## _wp04127

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---

### I. Introduction — Purpose and scope
- Designed as guidance for central bank or supervisory officials asked to “stress test the financial system.”
- Intended to answer basic process questions: what stress testing means, what is involved, and where to begin.
- Not focused on technical aspects; intended as a reference at the beginning of the stress-testing process.
- Structure:
  - Section II: discussion of stress testing in a financial system context.
  - Section III: overview of the stress-testing process.
  - Section IV: IMF experience in FSAPs.
  - Section V: conclusions.

### II. A brief overview of stress testing
- Why do a stress test?
  - Provides information on behavior of the system under exceptional but plausible shocks.
  - Helps assess significance of system vulnerabilities.
  - Value added derives from a consultative process integrating:
    - a forward-looking macroeconomic perspective,
    - focus on the financial system as a whole,
    - a uniform approach to the assessment of risk exposures across institutions (IMF and World Bank (2003)).
  - Complements institution-level stress tests and cross-checks other analyses.
  - Identifies weaknesses in data collection, reporting systems, and risk management.
  - Helps increase expertise in risk assessment and promotes cooperation across regulatory institutions.
  - Contributes to understanding links between financial sector and macroeconomy.
- What is a stress test?
  - At portfolio level: measures sensitivity of a portfolio to extreme but plausible shocks.
  - Described as a rough estimate of how portfolio value changes when large changes are made to risk factors; the term “rough estimate” emphasizes lack of scientific precision.
  - Involves judgments and assumptions; each choice can introduce wide margins of error.
  - Originally for trading-book market risks; now used broadly to assess groups of institutions or entire systems.
  - “System-focused” stress tests:
    - More macroeconomic in orientation, aiming to identify common vulnerabilities across institutions.
    - Involve greater aggregation and heterogeneity.
    - Are not a replacement for institution-level testing but a complement.
    - Can be implemented as simultaneous stress tests of multiple portfolios using a common scenario, or a single scenario applied to an aggregated portfolio/model of the entire system.
    - Where feasible, conducting both approaches provides maximum information on vulnerabilities.
- Methodological notes:
  - Stress tests estimate exposure to a specific event, but not the probability of that event.
  - Stress testing requires Annex I data requirements and other technical references (Blaschke and others (2001); Laubsch (1999)).

### III. The stress-testing process — stages and practical guidance
- Overall view:
  - Stress testing is a process: investigative, diagnostic, numerical, and interpretive.
  - Typical stages:
    - identification of vulnerabilities,
    - construction of a scenario within a consistent macroeconomic framework,
    - mapping scenario outputs into balance-sheet and income-statement impacts,
    - numerical analysis,
    - consideration of second-round effects,
    - summarizing and interpreting results.
  - Stages are iterative, not strictly sequential.
- A. Identifying vulnerabilities
  - First stage: identify main vulnerabilities to focus analysis and resources.
  - Use a mix of qualitative and quantitative elements; narrow focus for refined analysis.
  - Use numerical indicators at multiple levels:
    - macro-level,
    - broad structural indicators,
    - institution-focused or micro-level indicators.
  - A dedicated working group can facilitate the process.

### IV. Box 2 — Using a Working Group to Coordinate the Process
- Purpose and role:
  - Facilitate and coordinate complex interactions among specialists involved in stress testing a financial system.
  - Provide a forum for discussion and coordination of input collection; cross-disciplinary and cross-institutional involvement is crucial.
- Suggested composition — supervisory side:
  - Data collection and analysis (e.g., analyst from early warning systems or off-site supervision).
  - Internal risk models expertise.
  - On-site supervision.
  - Conglomerate supervision where relevant.
  - Nonbank supervision where relevant.
  - Accounting and balance sheet analysis.
- Suggested composition — macroeconomic side:
  - Representatives from macroeconomic modeling or forecasting team.
  - If a macro-econometric model will be used, include someone with in-depth knowledge of the model.
- Working group operations:
  - Periodic plenary meetings; technical sub-groups may meet more frequently.
- Data and indicator guidance — macroeconomic context:
  - Analyze volatile, misaligned, or out-of-equilibrium macro and financial variables to identify shock sources.
  - Relevant sectors and indicators:
    - Real sector: growth performance relative to potential; growth rates for consumption, investment, and incomes; unemployment rates; inflationary pressures on consumer, wholesale, and asset prices; household and corporate measures of indebtedness, leverage, income growth, and debt servicing ability.
    - Government sector: magnitude of the government deficit, debt stock, associated debt sustainability; size of the present fiscal impulse; how the government budget is financed.
    - External sector: magnitude of the current account deficit, official reserves, how the deficit is financed; relative size, maturity structure, and currency composition of external debt; extent of exchange rate misalignment and pressures on the exchange rate.
- Structural indicators to locate risks:
  - Ownership and market shares by institution and type.
  - Balance sheet structures from aggregate financial statements.
  - Flow-of-funds accounts to identify intermediation trends.
- Qualitative information:
  - Institutional and regulatory framework information and discussions with supervisors, regulators, private-sector analysts, and market participants.
- Financial Soundness Indicators (FSIs) — core examples (selected exactly as presented):
  - Regulatory capital to risk-weighted assets — Capital adequacy — Broad measure of capital including items giving less protection against losses, such as subordinated debt, tax credits, unrealized capital gains.
  - Regulatory Tier I capital to risk-weighted assets — Capital adequacy — Highest quality capital such as shareholder equity/retained earnings, relative to risk weighted assets.
  - Nonperforming loans net of provisions to capital — Capital adequacy — Indicates potential size of additional provisions that may be needed relative to capital.
  - Nonperforming loans to total gross loans — Asset quality — Indicates the credit quality of banks' loans.
  - Sectoral distribution of loans to total loans — Asset quality — Identifies exposure concentrations to particular sectors.
  - Return on assets — Earnings/profitability — Assesses scope for earnings to offset losses relative to capital or loan and asset portfolio.
  - Interest margin to gross income — Earnings/profitability — Indicates importance of net interest income and scope to absorb losses.
  - Noninterest expenses to gross income — Earnings/profitability — Indicates extent to which noninterest expenses weaken earnings.
  - Liquid assets to total assets — Liquidity — Assesses vulnerability to loss of access to market sources of funding or a run on deposits.
  - Liquid assets to short-term liabilities — Liquidity.
  - Net open position in foreign exchange to capital — Exposure to FX risk — Measures foreign currency mismatch.
- Encouraged set of FSIs (selected categories and indicators exactly as presented):
  - Deposit-taking institutions: Capital to assets; Large exposures to capital; Geographical distribution of loans to total loans; Gross asset position in financial derivatives to capital; Gross liability position in financial derivatives to capital; Trading income to total income; Personnel expenses to noninterest expenses; Spread between reference lending and deposit rates; Spread between highest and lowest interbank rate; Customer deposits to total (noninterbank) loans; Foreign currency-denominated loans to total loans; Foreign currency-denominated liabilities to total liabilities; Net open position in equities to capital.
  - Other financial corporations: Assets to total financial system assets; Assets to GDP.
  - Nonfinancial corporate sector: Total debt to equity; Return on equity; Earnings to interest and principal expenses; Net foreign exchange exposure to equity; Number of applications for protection from creditors.
  - Households: Household debt to GDP; Household debt service and principal payments to income.
  - Market liquidity: Average bid-ask spread in the securities market; Average daily turnover ratio in the securities market.
  - Real estate markets: Real estate prices; Residential real estate loans to total loans; Commercial real estate loans to total loans.
- Note: Other relevant indicators not formally part of the encouraged set may be added where available and relevant.

### V. Box 3 — Simulations Using Macro Models: Some Considerations
- Baseline assumptions:
  - Baseline could be no change from latest data, or the central forecast or most likely scenario from the most recent forecasting exercise.
- Policy response assumptions:
  - Different policy reaction functions may be embedded (e.g., a Taylor rule), or assume no change in policies.
  - Assuming no policy response typically implies larger macroeconomic effects, depending on model and scenario.
- Time horizon:
  - Quarterly models may produce forecasts over the next six to eight quarters.
  - Shorter horizons desirable when assuming no institutional adjustment.
- Variable fixation and shock selection:
  - Judgment required on which exogenous variables are held fixed.
  - Avoid changing a large number of exogenous variables unnecessarily.
- Shock calibration:
  - Calibrate on historical experience (e.g., largest change over chosen time horizon in last ten years) or hypothetical scenarios (e.g., a 20 percent fall in the exchange rate).
  - Historical experience may be intuitive; structural changes may invalidate historical calibration.
- Top-down vs bottom-up:
  - Bottom-up: portfolio-level responses estimated using disaggregated institution data; advantage: uses individual portfolio data; drawback: potential inconsistencies if institutions produce own estimates.
  - Top-down: derive common parameters from aggregated data; advantage: easier, consistent; drawback: relies on aggregate historical relationships that may not hold.
  - Ideally apply both methods when feasible.
- Execution, scope, and coverage:
  - Individual institutions should be heavily involved where possible.
  - Coverage: broad enough to represent meaningful critical mass while feasible (example: less than twenty).
  - In countries with many small institutions, aggregate or sample smaller institutions.
  - Contagion, interbank, and second-round effects: often not addressed but important; banks following Basel internal-ratings based approaches generally required to have comprehensive stress testing.

### VI. Box 6 — Stress Testing of Corporate Sector
- Overview:
  - Loans to corporate sector often significant; stress testing corporate balance sheets informs credit quality of bank portfolios.
- Key risk sensitivities:
  - Interest rate risk.
  - Foreign exchange rate risk.
  - Macroeconomic cycles (sales and firm income).
- Measuring debt-service capacity:
  - Use interest coverage ratio: earnings before interest, taxes, depreciation, and amortization divided by interest expenses.
  - Firms with interest coverage ratios below one face liquidation, funding needs, renegotiation, or default.
- What stress tests show:
  - Effects of shocks on interest coverage ratios and proportion of firms at risk.
- Calibrating shocks:
  - Scenarios should reflect exceptional but plausible events.
  - Can be based on historical data (e.g., largest observed changes or extreme values over a specified period) or hypothetical large movements.
  - Example calibration: largest change in a risk factor over the past ten years.
  - Joint probability of simultaneous factor movements is the relevant empirical measure.
- Mapping macro scenarios to balance sheets — bottom-up:
  - Two mappings required: macro adjustment to common risk factors; common risk factors to portfolio instruments.
  - Needed financial variables: interest rates (term structure), exchange rates (spot and forward, bilateral and trade-weighted), asset prices, credit exposures and quality.
  - Supplement macro output with term-structure models or equilibrium real exchange rate models as needed.
  - Individual institutions best placed to map risk factors into portfolios.
- Top-down approach:
  - Useful check on bottom-up results and practical where institutions lack capacity.
  - Examples include regression-based and macro-augmented models.
- Second-round effects:
  - Short horizons may justify ignoring behavioral change; longer horizons (a year or more) make ignoring feedback effects harder to justify.
  - Possible second-round effects: direct credit losses from counterparty failures; increased funding costs; portfolio adjustments affecting aggregate demand.
  - Contagion models: two-stage exercise—individual balance sheets then counterparty exposures—to construct systemic risk indices.
- Interpretation and presentation:
  - Stress tests identify latent exposures; regular stress testing tracks changes over time.
  - Common presentation: group aggregate impacts by type of risk/scenario; bottom-up outputs use descriptive statistics and peer-group analysis.
- Publication considerations:
  - Confidentiality and interpretation challenges exist.
  - Useful disclosure practices: publish summary information (mean and range); publish scenarios undertaken.

### VII. Box 7 — Financial Stability Reports
- Overview:
  - Increasing number of central banks produce stand-alone Financial Stability Reports; stress tests commonly published in these reports.
- Selected examples (institution — frequency — first year — stress tests published):
  - Austria — Austrian National Bank — Semi-annually — 2001 — No
  - Belgium — National Bank of Belgium — Annually — 2002 — No
  - Brazil — Central Bank of Brazil — Semi-annually — 2002 — Yes
  - Canada — Bank of Canada — Semi-annually — 2002 — No
  - Denmark — National Bank of Denmark — Annually — 2000 — No
  - Finland — Bank of Finland — Annually — 2003 — No
  - France — Bank of France — Semi-annually — 2002 — Yes
  - Hungary — National Bank of Hungary — Semi-annually — 2000 — No
  - Indonesia — Bank Indonesia — Semi-annually — 2003 — Yes
  - Norway — Bank of Norway — Semi-annually — 1995 — No
  - Sweden — Bank of Sweden — Semi-annually — 1997 — No
  - United Kingdom — Bank of England — Semi-annually — 1995 — No
- FSAP stress-testing role and trends:
  - Stress tests integral to FSAPs; performed for every participating country.
  - Designed to provide quantitative measures of system vulnerability.
  - Most FSAP analyses performed on a bank-by-bank (bottom-up) basis using single factor and scenario approaches.
  - Contagion and second-round effects typically not addressed in many FSAPs, though some include interbank contagion.
  - Recent trends: greater role for country authorities and institutions; increased use of internal models and macro-simulation models; increased coverage of nonbank financial institutions.
- Methodology and data issues:
  - Identify vulnerabilities using macro, structural, and micro indicators.
  - Construct scenarios using historical financial market price data (e.g., ten years of daily data) and macroeconomic time series.
  - Balance-sheet implementation best with institution-by-institution data; sensitivity tests require maturity breakdowns (example buckets include: one day or less, one day to one month, one month to three months, three months to six months, six months to one year, one to five years, over five years), net open position by currency, loan-loss provisions by asset categories, sources and uses of funds by maturity, stock of liquid and near-liquid assets.
  - Data quality considerations: apply IMF’s Data Quality Assessment Framework (DQAF) and adjust balance sheet items where accounting interpretation is in doubt.
- Interpretation, metrics, dissemination:
  - Purpose: identify vulnerabilities and estimate sensitivity of balance sheets to shocks.
  - Two main approaches: bottom-up (individual portfolios) and top-down (aggregated data).
  - Common metrics: tier one capital and total capital; income definitions such as EBITDA; assets measures such as total assets, quick assets, current assets.
  - Public dissemination feasible but must manage confidentiality and interpretation challenges.

### VIII. Key implementation guidance and practical remedies
- Use a working group to coordinate cross-disciplinary inputs and meetings.
- Prefer institution-level data where available; apply top-down methods where data limited.
- Calibrate shocks using historical extremes (e.g., largest change over the past ten years) or plausible hypothetical movements (e.g., a 20 percent fall in the exchange rate).
- For maturity breakdowns use buckets including: one day or less; one day to one month; one month to three months; three months to six months; six months to one year; one to five years; over five years.
- Coverage targets: include institutions representing a meaningful critical mass while keeping number feasible (example: less than twenty).
- Use FSIs to narrow focus; aim for FSI series that ideally extend back to cover at least one business cycle.
- Address data constraints by working with larger institutions to obtain or calibrate missing data.

*Source: _wp04127 — References (selected sections and Boxes 2, 3, 6, 7) from the source PDF.*

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

### _wp04127 - References

### I. Introduction — Purpose and scope
- Designed as guidance for central bank or supervisory officials asked to “stress test the financial system.”
- Intended to answer basic process questions: what stress testing means, what is involved, and where to begin.
- Not focused on technical aspects; intended as a reference at the beginning of the stress-testing process.
- Structure:
  - Section II: discussion of stress testing in a financial system context.
  - Section III: overview of the stress-testing process.
  - Section IV: IMF experience in FSAPs.
  - Section V: conclusions.

### II. A brief overview of stress testing
- Why do a stress test?
  - Provides information on behavior of the system under exceptional but plausible shocks.
  - Helps assess significance of system vulnerabilities.
  - Value added derives from a consultative process integrating:
    - a forward-looking macroeconomic perspective,
    - focus on the financial system as a whole,
    - a uniform approach to the assessment of risk exposures across institutions (IMF and World Bank (2003)).
  - Complements institution-level stress tests and cross-checks other analyses.
  - Identifies weaknesses in data collection, reporting systems, and risk management.
  - Helps increase expertise in risk assessment and promotes cooperation across regulatory institutions.
  - Contributes to understanding links between financial sector and macroeconomy.
- What is a stress test?
  - At portfolio level: measures sensitivity of a portfolio to extreme but plausible shocks (Box 1).
  - Described as a rough estimate of how portfolio value changes when large changes are made to risk factors; the term “rough estimate” emphasizes lack of scientific precision.
  - Involves judgments and assumptions; each choice can introduce wide margins of error.
  - Originally for trading-book market risks; now used broadly to assess groups of institutions or entire systems.
  - “System-focused” stress tests:
    - Are more macroeconomic in orientation, aiming to identify common vulnerabilities across institutions.
    - Involve greater aggregation and heterogeneity (adding or comparing “apples” and “oranges”).
    - Are not a replacement for institution-level testing but a complement.
    - Can be implemented as:
      - simultaneous stress tests of multiple portfolios using a common scenario, or
      - a single scenario applied to an aggregated portfolio/model of the entire system (noting aggregation is arduous).
    - Where feasible, conducting both approaches provides maximum information on vulnerabilities.
- Key methodological notes from the text:
  - Stress tests estimate exposure to a specific event, but not the probability of that event (Committee on the Global Financial System (2000)).
  - See Blaschke and others (2001) for a broad overview and Laubsch (1999, Ch. 2) for motivation and design.
  - Annex I provides further data requirements; Box 8 describes IMF use of stress tests.

### III. The stress-testing process — stages and practical guidance
- Overall view:
  - Stress testing is a process: investigative, diagnostic, numerical, and interpretive.
  - Typical stages:
    - identification of vulnerabilities,
    - construction of a scenario within a consistent macroeconomic framework,
    - mapping scenario outputs into balance-sheet and income-statement impacts,
    - numerical analysis,
    - consideration of second-round effects,
    - summarizing and interpreting results.
  - Stages are iterative, not strictly sequential; modification and review are expected.
- A. Identifying vulnerabilities
  - First stage: identify the main vulnerabilities to focus analysis and resources.
  - Narrowing focus allows more refined analysis; unrealistic to stress every possible risk factor.
  - Iterative process mixing qualitative and quantitative elements.
  - Use of numerical indicators at multiple levels:
    - macro-level (the “big picture”),
    - broad structural indicators,
    - institution-focused or micro-level indicators.
  - These indicators provide complementary information and should be used together.
  - A dedicated working group can facilitate the process (see Box 2).
  - Macro-level indicators provide context on potential sources of shocks and help assess what is “normal” for the economy.

### Boxes and ancillary materials referenced (as presented in the text)
- Box 1. Stress Tests: A Primer — defines stress testing, scope (market, credit, liquidity risk), examples of parameters to shock, and typical output (impact on capital).
- Box 2. Using a Working Group to Coordinate the Process — recommended but content not reproduced here.
- Additional boxes in the paper (titles only as provided): Box 3 through Box 8 covering simulations, Basel, insurance, corporate sector, Financial Stability Reports, and IMF scenario analysis.
- Tables listed in the source: Table 1 Core Set of Financial Soundness Indicators; Table 2 Encouraged Set of Financial Soundness Indicators.
- Annex I referenced for data requirements; specific contents not reproduced in the provided excerpt.

*Source: _wp04127 - References*

### Box 2. Using a Working Group to Coordinate the Process

### Box 2. Using a Working Group to Coordinate the Process

### Purpose and role of a working group
- Facilitate and coordinate the complex interactions among specialists involved in stress testing a financial system.
- Act as a forum for discussion of issues and coordination of collection of necessary inputs.
- Cross-disciplinary and cross-institutional involvement is crucial to ensure the stress testing process is well understood, appropriately implemented, and provides useful insights.
- Contacts and discussions with banks on stress testing can be helpful.

### Suggested composition and expertise — supervisory side
- Data collection and analysis (e.g., an analyst from the early warning systems team or off-site supervision) to identify vulnerabilities.
- Internal risk models to assist in numerical calculations or their interpretation (e.g., if financial institutions provide estimates for their own portfolios).
- On-site supervision to identify weaknesses and provide counterparty contacts at financial institutions.
- Conglomerate supervision, if financial conglomerates have a large presence in the financial system.
- Nonbank supervision, if nonbank institutions (e.g., insurance companies) play a significant role or represent a significant vulnerability.
- Accounting and balance sheet analysis.

### Suggested composition and expertise — macroeconomic side
- Representatives from the macroeconomic modeling or forecasting team to assist in preparation of scenarios and the macroeconomic framework.
- If a macro-econometric model will be used, include someone with in-depth knowledge of the workings of the model.

### Working group operations
- The working group can meet periodically to provide input on design and execution of stress tests.
- Various sub-groups can meet at a more technical level on a more frequent basis.

### Data and indicator guidance — macroeconomic context
- Analyze key macro and financial variables that are the most volatile, misaligned, or out of equilibrium to identify potential sources of shocks and to inform macro simulations.
- Relevant sectors and indicators:
  - Real sector: growth performance relative to potential; growth rates for consumption, investment, and incomes; unemployment rates; inflationary pressures on consumer, wholesale, and asset prices; for household and corporate sectors: measures of indebtedness, leverage, income growth, and debt servicing ability.
  - Government sector: magnitude of the government deficit, debt stock, associated debt sustainability; size of the present fiscal impulse; how the government budget is financed.
  - External sector: magnitude of the current account deficit, official reserves, how the deficit is financed; relative size, maturity structure, and currency composition of external debt; extent of exchange rate misalignment and pressures on the exchange rate.

### Structural indicators to locate risks
- Ownership and market shares by institution and type to identify linkages and systemically important institutions (data could include total assets or profits by bank or other institution and by sector).
- Balance sheet structures from aggregate financial statements to indicate significant exposures to particular asset/liability classes or income sources (analyzed by institution type and over time).
- Flow-of-funds accounts to identify changes in intermediation patterns and trends in fund raising by different sectors and instruments.

### Qualitative information
- Institutional and regulatory framework information and discussions with supervisors, regulators, private-sector analysts, and market participants provide context and may reveal likely sources of vulnerability, even if anecdotal.

### Financial Soundness Indicators (FSIs)
- Use FSIs to narrow focus on the financial system’s vulnerability to shocks and capacity to absorb losses; FSIs are typically micro-level, derived from individual institutions or sectors.
- Key FSI considerations:
  - Monitor FSIs for specific peer groups and measures of dispersion to identify common vulnerabilities and concentration of risks.
  - Ideally, FSI data series should extend back to cover at least one business cycle.
  - Review data underlying FSI ratios (numerators and denominators) to gauge sources of inter-temporal movements.
  - Pay close attention to definitions and treatment of accounting and consolidation issues (across borders and within business groups); assess general data reliability.
- Core set of FSIs for deposit-taking institutions (selected examples exactly as presented):
  - Regulatory capital to risk-weighted assets — Capital adequacy — Broad measure of capital including items giving less protection against losses, such as subordinated debt, tax credits, unrealized capital gains.
  - Regulatory Tier I capital to risk-weighted assets — Capital adequacy — Highest quality capital such as shareholder equity/retained earnings, relative to risk weighted assets.
  - Nonperforming loans net of provisions to capital — Capital adequacy — Indicates potential size of additional provisions that may be needed relative to capital.
  - Nonperforming loans to total gross loans — Asset quality — Indicates the credit quality of banks' loans.
  - Sectoral distribution of loans to total loans — Asset quality — Identifies exposure concentrations to particular sectors.
  - Return on assets — Earnings/profitability — Assesses scope for earnings to offset losses relative to capital or loan and asset portfolio.
  - Interest margin to gross income — Earnings/profitability — Indicates importance of net interest income and scope to absorb losses.
  - Noninterest expenses to gross income — Earnings/profitability — Indicates extent to which noninterest expenses weaken earnings.
  - Liquid assets to total assets — Liquidity — Assesses vulnerability to loss of access to market sources of funding or a run on deposits.
  - Liquid assets to short-term liabilities — Liquidity.
  - Net open position in foreign exchange to capital — Exposure to FX risk — Measures foreign currency mismatch.
- Encouraged set of FSIs (selected categories and indicators exactly as presented):
  - Deposit-taking institutions: Capital to assets; Large exposures to capital; Geographical distribution of loans to total loans; Gross asset position in financial derivatives to capital; Gross liability position in financial derivatives to capital; Trading income to total income; Personnel expenses to noninterest expenses; Spread between reference lending and deposit rates; Spread between highest and lowest interbank rate; Customer deposits to total (noninterbank) loans; Foreign currency-denominated loans to total loans; Foreign currency-denominated liabilities to total liabilities; Net open position in equities to capital.
  - Other financial corporations: Assets to total financial system assets; Assets to GDP.
  - Nonfinancial corporate sector: Total debt to equity; Return on equity; Earnings to interest and principal expenses; Net foreign exchange exposure to equity; Number of applications for protection from creditors.
  - Households: Household debt to GDP; Household debt service and principal payments to income.
  - Market liquidity: Average bid-ask spread in the securities market; Average daily turnover ratio in the securities market.
  - Real estate markets: Real estate prices; Residential real estate loans to total loans; Commercial real estate loans to total loans.
- Note: Other relevant indicators not formally part of the encouraged set may be added where available and relevant (e.g., additional balance sheet data, data on the life insurance sector, or information on the corporate and household sector).

*Source: Box 2. Using a Working Group to Coordinate the Process*

### Box 3. Simulations Using Macro Models: Some Considerations

### Box 3. Simulations Using Macro Models: Some Considerations

### Considerations for using macro models to simulate scenarios
- What are the baseline assumptions?
  - The baseline assumption could be no change from the latest data, or the central forecast or most likely scenario from the most recent forecasting exercise.
- What policy responses are assumed?
  - Depending on the model, different policy reaction functions may be imbedded (such as a Taylor rule relating monetary policy instrument settings to deviations in inflation and output from their targets) or an assumption of no change in policies may be used.
  - Assuming no policy response will typically imply a larger macroeconomic effect of any shock, but this will depend on the model and scenario.
- What is the time horizon of the simulations?
  - If a quarterly model is available, it may be possible to produce forecasts over the next six to eight quarters.
  - When applying the scenarios to individual balance sheets, a shorter time horizon is desirable if no reaction by institutions is assumed (i.e., if it is assumed that institutions do not adjust their balance sheets, the results can be interpreted as a comparative static exercise).
- Which variables are assumed fixed, and which are shocked?
  - Many macroeconomic models use a large number of exogenous variables. Implementing a particular scenario requires judgment as to which variables are assumed constant.
  - Changing a large number of exogenous variables may make the scenario unnecessarily complex, with little benefit in terms of realism and less acceptance of the results by participants.
- What size of shocks should be used?
  - Shocks can be calibrated on historical experience (e.g., largest change over the chosen time horizon seen in the last ten years), or can be set on the basis of a hypothetical scenario (e.g., a 20 percent fall in the exchange rate).
  - Historical experience may be more intuitive and easier to justify, but major structural changes may invalidate historical calibration (e.g., deregulation may change fundamental economic relations).

### Top-down and bottom-up approaches
- Bottom-up approach
  - The response to various shocks in a scenario is estimated at the portfolio level, using highly disaggregated data from individual financial institutions.
  - Results can then be aggregated or compared to analyze the sensitivity of the entire sector or group of institutions.
  - Advantage: makes better use of individual portfolio data.
  - Drawback: if individual institutions provide their own estimates, the approach may introduce inconsistencies in how each institution applies the scenario and produces its numerical estimates.
- Top-down approach
  - Used to estimate the responsiveness of a group of institutions to a particular scenario.
  - A common parameter is derived from all institutions in the data set (e.g., using a regression of aggregated information on macro variables) to arrive at an estimate of the aggregate impact.
  - Advantage: easier to implement, requires only aggregated data, consistent and uniform.
  - Drawback: based on aggregate historical relationships that may not hold in the future.
- Implementation guidance
  - Ideally, both methods should be applied, but data limitations may preclude this in many countries.

### Execution, scope, and coverage of system-focused stress tests
- Who should perform the empirical analysis?
  - Ideally, individual institutions should be as heavily involved in the process as possible, irrespective of whether a top-down or bottom-up approach is used, because they typically have the best access to data and knowledge of their own portfolios.
  - For institutions with sophisticated risk management systems or significant international operations, most will have systems and stress-testing procedures in place as part of their internal risk monitoring processes (see Box 4).
  - For countries with financial institutions that have more rudimentary systems and less expertise, involvement in the process may expand their knowledge; the central bank or supervisory agency may need to provide guidance or undertake parts of the empirical analysis while involving institutions as much as possible.
  - Having institutions cooperate may require moral suasion or other incentives, including the ability to benchmark their own results against their peer groups or the ability to learn from other participants.
  - The top-down approach is best undertaken by the agency with best access to the data and expertise necessary to perform the exercise.
  - Footnote: Banks that follow the Basel Committee’s internal-ratings based approach are required by their supervisors to have a comprehensive stress testing program in place. Many large banks have Value at Risk frameworks in place for internal monitoring of risk positions. See Jorion (2001) for a survey of Value at Risk methods.
- Which institutions should be included?
  - Coverage should be broad enough to represent a meaningful critical mass of the financial system, while keeping the number of institutions covered at a feasible level (e.g., less than twenty).
  - The total market share of the institutions involved (either in terms of assets, deposits, or some other criteria such as importance in the payment system) can be used to determine a cutoff point.
  - Depending on interlinkages and systemic importance, both banks and nonbank financial institutions should be included, although this may present difficulties if supervised by different entities or have different balance sheet reporting dates or practices.
  - In countries with a large number of small institutions, consider aggregating smaller institutions into a single balance sheet or taking a representative sample of institutions, or even ignoring them if they are not systemically important.
  - Stress tests can also be applied to nonfinancial companies to understand the sensitivity of corporate sector balance sheets.

### Stress testing of banks and supervisory guidance (Box 4 key points)
- Historical and regulatory context
  - In 1996 the Basel Committee on Banking Supervision (1996, 1998) recommended that banks using the internal models approach to capital adequacy for market risk have in place a “rigorous and comprehensive stress testing program.”
  - The 2004 revised Framework for the New Basel Capital Accord (or Basel II) (Basel Committee on Banking Supervision, 2004) expands recommendations regarding stress testing in line with the internal ratings based approach.
- Basel II specific guidance and expectations (paragraph references retained verbatim)
  - Banks should use stress tests to take account of the illiquidity of lower quality assets (para. 158).
  - Banks must have stress testing processes for use in the assessment of capital adequacy (para. 434): “Stress testing must involve identifying possible events or future changes in economic conditions that could have unfavourable effects on a bank’s credit exposures and assessment of the bank’s ability to withstand such changes. Examples of scenarios that could be used are (i) economic or industry downturns; (ii) market-risk events; and (iii) liquidity conditions.”
  - Supervisors must have minimum quantitative standards with regard to stress testing (para. 527j): “A rigorous and comprehensive stress-testing programme must be in place. Banks are expected to subject their internal model and estimation procedures, including volatility computations, to either hypothetical or historical scenarios that reflect worst-case losses given underlying positions in both public and private equities. At a minimum, stress tests should be employed to provide information about the effect of tail events beyond the level of confidence assumed in the internal models approach.”
  - Supervisors should consider how a bank provides for unexpected events in setting capital levels (paragraph 750): “This analysis should cover a wide range of external conditions and scenarios, and the sophistication of techniques and stress tests used should be commensurate with the bank’s activities.”
  - Banks should stress test credit concentration risk (para. 775): “A bank’s management should conduct periodic stress tests of its major credit risk concentrations and review the results of those tests to identify and respond to potential changes in market conditions that could adversely impact the bank’s performance.”
- Outcome
  - The Basel recommendations gave impetus to a growing awareness and familiarity of stress testing by banks.

### Stress testing of insurance companies (Box 5 key points)
- State of practice and regulatory context
  - Stress testing of insurance company balance sheets and income statements is not as well-developed as stress testing of banks.
  - The revised Insurance Core Principles issued in 2003 by the International Association of Insurance Supervisors (IAIS 2003a, p. 35) includes stress tests as an advanced criterion for Principle 20: “The supervisory authority requires that insurers undertake regular stress testing.”
  - The IAIS (2003b) issued a guidance paper on stress testing by insurers.
- Risk characteristics and methods
  - Insurance companies face underwriting risk, catastrophe risk, and risks on technical claims provisions; on the asset side they face market risk, credit risk, liquidity risk, operational risk, group risk, and systemic risk.
  - The complexity of insurance contracts can create difficulties in revaluing liabilities and may require detailed contract-by-contract data for accurate assessment.
  - Stochastic techniques are sometimes used by insurers to assess resilience; alternatively, simple deterministic tests (e.g., shifts in loss ratios or specified catastrophic events) can reveal useful information.
- Presentation and aggregation
  - Results are often expressed in terms of their impact on the solvency margin (the required solvency margin is the minimum level of capital and reserves intended to ensure with a high probability the insurer’s ability to meet its obligations).
  - Numerical estimates of impact can be expressed as a percent of the required solvency margin.
  - Aggregating insurance stress test results with banking results may be complicated because of differences in accounting and regulatory treatment, definitions of capital, and market valuation of investments; a separate presentation of results may be warranted.

### Data constraints and practical remedies
- Four main forms of data limitations (as noted in IMF and World Bank (2003))
  - Basic data availability, especially where information on balance sheet exposures may not be available.
  - Difficulty isolating specific exposures, especially among large complex financial institutions or institutions active in derivative markets.
  - Lack of risk data, e.g., duration or default measures, in countries where risk management systems are less sophisticated.
  - Confidentiality issues, or limitations on what supervisors are legally able to share with other parties.
- Ways to overcome data difficulties
  - Work with larger and more sophisticated institutions to obtain better data or to calibrate parts of the exercise.
  - Example: if the exposure of interest is the aggregate exposure to a specific borrower or sector, use available institution-level information to inform aggregate calibrations.

*Source: Box 3, "Simulations Using Macro Models: Some Considerations", _wp04127.*

### Box 6. Stress Testing of Corporate Sector

### Box 6. Stress Testing of Corporate Sector

### Overview
- Loans to the corporate sector often account for a significant portion of total lending; stress testing corporate balance sheets provides useful information on underlying credit quality of bank portfolios.
- See Glen (2004), Goldman Sachs (1998, 2000), and Heytens and Karacadag (2001) for examples of this approach.

### Key risk sensitivities to assess
- Interest rate risk: impact of interest rate changes on net interest expenses and interest earnings.
- Foreign exchange rate risk: effect of exchange rate changes on foreign earnings and interest expenses on the stock of foreign-currency denominated debt.
- Macroeconomic cycles: impact of changes in sales and firm income.

### Measuring debt-service capacity
- Use the interest coverage ratio, often defined as earnings before interest, taxes, depreciation, and amortization divided by interest expenses.
- Firms that fail to maintain their interest coverage ratios above one must eventually liquidate assets, gain new funding, renegotiate debt contracts, or default.
- The proportion of firms or their debts that have low interest coverage ratios (e.g., below one) provides a rough proxy for potential loan defaults.

### What stress tests show
- Stress tests can show effects of different shocks on interest coverage ratios and the proportion of firms at greater risk of defaulting.
- They are a useful indicator of the sensitivity of the underlying credit quality of bank loans to a variety of shocks.

### Calibrating shocks
- Scenarios should reflect exceptional but plausible events, beyond the normal range of experience.
- Scenarios can be based on historical data (e.g., largest observed changes or extreme values over a specified period) or hypothetical large movements thought to be plausible.
- Historical scenarios can be intuitive; hypothetical scenarios may be more realistic if financial structure has changed.
- Experiences of other countries can be a useful guide.
- Example calibration: a simple sensitivity test can be calibrated according to the largest change in a risk factor over the past ten years.
- Note: relevant empirical measure for scenarios is the joint probability of all factors moving simultaneously; attaching probabilities to hypothetical scenarios is often difficult and involves judgment.
- In some cases it may be useful to calibrate shocks to cause one or more institutions to breach their minimum capital requirement to determine shock magnitudes necessary to cause such a “failure.”

### Mapping macro scenarios to balance sheets — bottom-up approach
- Implementing bottom-up stress tests requires two mappings:
  - From macro adjustment scenarios to a set of common risk factors.
  - From common risk factors into all instruments in a portfolio.
- Financial variables needed may include:
  - Interest rates (term structure of the risk-free rate, credit quality spreads).
  - Exchange rates (spot and forward, bilateral and trade-weighted).
  - Asset prices (aggregate indices of market prices).
  - Credit exposures and quality.
- Supplement macro model output with additional estimates where necessary (e.g., term-structure models, equilibrium real exchange rate models).
- Examples:
  - If macro model only provides an overnight cash rate and a 10 year bond rate, use an empirical term-structure model to produce estimated rates for additional maturities and derive credit spreads.
  - If macro model provides only a trade-weighted exchange rate or a single bilateral exchange rate, use implicit weightings to produce bilateral rates or assume patterns of cross rates.
- Individual institutions usually best placed to map risk factors into portfolios due to access to detailed portfolio information and internal risk models.
- Where internal models are limited, institutions can adjust internal model parameters (credit scores, transition matrices, default probabilities) using macroeconomic changes, recent downturns, or expert judgment.

### Top-down approach
- A top-down approach provides a useful check on bottom-up results and is practical where institutions lack capacity to estimate impacts on their portfolios.
- Top-down exercises apply system-wide adjustment parameters or regression-based estimates to approximate impacts on individual institutions.
- Examples of top-down models and applications described:
  - Frøyland and Larsen (2002); Andreeva (2004).
  - Benito et al (2001) extending the Bank of England’s macro model to incorporate household and corporate balance sheets and stress testing housing prices and interest rates.
  - Hoggarth and Whitley (2003) using the Bank of England’s macro model to estimate impacts on new provisions.
  - Arpa et al (2000); Kalirai and Scheicher (2002) modeling effects of macro variables on provisions and earnings for Austrian banks.
  - Pesola (2001) estimating loan losses as a function of GDP, indebtedness, income and interest rate shocks, and deregulation.
- Caveat: regression-based estimates often provide partial equilibrium estimates; interpret results with care.

### Second-round effects
- Many stress tests assume no behavioral change or portfolio realignment in response to shocks; valid for short horizons or when behavioral changes take time.
- Example: limited behavioral response may be reasonable over a one- to three-month horizon.
- For horizons of a year or more, and for systemically important institutions, ignoring feedback effects is harder to justify.
- Possible second-round effects:
  - Direct credit losses from counterparty failures.
  - Increased funding costs for weakened banks.
  - Portfolio adjustments (e.g., tightening lending criteria) affecting aggregate demand.
- Contagion models help consider second-round effects and inter-institution linkages:
  - Two-stage exercise: stress-test individual balance sheets, then examine counterparty exposures (interbank loans, cross shareholdings, deposits, other exposures).
  - Results can be used to construct indices of systemic risk based on the impact of failure of key institutions.

### Interpretation of stress-test results
- Stress tests are useful for identifying latent risk exposures and likely significance of losses in a systematic manner.
- Regular stress testing provides information about changes in the risk profile of the system over time.
- Stress tests are useful for evaluating effects of large movements (tail events), but should not be portrayed as providing precise measures of loss magnitudes; typically, no probabilities are attached to outcomes.
- Risks to validity:
  - Model specification or estimation errors (“model error”) can invalidate conclusions.
  - Stress tests may not capture full range and interaction of risks (operational risk, legal risk) and may give only a partial picture.
  - Stress tests typically consider only part of a bank’s income-generating operations; banks may have significant income flows unaffected by the scenarios.
- Complementary measures (e.g., financial soundness indicators) help validate stress-test results.
- Presentation of results:
  - Group aggregate (sector level) impact by type of risk and/or by scenario.
  - Use composition of expected losses (as a proportion of capital or income) to summarize central results.
  - Bottom-up outputs: use descriptive statistics (mean, median, standard deviation, minimum, maximum, number of institutions in each decile) and peer-group analysis to show distribution across institutions.
  - Supervisory agencies applying a common framework to reported balance sheet data can act as an accuracy and consistency check.

### Publication considerations
- Public dissemination poses confidentiality and interpretation challenges; institutions may fear negative market reactions or competitive disadvantage.
- Disclosure risks: some analysts may interpret chosen scenarios as an official view on most likely or most problematic scenarios.
- Many countries publish summary or aggregated information; such disclosure difficulties can be overcome.
- Useful disclosure practices:
  - Publish summary information (mean and range) to inform markets and allow benchmarking without revealing identities.
  - Publish scenarios undertaken to raise awareness of risks for institutions’ own stress testing programs.

*Source: Box 6. Stress Testing of Corporate Sector, _wp04127 - Box 6. Stress Testing of Corporate Sector*

### Box 7. Financial Stability Reports

### Box 7. Financial Stability Reports

### Overview
- A growing number of central banks regularly produce stand-alone publications devoted to assessing the condition and stability of the financial system, generally making use of a range of financial sector indicators to guide and illustrate the analysis.
- Stress tests are commonly published in these reports and are used to assess the resilience of domestic financial systems to predetermined risk scenarios.

### Selected Financial Stability Reports (institutions and features)
- Austria — Austrian National Bank — Semi-annually — 2001 — No
- Belgium — National Bank of Belgium — Annually — 2002 — No
- Brazil — Central Bank of Brazil — Semi-annually — 2002 — Yes
- Canada — Bank of Canada — Semi-annually — 2002 — No
- Denmark — National Bank of Denmark — Annually — 2000 — No
- Finland — Bank of Finland — Annually — 2003 — No
- France — Bank of France — Semi-annually — 2002 — Yes
- Hungary — National Bank of Hungary — Semi-annually — 2000 — No
- Indonesia — Bank Indonesia — Semi-annually — 2003 — Yes
- Norway — Bank of Norway — Semi-annually — 1995 — No
- Sweden — Bank of Sweden — Semi-annually — 1997 — No
- United Kingdom — Bank of England — Semi-annually — 1995 — No
- Note: List based on IMF (2003b).

### Examples of published stress tests in Financial Stability Reports
- United Kingdom: A range of macroeconomic stress tests carried out in the context of IMF’s FSAP are described in the Bank of England’s June 2003 Financial Stability Review. See Hoggarth and Whitley (2003).
- Denmark: Sensitivity analyses and stress tests examining whether earnings and capital of the Danish banking system are sufficient to withstand predetermined risk scenarios are reported in the National Bank of Denmark’s 2003 Financial Stability Report. See National Bank of Denmark (2003).
- Austria: Stress tests focusing on the interdependence of banking sector credit risk and economic developments are reported in the Austrian National Bank’s Financial Stability Report (Number 3). See Kalirai and Scheicher (2002).
- Hungary: The effect of interest rate and credit shocks on the capital position of the Hungarian banking system are reported in the Hungarian National Bank’s December 2003 Report on Financial Stability. See Hungarian National Bank (2003).
- Indonesia: The effect of changes in NPLs on the capital position of the Indonesian banking system are reported in Bank Indonesia’s June 2003 Financial Stability Report.
- IMF: A summary of stress test results from selected FSAP missions have also been published by the IMF as part of Financial System Stability Assessments.

### FSAP stress testing: role, scope, and recent trends
- Role and scope
  - Stress tests are an integral part of FSAPs conducted by the IMF and World Bank, and have been performed for every country participating in the FSAP.
  - Designed to provide a quantitative measure of the vulnerability of the financial system to different shocks.
  - Complement other assessment components: legal, institutional, regulatory, supervisory frameworks; observance of standards and codes; financial system structure and vulnerabilities; empirical analysis of financial soundness indicators.
- Implementation features
  - Data availability is a key factor in determining the approach and sophistication of stress tests performed as part of the FSAP.
  - Most analyses are performed on a bank-by-bank (bottom-up) basis, based on single factor and scenario approaches.
  - Contagion risks and second round effects have typically not been addressed in many FSAPs, although some have incorporated elements of interbank contagion.
  - The involvement of the authorities has varied, with some precluded from providing data on individual institutions by bank secrecy laws or conventions.
  - For countries that have published the IMF’s summary assessment of the FSAP mission (the Financial System Stability Assessment), most have included a summary of the stress testing results.
- Recent trends in FSAP stress testing
  - Country authorities and individual financial institutions now play a greater role in the design and implementation of stress tests; increased reliance on using the internal models of banks to evaluate the impact of shocks, including their off balance-sheet exposures.
  - The use of macro-simulation models to calibrate a macro scenario has increased.
  - Coverage of nonbank financial institutions has increased, with large insurance companies now being included in many cases as part of the analysis.
  - Many country authorities are now implementing their own stress-testing programs, partly as a result of FSAP-related work.

### Stress testing methodology and data issues
- Identifying vulnerabilities
  - Use a variety of macro-level, structural, and micro-level indicators to isolate key vulnerabilities.
  - Macroeconomic indicators include: national accounts data and other real sector data (labor markets, production, prices, household and corporate sector performance); fiscal accounts (government operations and debt stocks); external sector accounts (balance of payments, international investment position, international reserves and liquidity, exchange rate developments); financial sector accounts (accounts of banks and the central bank, structure of interest rates, trends in asset prices).
  - Structural indicators: ownership and market shares, aggregated balance sheet data, flow of funds accounts.
  - Financial soundness indicators (see Tables 1 and 2 in source) provide information on health of the financial sector.
- Constructing and calibrating scenarios
  - Historical data on financial market prices can be useful: a long time series of daily data (e.g., ten years) on interest rates, exchange rates and equity prices helps inform plausible shock magnitudes.
  - A similar time series for broader macroeconomic variables helps calibrate simulation models.
- Balance-sheet implementation (key data requirements)
  - Preferably collect data on an institution-by-institution basis.
  - Sensitivity (single-factor) tests require:
    - Interest rate risk: maturity breakdown (maturity “buckets”) for assets and liabilities (examples of buckets: one day or less, one day to one month, one month to three months, three months to six months, six months to one year, one to five years, over five years); maturity breakdowns by local and foreign currencies; duration measures.
    - Foreign exchange rate risk: net open position by currency.
    - Credit risk: loan-loss provisions by asset/exposure categories; banks’ internal credit ratings distributions and metrics (default and recovery rates, transition matrices); exposures by geographic region, industry, or product type.
    - Liquidity risk: sources and uses of funds broken down by maturity; structure of deposits and other liabilities (including interbank lines) and turnover rates; stock of liquid and near-liquid assets usable as collateral or sold quickly.
- Data quality
  - The IMF’s Data Quality Assessment Framework (DQAF) addresses integrity, methodological soundness, accuracy and reliability, serviceability, and accessibility.
  - Where data quality or accounting interpretation is in doubt, supervisors may adjust balance sheet numbers prior to shocking or when expressing results in ratios (e.g., disallowing some items in tier one capital).

### Interpretation, metrics, and dissemination
- Purpose: Stress testing is a process to identify vulnerabilities and provide a rough estimate of sensitivity of balance sheets to shocks; system-focused stress tests combine a forward-looking macro perspective with institution-level sensitivity analysis.
- Translating macro scenarios into balance sheets: two main approaches
  - Bottom-up: impact estimated using data on individual portfolios.
  - Top-down: impact estimated using aggregated data.
- Common metrics for summarizing results (denominators used)
  - Capital: tier one capital (shareholders funds: common stock, disclosed reserves, retained earnings) and total capital.
  - Income: definitions include EBITDA, ordinary income, profits before and after taxes.
  - Assets: total assets; quick assets; current assets.
- Dissemination
  - Public dissemination of results may present challenges, but publication by many countries demonstrates feasibility.
  - Stress tests provide quantitative measures of vulnerability and, combined with other analyses, support conclusions about overall financial system stability.

*Source: Box 7. Financial Stability Reports, from IMF Working Paper _wp04127.*

### REFERENCES

### _wp04127 - REFERENCES

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### Interbank exposures, contagion, and systemic risk
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### Financial soundness indicators, IMF and FSAP-related work
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### Corporate vulnerability, real estate, and sectoral impacts
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- Goldman Sachs, 2000, Asia Bank NPLs III: How high, how structural? Goldman Sachs Global Equity Research Report (Hong Kong: Goldman Sachs).
- Gereben, Aron, Ian Woolford, and Melleny Black, 2003, The macroeconomic impacts of a foot-and-mouth disease outbreak: an information paper for Department of the Prime Minister and Cabinet, information paper (Wellington: Reserve Bank of New Zealand), available on the Web at http://www.rbnz.govt.nz/research/0130346_2.pdf.
- Heytens, Paul, and Cem Karacadag, 2001, An Attempt to Profile the Finances of China's Enterprise Sector, IMF Working Paper, WP/01/182, November (Washington: International Monetary Fund) available on the Web at http://www.imf.org/external/pubs/ft/wp/2001/wp01182.pdf.

### Risk management, modeling, and technical methods
- Bunn, Philip, 2003, “Company-accounts-based Modelling of Business Failures,” Financial Stability Review, Issue 15, December 2003 (London: Bank of England)., available on the Web at http://www.bankofengland.co.uk/fsr/fsr15art8.pdf.
- Kim, Jongwoo, Allan M. Malz, and Jorge Mina, 1999, Long Run Technical Document, RiskMetrics Technical Document (New York: RiskMetrics Group) available on the Web at http://www.riskmetrics.com/pdf/LongRunTechDoc.pdf.
- Laubsch, Alan J., 1999, Risk Management: A Practical Guide, RiskMetrics Technical Document (New York: RiskMetrics Group) available on the Web at http://www.riskmetrics.com/pdf/RMGuide.pdf.
- Gropp, Reint, and Jukka Vesala, 2004, Bank Contagion in Europe, paper presented at the Financial Intermediation Research Society Conference on Banking, Insurance and Intermediation, Capri, Italy, May 13-15, 2004 (Gainesville Florida: The Financial Intermediation Research Society) available on the Web at http://finance.wharton.upenn.edu/~allenf/capri/papers/159gropp.doc.
- Sahel, Benjamin, and Jukka Vesala, 2001, “Financial stability analysis using aggregated data,” BIS Papers, No. 1 (Basel: Bank for International Settlements) available on the Web at http://www.bis.org/publ/bispap01f.pdf.
- Schachter, Barry, 1998, The Value of Stress Testing in Market Risk Management, memorandum, Chase Manhattan Bank available on the Web at http://www.gloriamundi.org/download.asp?ResouceUrl=drms.pdf.

*References list as provided in the source PDF.*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2004/_wp04127.pdf_