26.8 percent (16.6 percent).
  - Basel III schedule simulated a gradual phase-out by 10 percent of the current capital from 2013 on.
  - For core tier 1 capital, the phase-out rate is 20 percent and begins from 2014.
  - The phase-out ratio is 41.3 percent (24.7 percent).
- Income retention / pay-out behavior:
  - Basel III can be applied in terms of the income retention rate via uniform pay-out ratios (drop-down menu) or bank-specific behavior.
  - Maximum pay-out ratios (i.e., minimum retention rates) are pre-defined under Basel III as specified in BCBS 2010a, para. 129f.
- Figure 5 referenced: Overview of Basel III Phase-in Agreements (Source: BCBS (2010a)).

### IV. Stress Testing Framework — overview and design
- Framework built on a modular kernel with extendable modules; organization of chart:
  - Upper left: external parameterization and models.
  - Lower right: input data.
  - Main sequence: define assumptions → calculate solvency impact → calculate name concentration impact → aggregate → summarize results.
- Excel tool design features:
  - (a) based on Excel;
  - (b) users guided through the sheet with documentation and help menus;
  - (c) layout facilitates setting assumptions, including without satellite models (using pre-defined, simple rules);
  - (d) drop-down lists allow switching between different settings (e.g., scenarios);
  - (e) framework tested and improved in various contexts.
- Figure 6 referenced: The Modular Design of the Stress Testing Framework (Source: Authors).
  - Note: As the framework is based on an Excel-template, the modules correspond to different tabs; result sheets aggregate data, assumptions, parameters and summarize outcomes at bank and system level.
  - Dashed boxes refer to modules available in follow-up releases.

### B. How the framework actually works — three execution steps
- Three required activities to run a stress test:
  - (a) define the scenario, configure the framework and enter input data (Step 1);
  - (b) link the (macro-)scenario to financial risks (Step 2);
  - (c) execute the stress test (Step 3).
- Step 1 — The (Macro-)Scenario Definition:
  - Outside the tool, stress testers decide on a shock or macro-economic scenario (model-driven or expert judgment).
  - Inside the tool, users perform parameterization that alters the template according to number of banks and (credit) portfolio granularity.
  - Recommendation: run reverse stress tests in addition to scenario tests; reverse tests should include simulations of uniform scenarios (example provided: "stress level of, say 3 percent").
- Step 2 — From (Macro-)Scenarios to Micro Impact:
  - Simplest case: sensitivity tests for specific risk types (credit, market, operational, concentration) — often based on expert judgment.
  - Complex case (macro stress test): link macro-economic risk factors to financial risks via satellite models (econometric models).
- Step 3 — Execution of the stress tests:
  - Tests run "on the fly" once settings and calibrated satellite models are set.
  - Outputs: bank-by-bank solvency under stress, aggregate system figures (capital adequacy, recapitalization needs), and various financial soundness indicators (FSIs).
  - Risk contributions reported include operating income buffer, credit losses, and trading and investment losses.

### The (Macro-)Scenario Definition — parameterization and configuration
- Parameterization steps before starting stress tests:
  - (a) set technical parameters;
  - (b) set economic parameters (can be changed on-the-fly);
  - (c) run configuration;
  - (d) begin data input.
- Technical Parameters (Sheet: Variables):
  - Framework comes fully configured; Variables sheet exposes fundamental parameters for expert users to change (banking aggregates, available Basel II approaches, scenario and VB variable names, VB look-up tables).
  - Novices need not modify technical parameters; changes can have vast knock-on effects.
- Economic Parameters (Sheet: Parameter):
  - Framework is fully configured; Parameter sheet allows reconfiguration including under-year adjustment, scenario labels, interest rate shocks, and reduced form approximations defining relationships among risk factors.
  - Relationships explicitly listed:
    - i. The relationship between PDs and LGDs.
    - ii. The relationship between PDs and RWAs.
    - iii. The relationship between Asset Correlations and RWAs.
    - iv. The rescaling of credit-risk related RWAs based on StA into QIRB RWAs.
  - For detailed explanations, refer to the Parameter tab in the tool or Section III.
- Configuration (Sheet: Setup):
  - Mandatory final configuration for every user; defines scope of stress test.
  - Framework accounts for:
    - (a) the number of banks included in the test;
    - (b) choice of credit portfolio granularity — by economic sector, Basel II asset class, or by geography (regions within a country and/or other countries/world regions banks lent to);
    - (c) general granularity of data available (minimum set, extended set, maximum set).
  - Templates tailored to display only relevant information via VB macros.

### Input Data requirements and options
- Input types required:
  - System-level data (e.g., GDP for the system, country-level PDs and LGDs).
  - Bank-specific information (balance sheet data, financial statements, regulatory data).
  - Econometric models if applicable.
- Three input-data sets offered:
  - Minimum set:
    - About 30 inputs needed to run a solvency test (includes bank names, reporting year and month, country of origin).
    - Using minimum set yields lowest precision but retains most functionalities.
  - Extended set:
    - Includes bank-specific credit risk parameters (EADs, PDs, LGDs) for key economic sectors (e.g., corporate, retail, public, financials).
  - Maximum set:
    - Comprises about 600 inputs.
    - Intended for meaningful stress tests for a first tier international bank; suitable as a top-down benchmark for large exercises.
- Mixed-data-sample capability:
  - Framework allows running tests where different banks have different input sets (e.g., extended/maximum for larger banks, minimum for smaller banks); tool will use the most granular information available per bank.
- Publicly available data (annual reports, risk reports, Basel Pillar 3 reports) can support minimum and extended sets, sometimes maximum set.
- Proxies:
  - For banks that have not implemented advanced Basel II approaches, proxies can be used (outlined in Box 1).
- Footnotes and operational notes:
  - Where “_X” stands for either: Banks, Country or Satellite.
  - In simplest case, non-performing loans (NPLs) (i.e., the stock) can be used as a proxy for PDs.
  - It is foreseen that credit risk parameters (NPLs or provisions) are available at the bank level; otherwise country-level parameters can be used as a proxy.
  - The extended and maximum information sets have been compared empirically for a solvency stress test outcome.

### From (Macro-)Scenarios to Micro Impact — guidance and satellite-model handling
- Sensitivity tests:
  - Typically expert-judgment driven; specify increases in risk parameters by reference to past stress levels.
  - Guided by available risk factors and scope definition (which assets the stress refers to).
- Scenario (macro) stress tests:
  - Multivariate and based on stressed macro conditions; translate macro forecasts to banks’ asset quality using satellite models.
  - Satellite models are not part of the framework; framework provides a "user exit" tab Input_Satellite to specify linking models for PDs, credit growth and changes in profitability.
  - Input_Satellite features:
    - Allows up to five different explanatory variables per equation (extendable).
    - Allows up to four different scenarios (baseline and three stress scenarios) for sensitivity analysis on results sheet.
  - Linking equations must be estimated outside the framework; guidance on handling satellite models provided in Appendix II and the roadmap in the tool.

*Source: Authors.*

### Box 1. How to do a Meaningful Stress Test as a non-IRB Bank?

### Box 1. How to do a Meaningful Stress Test as a non-IRB Bank?

### Preconditions for meaningful stress tests
- Forward-looking credit risk parameters (PDs, LGDs) estimated by banks under IRB are the first-best input because they reflect expected future losses rather than past losses.
- When IRB parameters are unavailable, successive best-practice proxies are proposed:
  - Second best: (a) use available NPL inflows or (b) translate NPL stocks into flows based on expert judgment (ensuring consistency with default rates); or (c) use flow data of credit impairments from the P&L (specific provisions and/or write-offs).
  - Third best: use NPL stocks.
  - Fourth best: use country-specific data or data from peer countries as proxies.
- LGDs:
  - Bank- or sector-level LGDs are first best; country-level LGDs are often available and are a meaningful proxy, especially for corporate exposure.
  - Basel II FIRB calibrations reflect advanced-country LGD levels, which are typically substantially lower than LGDs in emerging economies and low income countries.
  - The Doing Business database by World Bank can provide country-level data for many countries.

### Translating statutory (StA) capital to economic capital (quasi-IRB RWAs)
- Economic capital ratios are derived by calculating quasi-IRB RWAs for credit risk based on implied credit risk parameters (PDs and LGDs or credit losses).
- Market risk RWAs can be derived from internal experience or benchmark data; operational risk RWAs could be based on statutory data.
- Translation typically uses sector composition of each bank’s credit portfolio and applies the respective Basel II IRB formula across asset classes (SMEs, retail credit, other counterparties).
- A scaling factor captures the relative difference between statutory and economic capital ratios (example provided below: scaling factor 1.34).
- A granularity (name concentration) surcharge can be calculated and added to RWAs to reflect borrower concentration; conservative benchmark: EU definition of related counterparties.

### Assumptions and scenario design (Sheets: Assumptions; Parameter tab)
- The tool allows selecting scenarios on results sheets and running sensitivity tests without changing tabs.
- Stress levels can be defined in absolute terms (“to x percent”) or relative terms (“by x percent”); example: increase from 1 percent to 2 percent (increase by 100 percent).
- Nine stress-test parameters must be assumed for comprehensive scenario tests (Table 4):
  - Credit Risk (CR): PDs (set bank-/sector-level), Change in Ratings (simulate up to 9 notches), LGD (set bank-/sector-level), Credit Losses (PD*LGD; can substitute), Asset Correlations (ACs), Largest Exposures (simulate default), Credit Growth.
  - Market Risk (MR): FX rate, interest rate, asset prices; Change in RWAs.
  - Operational Risk (OR): Increase in RWAs for operational risk.
  - Pillar 2 RWAs: Increase in RWAs for Pillar 2 exposure (and other Pillar 1 risks).
  - Change in Income: changes to operating income (net interest income, fee and commission income, other operating income) and other income.
  - Basel III: simulate (a) increase in RWAs (according to QIS 6 results); (b) phase-out of capital (according to QIS 6 results); and (c) minimum capitalization rates as scheduled (for Total Capital, Tier 1 capital and Common/Core Tier 1).
- Simplified macro-to-credit rules of thumb (on Parameter tab) link changes in GDP to credit risk parameters for advanced countries and emerging economies; these are based on forthcoming research by Hardy and Schmieder (2011) and are “average” situations only.
- Optionally, LGDs can be empirically linked to PDs so that only stressed PDs need be defined and LGDs are derived by an empirical model.

### Other controllable assumptions (Table 5)
- Scenario type: macro scenario, expert-based scenario, or manual input.
- Sector classification: choose sector breakdown if data entered.
- Method to stress RWAs for credit risk:
  - StA method: keep RWAs constant (StA-style).
  - Basel II IRB approach: RWAs change with credit risk parameters (greater sensitivity, non-linearity).
  - If starting from StA, a scaling factor may be used to translate pre-stress RWAs into QIRB RWAs—tester must verify appropriateness.
- Name concentration: option to add RWAs for name concentration.
- Bank behavior: set income retention rate (significant effect); set assumptions on balance sheet changes (credit exposure growth).
- Capital definition and hurdle rates: simulate for Total capital, Tier 1, Common Tier 1 and set hurdle rates (example: 8 percent).

### Execution mechanics and outputs
- Tests run “on the fly”; results shown immediately in result tabs.
- Outputs include bank-by-bank solvency under stress (capital ratio, recapitalization needs) and aggregate system metrics (capital adequacy, recapitalization needs), plus FSIs and risk-driver contributions (credit losses, trading losses, income as first buffer).
- Road-map tab summarizes spreadsheet mechanics step-by-step.
- Results sheets present both system-level and institution-specific outcomes; illustrative Figure 8 shows distribution of capital ratios across quantiles for 12 international banks through 2014 (table and chart showing percentiles and counts across capital buffer ranges).

### Stylized numerical example (single bank, single period, credit risk focus)
- Bank baseline:
  - Total assets: $10 billion
  - Credit portfolio: $5.7 billion
  - Total regulatory capital: $1.3 billion
  - Expected loss: $0.1 billion (EAD: 5.7 billion; PD: 2.4 percent; LGD: 71.8 percent)
  - Total RWAs (StA, incl. market & operational risk): $10 billion
  - QIRB RWAs: $13.4 billion
  - Scaling factor (QIRB/StA): 1.34
- Two stress scenarios simulated:
  - Both scenarios: PDs increase by 100 percent (from 2.4 to 4.7 percent).
  - Scenario 1: LGDs unchanged at 71.8 percent; correlations unchanged at 15.7.
  - Scenario 2: LGDs increase to 76.8 percent (+7.2 percent); correlations increase to 18.8 (+20 percent); concentration risk added equal to 4.0 percent of total credit RWAs.
- Table 6 assumptions snapshot:
  - Pre-stress PDs: 2.4; Scenario 1 PDs: 4.7 (+100%); Scenario 2 PDs: 4.7 (+100%).
  - Pre-stress LGDs: 71.8; Scenario 1 LGDs: 71.8 (no change); Scenario 2 LGDs: 76.8 (+7.2%).
  - Correlations: Pre-stress 15.7; Scenario 2 correlation 18.8 (+20%).
  - Concentration Risk: Scenario 2 increases RWAs by 4.0%.
  - Retained Profit: 100 (pre-stress and both scenarios).
- Outcome summary under different RWA treatments (Table 7):
  - If StA RWAs used and RWAs adjusted only for losses/credit growth (no economic RWA change):
    - Pre-stress RWAs: 10; CAR pre-stress: 13.0 percent
    - Scenario 1 CAR after stress: 13.5 percent
    - Scenario 2 CAR after stress: 13.4 percent
  - If StA RWAs are adjusted to reflect economic change in riskiness:
    - Pre-stress CAR: 13.0 percent
    - Scenario 1 CAR after stress: 9.5 percent
    - Scenario 2 CAR after stress: 7.6 percent
  - If QIRB RWAs used (pre-stress CAR shown as 9.6 percent):
    - Scenario 1 CAR after stress: 5.9 percent
    - Scenario 2 CAR after stress: 4.0 percent
- Interpretation:
  - Using economic RWAs (QIRB or StA adjusted for economic changes) produces substantially lower CARs under stress than leaving RWAs unchanged.
  - Net income under the stylized scenarios remains positive; scenarios illustrated are not particularly severe but show material differences when risk-weight adjustments are applied.

### Key policy-relevant findings and recommendations
- Economic stress tests that adjust RWAs for increased riskiness of credit exposure are essential to identify upcoming risk and avoid false sense of security, particularly in emerging economies and low income countries.
- Improving data quality for credit risk (to allow forward-looking PDs and better LGD estimates) is a critical precondition for meaningful stress testing.
- Granularity/name-concentration adjustments are important, especially for medium-sized and smaller banks.
- Stress testers must judge plausibility of macro-financial linkages and scenario severity; simplified “rules of thumb” should be used cautiously and adapted to country-specific circumstances.
- The framework facilitates designing flexible stress tests, enables comparison of StA-type and economic (IRB-like) tests, and provides an accessible Excel-based tool to support policy makers, senior bank managers, and market participants.

*Source: Authors (Box 1, “How to do a Meaningful Stress Test as a non-IRB Bank?”).*

### Appendix I.1 Adoption of Foundation and Advanced IRB (Survey Carried out by

### _wp1183 - Appendix I.1 Adoption of Foundation and Advanced IRB (Survey Carried out by

### Appendix I.2 — Supervisory Stage of Basel II Implementation
- Reference: (Survey Carried out by the FSI, 2010, p.20)

### Appendix II — Derivation of Macro Scenarios
- Framework overview:
  - Macro scenarios are derived based on satellite models, i.e., econometric models linking macroeconomic variables to financial risk parameters.
  - The framework foresees that such models are calibrated before running the tests, and that the outcome of the regressions is entered into a specifically foreseen tab.
  - The advantage is that assumptions entered in the template can be changed readily and one can assess the sensitivity of the stress test outcome to changes in the macroeconomic assumptions.
- Scenario design:
  - The framework foresees the definition of three macro scenarios, namely:
    - mild stress (yellow, macro 1)
    - stress of medium severity (orange, macro 2)
    - severe stress (red, macro 3)
  - Once the model specification has been entered into the “Satellite Model” tab, the credit parameter scenarios are directly linked to the respective column in the assumptions tab.
- Illustrative models and caution:
  - The framework contains illustrative models that link macroeconomic conditions to PDs/Default Rates/NPLs, credit growth and income.
  - Stress testers are cautioned not to use these models unless there is a reason to believe that they are suitable for the circumstances of their test.

### Appendix III — Corporate Recovery vs. Default Rates
- Figures and sources:
  - Source: Moody’s (2009) Corporate default and recovery rates, 1920-2008.
  - Source: S&P (2010) Corporate default and recovery rates for speculative grade credit.
- Chart annotation (as described):
  - One plot shows Moody’s series (1920-2008) of corporate default and recovery rates.
  - Another plot titled "S&P's Speculative Grade Default and Recovery Rates" displays PD on the x-axis and Recovery Rate on the y-axis, with the y-axis scale including 0% to 80% and the x-axis scale shown as 0%2%4%6%8%10%12% (as presented in the source).

### Selected references cited in the content unit (preserving original entries)
- Aikman, David, and others, 2009, “Funding liquidity risk in a quantitative model of systemic stability,” Bank of England, Working Paper No. 372.
- Altman, Edward I., Brooks Brady, Andrea Resti, and Andrea Sironi, “The Link Between Default and Recovery Rates: Theory, Empirical Evidence and Implications,” NYU Working Paper No. S-DRP-03-08, March.
- Alessandri, Piergiorgio, and others, 2009, “Towards a Framework for Quantifying Systemic Stability,” International Journal of Central Banking 5, pp. 47-82.
- Alfaro, Rodrigo A., and Mathias Drehmann, 2009, “Macro Stress Tests and Crises: What Can We Learn,” BIS Quarterly Review December.
- Basel Committee on Banking Supervision (BCBS), 2006, “Basel II: International Convergence of Capital Measurement and Capital Standards: A Revised Framework–Comprehensive Version”, June. http://www.bis.org/publ/bcbs128.htm.
- Basel Committee on Banking Supervision (BCBS), 2010a, “Basel III: A Global Regulatory Framework for More Resilient Banks and Banking System,” December.
- Basel Committee on Banking Supervision (BCBS), 2010b, “Results of the Comprehensive Quantitative Impact Study,” December.
- Breuer,Thomas, Martin Jandacka, Klaus Rheinberger, and Martin Summer, 2009, “How to Find Plausible, Severe, and Useful. Stress Scenarios,” International Journal of Central Banking 5, 205-224.
- Borio, Claudio, and Mathias Drehmann, 2009, “Towards an Operational Framework for Financial Stability: ‘Fuzzy’ Measurement and its Consequences,” in Banco Central de Chile (ed), Financial Stability, Monetary Policy and Central Banking: also available as BIS Working Paper no. 284.
- Boss, Michael, Gerald Krenn, Claus Puhr, and Martin Summer, 2006, “Systematic Risk Monitor: A Model for Systematic Risk Analysis and Stress Testing of Banking Systems,” Austrian National Bank, Financial Stability Report 11.
- Boss, Michael, and others, 2008, “Stress Tests for the Austrian FSAP Update 2007: Methodology, Scenarios and Results,” Austrian National Bank, Financial Stability Report 15.
- Čihák, Martin, 2007, “Introduction to Applied Stress Testing,” IMF Working Paper 07/59 (Washington: International Monetary Fund).
- Djankov, Simeon, Caralee McLiesh, and Andrei Shleifer, 2007, “Private Credit in 129 Countries,” Journal of Financial Economics 84, pp. 299–329.
- Drehmann, Mathias, Steffen Sorensen, and Marco Stringa, 2008, “The Integrated Impact of Credit and Interest Rate Risk on Banks: An Economic Value and Capital Adequacy Perspective,” Bank of England Working Paper No. 339.
- Eisenberg, Larry K. and Thomas H. Noe, 2001, “Systemic Risk in Financial Systems,” Management Science, Vol. 47(2): pp. 236–249.
- Elsinger, Helmut, Alfred Lehar, and Martin Summer, 2006, “Risk Assessment for Banking Systems,” Management Science, Vol. 52(9), pp. 1,301–1,314.
- Federal Reserve Board of Governors, 2007, “Draft Federal Register Notice,” p. 119.
- Financial Stability Institute, 2010, “2010 FSI Survey on the Implementation of the New Capital Adequacy Framework—Summary of Responses to the Basel II Implementation Survey,” Occasional Paper No 9, August.
- Foglia, Antonella, 2008, “Stress Testing Credit Risk: A Survey of Authorities' Approaches,” Banca d’Italia, Occasional Papers no. 37, December.
- Goodhart, Charles A.E., Pojanart Sunirand, and Dimitrios P. Tsomocos, 2003, “A Model to Analyze Financial Fragility,” London School of Economics, Discussion Paper 417.
- Gordy, Michael and Eva Lütkebohmert, 2007, “Granularity Adjustment for Basel II.” Deutsche Bundesbank Discussion Paper (Series 2), No 1, 2007.
- Gray, Dale F., Zvi Bodie, and Robert C. Merton, 2007, “New Framework for Measuring and Managing Macrofinancial Risk and Financial Stability,” NBER Working Paper No. 13607
- Hardy, Daniel, and Christian Schmieder, “Rules of Thumb to Stress Test Credit Risk,” Forthcoming IMF Working Paper.
- Mager, Ferdinand, and Christian Schmieder, 2009, “Stress Testing German Credit Portfolios,” Journal of Risk Model Validation 3(3), pp. 61-77.
- Moody’s, 2009, “Corporate Default and Recovery Rates”, 1920-2008, Special Comment, February.
- Schmieder, Christian, and others, 2011, “Second Generation Applied Stress Testing—Liquidity Module,” Forthcoming IMF Working Paper.
- Schmieder, Christian and Philipp Schmieder, 2011, Impact of Legislation on Credit Risk—Comparative Evidence From the United States, the United Kingdom, and Germany, “IMF Working Paper 11/55 (Washington: International Monetary Fund).
- Schuermann, Til, 2004, “What Do We Know About Loss Given Default?” Working Paper 04-01, Wharton Financial Institutions Center Working Paper Series, www.defaultrisk.com/pp_recov_40.htm.
- Standard & Poor’s, 2010, “Default, Transition, and Recovery: 2009 Annual Global Corporate Default Study and Rating Transitions”.

*Source: _wp1183 - Appendix I.1 Adoption of Foundation and Advanced IRB (Survey Carried out by — content as provided).*

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