## Introduction to Applied Stress Testing ## Source details **Canonical URL:** [Introduction to Applied Stress Testing](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2007/_wp0759.pdf) ## Other formats - [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2007/_wp0759.pdf.md) - [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2007/_wp0759.pdf.json) --- ### Abstract, Purpose, and Scope - Stress testing: method for analyzing resilience of financial systems to adverse events; paper aims to demystify stress tests and illustrate strengths and weaknesses. - Approach: Excel-based, institution-by-institution exercise using a small fictional banking system (Bankistan) and accompanying Stress Tester 2.0.xls. - Focus: system-oriented stress tests on bank-by-bank data; introduction emphasizing application to actual data rather than a comprehensive cookbook. - Core messages: - Assumptions matter; transparency of assumptions and robustness checks are essential. - Stress testing stages are not strictly sequential; iterative modification is common. - JEL Classification Numbers: G10, G20. - Keywords: stress testing, financial soundness indicators, early warning systems. ### Bankistan: Macroeconomic and Banking Sector Background (Box 1) - Macroeconomy and policy: - Real activity: sharply contracting. - Inflation: almost doubled to 65 percent. - Government deficit: more than doubled in 2005. - Central bank financing: sharp increase accelerating money growth. - Monetary policy: expansionary measures (e.g., lowering reserve requirements) → excess liquidity → treasury bill rates dropped from 60 percent to below 15 percent → real interest rates sharply negative. - Exchange rates: - Official exchange rate: fixed at 55 B$/US$. - Black market exchange rate: depreciated from about 60 B$/US$ to about 85 B$/US$. - Banking sector condition and asset quality: - Reported high capital adequacy ratios overstated due to insufficient provisioning. - Gross NPLs to total loans: increased from 15 percent at end-2004 to 20 percent at end-2005. - Banking system structure: - 12 banks: three state owned (SB1–SB3), five domestic private (DB1–DB5), four foreign-owned (FB1–FB4). - Data coverage and units: - All data relate to end-2005 unless indicated otherwise. - Data expressed in millions of Bankistan dollars (B$), except ratios (percent). ### Stress Tester 2.0: Tool Design and Workbook Contents - Accompanying file: Stress Tester 2.0.xls; capital letters A–H denote spreadsheet order; numbers denote table order. - Cell color coding: - Yellow: data reported by National Bank of Bankistan (NBB) — found only in “Data” worksheet. - Blue: sizes of shocks to risk factors — Assumptions worksheet. - Green: numerical assumptions (parameters) — Assumptions worksheet. - No background: formulas linked to yellow/green/blue cells; results update automatically. - Yellow stripes: consistency checks. - Green/white and blue/white stripes: imported numerical assumptions editable with caution. - Workbook: nine worksheets — Read Me, Data, Assumptions, Credit Risk, Interest Risk, FX Risk, Interbank, Liquidity, Scenarios. - Key worksheet tables (selected): - Data: Table A1–A6 (basic balance sheet/income statement, prudential indicators, FSIs, sector structure, supervisory rankings, conversion of rankings into PDs). - Assumptions: Table B (all assumptions; charts illustrating sensitivity). - Credit Risk: Table C1 (asset quality) and Table C2 (credit stress tests: 1–4). - Interest Risk: Table D1 (repricing buckets) and Table D2 (interest rate stress). - FX Risk: Table E1 (direct FX exposure) and Table E2 (indirect FX shock via FX loans). - Interbank: Table F1 (net interbank exposures), Table F2 (pure contagion), Table F3 (macro contagion). - Liquidity: Table G1 (proportional liquidity drain), Table G2 (liquidity contagion). - Scenarios: Table H1–H4 (combined shocks, post-shock FSIs, post-shock ratings, post-shock PDs). ### Stress Testing Framework and Stages - Conceptual process: - (i) identify vulnerabilities; - (ii) construct scenario; - (iii) map scenario outputs to balance sheet/income statement formats; - (iv) perform numerical analysis; - (v) consider second round effects; - (vi) summarize and interpret results. - Modular implementation: - External shocks → Macroeconomic model → Satellite model → Balance sheet implementation → Impacts (e.g., capital injection as percent of GDP) → Feedback-effects module. ### Credit Risk: Shocks, Calibration, and Examples - Four credit shocks in Stress Tester 2.0: - Credit Shock 1: Adjustment for Underprovisioning — align reported regulatory capital to economic net worth via corrective provisioning. - Credit Shock 2: Increase in NPLs — default settings: NPL increase value cell B46 = 25 (percent); total additional NPLs (cell B50) = B$ 2,206 million. - Bank-by-bank allocation options: proportional to existing NPLs (default) or proportional to performing loans (alternative: required NPL increase ≈ 4.3 percent of performing loans; state-owned banks’ post-shock capital examples: cell C53 = B$ -437 million under default allocation; alternative allocation yields cell C53 = B$ -296 billion in source example). - Provisioning and RWA weighting adjustable via green cells (e.g., B40, B48, B49). - Credit Shock 3: Sectoral Shocks — target sectors (e.g., tourism, trade); shocks allocated proportional to banks’ exposures to sectors; interface cells B43–B49 in Assumptions connect econometric outputs to balance-sheet implementation. - Credit Shock 4: Concentration Risk — failure of largest counterparties and provisioning for those failures; applicable to exposures to nonbank financial institutions if data available. - Prescribed loan provisioning rules (Credit Shock 1 example): - 1 percent general provision for pass loans. - 3 percent general provision for special mention loans. - 20 percent specific provision for sub-standard loans. - 50 percent specific provision for doubtful loans. - 100 percent for loss loans. - Collateral valuation assumption: actual collateral value assumed to be 25 percent of reported values (75 percent haircut). ### Interest Rate Risk: Direct and Indirect Effects - Direct interest rate risk: - Flow impact from repricing gap across three repricing buckets: <3 months, 3–6 months, 6–12 months. - Stock impact from marked-to-market valuation of bond holdings using duration; durations calculated in Assumptions rows 57–59. - Duration gap formulations: duration of assets D_A and liabilities D_L; simplified impact equation links change in capital adequacy to duration gap and interest rate changes under ΔA_RW/A_RW = ΔA/A. - Indirect interest rate risk: - Higher nominal interest rates can raise real rates, increasing borrowers’ repayment stress and NPLs; typically estimated via regression linking interest rates to NPLs. - Combined interest rate and credit shocks simulated in Scenarios worksheet. ### Foreign Exchange Risk: Direct and Indirect Channels - Direct FX risk: - Measured by net open position in foreign exchange (core FSI) and linear approximation linking exchange rate change to capital change (useful for small changes; option positions can be nonlinear). - Bankistan example: assumed depreciation from 55 B$/US$ to parallel market 85 B$/US$; direct depreciation effects small and some banks benefit. - Supervisory ceilings on net open positions: typically 10–20 percent of capital. - Indirect FX risk: - Exchange rate changes affect corporate leverage (D_c/E_c) and via parameter a link to changes in NPL/TL (Δ(NPL/TL)/Δ(D_c/E_c) = a > 0). - Empirical reference: IMF (2003) panel of 47 countries — 10 percentage point rise in corporate leverage associated with 1.1 percentage point rise in NPL/TL after one year lag. - Stress Tester 2.0 Table E2 approximates change in NPLs proportional to volume of FX loans per bank. ### Interbank Contagion: “Pure” and “Macro” Tests - Net interbank exposure matrix derived for 12 banks; converted to creditor exposures by taking positive entries. - “Pure” contagion (Table F2): - Simulate failure of each bank; unpaid interbank borrowing reduces counterparties’ capital; iterative contagion allowed. - Simplifying rule: banks with positive capital after an iteration repay obligations; if negative → fail and do not repay. - Example systemically important bank by criterion: FB2 yields post-shock systemic capital B$ 3,570 million (cell B138) and post-contagion CAR 9.7 percent (cell B152). - Interbank loans risk weight default: 20 percent (cell B77). - “Macro” contagion (Table F3): - Starts from post-shock capital/RWA from macro scenario (Scenarios sheet); initial failures triggered by macro shock feed into contagion iterations. - Bankistan example default iteration sequence: first iteration failures SB2 and SB3 → second iteration failures SB1, DB1, DB2 → third iteration failure DB4 → stops after third iteration. ### Liquidity Tests and Liquidity Contagion - Liquidity measures presented as number of days a bank could survive a liquidity drain without external liquidity. - Two tests: - Table G1 — proportional withdrawals across banks based on demand and time deposit volumes; user-configurable percentage withdrawal per day and convertibility of assets per day. - Table G2 — liquidity contagion / flight to safety: run originates in smallest/weakest banks (safety measures: total assets; assets with premium for state ownership; pre-shock rating); can combine government bond default impact by changing assumed share of government bonds in default. - Practical rule of thumb: some supervisors view 5 days as threshold for survival in a liquidity run. ### Scenarios: Combining Risk-Factor Shocks and Presentation - Scenarios worksheet (Tables H1–H4): - Table H1: summary of combined credit, interest rate, exchange rate, and liquidity shocks and comparison of impact on profits (allows autonomous shock to profits/net interest income). - Table H2: post-shock financial soundness ratios. - Table H3: post-shock ratings. - Table H4: post-shock probabilities of default. - Scenario presentation: - Impacts decomposed into individual risk-factor contributions (percentage points of CAR). - Charts in Assumptions show baseline (black), post-shock (red), and post-shock after contagion (yellow) CAR values. - Users choose alternative specifications via green cells B69–B75 in Assumptions; charts update automatically. - Scenario selection approaches: - Worst case approach: for a chosen plausibility level, find most damaging combination. - Threshold approach: for a given impact threshold (e.g., CAR = 0), find most plausible combination reaching it. - Box 5 caution: simply adding aggregate losses overlooks concentration of risks; bank-by-bank calculations reveal concentration and allow mapping to supervisory ratings and PDs (though PDs do not aggregate easily to a system measure). ### Presentation Variables and Metrics (Appendix II excerpts) - Common impact variables and considerations: - Capital (absolute B$) — links to macroeconomy via Other Items Net but needs scaling for comparability. - Capitalization (capital/equity to assets or to RWA) — scaled comparison across banks. - Capital injection needed (for example as percent of GDP) — upper bound on fiscal cost. - Profits and profit buffer — average annual profits over last 10 years used as first line of defense; profit buffers shown separately. - Profitability ratios (ROE, ROA) — scaled comparisons. - Net interest income and components — can be stressed separately. - Z-score: z ≡ (k + μ) / σ where k = equity capital (% of assets), μ = average after-tax return (% of assets), σ = standard deviation of after-tax return on assets; higher z implies lower insolvency probability. - Loan losses — easier in top-down but may understate impact if buffers concentrated in weak institutions. - Liquidity indicators — measure survival and liquidity stress rather than solvency. - Ratings and probabilities of default (PDs) — combine solvency and liquidity into single measures; example step-function conversion used in Stress Tester 2.0: - rating 1 → 0.1 percent PD per year, - rating 2 → 1 percent PD per year, - rating 3 → 5 percent PD per year, - rating 4 → 30 percent PD per year. - Solvency assessment metric in Stress Tester 2.0: - Capital adequacy ratio (CAR) metric; Bankistan supervisory minimum CAR assumed 10 percent (user-changeable; cell B71 in Assumptions). - Basel original minimum CAR: 8 percent (noted). - Government capital injection formula (accounting relationship and derived expression): - Definitions: C = existing total regulatory capital; RWA = existing risk-weighted assets; I = capital injection; q = percentage of capital injection immediately used to increase RWA; ρ = regulatory minimum CAR (ρ = 10 percent in Bankistan example). - Piecewise outcome: - I = 0 if CRWA ≥ ρ RWA (source phrasing retained as context clarifies variables). - Otherwise I = (ρ RWA − C)/(1 − ρ q). - If q = 0 and ρ = 10 percent (Bankistan), then I = 0.1*RWA – C. - Parameters ρ and q adjustable in Assumptions (green cells B71 and B72); q>0 increases necessary injection, though impact generally small. ### Data Limitations, Methodological Choices, and Implementation Modalities - Top-down vs bottom-up: - Top-down disadvantage: may miss concentration and interbank linkages. - Bottom-up advantage: captures concentrations and contagion; disadvantage: data and computational complexity. - Common practice: combine approaches — estimate macro-to-loss mapping on aggregate data, implement bank-by-bank in Stress Tester 2.0. - Centralized vs decentralized implementation: - Centralized (single center like central bank): focused on macro linkages, consistent implementation, better contagion/network analysis. - Decentralized (banks run their own tests): richer modeling using internal data, but aggregation may misstate systemic impacts and contagion; recommended to complement decentralized with centralized calculations. - Data and input considerations: - Time to repricing (not residual maturity) is key for interest rate risk (e.g., a 20 year mortgage repricing every 6 months treated as 6-month instrument). - Off-balance-sheet items, option delta equivalents, and bank-to-bank exposures (matrix) required for contagion analysis. - For scarce data, reduced-form or mechanical approaches, calibration from other countries, or expert judgment may be used (see Box 3 / reduced-form methods). ### Use in FSRs and FSAPs; Prevalence and Recommendations - Use in FSRs (survey highlights): - As of end-2005, share of central banks’ FSRs that included summaries of stress tests ≈ "75 percent" (Čihák, 2006). - Appendix Table 1 survey statistics (percent of FSRs): - Stress testing included — 55 - Stress testing follows a recent FSAP — 38 - Credit risk stress testing included — 55 - Interest rate risk stress testing included — 45 - Exchange rate risk stress testing included — 33 - Other risks included — 33 - Scenario analysis included — 38 - Contagion analysis included — 10 - Credit risk based on an econometric model — 8 - FSAP practice and evolution: - All FSAPs include some form of stress testing; trend toward scenario analysis, greater involvement of authorities and institutions, more contagion inclusion. - IEO review: overall quality high but recommended clearer disclosure of limitations and “health warnings.” - Recommendations for FSRs and FSAPs: - Make greater use of scenarios and justify assumptions. - Integrate impacts and buffers (capital, profitability) and present institution-level outcomes. - Place greater focus on liquidity tests and contagion analysis. - Employ more stressful scenarios and justify assumptions; use threshold approach complementarily. - Improve data collection (loan-level exposures by sector, off-balance-sheet items) and model calibration (satellite models linking macro to credit outcomes). ### Practical Aids, Pedagogy, and Suggested Extensions - Pedagogical materials: boxes, figures, tables, Appendix I tasks for hands-on exercises with Excel file; fictional Bankistan serves as realistic non-confidential dataset for workshops. - Suggested extensions for advanced users: - Econometric estimation of macro-to-credit relationships. - Additional risk modules: asset price risk, commodity risk, longer multi-period frameworks. - Interface modules with external macroeconomic models. - Expand number of institutions and sophistication (credit VaR, factor models, combined structural bank models). *Source: Introduction to Applied Stress Testing, Martin Čihák, IMF Working Paper WP/07/59, March 2007 (content as provided).* ### Introduction to Applied Stress Testing ### Introduction to Applied Stress Testing ### Abstract and Purpose - Stress testing is a method for analyzing the resilience of financial systems to adverse events; the paper aims to demystify stress tests and illustrate their strengths and weaknesses. - The paper uses an Excel-based, institution-by-institution exercise to walk readers through stress testing for credit risk, interest rate and exchange rate risks, liquidity risk, and contagion risk, and guides the design of stress testing scenarios. - The paper describes links between stress testing and other analytical tools, such as financial soundness indicators and supervisory early warning systems, and includes surveys of stress testing practices in central banks and the IMF. - JEL Classification Numbers: G10, G20. - Keywords: stress testing, financial soundness indicators, early warning systems. ### Scope, Approach, and Key Messages - Focus: system-oriented stress tests carried out on bank-by-bank data, demonstrated with a small, non-complex fictional banking system (Bankistan). - Emphasis on application to actual data; the paper is an introduction rather than a comprehensive “stress testing cookbook.” - Core message: assumptions matter in stress testing; transparency of assumptions and robustness checks are essential. - The paper highlights that stress testing stages are not necessarily sequential and iterative modification of components is common. ### Accompanying Tool: Stress Tester 2.0 - The accompanying Excel file is titled “Stress Tester 2.0.xls” and is an essential part of the document. - References to Excel tables use the convention: capital letters A–H denote spreadsheet order and numbers denote table order within a spreadsheet (e.g., Table A2). - The file groups and highlights assumptions (in blue and green) for transparency. - Users should be proficient in operating standard Excel files and should have read the document; knowledge of intermediate macroeconomics is useful. ### Stress Testing Process (Framework and Stages) - Stress testing can be conceptualized as a process including: - (i) identification of specific vulnerabilities or areas of concern; - (ii) construction of a scenario; - (iii) mapping scenario outputs into formats usable for balance sheet and income statement analysis; - (iv) performing the numerical analysis; - (v) considering any second round effects; - (vi) summarizing and interpreting the results. - The exercise in the paper models stress tests used in Financial Sector Assessment Program (FSAP) missions but is simplified for workshop use. ### Structure of the Document (Contents Overview) - The document contains 10 sections, 3 appendixes, and an accompanying Excel file. - Section coverage (by section number): - I. Introduction - II. Overview of the File and of the Stress Testing Process - III. Understanding And Analyzing the Input Data - IV. Credit Risk - V. Interest Rate Risk - VI. Foreign Exchange Risk - VII. Interbank (Solvency) Contagion Risk - VIII. Liquidity Tests and Liquidity Contagion - IX. Scenarios - X. Conclusions and Extensions - Appendixes: - Appendix I: Questions for the Hands-On Exercise - Appendix II: Stress Testing in Financial Stability Reports - Appendix III: Stress Testing in the Financial Sector Assessment Program ### Practical Coverage and Topics Demonstrated - Input data discussion includes coverage of stress tests, balance sheets, income statements, and other input data; indicators of financial sector soundness and structure; ratings and probabilities of default. - Credit risk tests demonstrated include: Credit Shock 1 (“Adjustment for Underprovisioning”), Credit Shock 2 (“Increase in NPLs”), Credit Shock 3 (“Sectoral Shocks”), Credit Shock 4 (“Concentration Risk”). - Interest rate risk treatment includes direct and indirect interest rate risk. - Foreign exchange risk treatment includes direct and indirect foreign exchange risk. - Interbank contagion is split into “Pure” interbank contagion and “Macro” interbank contagion. - Liquidity tests and liquidity contagion are demonstrated. - Scenario design topics include designing consistent scenarios, linking stress tests to rankings and probabilities of default, and modeling feedback effects. ### Pedagogical and Practical Aids - The paper includes concrete pedagogical material: - Boxes (examples and methodological notes), Figures (frameworks, illustrative charts), and Tables (file worksheet descriptions). - Appendix I contains tasks and questions to support workshops or self-practice with the Excel file. - Appendix II gives an overview of stress tests in selected financial stability reports. - Appendix III overviews stress tests in FSAP missions. - A fictional country, Bankistan, is used to provide realistic but non-confidential data for hands-on exercises. ### Limitations and Extensions - The paper covers basic versions of the most common stress tests; more sophisticated systems may require elaborations such as econometric estimation of relationships or modules for additional risks (asset price risks, commodity risks). - The accompanying file is modular and can be extended to capture additional risks or elaborate existing ones. *Source: Introduction to Applied Stress Testing, Martin Čihák, IMF Working Paper WP/07/59, March 2007.* ### Box 1. Background Information on Bankistan’s Economy and Banking Sector ### Box 1. Background Information on Bankistan’s Economy and Banking Sector ### Macroeconomic environment - Real activity is sharply contracting. - Inflation has almost doubled to 65 percent. - Unsustainable fiscal imbalances and loose monetary conditions were key to the deteriorating situation. - The government deficit more than doubled in 2005. - A sharp increase in central bank financing of the government has significantly accelerated money growth. ### Policy response and interest rates - Expansionary monetary policy measures (e.g., a lowering of reserve requirements) have induced a further easing of liquidity conditions. - Excess liquidity induced a drop in treasury bill rates from 60 percent to below 15 percent. - With inflation at 65 percent, real interest rates are sharply negative. - (Note: This is used for assessing interest rate risk.) ### Exchange rate and foreign exchange risk - Official exchange rate: fixed at 55 B$/US$. - Black market exchange rate depreciated from about 60 B$/US$ to about 85 B$/US$ in recent months. - (Note: This is important information for assessing foreign exchange risk.) ### Banking sector condition and asset quality - The deteriorating macroeconomic environment has put considerable strain on the financial condition of the banking system. - Some banks have been weakened considerably and are prone to further deterioration given the significant risks. - Reported high capital adequacy ratios were found to be overstated due to insufficient provisioning. - (Note: This information is used for the assessment of asset quality.) - Asset quality has deteriorated: the ratio of gross nonperforming loans (NPLs) to total loans increased from 15 percent at end-2004 to 20 percent at end-2005. - (Note: This information will be used for assessing credit risk.) - An assessment of compliance with the Basel Core Principles for Banking Supervision (BCP) suggests existing loan classification and provisioning rules are broadly adequate but not well implemented; banks are underprovisioned. ### Banking system structure - The banking system consists of 12 banks: - Three state owned: code names SB1 to SB3. - Five domestic privately owned banks: DB1 to DB5. - Four foreign-owned banks: FB1 to FB4. - The banking system, particularly the state-owned banks, have been plagued by a large stock of NPLs and weak provisioning practices. - Data on the structure and performance of the 12 banks are provided in the “Data” sheet of the accompanying Excel file. ### Stress testing framework and workbook (general design) - Focus: calculate bank-by-bank impacts from external shocks and express impacts in variables such as capital adequacy or capital injection as a percent of GDP. - Modular design: - External shocks → Macroeconomic model (links to GDP, interest rates, exchange rate). - Macroeconomic variables → Satellite model (maps to banks’ asset quality, ideally bank-by-bank). - Satellite model + macro model → Balance sheet implementation → Impacts (e.g., capital injection needed). - Results cells (e.g., capital injections as a percent of GDP) can interface with a feedback-effects module. ### Data coverage and units - All data in the file relate to end-2005, unless indicated otherwise. - Data are expressed in millions of Bankistan dollars (B$), except for ratios (shown in percent). ### Color coding of workbook cells - Yellow: data reported by the National Bank of Bankistan (NBB); found only in the “Data” worksheet. - Blue: assumed sizes of shocks to risk factors (e.g., an increase in interest rates); found only in the Assumptions worksheet. - Green: numerical assumptions (parameters) of the stress test; found only in the Assumptions worksheet. - No background (normal black font): formulas linked to yellow, green, and blue cells; results recalculated automatically when inputs change. - Yellow stripes: consistency checks (sums or other functions of input data). - Green/white stripes: numerical assumptions imported from the Assumptions sheet; editable but may break links if saved. - Blue/white stripes: numerical assumptions imported from the Assumptions sheet; editable with caution to avoid breaking links. ### Workbook contents and worksheet descriptions - The file contains nine worksheets: Read Me, Data, Assumptions, Credit Risk, Interest Risk, FX Risk, Interbank, Liquidity, and Scenarios. - Data worksheet: - Six tables; input data as compiled by the NBB (collected in March 2006 and generally relate to end-December 2005). - Table A1: basic balance sheet and income statement data. - Table A2: other prudential indicators important for the stress tests. - Table A3: FSIs (key ratios based on input data). - Table A4: structure of the banking sector. - Table A5: institution-by-institution rankings using a supervisory early warning system calibrated by the NBB. - Table A6: converts rankings into probabilities of default. - Assumptions worksheet: - One table (Table B) putting together all assumptions; contains charts to see how changes affect results. - Credit Risk worksheet: - Two tables: Table C1 (reported data on asset quality) and Table C2 (credit risk stress test). - Credit risk stress test components: (1) correction for underprovisioning of NPLs; (2) an aggregate NPL shock; (3) a sectoral shock; (4) a shock for credit concentration risk (large exposures). - Interest Risk worksheet: - Two tables: Table D1 sorts assets and liabilities into three time-to-repricing buckets; Table D2 shows the corresponding interest rate stress test. - Interest rate test components: (1) flow impact from gap between interest sensitive assets and liabilities; (2) stock impact from repricing of bonds. - FX Risk worksheet: - Two tables: Table E1 (foreign exchange exposure and direct exchange rate risk shock); Table E2 (indirect foreign exchange shock using FX loans to approximate impact on credit quality). - Interbank worksheet: - Three tables: Table F1 (matrix of net interbank exposures); Table F2 ("pure" interbank contagion from one bank failing to repay obligations); Table F3 ("macro" contagion where failures result from modeled macro shocks). - Liquidity worksheet: - Two tables: Table G1 models a liquidity drain affecting all banks proportionally; Table G2 models "liquidity contagion" with faster drains in banks perceived similarly weak by depositors and allows testing liquidity impact of government default. - Scenarios worksheet: - Four tables: Table H1 (summary of combined credit, interest rate, exchange rate, and liquidity shocks and comparison of impact on profits with allowance for an autonomous shock to profits); Table H2 (post-shock financial soundness ratios); Table H3 (post-shock ratings); Table H4 (post-shock probabilities of default). ### User guidance and further development - Yellow cells in “Data” should be replaced when new NBB data arrive to automatically recalculate results. - Users can change blue (shock sizes) and green (parameters) cells in the Assumptions worksheet to observe impacts; charts in Assumptions provide graphical feedback. - Green/white and blue/white striped cells allow in-sheet edits but may break links if saved. - Expert users are invited to suggest improvements or develop the file further (e.g., new risk types, more realistic modeling, more institutions, multi-period framework); modules can interface with external macroeconomic models. *Source: Box 1. Background Information on Bankistan’s Economy and Banking Sector (content as provided).* ### Appendix II for a more detailed overview of stress tests in FSRs). ### _wp0759 - Appendix II for a more detailed overview of stress tests in FSRs) ### Top-down versus bottom-up approaches - Disadvantages of top-down: - Applying tests only to aggregated data can overlook concentration of exposures at the level of individual institutions and linkages among institutions, and therefore risks that failures in a few weak institutions can spread to the rest of the system. - Advantages and disadvantages of bottom-up: - Should capture concentration of risks and contagion and generally lead to more precise results. - May be hampered by insufficient data and by calculation complexities; detailed institution-by-institution exposures can lead to insurmountable computational problems in large and complex systems. - Common practice: - Most macroprudential stress tests try to combine advantages and minimize disadvantages of both approaches. - Example workflow: use a model estimated on aggregate data to map macroeconomic shocks into an increase in nonperforming loans; use Stress Tester 2.0 to calculate how this aggregate impact influences individual banks and the system. ### Centralized versus decentralized implementation - Centralized approach (illustrated in the spreadsheet): - All calculations done in one center (e.g., central bank, supervisory agency, or IMF expert). - Advantages: (i) more focused on linkages to macroeconomic factors; (ii) better integration of credit and market risks; (iii) consistent implementation across institutions; (iv) better analysis of correlation across institutions (inter-portfolio correlation); (v) ability to analyze network effects (contagion). - Less refined for computational complexity and data availability reasons. - Decentralized approach (often used in advanced-country FSAPs): - Involves banks themselves in carrying out stress testing calculations. - Advantages: richer, more detailed modeling using wider data and banks’ risk management expertise and capacity. - Disadvantages: may not sufficiently reflect contagion effects among banks; aggregating individual banks’ results may misstate systemic impacts; ensuring consistent implementation of assumed shocks across many banks can be a major challenge. - Recommendation: - Even if decentralized calculations are carried out, complement them with centralized calculations as discussed here. ### Variables that can be used to present stress test impacts - General criteria: variable should (i) be interpretable as a measure of financial soundness, and (ii) be credibly linked to the risk factors. - Commonly used variables (advantages and cautions preserved): - Capital - Motivation: material impact on solvency; commercial banks’ capital is part of Other Items Net in monetary surveys, facilitating links to financial programming. - Disadvantage: capital in absolute terms (B$) needs comparison to other indicators (e.g., risk-weighted assets, GDP). - Accompanying Excel file illustrates presentation in terms of capital. - Capitalization (capital or equity to assets, or capital to risk-weighted assets) - Scaled measure allowing comparison across institutions of different size. - Disadvantage: change in capitalization does not by itself indicate macroeconomic relevance; needs accompaniment by other measures. - Accompanying Excel file uses capitalization as a key indicator. - Capital injection needed (for example as a percentage of GDP) - Direct link to macroeconomy; provides an upper bound on potential fiscal costs of bank failures. - Accompanying Excel file illustrates capital injection. - Profits - Baseline profits are first line of defense before dipping into capital; expressing shocks only in terms of capital may overestimate impacts if banks were profitable in baseline. - Accompanying Excel file indicates the “profit buffer” based on the average annual profits over the last 10 years and allows a separate “test” for an autonomous shock affecting profits or net interest income. - File shows profit buffers as a separate item rather than directly deducting impacts from profits. - Profitability (return on equity, assets, or risk-weighted assets) - Scaled by bank size, enabling comparison across banks. - Excel file shows profit buffers as ratios to risk-weighted assets. - Net interest income and other profit components - Can be stressed separately; net interest income relates more directly to interest rates and may be amenable to econometric analysis. - Provides only a partial picture of economic value and resilience. - Z-scores - Formula: z≡(k+μ)/σ, where k is equity capital as percent of assets, μ is average after-tax return as percent on assets, and σ is standard deviation of the after-tax return on assets. - Interpretation: number of standard deviations a return realization must fall to deplete equity under normality assumption; higher z-score implies lower probability of insolvency. - Accompanying Excel file illustrates z-score presentation (including peer-group z-scores), with caution that portfolio-level translations may overlook contagion. - Loan losses - Easier to implement in top-down calculations. - Drawback: does not take into account banks’ buffers (profits and capital) and may underestimate overall impact if losses concentrate in weak institutions. - Liquidity indicators - Liquidity stress tests measure impacts in terms of liquidity indicators rather than solvency measures. - Excel file illustrates liquidity presentation. - Ratings and probabilities of default (PDs) - Combine solvency and liquidity risks into a single measure; can model how changes in variables translate into rating or PD changes. - Excel file illustrates this presentation. - Market-based indicators (e.g., relative prices of securities, distance to default for bank stocks, credit default swap premia) - Advantages: higher frequency than accounting data. - Disadvantages: lack of sufficiently deep markets in many countries; bank stocks may be untraded or illiquid. - Limited work linking market-based indicators to macroeconomic variables for stress tests. ### How results are presented in Stress Tester 2.0 - Two main questions addressed by each stress test: 1. Which banks could withstand the assumed shocks and which ones would fail? 2. What are the associated potential costs for the government given the failure of banks in times of stress? - Solvency assessment example: - Capital adequacy ratio (CAR) used as assessment metric. - Basel original minimum CAR: 8 percent. - Bankistan supervisors assume minimum CAR of 10 percent; whenever a bank’s CAR falls below 10 percent, owners are obliged to inject capital or the bank is closed and license withdrawn. - CAR below 0 indicates negative capital and insolvency. - Note: the 10 percent minimum is an assumption in Stress Tester 2.0 contained in cell B71 of the “Assumptions” worksheet and is user-changeable. - Total capital may differ from regulatory capital; workbook uses the same numbers for simplicity but allows differences between equity and regulatory capital. - Profits and profit buffer: - Stress Tester 2.0 allows profits to be taken into account. - Profit buffer: based on average annual profits over the last 10 years; file allows separate test of autonomous shocks to profits or net interest income. - Profit buffers are shown as a separate item (to permit a prudent alternative of disregarding profits). - Some banks may have non-existent or negative profit buffers. - Government capital injection calculation: - Accounting relationship used: - ρ = (C + I)/(RWA + q I) (expressed in the source as ρ = + / qIRWA IC; context clarifies variables) - Definitions: C = existing total regulatory capital; RWA = existing risk-weighted assets; I = capital injection; q = percentage of capital injection immediately used to increase RWA; ρ = regulatory minimum CAR (ρ = 10 percent in Bankistan). - Derived expression for necessary capital injection: - I = 0 if CRWA ≥ ρ RWA - Otherwise I = (ρ RWA − C)/(1 − ρ q) (expressed in source as the piecewise formula with q and ρ terms) - Specific illustrative case: - If q = 0 and ρ = 10 percent (Bankistan), then I = 0.1*RWA – C. - Parameters ρ and q are assumed and changeable in Stress Tester 2.0 (green cells B71 and B72 in “Assumptions” worksheet). - If ρ is lower than 10 percent, necessary capital injection is lower, and vice versa; if q>0 (RWA increase with capital), necessary capital injection is higher, though impact of q changes is generally small. ### Understanding and analyzing the input data; coverage and peer groups in the example - “Data” sheet summarizes input data as reported by the NBB and shows key ratios and illustration of off-site supervisory assessment tables. - Coverage in example: - Stress tests cover all 12 commercial banks in the country. - FSAP practice: only a minority of FSAPs have covered all banks; most cover a subsample of large banks accounting for generally 70–80 percent of system assets. - Trade-offs: including all banks is more comprehensive and favored by supervisors; excluding others can be practical for computational complexity and for macroprudential users focusing on systemically important institutions. - Peer-group analysis in Stress Tester 2.0 example: - 12 banks grouped into 3 peer groups by ownership: - State-owned banks: SB1 to SB3 - Domestic privately-owned banks: DB1 to DB5 - Foreign-owned banks: FB1 to FB4 - Alternative groupings possible (e.g., by size or financial performance). - Treatment of foreign banks: - Example has foreign banks only through locally-incorporated subsidiaries. - Branches typically do not have their own capital against which shocks could be shown; impacts for branches should be expressed in other variables (e.g., profits) if separate data are available. - Scope focus: - This document mirrors FSAPs and FSRs by focusing on banks and banking systems, as banks tend to dominate financial systems and are key to systemic risk assessment. - Some FSAPs and FSRs have included explicit stress tests of insurance companies and pension funds; stress testing these sectors can be complex and may involve different risk modeling approaches. *Source: Appendix II text from _wp0759 - Appendix II for a more detailed overview of stress tests in FSRs).* ### Box 2. Stress Tests for Insurance Companies ### Box 2. Stress Tests for Insurance Companies ### Risks Addressed by Insurance Sector Stress Testing - Underwriting risk: - rapid growth or decline in underwriting portfolio - uncertainty of the claims experience - length of tail of the claims development - dependence on intermediaries - possibility of reinsurance rates increasing substantially - uncertainty in pricing in new or emerging underwriting markets - geographical mix of the portfolio - tolerance for variations in expenses - Catastrophe risk: - ability to withstand catastrophic events, increases in unexpected exposures, latent claims or aggregation of claims - possible exhaustion of reinsurance arrangements - appropriateness of catastrophe models and underlying assumptions - Deterioration of technical provisions: - adequacy and uncertainty of technical claims provisions and other underwriting provisions - frequency and size of large claims; outcomes of disputed claims (legal proceedings) - effects of inflation; effects of increasing longevity on pension products - guarantees and options in policy terms; risks of early policy termination linked to interest rate variations - social, economic, legislative, and technological changes - Market risk: - adverse movement in the value of an insurer’s assets and liabilities affected by market movement - modeling similar to banking - Credit risk: - failure of counterparties (debtors, brokers, policyholders, reinsurers, guarantors) - modeling similar to banking - Liquidity risk: - inability to realize assets to fund obligations as they fall due - modeling similar to banking - Other risks: - operational risk, group risk, and systemic risk (e.g., impact of failures/downgrades in other insurers or banks) Note: This list is based broadly on IAIS (2003). ### Incorporating Failures in Nonbank Financial Institutions - Failures in nonbank financial institutions can be assessed as part of credit risk. - Two methods provided in the accompanying Excel file: - Incorporate nonbank financial institutions as one sector in sectoral credit risk; run a stress test for a certain percentage of loans to the nonbank financial sector becoming nonperforming. - Incorporate as part of large exposures tests: if data on largest exposures of banks to nonbank financial institutions are available, run a test on banks’ solvency should their largest counterparties in the nonbank financial sector fail. ### Balance Sheets, Income Statements, and Other Input Data - Tables A1 and A2 in the “Data” worksheet illustrate typical data needed for stress tests (not minimum requirements). - Data layout in the file: - first data column: aggregated data for whole banking system - next three columns: aggregated data for three peer groups (state banks, private domestic banks, foreign banks) - remaining twelve columns: data for individual banks - Top part of “Data” worksheet (Table A1) contains balance sheets and income statements; aggregated and peer group data can be calculated as sums of bank-by-bank data (interbank exposures disregarded initially; addressed later in interbank contagion risk). - Table A2 lists additional key input data for system aggregate, peer groups, and individual banks: - (i) regulatory capital and risk-weighted assets - (ii) asset quality and structure of lending by sector and by size of borrower - (iii) provisioning and collateral (for credit risk calculation) - (iv) structure of assets, liabilities, and off-balance sheet items by time to repricing - (v) structure of the bond portfolio (for interest rate risk calculation) - (vi) net open positions in foreign exchange and lending in foreign currency (for foreign exchange solvency risk) - (vii) average profits and standard deviation of profits over time (to measure “baseline” profitability) - (viii) liquidity structure of assets and liabilities (for liquidity risk calculation) - (ix) bank-to-bank uncollateralized exposures, presented in matrix form (for interbank solvency contagion risk) - Data sources and caveats: - Most Table A2 data usually available through standard regulatory returns. - Stress tests analyze economic position (net worth) and this may differ from reported regulatory capital due to overvalued assets or liabilities treated as capital; analysts should adjust input data for such biases (file shows an example when banks underprovision their nonperforming loans). - Input data should reflect off-balance sheet positions (e.g., net open FX positions should reflect delta equivalents of FX options). - Bank-to-bank exposure data may be difficult to collect; approximate calculations (e.g., exposure to rest of system as a whole) can be used but may overlook exposures. - For interest rate risk, time to repricing is important: a 20 year mortgage with rate repricing every 6 months should be treated like a 6 month fixed rate loan from an interest rate risk perspective; using maturity or residual maturity as proxy for time to repricing can overstate interest rate risk. - Additional data for other risks: - Equity price risk and commodity price risk require data on net open positions in equities and commodities. - Breakdown of assets and liabilities by residual maturity/time to repricing and currency is needed to perform stress tests separately for foreign currency. ### How To Do Stress Tests When NPLs or Other Input Data Are Unavailable (Box 3) - Rudimentary stress tests can be performed with basic financial statements over a sufficient number of periods, using observed or assumed relationships between risk factors, income statement items, and balance sheet items. - Examples: - Interest rate risk: regress past net interest income of individual banks on interest rates and other variables; use estimated slope coefficient(s) to translate interest rate changes into impact on profits (and potentially capital). If long time series unavailable, slope coefficients can be calibrated using expert information or experience from other countries. - Credit provisioning: regress provisions for loan losses on risk factors and other explanatory variables to analyze impact on profitability. - Reduced-form stress tests: - If individual financial statement items are unavailable, but reliable time series exist, reduced-form tests can use capital, asset, and return data over time to calculate z-score as proxy for individual bank soundness. - z-scores can be regressed on macroeconomic variables (e.g., real GDP growth rate, interest rate, exchange rate) and bank-level variables (e.g., asset size, loan to asset ratio). Resulting slope coefficients map macro scenarios into z-scores. - Challenge: aggregating bank-by-bank soundness data into a system-wide indicator (see Čihák, 2007). ### Indicators of Financial Sector Soundness and Structure - Table A3 contains core FSIs and other ratios characterizing the banking sector and components; ratios provide a summary of soundness for sector, peer groups, and individual banks. - z-score definition and usage: - z ≡ (k + μ) / σ - where k is equity capital as a percent of assets - μ is average after-tax return as percent on assets - σ is standard deviation of the after-tax return on assets (proxy for return volatility) - z-scores are linked to probability of a bank’s insolvency. - Table A3 shows z-scores for peer groups using a methodology similar to translating bank-by-bank distance to default measures to a “portfolio distance to default”; calculations should be treated with caution as they may overlook contagion. - Banking sector structure (Table A4) highlights: - share of foreign-owned banks is relatively high—about 55 percent in terms of assets, and 83 percent in terms of capital - total assets as ratio to GDP is used to indicate banking system size relative to the economy and to put into perspective capital injections needed to meet minimum capital adequacy requirement. ### Ratings, Probabilities of Default, and Supervisory Early Warning Systems - Tables A5 and A6 combine banking sector ratios into institution-by-institution rankings using a supervisory early warning system. - Off-site supervisory ranking example (NBB): - system has three thresholds for each indicator determining numerical rankings (1 best to 4 worst) - rankings for individual variables are weighted (weights provided in the “Assumptions” worksheet) to derive an overall ranking - Conversion from rankings to probabilities of default (Table A6) uses a “step function”: - bank with rating of 1: 0.1 percent probability of default in a given year - bank rated 2: 1 percent probability of default - bank rated 3: 5 percent probability of default - bank rated 4: 30 percent probability of default - Parameters of step functions: - sometimes based on expert estimates - supervisory agencies may “back-test” systems to check identification of failed or intervention-needed institutions; re-estimated parameters should be entered in row 22 of the “Assumptions” worksheet - Back-testing example (Figure 3): - using two variables (capital adequacy and gross NPL to total loans) and one threshold per variable, the early warning system can reduce Type II errors: from 88 percent (15/17 without thresholds) to 33 percent (1/3 for the subset identified by thresholds) while capturing all failed banks (eliminating Type I errors). ### Credit Risk: Approaches and Credit Shock 1 - Credit risk is central to banking; three basic modeling approaches for credit risk in stress tests: - Mechanical approaches (used when insufficient data or shocks differ from past ones) - Approaches based on loan performance data and regressions (e.g., probabilities of default, losses given default, NPLs, provisions; single equation, structural, VAR) - Approaches based on corporate sector data (e.g., leverage, interest coverage) and possibly household sector data - The exposition starts with mechanical approaches and extends to more realistic ones; Box 4 discusses links between credit risk and macroeconomic risk. - Worksheet “Credit Risk”: - Table C1 summarizes reported data for asset quality - Table C2 includes credit risk stress tests with four different types of credit shocks labeled 1, 2, 3, and 4 - Credit Shock 1 (“Adjustment for Underprovisioning”): - Purpose: align stress testing focus on economic value (net worth) rather than reported regulatory capital - Reported capital may include items that are not true capital or may overstate assets - Analysts should adjust reported data to better reflect baseline economic situation before applying stress tests - Credit Shock 1 is presented as an example of such an adjustment (a starting-point adjustment rather than a stress test per se); if reporting already reflects economic value, no adjustment is needed and one can proceed to Credit Shock 2 and beyond *Source: Box 2. Stress Tests for Insurance Companies, _wp0759 - Box 2. Stress Tests for Insurance Companies* ### Box 4. Linking Credit Risk and Macroeconomic Models ### Box 4. Linking Credit Risk and Macroeconomic Models ### Literature and empirical approaches - Econometric linkages between credit risk and macroeconomic variables have been applied across countries and contexts, including: - Pesola (2005): Nordic countries, Belgium, Germany, Greece, Spain and the UK (early 1980s to 2002). - IMF (2003): broader cross-country analysis. - Boss (2002) and Boss and others (2004): Austria. - Virolainen (2004): Finland — macroeconomic credit risk model estimating probability of default by industry. - Norges Bank (Eklund, Larsen, and Berhardsen, 2003): single-equation models for household debt and house prices; corporate bankruptcies model. - Peng and others (2003); Gerlach, Peng, and Shu (2004): Hong Kong SAR (aggregate and panel approaches). - Babouček and Jančar (2005): Czech Republic — vector autoregression with nonperforming loans and macro variables. - FSAP missions commonly employ similar models (example: Spain FSAP regression explaining nonperforming loans with financial sector and macro indicators). ### Issues in interpreting macroeconomic credit-risk models - Dominance of linear statistical models; linearity may be reasonable for small shocks but non-linearities are likely important for large shocks (doubling the shock may more than double the impact). - Micro-level models and macro analysis (Drehmann, 2005) report nonlinear links between shock scale and default likelihood. - Models are subject to the Lucas critique; parameters/functional forms may become unstable under major stress (example: de-pegging in a currency-board regime makes past-data models unreliable). - In extreme or structural-change scenarios, calibration using parameters based on experience from other countries may be preferable. ### Credit shock framework (Stress Tester 2.0) - Credit Shock 1: corrective provisioning to meet existing provisioning requirements. - Prescribed loan provisioning rules: - 1 percent general provision for pass loans - 3 percent general provision for special mention loans - 20 percent specific provision for sub-standard loans - 50 percent specific provision for doubtful loans - 100 percent for loss loans - Collateral valuation assumption: actual collateral value assumed to be 25 percent of reported values (i.e., a 75 percent “haircut” on collateral). - Credit Shock 2 (“Increase in NPLs”): - Models a general decline in asset quality, affecting all banks proportionately. - Assumption: nonperforming loans (NPLs) increase by a certain percentage; default values being 25 percent of the existing stock of NPLs (i.e., additional provisioning by 25 percent for each of substandard, doubtful, and loss loans). - Impact on RWA and capital: increased provisioning reduces both RWA and capital; default assumption often that full increase in NPL is subtracted from RWA, but user can adjust assumed weight (e.g., from 100 percent to 80 percent) via green cell (B40) in “Assumptions”. - Bank-by-bank allocation options: - Proportional to existing NPLs (default). - Proportional to overall stock of loans or to stock of performing loans. - Green cells allow choosing weights for existing NPLs and performing loans (cells B48 and B49 in “Credit Risk”). - Numerical example (default settings): - Default NPL increase value in cell B46 = 25 (percent). - Total volume of additional NPLs (cell B50) = B$ 2,206 million. - State-owned banks’ post-shock capital (cell C53) = B$ -437 million. - Alternative allocation (increase proportional to performing loans, keeping total additional NPLs equal to B$ 2,206 million via goal-seek): - Required NPL increase ≈ 4.3 percent of performing loans. - State-owned banks’ post-shock capital (cell C53) = B$ -296 billion. - Policy implication: distribution of credit risks and buffers across banks affects fiscal costs significantly. - Credit Shock 3 (“Sectoral Shocks”): - Allows shocks targeted to economic sectors; bank impact depends on banks’ exposures to sectors (approximated by total loans to that sector). - Example scenario in file: “terrorist attack” increasing credit risk in tourism and trade sectors. - Calibration can be historical scenario or econometric model; interface cells for linking econometric outputs to balance-sheet implementation: B43–B49 in “Assumptions”. - Sectors can be redefined (e.g., households, nonfinancial enterprises, nonbank financial institutions, government). - Increase in NPLs assumed proportional to bank’s credit exposure to the sector; can relax to reflect existing NPLs or total loans to each sector. - Credit Shock 4 (“Concentration Risk”): - Tests failure of largest counterparties per bank by changing assumed number of failures and provisioning rate for those failures. - Can be applied to banks’ exposures to NBFIs if supervisors have such data. ### Interest rate risk - Direct interest rate risk: - Calculated in two parts reflecting flow and stock impacts. - Flow impact: repricing gap (assets/liabilities) across three repricing buckets (due in less than 3 months, due in 3 to 6 months, due in 6 to 12 months). - Stock impact: marked-to-market valuation of bond holdings using duration; bond duration data provided by NBB and calculated with Excel “Duration” function (cells H58 and H59). - Definitions and formulas: - Duration of assets (D_A) and liabilities (D_L) defined as weighted average term-to-maturity. - First-order approximations shown (equations (1)–(4)); duration gap GAP_D specified; simplified impact equation (3) relates change in capital adequacy to duration gap and interest rate changes, assuming ΔA_RW/A_RW = ΔA/A. - Typical banking structure: D_A >> D_L, r_A > r_L, GAP_D > 0; increase in interest rates typically reduces net worth and capitalization. - Bankistan example: two government-issued bonds available; durations calculated in “Assumptions” rows 57–59. - Indirect interest rate risk: - Higher nominal interest rates can increase real interest rates and weaken borrowers’ ability to repay, raising credit risk (positive relationship found in country case studies between higher interest rates and NPLs or loan losses). - Assessment typically requires regression estimating the impact of interest rate changes on NPLs. - Combined impact of interest rate and credit quality changes can be simulated in the “Scenarios” worksheet. ### Foreign exchange (FX) risk - FX risk categories: direct solvency risk (banks’ net open positions), indirect solvency risk (borrowers’ FX positions affecting creditworthiness), and FX liquidity risk. - Direct FX risk: - Measured using net open position in foreign exchange (core FSI); example methodology linking change in exchange rate e to change in capital through net open position F and capital C (equations (5)–(6)). - Linear approximation useful for small changes; option positions can induce strong non-linearities. - Bankistan example: assumed depreciation from official exchange rate of 55 B$/US$ to parallel market rate of 85 B$/US$ (at constant cross exchange rates to the US$). - Observation: very limited number of banks have short positions; direct depreciation effects small and some banks benefit. - Supervisory limits: net open positions often limited as percent of capital, ceilings typically in the range of 10–20 percent of capital. - Indirect FX risk: - Exchange rate changes affect corporate competitiveness and corporate balance sheets via net FX positions, influencing corporate leverage (D_c/E_c) and thereby NPL/TL ratio. - Analytical relationships provided: - Change in corporate leverage due to FX: equation (7). - Corporate leverage linked to NPL/TL via parameter a: Δ(NPL/TL)/Δ(D_c/E_c) = a > 0. - Resulting change in NPL/TL due to FX: equation (8). - Impact on capital adequacy, assuming provisions are fixed percentage π of NPLs and deducted from capital: equation (9). - Empirical reference: IMF (2003) — panel of 47 countries shows a 10 percentage point rise in corporate leverage associated with 1.1 percentage point rise in NPL/TL after one year lag. - Practical implementation in Stress Tester 2.0: Table E2 approximates change in NPLs proportional to volume of foreign exchange loans in a bank. ### Interbank (solvency) contagion risk - Framework: - Matrix of net interbank credits derived for twelve banks in Bankistan; positive cell = column bank is net creditor to row bank; diagonal cells empty. - Converted into net interbank exposures by focusing on positive numbers (creditor exposures). - “Pure” interbank contagion (Table F2): - Series of 12 separate stress tests simulating failure of each bank and impact on other banks’ capital through unpaid interbank borrowing. - Iterative contagion: first iteration failures can lead to further failures in subsequent iterations. - Simplifying assumption: if a bank’s capital remains positive after an iteration it repays obligations; if negative it fails and does not repay. - Example outcomes: - Two banks would fail as a result of others’ failures: DB1 can fail as result of failures in SB2 or FB3 (cells I62 and I71); DB2 can fail as result of failures in SB1, SB2, FB1, and FB3 (cells J61, J62, J69, and J71). - Interbank loans’ risk weight assumed at 20 percent by default (cell B77 in “Assumptions”), reflecting typical Basel weight. - Systemic importance metric: decline in system capital or CAR when individual bank fails. Example: FB2 is most systemically important by this criterion because its assumed failure yields lowest post-shock systemic capital B$ 3,570 million (cell B138) and post-contagion CAR 9.7 percent (cell B152). - “Macro” interbank contagion (Table F3): - Starts from post-shock capital and RWA from macro scenario in “Scenario” sheet; failures triggered by macro shock are inputs to contagion iterations. - Bankistan default settings example: - First iteration simultaneous failures: SB2 and SB3. - Second iteration failures triggered: SB1, DB1, and DB2. - Third iteration failure: DB4. - Process stops at third iteration (no further failures). - Key difference vs “pure” test: “macro” test accounts for varying likelihoods of failure across banks induced by common external shocks. ### Liquidity tests and liquidity contagion - Liquidity testing is less common than solvency testing due to data and modeling complexity, but important because stress often manifests as liquidity runs. - Stress Tester 2.0 liquidity measures: - Presentation: number of days each bank could survive a liquidity drain without external liquidity. - Two example tests in “Liquidity” worksheet (Figure 5 illustrates results): - Table G1 — proportional withdrawals: liquidity drain affecting all banks proportionally based on demand and time deposit volumes; user can change percentage withdrawal per day and percentage of liquid/convertible assets per day. - Table G2 — liquidity contagion / flight to safety: run starts in smallest or weakest banks; three measures of bank safety available: - total assets; - total assets with premium for state ownership; - pre-shock rating. - Table G2 can combine liquidity impact of government default with a bank run by changing assumed percentage of government bonds in default. - Practical rule of thumb: some supervisors view 5 days as important threshold for bank survival in a liquidity run (gives “breathing time” for management and supervisors), though internet/direct banking has diluted this. ### Scenarios and combining shocks - “Scenarios” worksheet (Tables H1–4) shows how to combine shocks across risk factors because macro changes are interrelated (e.g., nominal interest rate increases can raise real rates and NPLs). - The worksheet aggregates impacts from “Credit Risk”, “Interest Risk”, “FX Risk”, “Interbank”, and “Liquidity” sheets into an aggregate impact on capital adequacy. - Users can select alternative specifications via green cells B69–75 in “Assumptions”; summary of chosen scenario shown atop Table H. - Presentation: - Impacts shown in terms of capital adequacy and decomposed into individual risk-factor contributions (in percentage points of the CAR ratio). - Charts in “Assumptions” show baseline (black), post-shock (red), and post-shock after contagion (yellow) CAR values. - Comparison with banks’ profits included; users can assume autonomous shock to net interest income in a green cell. - Scenario design approaches: - “Worst case approach”: for given level of plausibility, which scenario has worst impact on system. - “Threshold approach”: for a given impact on system, what is most plausible combination of shocks required to cause that impact. *Italic: Box 4. Linking Credit Risk and Macroeconomic Models — extracted from the provided source content.* ### Box 5. Can We Add The Impacts of Shocks? ### Box 5. Can We Add The Impacts of Shocks? ### Combining shocks and concentration of risks - Simply adding up aggregate losses from individual shocks can overlook concentration of risks in institutions. - Stress Tester 2.0 calculates impacts bank-by-bank to reveal that some banks can be hit much harder than others. - Combining solvency and liquidity risks is nontrivial; Stress Tester 2.0 uses the NBB’s supervisory early warning system to: - combine changes in solvency and liquidity (and other measures), - identify the change in the supervisory rating, - infer the implied change in probability of default (PD). - Limitation: the PDs cannot be easily aggregated for the system as a whole, though the approach provides a useful illustration. ### Scenario selection: worst case approach vs. threshold approach - Illustration context: simplified case with two risk factors (e.g., changes in interest rates and exchange rates). - Geometric interpretation: - Each ellipse depicts combinations of the two risk factors with the same probability of occurrence; ellipse shape reflects correlation, size reflects plausibility (larger ellipse = smaller plausibility). - Diagonal lines depict combinations leading to the same overall impact, measured by change in the system’s capital adequacy ratio (CAR). Impact increases with size of shocks, so CAR decreases in the northeast direction. - Diagonal lines can be nonlinear; depicted straight here for simplicity. - Worst case approach: - Select a level of plausibility (example: 1 percent). - Search the combination of shocks with this plausibility that has the worst impact (point on the largest ellipse as far northeast as possible — point A in Figure 7). - Threshold approach: - Select a threshold (a diagonal line, e.g., CAR = 0%). - Search for the most plausible (smallest) shocks reaching this threshold. - With the specific correlation pattern in Figure 7, selecting a threshold of zero capital adequacy leads to the combination corresponding to point A. - Calibration guidance: - For risk factors with good historical time series (particularly market risks), base scenarios on past volatility and covariance patterns. - Single-factor calibration example: an exchange rate shock can be based on 3 standard deviations of past exchange rate changes (corresponding roughly to a 1 percent confidence level). - With multiple risk factors, use covariance statistics or stochastic simulations based on macroeconomic models. - Caveat: models can break down for large shocks; use cautiously as a first-cut approximation. ### Box 6 — Picking the ‘Right’ Scenario (summary) - Theoretical ideal: scenarios should be internally consistent; in practice, consistency assessment is tricky because scenarios must be exceptional but plausible. - Approaches: - Historical extreme scenario (e.g., East Asian crisis of 1997): - Advantages: easy to communicate and implement; plausible because it happened. - Disadvantages: past crises may not model future crises; probability level of the historical scenario may be unclear. - Macroeconomic model–based stochastic simulations: - Often require a “satellite” model linking credit risk measures (e.g., nonperforming loans to total loans) to macro variables. - Satellite model should be estimated on individual bank (or borrower) data when available; used for balance sheet implementation. - Direct plotting of observed risk factors against a soundness measure (e.g., CAR) to identify most stressful combinations (north-east-most points in Figure 7). - Practical emphasis: - A range of methods exists; choose a scenario that is stressful and tells a consistent story. - Identifying “the right scenario” is often infeasible — more important are: - (i) transparency about underlying assumptions; - (ii) transparency about sensitivity of results to assumptions; - (iii) showing how results with the same assumptions change over time. ### Linking stress tests to rankings and probabilities of default - The “Scenarios” sheet illustrates links between stress tests and the supervisory early warning system using post-shock bank-by-bank data. - Workflow: - Table H2: post-shock FSIs and other ratios for individual banks (compared with pre-shock ratios in Table A3). - Table H3: converts post-shock ratios into post-shock supervisory ratings using the same “step functions” applied pre-shock (specified in “Assumptions” worksheet, rows 3-22). Table H3 provides averages weighted by banks’ total assets for three peer groups and the system. - Table H4: converts post-shock ratings into post-shock probabilities of default for each bank (compare with pre-shock PDs in Table A6). - Visualizations: - Figures 8 and 9: charts showing baseline (black) and stress (red) values for ratings and PDs; stress values reflect default sizes of shocks and starting assumptions. - Figure 10: shows impact of stress on banks’ z-scores (higher z-scores correspond to lower PDs); z-scores decline under stress, generally mirroring increases in PDs shown in Figure 9. - User interactivity: changing key shock sizes and assumptions in the accompanying Excel file updates the charts automatically. ### Modeling feedback effects - Focus of presented stress tests: impacts of macroeconomic shocks on the financial sector. - Important macro question: do financial-sector shocks feed back to the macroeconomy? - Practical modeling limitations: numerous potential feedback channels; only some are tractable. - Directly incorporable effect in the Fund’s financial programming framework: impact on capital via “Other Items Net” in the monetary survey and consequent effects on other macro variables. - Other channels: asset fire-sales (e.g., real estate) lowering asset prices and affecting sectors such as household consumption; bank failures causing credit crunches. - Approximation used in the Excel example: - Capital injection needed to bring all banks to the minimum required capital adequacy ratio is used as a proxy for potential macroeconomic impacts. - This indicator is an upper-bound estimate of potential fiscal costs to avert failures. - Public sector likely to inject capital preferentially into state-owned banks; injections into privately owned banks are less certain and more likely for larger banks considered “too big to fail.” - Charts in the “Assumptions” worksheet (reproduced as Figure 11) show capital injection breakdown by ownership, reflecting default shock sizes and assumptions. ### Conclusions, main challenges, and recommended steps - Hands-on stress testing is essential for understanding stress testing mechanics; users can change assumptions and observe results. - Stress tests complement other financial stability tools: - Complementary to FSIs for benchmarking under no stress and for describing impact of stress. - Complementary to supervisory early warning systems for producing ratings and PDs under stress. - Complementary to assessments of compliance with regulatory standards and to evaluation of the broader financial stability framework (financial safety nets, liquidity support, deposit protection, crisis management). - Main challenges highlighted: - Stress testing is data intensive; low-probability events mean persistent data scarcity and the need for simplifying assumptions — analysts must be transparent about assumptions. - Nonlinearities are likely for large shocks. - Macroeconomic and other models tend to break down in crises; past crises may not be a good guide for the future. - Impact of shocks is distributed over time; deterioration in asset quality and crisis evolution can span many years. Modeling should account for time dimension (example: Bank of England stress tests look at 2–3 years). - Mitigating measures by participants and authorities, and feedback effects, gain importance over longer horizons. - Two main steps to address challenges: - Keep assumptions transparent and show sensitivity of results to assumptions. The accompanying file centralizes assumptions and allows experimentation. - Present stress test results over time to identify changes in the overall pool of risks and the structure of risks. Stress Tester 2.0 is a one-period snapshot intended to be run repeatedly with updated input data. - Suggested extensions (select): - Credit risk–macro nexus: - Need more detailed data on loan exposures and loan performance by economic sector and data on corporate and household financial soundness. - Use time series of historical data to establish linkages between macro variables and loan performance; if unavailable, use estimates from other countries. - The exercise conveys the gist of credit risk stress testing without full technical detail; more granular implementation is desirable. *Source: Box 5. Can We Add The Impacts of Shocks? (from the supplied IMF content unit).* ### Box 4 provided references to studies that analyzed this nexus in more detail. ### _wp0759 - Box 4 provided references to studies that analyzed this nexus in more detail. ### Stress-testing methodologies and model types - Credit VaR models - Purpose: determine the probability distribution of losses on a portfolio of loans and other debt instruments to compute economic capital required by credit operations. - Implementation challenges at the macroprudential level: - (i) less banks use them; - (ii) risk factors and their parametrization differ across banks, complicating comparability and aggregation. - Feasibility: implementing credit risk models on a macroprudential level is possible and can provide a useful benchmark (example: Avesani and others (2006) on the CreditRisk+ model). Some recent FSAPs have used these approaches. - Stress-testing based on factor models - Forms: - (i) portfolio risk management models using structural credit risk models of obligors’ assets and risky debt based on domestic and international factor models (examples: KMV portfolio manager models, CreditMetrics, default and conditional probability of default models such as Segoviano and Padilla, 2006); - (ii) Merton-type structural models of banks which calibrate risk-adjusted balance sheets and implied assets of banks linked to domestic and international factor models. - Application: analyze how changes in key international and domestic factors drive individual bank risk and systemic risk. - Coverage: applicable to banking systems in "30 or so" middle and some low income countries and to banking systems in developed countries. - Combined structural bank model with interest rate term structure model - Objective: assess impact of interest rate level, interest rate volatility, and asset–interest rate correlations on individual bank risk and systemic risk. - Example: Shimko-Tejima-van Deventer model for bank soundness and capital adequacy (e.g., Belmont, 2004). - Other risk-factor stress tests - Depending on financial system sophistication and exposures, include asset price shocks (e.g., real estate prices) and commodity price shocks (especially for developing countries with significant commodity exposures). ### Hands-on exercise: credit, interest rate, FX, liquidity, contagion, and scenario construction - Credit risk exercises (examples of questions) - Underprovisioning: identify undercapitalized or insolvent banks after applying provisions; compute government capital injection needed to restore capital asset ratio to required minimum of 10 percent; test sensitivity to provisioning rates (example alternative provisioning rates: 2 percent for pass loans and 5 percent for special mention loans vs. Bankistan's 1 percent and 3 percent). - Increase in NPLs: identify banks that cannot withstand a 25 percent increase in NPLs; compute government capital injection to restore 10 percent CAR; consider the effect if only 0 percent risk-weight assets (government bonds) are affected. - Sectoral shocks: identify banks most exposed to shocks to tourism and agriculture; propose methodological improvements and alternative loan breakdowns. - Large exposures: identify banks most exposed to concentration risk; adapt exercise to model risks from non-bank financial institutions. - Interest rate risk - Identify banks that can withstand an increase in interest rates and those that would fail; estimate potential government costs; discuss weaknesses and remedies for interest rate risk calculations. - Foreign exchange (FX) risk - Direct FX risk: on basis of a depreciation rate of 55 percent, identify banks that can withstand the shock and those that would fail or be undercapitalized; estimate potential government costs. - Indirect FX risk: assess how inclusion of indirect FX risk changes stress-test results; examine ways to make indirect FX incorporation more realistic (reference to Table E2). - Liquidity risk - Model different withdrawal rates for domestic and foreign currency deposits; identify additional variables to approximate depositor perceptions and how to model them; improve realism of government default tests. - Interbank contagion - Compute the impact of further contagion iterations (third iteration) in "pure" and "macro" contagion exercises; incorporate bank profits into contagion exercises; account for failures of banks with positive but small capital adequacy ratios. - Creating consistent scenarios - Assess consistency of shocks across three risk factors in worksheet scenarios; evaluate reasonableness given macroeconomic vulnerabilities; adjust scenarios for consistency. - Compare vulnerability across peer groups and sensitivity to assumptions on profits and shocks to net interest income. ### Use of stress testing in Financial Stability Reports (FSRs): prevalence, characteristics, and gaps - Prevalence and evolution - As of "end of 2005", the share of central banks’ FSRs that included summaries of stress tests was about "75 percent" (Čihák, 2006). - Typical pattern: early FSRs omit stress tests; stress tests are included in subsequent reports as central banks become comfortable with presentation. - Observation: a number of central banks may conduct internal stress tests without publishing results. - Common features and data coverage - Stress tests in FSRs tend to cover either all banks or virtually all in terms of market share; other financial sectors are covered much less often (exceptions exist). - A majority of stress tests are based on bank-by-bank data; central banks without supervisory access often rely on top-down approaches or non-supervisory data. - Risk coverage frequency: - Credit risk is covered in almost all stress tests. - Interest rate risk is covered in most stress tests. - Exchange rate risk is covered in some FSRs, often only as discussions of open foreign currency positions rather than formal stress tests. - Methodologies commonly used - Most stress tests in FSRs are sensitivity calculations; some include scenario analysis (historical or hypothetical); few use econometric models. - Inclusion of indirect exchange rate effects and contagion is rare; when included, contagion exercises are often basic and based on net interbank market exposures. - Virtually all surveyed FSR stress tests have been positive in overall assessment of the financial sector’s stability. - Cross-country variation - There is substantial cross-country variation in size and range of shocks, and in methodologies applied, reflecting differences in financial systems, risks, and data quality. ### Recommendations and improvements for stress testing in FSRs - Make greater use of scenarios - Move beyond narrow single-factor shocks; justify scenarios and relate scenario design to recent history or future risks. - Integrate impacts and buffers - Present impacts in terms of capital, capital adequacy, or profitability rather than only loan loss provisions to assess concentration of risks across institutions. - Importance of institution-level data to carry out this analysis. - Place greater focus on liquidity tests - Solvency tests predominate; explicit liquidity testing is rare but almost as important. - Add contagion analysis - Analyze contagion among banks and between nonbanks and banks. - Requirements: - For insolvency-focused contagion: matrix of net uncollateralized interbank exposures; implement either single-institution failure scenarios or macro-related contagion tests where initial failures are triggered by macroeconomic stress. - For liquidity-run contagion: detailed data on withdrawals in past bank-run episodes. - Employ more stressful scenarios and justify assumptions - Avoid relying on narrow and mild assumptions (e.g., banks earning satisfactory earnings during stress). - Ensure scenario assumptions are consistent across FSRs to allow comparability and to avoid optimistic assumptions during weakness. - Include approaches to defining scenarios that do not start from plausibility alone. - Employ a threshold approach - Complement probabilistic-style scenarios with "threshold approach" tests that ask what shock would be required to reach a specified system threshold (e.g., system capital adequacy of 8 percent or a given share of institutions insolvent). This approach has been used in several FSAPs and FSRs (example: National Bank of Poland’s Financial Stability Review). ### Key statistics and survey findings (Appendix Table 1) - Topic — Percent of FSRs - Stress testing included — 55 - Stress testing follows a recent FSAP — 38 - Credit risk stress testing included — 55 - Interest rate risk stress testing included — 45 - Exchange rate risk stress testing included — 33 - Other risks included — 33 - Scenario analysis included — 38 - Contagion analysis included — 10 - Credit risk based on an econometric model — 8 - Additional contextual figures - Share of FSRs that included summaries of stress tests was about "75 percent" as of the "end of 2005". - Coverage anecdote: stress-testing approaches described can be applied to banking systems in "30 or so" middle and some low income countries. *Source: _wp0759 - Box 4 provided references to studies that analyzed this nexus in more detail.* ### Appendix Table 2. Examples of Stress Te ### Appendix Table 2. Examples of Stress Te ### Country examples (selected rows) - Poland — Coverage: All banks - Main conclusion: The system exhibits high stability. - Credit shock: Three shocks: (i) satisfactory and special mention loans migrate to doubtful; (ii) substandard and doubtful migrate to loss; and (iii) bankruptcy of three largest borrowers. - Interest rate shock: Not a stress test, but an analysis of gains/losses on interest-sensitive instruments, and the maturity of debt securities. - Exchange rate shock: Not a stress test, but an analysis of VaR and open positions. - Other shock: Equity price risk and property market risks analyzed (but without a stress test) - Indirect FX risk: No - Contagion: No - Netherlands 2/ — Coverage: Major fin. institutions (84% banks, 54 % insur.c., 50 % pens.f.) - Main conclusion: Banks are sufficiently shock-resistant. - Credit shock: +/-50 bps change in credit spreads (larger for insurance and pensions) - Interest rate shock: +/-100 bps parallel move; 50 bps flattening/steepening of yield curves (larger for ins&pen) - Exchange rate shock: +/-10 % change in the exchange rate of EUR vs. other currencies - Other shock: +/-15 % change in all relevant stock indices; 25 % increase in market volatilities - Indirect FX risk: Yes, “domestic crisis of confidence, “dollar crisis” - Contagion: No - Norway — Coverage: All banks / seven largest conglome-rates. - Main conclusion: Short-term stability outlook satisfactory. However, increased vulnerability of household sector. - Credit shock: Decline in economic growth, increased unemployment. - Interest rate shock: Interest rates unchanged, but interest burden of real sector increased appreciably. - Exchange rate shock: (not specified as a shock column entry) - Other shock: A fall in property prices reduces mortgage values, causing a rise in loss given default. - Indirect FX risk: Yes, all tied to credit risk. - Contagion: No - Sweden — Coverage: Four major banks - Main conclusion: The major banks improved their potential for coping with shocks. - Credit shock: Failure of the largest counterparty, assumed recovery ratio of 25 percent. - Interest rate shock: Increase in interest rates by 1 pct points, and a 30 percent fall in the stock market. - Exchange rate shock: (not indicated) - Other shock: (not indicated) - Indirect FX risk: No - Contagion: Yes ### Appendix III — Stress testing in the Financial Sector Assessment Program (FSAP): key findings and evolution - Role and practice - Stress tests are a crucial tool of the quantitative part of the stability assessments in the FSAP. - All FSAP missions have included some form of stress tests, ranging from very basic sensitivity assessments to elaborate exercises involving Monte Carlo simulations or models developed by financial institutions themselves. - Tests are tailored to country-specific circumstances, reflecting complexity of the financial system and data availability. - Independent Evaluation Office (IEO) review (Independent Evaluation Office, 2006) - Overall quality of stress testing work was very high. - Reporting often takes a “black-box” approach, with too little discussion of limitations implied by data and methodological constraints and choices on which shocks to analyze. - Recommendation: greater “health warnings” about interpretation of results. - Noted gap between “good practice” modeling approaches and those used in many cases. - Some assessments avoided politically sensitive shocks (e.g., public debt defaults). - Trends over time - Older assessments: mostly single-factor sensitivity analysis, based on historical extremes. - More recent assessments: greater focus on scenario analysis; greater involvement of authorities (including macroeconomic models or micro-level credit models); greater involvement of financial institutions (internal models and value-at-risk calculations); more frequent inclusion of interbank contagion and nonbank financial institutions. ### Quantitative indicators and tables (high-level highlights) - Appendix Table 3. Evolving Role of Stress Testing in the FSAP, 2000–2005 (Percent of all FSAPs Initiated in the Period) - 2000–2002: Scenario analysis 64; Contagion analysis 11; Insurance sector stress testing 25 - 2003–05: Scenario analysis 95; Contagion analysis 38; Insurance sector stress testing 37 - Who conducted calculations in European FSAP stress tests (Appendix Table 4) — examples of institutions involved: - Supervisory agency/central bank: Austria, Belgium, Denmark, Estonia, France, Germany, Hungary, Ireland, Israel, Malta, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, United Kingdom - FSAP team: Belarus, Belgium, Bosnia and Herzegovina, Croatia, Czech Republic, Denmark, Estonia, Iceland, Ireland, Israel, Latvia, Lithuania, Macedonia, Moldova, Norway, Poland, Portugal, Romania, Russia, Slovakia, Slovenia, Serbia, Spain, Ukraine, United Kingdom - Financial institutions: Belgium, Denmark, Estonia, France, Germany, Ireland, Israel, Luxembourg, Malta, Netherlands, Norway, Portugal, Spain, United Kingdom - Institutions covered in European FSAP stress tests (Appendix Table 5) — selected coverages: - All banks (bank by bank): Belarus, Belgium, Lithuania, Moldova, Ukraine - Large/systemically important banks (bank by bank): Austria, Belgium, Bosnia and Herzegovina, Croatia, Czech Republic, Denmark, Estonia, Finland, France, Germany, Hungary, Iceland, Ireland, Israel, Latvia, Luxembourg, Malta, Netherlands, Norway, Poland, Romania, Russia, Slovakia, Slovenia, Serbia, Spain, Sweden, Switzerland, United Kingdom - Insurance companies: Belgium, Denmark, Finland, France, Netherlands, Norway, Portugal, Spain, Sweden, United Kingdom - Pension funds: Netherlands, United Kingdom - Approaches to credit risk modeling (Appendix Table 6) — examples: - NPLs, provisions: historical or macro-regressions: Austria, Czech Republic, France, Iceland, Israel, Russia, Romania, Sweden - NPLs, provisions: ad hoc approaches: Belarus, Bosnia and Herzegovina, Bulgaria, Croatia, France, Hungary, Israel, Latvia, Lithuania, Macedonia, Malta, Moldova, Poland, Serbia, Slovakia, Slovenia, Switzerland, Ukraine - Shocks to probabilities of default based on historical observations or regressions: Austria, Belgium, Denmark, Luxembourg, Russia, Spain - Shocks to probabilities of default (ad hoc): Germany, Netherlands, Norway, United Kingdom - Explicit analysis of cross-border lending: Austria, Spain - Explicit analysis of foreign exchange lending: Austria, Croatia - Explicit analysis of loan concentration: Malta, Netherlands, Russia, Serbia - Interest rate shocks and modeling (Appendix Tables 7–8) — examples of shock sizes and approaches: - Examples of shock sizes (Table 7): 3 standard deviations of 3-month changes; 50%-100% increase; three-fold increase in nominal rate; 100 basis point shock to interest rates; 100 basis point shock to dollar interest rates and a concomitant 300 basis point shock to local currency interest rates; 300 basis point increase - Approaches (Table 8): Repricing or maturity gap analysis (Austria, Belarus, Belgium, Croatia, Czech Republic, Hungary, Lithuania, Macedonia, Malta, Moldova, Poland, Russia, Romania, Serbia, Ukraine); Duration (Belgium, Iceland, Israel, Latvia, Norway, Slovakia, Switzerland); Value at Risk (France, Denmark, Germany, Israel, Netherlands, United Kingdom); Others (Norway, Sweden) - Exchange rate shocks and approaches (Appendix Tables 9–10) — examples: - Shock sizes (Table 9): 20%-50% devaluation; 30% devaluation; 10% depreciation; 20% depreciation/appreciation; 40% depreciation/appreciation of Euro/Dollar exchange rate - Approaches (Table 10): Sensitivity analysis on the net open position (Austria, Belarus, Belgium, Bulgaria, Croatia, Czech Republic, Hungary, Iceland, Latvia, Lithuania, Macedonia, Malta, Moldavia, Norway, Poland, Russia, Romania, Serbia, Slovakia, Slovenia, Sweden, Switzerland, Ukraine); Value at Risk (France, Germany, Israel, Netherlands, United Kingdom) - Other risk modeling approaches (Appendix Table 11) — selected items: - Liquidity risk (ad-hoc decline in liquidity): Austria, Belarus, Belgium, Bosnia and Herzegovina, Germany, Lithuania, Netherlands, Russia, Spain, Ukraine, United Kingdom - Liquidity risk (historical shock): Croatia, France - Shock to main stock market index: Austria, Belgium, Finland, France, Germany, Israel, Latvia, Lithuania, Malta, Netherlands, Norway, Slovakia, United Kingdom - Housing price shock: Netherlands, Norway, United Kingdom, Ukraine - LTV ratios, mortgage PDs: Croatia, Sweden - Commodity price: Finland - Interbank contagion: Austria, Belgium, Luxembourg, Netherlands, Romania, United Kingdom - Slowdown in credit growth: Bosnia and Herzegovina - Country risk: Luxembourg - Competition risk (i.r. margin): Lithuania, Slovenia - Shock to specific sector(s): Belarus, Finland ### Notes, abbreviations, and table notes (as presented) - Abbreviations: NPL ... nonperforming loans, TL ... total loans, pct... percentage, bp ... basis points, st. dev. ... standard deviation, int. rate ... interest rate, EUR ... Euro, USD ... U.S. dollar, CHF ... Swiss Frank, and YEN ... Japanese yen. - Note 2/: The latest FSR contained the stress tests carried out by (or in collaboration with) an FSAP mission. - Note 3/: Based on the FSR at the end 2003. The subsequent two FSRs presented only the “stress CAR,” which shows a bank’s financial position in a situation where all NPLs are written off. - Source of Appendix Table 2 and accompanying text: The author, based on central banks’ recent financial stability reports. Austrian National Bank: Financial Stability Report 7, June 2004. Danmarks Nationalbank: Financial Stability 2003. Deutsche Bundesbank: Report on the Stability of the German Financial System, Monthly Report, October 2004. De Nederlandsche Bank: Overview of Financial Stability in the Netherlands, December 2004, Issue No. 1. Hungarian National Bank: Report on Financial Stability, June 2003. National Bank of Poland: Financial Stability Review, First Half of 2004. Norges Bank: Financial Stability, 2004:1, June 2004. Sveriges Riksbank: Financial Stability Report, 2004:2. *Source: Excerpt from the PDF content provided.* --- _Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2007/_wp0759.pdf_