A Guide to IMF Stress Testing

Chapter 5. Next-Generation Applied Solvency Stress Testing

Li Ong
Published Date:
December 2014
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Christian Schmieder, Claus Puhr and Maher Hasan This chapter is an abridged version of IMF Working Paper 11/83 (Schmieder, Puhr, and Hasan, 2011). The working paper benefited from comments from Martin Čihák, Andreas Jobst, Liliana Schumacher, Hiroko Oura, Elena Loukoianova, Joseph Crowley, Aidyn Bibolov, Jay Surti, Heiko Hesse, and Torsten Wezel; as well as from the participants of the Monetary and Capital Markets Department and European Department seminar.

This chapter provides an overview of the building blocks of a new solvency stress testing tool. The framework enriches solvency stress tests by enhancing their risk sensitivity while keeping them flexible, transparent, and user-friendly. The framework is Excel-based, and explicitly allows running multiperiod scenarios (up to 5 years), providing both regulatory and economic capitalization ratios under stress. The framework can be applied to single banks with a “simple” risk structure and to systemically important financial institutions and can be used for financial stability analysis that includes hundreds (and even thousands) of banks.

Method Summary

Method Summary
Overview• The framework seeks to enrich solvency stress tests in terms of their risk sensitivity while keeping them flexible, transparent, and user-friendly.
• It generates both regulatory and economic capitalization ratios under stress.
ApplicationThe framework enables the conduct of multiperiod solvency stress tests for banks (and, in principle, also other financial institutions). Its main contributions include
1. increasing the risk sensitivity of stress tests by capturing changes in risk-weighted assets under stress, including for non–Internal Ratings Based (IRB) banks (through a quasi-IRB approach);
2. providing stress testers with a comprehensive platform for using satellite models for defining various assumptions and scenarios;
3. allowing stress testers to run multiyear scenarios (up to 5 years) for hundreds of banks, depending on the availability of data.
Nature of approachBalance sheet data based.
Data requirementsAccounting information and supervisory data, including comprehensive information on banks’ assets, income components, and capitalization ratios, as well as banks’ off-balance-sheet positions. Satellite models are also needed; the scenarios are expert based.
StrengthsThe method caters for the need to run more risk-sensitive, granular, and comprehensive solvency stress tests and takes into account the fact that meaningful data to run IRB-type stress tests remain limited at this stage.
Weaknesses• The scenario design requires expert judgment or reliance on rules of thumb (some gathered from experiences with other countries, which may not be applicable to the country being analyzed).
• The framework does not explicitly capture dependencies across banks (as portfolio models may do).
ToolThe Excel spreadsheet macro is available in the toolkit, which is on the companion CD and at www.elibrary.imf.org/stress-test-toolkit.
Contact author: C. Schmieder.

The recent past has clearly revealed the importance of stress tests not only as a risk management tool and key component of financial stability analysis but also as a crisis management tool. This last role of stress tests became evident in the U.S. Supervisory Capital Assessment Program1 (SCAP) as well as in European stress tests that were used to decide the required level of capital backstops. In addition, emerging macro-prudential tools such as capital conservation buffers, countercyclical capital conservation buffers, systemic risk charges, and Pillar 2 capital charges (and even Pillar 1 charges for market risk) can be and are determined on the basis of stress tests. Stress tests also are used for internal bank capital allocation and risk management purposes, such as limit setting.

In developing the new framework, we take into account three key dimensions. First, a stress test framework needs to allow its users to conveniently run (a series of) severe yet plausible scenarios to assess the sensitivity of the stress to the underlying assumptions. Second, a useful stress test framework needs to be risk sensitive. This requires that changes to risk parameters be based on economic measures of solvency, in addition to statutory regulatory ones. Last, the effectiveness of stress testing depends on the ease with which the output can be communicated to decision makers (e.g., policymakers, senior bank managers) and market participants. Although these concepts seem straightforward, they might pose challenges in practice as higher risk-sensitivity exercises are expected typically to require the use of technically complex, “sophisticated” frameworks.

We develop a “next-generation”2 Excel-based tool, designed to be transparent, flexible, and user-friendly. The last two features make the tool accessible to banks, regulators, and rating agencies in advanced, emerging, and developing economies. The tool is particularly geared toward evolving risk management practices, spurred by regulatory changes (Basel II/III). The key conceptual contribution of this framework is that it allows for an assessment of economic solvency under stress. This is done by adjusting the denominator of capitalization, risk-weighted assets (RWA), for potential unexpected (worst case) losses, not only in terms of volume (as in the past) but also for changes in the risk profile of a bank’s business. The rationale for that is to make potential losses visible well before they materialize in terms of losses in the numerator of capitalization ratios (in terms of a reduction in capital through losses). Although economic solvency tests (ideally) require various inputs, the framework has been designed to make economic solvency tests possible also for banks that are currently under Basel I or the Standardized Approach (StA) through a quasi-Internal Ratings Based (QIRB) approach. With various banks moving to the Foundation Internal Ratings Based (FIRB) and Advanced Internal Ratings Based (AIRB) approach during the next years, the tool caters to the needs across various financial systems.

With these overarching objectives, our framework can be contrasted with other comprehensive stress testing frameworks that have been developed during the last decade. Two notable integrated ones come to mind: the Risk Assessment Model for Systemic Institutions (RAMSI) by the Bank of England (Aikman and others, 2009) and the Systemic Risk Monitor (SRM) by the Austrian Central Bank (Boss and others, 2006). Other institutions also have recently developed or upgraded their (already sophisticated) stress testing frameworks, such as in Brazil, Canada, Chile, the Czech Republic, France, Germany, Italy, Japan, the Netherlands, Norway, Spain, Sweden, Switzerland, and the United States as well as the European Central Bank (ECB)3. Most of these approaches were discussed by Foglia (2009), and details are presented in the recent Financial Stability Reports of the respective countries and/or institutions.

Our stress testing framework is based on three dimensions: risk sensitivity, scope, and ease of use (Figure 5.1). Risk sensitivity is key but should not come at the expense of it being analyzed through a “black box.” The scope should be wide, allowing for extensions when need arises. The ease of use is very important not only to make the output of a tool readily understandable and credible but also to focus on the stress tests as such rather than struggling with details on techniques.

Figure 5.1Comparison of Key Stress Testing Frameworks

Source: Authors.

Notes: BoE = Bank of En gland; OeNB = Austrian National Bank/Oesterreichische Nationalbank; RAMSI = Risk Assessment Model for Systemic Institutions; SRM = Systemic Risk Monitor.

The most important difference between our framework and the aforementioned integrated stress testing tools lies in the scope. Although the next-generation framework allows the use of satellite models (i.e., econometric models) to establish macro-financial linkages over the stress horizon, these models have to be estimated outside the framework (e.g., by means of an econometric software). In that sense, other stress testing tools, including those focusing on single risks (such as credit portfolio models, usually run based on market data), are more sophisticated than the next-generation framework in its standard form (i.e., without additional input).

In order to (at least partially) close this gap, certain considerations have been incorporated:

  • Work by Hardy and Schmieder (2013) in establishing rules of thumb for credit risk and income under different levels of stress has been built into the tool. These rules of thumb allow credit losses (default and recovery rates), correlations, and income to be linked to macroeconomic conditions. Hence, macro stress testing is possible without calibrating satellite models—a key feature of the tool4.

  • Likewise, the framework is based on a set of reduced-form models to run stress tests based on quasi-portfolio credit risk models—the other key instrument of the framework. The framework has been used recently for various types of risk analysis and stress tests carried out by the IMF and the ECB.

The rest of the chapter is organized as follows: Section 1 provides an overview on the methodological framework, including the concepts on the one hand and the technical solution on the other. Section 2 concludes the chapter.

1. Methodology

A. Concept

The methodology underlying the framework is a set of reduced-form models that enable quasi-portfolio model calculations. They are discussed below.

Stress Test Metric

The major output of the tool is banks’ capitalization levels under different scenarios. It allows stress testers to determine whether banks (1) are resilient enough to stay above the regulatory minima; (2) are resilient enough to meet market expectations (i.e., certain hurdle rates that are considered best practice by market participants);5 or (3) are sufficient to safeguard any particular bank from an additional idiosyncratic shock (in case of a common macroeconomic scenario). Moreover, the stress test can also help in determining banks’ potential capital needs in case either of these thresholds is not met.

Capitalization under stress is measured as follows:

If net income becomes negative, capital will be reduced; otherwise, capital increases subject to taxation and the earnings retention rate. The latter is common under baseline scenarios; otherwise, banks would be in a difficult position. Besides preshock capitalization (which is given as an input), the two main drivers of solvency risk for banks are credit losses and pre-impairment income.

When using a Basel I/II StA type definition of RWA for credit risk, RWA under stress evolves conditional to portfolio volume (i.e., credit growth and credit losses), except for some positions subject to risk weighting (such as sovereign bonds). For IRB banks (and when using economic capitalization measures), RWA is also adjusted for risk to reflect the change in the risk profile of banks’ business and thereby the increase or decrease of potential unexpected (worst case) losses. In the latter case, RWA allows banks’ portfolio quality to be monitored and thereby help to identify the buildup of risk early on—subject to the availability of timely and precise risk information. The framework also allows for an adjustment of RWA for market risk, operational risk, and other Pillar 1 and Pillar 2 risks under stress.


Income is banks’ first line of defense against unforeseen losses but also, at the same time, supports asset growth and represents a buffer for absorbing any impact from regulatory changes such as Basel III. Therefore, income should be a major element in any stress test framework, even more so for multi-period stress testing exercises. However, the modeling of income remains far less prominent (and developed) relative to loss modeling. The simulation of pre-impairment income (and/or of its specific components) should be guided by satellite models. In the published version of the tool, postshock income is determined as shown in Table 5.1.

Table 5.1Income under Stress
Income ElementDescription
Net operating income including impairmentsBy default, nonrecurring income is not considered; hence, net operating income is modeled as the sum of net interest income, net fee and commission income, and other operating income (including expenses). All three components can be adjusted separately if deemed appropriate.
• Add: Change in net operating income vs. reporting yearStress testers can define changes in net interest income, both expert based and model based; in addition to that, foregone interest owing to losses and additional interest income from credit growth are taken into account.
Moreover, changes in net fee and commission income and other operating income (including expenses) are accounted for (again, where available, the application of satellite models is possible).
• Less: Impairments for credit losses exceeding those in reporting yearOutcome of stress test of credit risk.
• Add: Changes in trading and investment income including marked-to-market gains/ losses (interest rate shock in the banking book, foreign exchange [FX] rate shock)The evolution of the trading income can be based on expert judgment by means of satellite models; in addition to that, marked-to-market gains/losses can be simulated through shocks affecting interest rates in the banking book and/or FX rates provided that bank-specific data are available.
• Add: Change in other income

Equal to: Net income (scenario, year t)
Other sources of income are foreseen to be simulated based on expert judgment. The sum of all the above components.
Source: Authors.
Source: Authors.

The reported operating income net of impairments serves as a benchmark for the income of the following years6. The guiding idea is that nonrecurring income as well as other sources of income (not part of operating income) is not taken into account, as these elements are not an integral part of the (medium-term) earning capacity of banks7. The calculation of income strikes a balance between setting straightforward assumptions and more sophisticated modeling. If the resulting net income after stress is positive, then the portion foreseen to be retained (after tax) based on the stress test assumptions will be added to the capital; otherwise, losses will be deducted from capital. Rather than sticking to a general assumption about retained income, rules depending on the postshock capitalization of each specific bank could be referred to (e.g., in line with Basel III maximum pay-out rules or based on empirical evidence, as discussed in Hardy and Schmieder, 2013), but such rules are not part of the standard version of the tool. Further information on the subcomponent of income can be found in Schmieder, Puhr, and Hasan (2011).

Credit Risk

The treatment of credit risk is the key innovation of the framework, which is based on a Basel II/III type notion of credit risk. The simulation of credit risk under stress is foreseen to be based on the credit risk parameters used for the computation of IRB capital charges, namely, (1) probabilities of default (PDs) and losses-given-default (LGDs); or (2) credit losses (such as impairments) as well as exposures at default and asset correlations. The tool offers a conceptual framework for determining credit losses under stress on the one hand (which informs the numerator of capital adequacy) and RWA for credit risk under stress on the other (the denominator of key capitalization ratios). It is worth highlighting that credit risk analyses (and stress tests more generally) are assumed to be carried out for all assets subject to default risk, that is, including counterparty credit risk and off-balance-sheet items. The market risk of the liquid assets is simulated separately through income.

The Relationship between PDs and LGDs. It was discovered a while ago that there is a positive correlation between the PDs and LGDs of bonds. This implies that, in times of stress (i.e., when PDs are higher), LGDs are higher than in “normal” times. With more data becoming available in recent years, this observation has also been confirmed for loans. In order to provide stress testers with the possibility of linking stressed LGDs to stressed PDs (and thus avoiding the need to make a separate assumption about the development of LGDs under stress), we combine evidence determined by Moody’s (2009) with an approximation formula proposed by the Board of Governors of the Federal Reserve System (Fed, 2006) to determine downturn LGDs, that is, LGDs under stress condi-tions8. Using the formula in Fed (2006):

A nonlinear formula is derived, accounting for the finding that the relationship is nonlinear (Standard & Poor’s, 2010): 9, 10

The intercept of equation (5.1) can be modified to match the actual levels of LGDs in specific countries. We propose using the World Bank’s Doing Business data to do so, drawing on work by Djankov, McLiesh, and Schleifer (2007), for countries for which no specific studies have been done (unlike the United States, the United Kingdom, Germany, and France, for example). The LGDs published by the World Bank can serve as a rough (and rather benign, in some cases) proxy for corporate LGDs. To arrive at a bank-level or country-level LGD, a weighted average is computed, to account for the portion of retail and other types of credit, and expert judgment is applied. The studies by Schmieder and Schmieder (2011) and Hardy and Schmieder (2013) on the implications of the legal framework could also be used to guide the calibration of LGDs.

RWA for Credit Risk. A portfolio credit risk model that captures credit correlations is needed to compute RWA for credit risk in economic terms. This framework uses the one-factor model underlying the IRB approach to determine changes in RWA conditional on changes in credit risk parameters (PDs, correlations, name concentration). LGDs exhibit a linear relationship with RWA, so no model is necessary, although it underscores the importance of LGDs. An illustrative example is provided in Schmieder, Puhr, and Hasan (2011).

RWA Sensitivity of PDs. The stress test framework uses the Basel II IRB formula to translate increases in PDs into stressed RWA. If one keeps LGDs and correlations constant,11 one can simulate the marginal effect of an increase in PDs on RWA. The RWA elasticity of PDs is higher the lower the pre-stress PDs, and the elasticity decreases when PDs increase12. For low levels of pre-stress PDs, the RWA elasticity of PDs is 0.6, that is, an increase in PDs by 1 percent yields an increase in RWA by 0.6 percent. For higher PDs, the elasticity goes down: for PDs of 5 percent, the effect is about 0.35 and for PDs of 10 percent about 0.2. The nonlinear effect is captured by means of a polynomial fit function. Further details are available in Schmieder, Puhr, and Hasan (2011).

RWA Sensitivity of Asset Correlations. For correlations, the elasticity depends on the characteristics of the counterpart, that is, their relationship with macroeconomic conditions. In simplified terms, one can refer to asset classes, such as (large) corporates, small- and medium-sized enterprises (SMEs), and retail customers. Corporates are expected to be most correlated with the cycle (on average), whereas idiosyncratic performance plays a more important role in debt service by SMEs and even more so for retail counterparts. The Basel II IRB framework takes a shortcut by linking correlations to PDs, using the empirical relationship that larger firms exhibit better ratings, that is, lower PDs. For the corporate IRB formula, the effect is more than linear (i.e., the PD elasticity is above unity) for PDs lower than 2 percent (see Schmieder, Puhr, and Hasan, 2011, for details).

We compared the IRB-based results with empirical evidence provided by Mager and Schmieder (2009) as a robustness check13. On the basis of stress tests of realistic German credit portfolios, we estimate the RWA elasticity of asset correlations for small banks at 0.45; for medium-sized banks, the elasticity is 0.7; and for large German banks, elasticity is 1.25, all of which confirm the above findings. As a default, the framework assumes a linear relationship between asset correlations and RWA, but stress testers can modify this assumption. The findings of Hardy and Schmieder (2013) could also be used as a reference point to determine the level of asset correlations under stress.

In sum, the framework performs similar functions to those of an economic capital model (such as CreditMetrics, Credit-Risk+) but with simple means. Combined with its ability to include capital charges for name concentration, as outlined below, the framework comes close to a full-fledged portfolio model.

Name Concentration and RWA. Basel II IRB minimum capital requirements do not account for name concentration, as the underlying (one-factor portfolio) model assumes that banks’ credit portfolios are perfectly granular. Although this assumption keeps the underlying model relatively simple, capital requirements may be underestimated. In order to avoid such underestimation, which is most likely for small banks, concentration risk is subject to Pillar 2, that is, supervisory scrutiny. The study by Gordy and Lütkebohmert (2007) offers a framework for estimating name concentration. The outcome of a numerical example provided by the authors was used to determine an approximation formula that translates name concentration into additional RWA (in percent). This approximation depends on the actual level of name concentration as measured in terms of the Herfindahl-Hirschman Index (HHI)14 and the aggregate bank-level PD:

Schmieder, Puhr, and Hasan (2011) provide an illustrative example.

Translation of RWA Based on the Standardized Approach into QIRB RWA. The use of a risk-sensitive measure of bank capitalization is essential for stress testing, as the evolution of risk and also the level of risk assumed before stress could otherwise be misleading. The framework using QIRB RWA to translate risk-invariant RWA into risk-sensitive measures allows banks that have not moved to the IRB approach to run meaningful stress tests. The idea is to

  • rescale the RWA of banks by means of an approximation (QIRB); and then

  • run risk-sensitive tests and simulate scenarios based on the IRB approach. In case stress testers do not feel comfortable with rescaling RWA, the reported RWA can be used as a starting point for risk-sensitive tests15.

A key precondition for calculating QIRB RWA is to use meaningful credit risk parameters. A second-best solution is needed for non-IRB banks. For many banks, nonperforming loans (NPLs) are available, usually including time series. However, NPLs are often stock figures, and definitions vary widely across countries, so a feasible solution has to be found to determine PD-like numbers (see Box 1 in Schmieder, Puhr, and Hasan, 2011). As discussed earlier, LGDs are often available at a country level only, which appears to be a good proxy for corporate exposure. For retail exposure, an alternative proxy has to be found, which may also apply to other asset classes. Aside from NPLs, data on (specific) provisions and write-offs also could be used to determine implied PDs or to directly measure credit losses, wherein PDs and LGDs do not have to be determined separately16.

An illustrative example for a hypothetical bank is shown below. Under the StA, the capital requirements are assumed to be at 8 percent of total exposure and do not fluctuate over time17. For the IRB approach, the capital requirements have been determined as a fraction of exposures by using default rates observed by Moody’s during the last decade (for the universe of the firms rated by them) and an LGD of 40 percent, which is a realistic through-the-cycle (TTC) benchmark for advanced countries18. In the example, the capital requirements under the IRB approach fluctuate significantly over time and are lower in most years (e.g., through 2003 to 2008)19. The scaling factor compares the relative level of capital requirements between the StA and the IRB approaches over time (Figure 5.2). The scaling factor thus adjusts the level of the StA RWA to the level of the IRB capital requirements. Given the high level of LGDs for most emerging markets and low-income countries, the scaling factor would be above unity except for very benign years with very low PDs, indicating that economic risk is often underestimated by the StA capital ratio, which might provide a false sense of security (see also Hardy and Schmieder, 2013).

Figure 5.2Illustrative Example for the Scaling Factor (Advanced Economy)

Source: Author

Note: IRB = Internal Ratings Based; LHS = left-hand side; RHS = right-hand side; StA = Standardized Approach.

Basel III

Our tool allows a general assessment of the potential impact over time from the Basel III phase-in, informed by the aggregate outcome of the Quantitative Impact Study (QIS) 6 (Basel Committee on Banking Supervision, 2010b). More specific assumptions can be defined provided that bank-specific data are available. The simulation of the effect of Basel III rules on bank solvency includes three key elements (Basel Committee on Banking Supervision, 2010a):

  • an increase in RWA in 2011;

  • the phase-out of eligible capital beginning in 2013 (Total, Tier 1) and 2014 (Common Equity/Core Tier 1), respectively; and

  • changes in minimum capital ratios over time20.

Changes in the first two elements are simulated based on the outcome of the QIS 6 and are applied to banks according to their size (banks with equity of less than $3 billion are classified as Group 2 banks). For the increase in RWA, stress testers can define a portion of behavioral adjustment. If one assumes that there is a behavioral adjustment of 50 percent, for example, then banks are assumed to mitigate 50 percent of the expected increase of RWA, for example, through a change in their asset composition. Basel III can also be applied in terms of the profit retention rate. This can be done by either using uniform payout ratios (from the drop-down menu) or by defining bank-specific behavior (see Hardy and Schmieder, 2013, for a discussion on typical bank behavior).

B. Technical overview


The stress test framework is built on a modular kernel, which conveniently allows extensions and refinements (Figure 5.3). As a guide, the upper left-hand side contains the external parameterization and models, the lower right-hand side the input data. Once these are settled, the main sequence of the framework’s mechanics goes from top-right to bottom-left (i.e., define assumptions of the stress test, calculate impact on the solvency, calculate the impact of name concentration, aggregate, and finally summarize results). The solvency tool is designed to be easy to use, both to simplify stress tests for the growing community of stress testers (with heterogeneous needs) and to provide interested stakeholders with an opportunity to smoothly access the field:

  • It is Excel-based;

  • users are systematically guided through the sheet (based on a user-friendly layout, documentation, and help menus);

  • the layout makes it easy to set assumptions, including without the use of satellite models (or using predefined, simple rules, per Hardy and Schmieder, 2013);

  • drop-down lists allow the user to switch between different settings (for example scenarios); and

  • the framework has been tested and improved in various contexts.

Figure 5.3The Modular Design of the Stress Testing Framework21

Source: Author

Note: Dashed boxes refer to modules made available separately.

How Does the Framework Work? Running a stress test requires several steps (Figure 5.4): defining the scenario, configuring the framework, and entering the input data (see Step 1); linking the (macroeconomic) scenario to financial risks (Step 2); and executing the stress test (Step 3).

  • Step 1: The (macro) scenario definition. Outside the tool, the stress tester has to decide on the shock and, in the case of a macro stress test, a macroeconomic scenario (either with the help of a model or using expert judgment). Within the tool, the user has to first implement a straightforward parameterization that alters the template according to the number of banks, the granularity of the (credit) portfolio, and so forth. Last but not least, bank data have to be input, which are limited to about 30 variables in the minimum setup.

  • Step 2: From (macro) scenarios to micro impact. In the simplest case, stress testers run sensitivity tests for specific risk types, such as credit risk, market risk, operational risk, or concentration risk. In the more demanding case, including when an assessment is linked to a macroeconomic scenario (referred to as macro stress test), multiple risk factors are accounted for at the same time. In case of a macro stress test, the test is performed by linking macroeconomic risk factors to financial risks (i.e., banks’ asset quality) by means of so-called satellite models (i.e., econometric models).

  • Step 3: The execution of the stress test. The actual run of the test happens “on the fly”—that is, once the specific setting has been chosen and the satellite models calibrated, the final outcome in terms of banks’ balance sheets and capitalization is generated immediately. The solvency tests reveal bank-by-bank solvency under stress and the aggregate figures for the system (capitalization, number of banks failing the tests, capital needs, and so forth) as well as various financial soundness indicators (FSIs), including the risk contributions of various elements (credit losses, trading and investment losses, profit serving as a first buffer against losses) to stress.

Figure 5.4Stress Testing Framework—Conceptual Overview

Source: Author

Note: The elements in italics will be available through separate pieces of work. EAD = exposure at default; LGDs = losses given default; NPL = nonperforming loan; PDs = probabilities of default; P&L = profit and loss; RWAs = risk-weighted assets.

The Execution of the Stress Tests. A key advantage of the framework is that the actual run of the tests takes place immediately. Once the setting has been specified, the outcome of the tests is generated under the respective results tabs. The mechanics of the spreadsheet are summarized step by step under the roadmap tab. The results sheets not only define the methods but also display the results of the tests at both the level of the financial system (or the overall sample of banks) and on an institution-specific level.

The dispersion of the bank-specific outcomes of a macro stress test for 12 international banks through 2014 is shown in Figure 5.5. The output shows the evolution of different quantiles of the total regulatory capital ratios (the setting can easily be changed to Tier 1 and Core Tier 1 ratios) over time and the number of banks in different capital buffer ranges. The outcome for the system (which is not shown here) includes the number of banks failing the tests, capitalization needs in absolute and relative terms, as well as the contribution of different risk drivers to stress. An illustrative numerical example is available in Schmieder, Puhr, and Hasan (2011).

Figure 5.5Screenshot of Bank-Specific Results

Source: Author

2. Conclusion

To date, the methods used to carry out stress tests tend either to be too simplified to identify important risks or are black boxes, wherein the economics of the tests becomes less important than the technique itself. Our framework seeks to close this gap, using conceptual elements from more sophisticated tools but making them accessible in a convenient and flexible manner. The framework is designed for banks and could, in principle, also be used for other financial institutions provided that adjustments are made to account for the pertinent differences in the types of business in general and the associated vulnerabilities in particular.

This stress testing framework contributes to the growing body of applied stress testing work, by providing a tool that satisfies three main objectives. It (1) facilitates the design and running of a series of meaningful scenarios to derive an overview of key risk drivers and their sensitivities; (2) allows the user to run risk-sensitive tests based not only on statutory regulatory rules but also on economic measures of solvency; and (3) provides ease of use for the stress tester and facilitates the communication of the result to decision makers. In the last context, the framework is flexible to amendments, as it is Excel based and is thus a versatile tool for stress testers. An example of an amendment to the tool is the ability to simulate the impact of an increase in funding costs.

The stress test framework presented in this chapter represents a work in progress. The tool will continue to be calibrated to account for ongoing regulatory changes and the evolution of best practice. At the same time, it is important not to lose sight of the fact that the primary responsibility of the stress tester is to run meaningful stress tests. For instance, it is up to the stress tester to decide how financial risks of specific banks link to macroeconomic stresses but to also make sure that the scenarios are plausible in any given situation. Further, an important requirement for running meaningful stress tests lies in the quality of input data.


The SCAP covered the 19 largest U.S. bank holding companies (BHCs), accounting for two-thirds of aggregate assets of the banking system. The SCAP assessed the capital positions of these firms against a baseline macroeconomic scenario, based on market and consensus forecasts, and an adverse scenario defined by the authorities. The results for each institution were published in May 2009.

The “next-generation” framework presented in this chapter extends the work on applied (macro) stress testing by Čihák (2007).

This list is not exhaustive.

As a caveat, this simplified approach has to be carefully applied to avoid misleading results under specific circumstances and/or for specific banks.

In recent months, Core Tier 1 ratios of at least 10 percent became more common, whereas 4–8 percent was a more common benchmark in the past.

If a stress test is to be based on a different initial value (e.g., net interest income as the average ratio of net interest income over total loans to customers over the last x number of years), minor adaptations in the Excel links of the framework would be necessary.

Stress testers should alter these assumptions as appropriate under specific conditions.

Downturn LGDs are defined in paragraph 468 of the Basel II framework (Basel Committee on Banking Supervision, 2006).

Standard and Poor’s does not reveal the equation for its logarithmic approximation.

LGD is capped at 100 percent.

When the Basel II formula is applied without adjustments, correlations would go down when PDs are increased, which would be inconsistent from a risk perspective.

The reason is that for the highest-rated borrowers, default is very unlikely, unlike for their lower-rated counterparts. In the latter case, default is “expected” (i.e., there would be little surprise), whereas in the former case, a downgrade would make default increasingly more likely. That said, it remains relatively unlikely for highly rated counterparts, that is, not expected but rather unexpected.

This is also to account for the fact that the correlations in the IRB framework are modeled conditional on the PD.

The HHI is the sum of the squared exposure portions. Gordy and Lütkebohmert (2007) refer to an HHI calculated based on exposures to groups/borrower units.

Although this is less than ideal from a risk perspective, it is a step forward compared with traditional tests based on Basel I type capitalization measures.

With the advent of Basel II, provisions are meant to reflect expected losses, which is a required input.

There will be some changes in external ratings and in the value of collateral, but for most banks, they will be limited.

For emerging markets and low-income countries, LGDs are typically higher, at 60–80 percent, which has a significant effect on the scaling factor. The reasons are manifold, but legislation is a key factor (which would be important for the duration of the workout process, for example). Further elaboration on this subject is provided in Schmieder and Schmieder (2011).

The reason is that the Basel II framework has been calibrated with a view that IRB capital charges are, on average, lower than the ones under StA in the primary recipient countries (i.e., not the ones that voluntarily adopt Basel II), reflecting economic reasons on the one hand and providing banks with incentives to move to the IRB on the other.

The leverage ratio has not been added because of the late phase-in but will be part of future releases.

As the framework is based on an Excel template, the modules are characterized by different tabs. At the heart of the framework are the result sheets, which bring various sources of data, assumptions, and parameters together and summarize the outcome of the stress tests, both on the bank level and on the system level.

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