United Kingdom Financial Stability Assessment Program (FSAP) Update 2011 Guidelines for Solvency Stress Test

In recent years, the IMF has released a growing number of reports and other documents covering economic and financial developments and trends in member countries. Each report, prepared by a staff team after discussions with government officials, is published at the option of the member country.


In recent years, the IMF has released a growing number of reports and other documents covering economic and financial developments and trends in member countries. Each report, prepared by a staff team after discussions with government officials, is published at the option of the member country.

I. Introduction

1. This note summarizes key assumptions related to the calibration and estimation of the bottom-up, system-wide solvency stress testing component of the IMF’s United Kingdom FSAP Update. It contains specific instructions regarding the implementation of such a stress test using end-2010 data.

2. The objective of this stress test, as part of the FSAP mission’s analysis of financial stability, is to assess the capital adequacy of the banking sector under different macroeconomic scenarios. It is anticipated that this exercise will contribute to a more comprehensive understanding of the U.K. financial system’s general vulnerabilities to shocks without identifying individual institutions. The stress test will incorporate specific risk factors, including cross-border developments (particularly sovereign risk), funding risks, upcoming regulatory reforms, as well as the behavioral changes of banks.

3. Thus, the focus and consequences of the stress test differs from that of other stress testing exercises in which U.K. banks have involved. In particular, the recent European effort coordinated by the Committee of European Banking Supervisors (CEBS) and the forthcoming one by the European Banking Authority (EBA) jointly with European Central Bank (ECB), are aimed at analyzing inherent risks in the near term and to assess potential capital needs of specific institutions, from which management actions may be required. In contrast, no management action would be expected as a result of the FSAP stress tests.

4. A summary of the macro scenarios, key assumptions and hurdle rates is presented in Appendix I.

5. Firms are requested to conduct their bottom-up stress tests, using end-2010 data, and to report their results to the Financial Services Authority (FSA) by Wednesday, May 4, 2011. The FSA will perform due diligence analysis and report aggregate findings to the IMF FSAP team.

II. Macro Scenarios

6. The FSAP will examine three adverse macro scenarios based on the deviation of GDP projections from the central growth forecast—the IMF’s World Economic Outlook (WEO) baseline projection of real GDP growth Table 1 In portraying the stress scenarios as a “mark-up” over the most likely outcome, one can take into account perceived risk, i.e., the potential for central expectations to vary due to uncertainties as well as revisions in light of new information.

Table 1.

Overview of Macroeconomic Scenarios

(In percent)

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7. In line with the system-wide supervisory stress test conducted by the FSA, the FSAP also considers two additional adverse scenarios that amplify the adversity of stress in terms of severity and duration. These adverse scenarios comprise:

  • “Double dip recession” scenarios (mild/severe and short-term), namely,

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      one standard deviation of real GDP growth (based on the volatility of the two-year growth rate between 1980 and 2010) from the baseline growth trend over a five-year horizon (with positive adjustment dynamics during the subsequent three years), in which a shock to economic growth results in a sharp decline of output and rising employment over two years; and

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      two standard deviations of the same.

  • A “slow growth” scenario (severe and long-term) with a cumulative negative deviation of about 7.3 percentage points in real GDP, or an average annual growth rate of about 0.9 percent over a five-year horizon, as a result of a permanent shock to productive capacity amid rising inflation expectations.

8. The macro scenarios are in line with the spectrum of economic shocks considered in the context of other stress testing exercises (Figure 1):

Figure 1.
Figure 1.

Overview of Macroeconomic Scenarios: GDP Growth

Citation: IMF Staff Country Reports 2011, 227; 10.5089/9781462335510.002.A002

  • The stress tests completed by the CEBS, the FSA, as well as the FSAP have in common a “double dip”-like adverse scenario.

  • The mild and severe “double dip” scenarios are consistent with the adverse scenarios of the stress test conducted by the EBA for 2011 (over the first two years) and the new “anchor scenario” of the FSA’s, respectively.

  • The prolonged slow growth scenario remains unique to the FSAP stress testing exercise, and is considered the “tail shock” scenario.

  • The other macro variables used for the stress test (short-term interest rate represented by the 3-month LIBOR; the long-term interest rate represented by the 10-year Treasury bond yield; unemployment and headline CPI inflation) are determined using the U.K. authorities’ macro models.

9. The adverse scenarios are underpinned by the following possible narratives:

  • For the “double dip” scenario, useful approach would be to simulate a semipermanent commodity price shock (e.g., oil price), a large shock to foreign demand, and possibly, a small endogenous shock to the uncovered interest rate parity governing the sterling-dollar exchange rate (i.e. a risk premium). This shock can be interpreted as a shift of investors away from dollar assets towards sterling assets, thereby aggravating the appreciation of the sterling and leading at least to a small output loss in the United Kingdom in the short-term.

  • For the “slow growth” scenario, a useful approach would be to simulate a negative global shock to technical progress. As this is a negative supply shock and price pressures do not abate, short-term interest rates are not lower after the shock. This might prevent otherwise lower short-term interest rates if one were to assume temporary shocks to labor participation or a slowdown of productivity. By keeping consumption and saving endogenous there is no shock variable for the saving rate. Increasing savings by introducing a negative demand shock (via consumption) would otherwise be countered by lower policy rates.

10. Cross-border effects are considered in all macro scenarios. Assumptions about the type of shocks (temporary or permanent), and the degree to which they affect relevant countries have to be aligned:20

  • The WEO baseline GDP growth rates are applied to all countries affecting the macro projections and the macro-financial linkages of banks with significant footprints in other parts of the world, financial sector performance.

  • In absence of a Fund-imposed macro model for the adverse scenario of multiple countries, the simulated estimates from the IMF’s Growth Projection Model (GPM) should be used as a guide for a bank’s individual country projections.

  • The GPM simulates the spillover of a hypothetical EU shock to the other regions in the world, in terms of growth, inflation and interest rates (Appendix II). Additionally, a uniform change in the short- and long-term interest rates in both the euro area and the United States is provided. Firms are requested to scale the interest rate shock to the magnitude of changes in nominal GDP.

  • Conditioning on these effects should result in findings that are similar to the ones obtained under the adverse scenario in the CEBS/EBA stress tests, where spillover shocks from EU countries to the rest of the world are examined in a mild adverse scenario.21

III. Satellite Models

11. Satellite models should be used to specify the macro-financial linkages of firm performance over the forecast horizon. Firms are required to determine credit losses and various elements of profit, including funding costs in response to changing capitalization via so-called “satellite models” or expert judgment. When expert-judgment is used, it should be closely aligned with the output of satellite models.22 For satellite models should at least cover the last five years and include a lagged term, GDP growth, interest rates, other macroeconomic variables, and firm-specific variables, such as leverage, loan-to-asset ratio and the funding gap:

  • Credit losses are forecast based on separate models for write-downs and write-ups specific to each sector (corporate, retail, public, financial institutions).

  • Profits are estimated using separate models for interest income,23 interest expenses, net fee and commission income, and the operational expenses. Income taxes are assumed to be 25 percent for firms recording a profit and zero otherwise.

  • Funding costs are simulated through interest expenses (see below).

  • Trading income under stress should be aligned with GDP growth, based on historical data.24 To this end, GDP growth under each scenario and year can be matched to the corresponding GDP growth rate during the last 15 years (i.e. the growth rate closest to the simulated one). However, firms that experienced exceptionally high trading losses during the recent credit crisis (relative to the historical experience) may wish to model the probability distribution of trading income and match point estimates to the percentile level of projected GDP growth. Thus, a high-dimensional parametric fit function can be used to align GDP with trading.

12. The stress test should allow for the impact of losses on both the trading and banking books in order to cover all material exposures (such as sovereign debt) in economic terms, irrespective of their accounting treatment, and then estimate the effects on income and expenses.

13. As a general rule, satellite models need to be clearly documented and back-tested. Since firms conduct their own stress test (“bottom-up”), the FSA, together with the IMF FSAP team, will require full disclosure of the various satellite models and expert judgments on earnings capacity, market and credit losses as well as the change in funding conditions under the various scenarios.

IV. Key Assumptions

14. This section describes the various assumptions that should be applied to the bottom-up solvency stress test. Firms are also encouraged to conduct additional solvency stress tests without these restrictions so that the aggregate impact of business strategies and idiosyncratic assumptions can be compared and assessed.25

15. The sample of firms involved in the IMF’s solvency stress testing exercise includes the seven largest banks: The five largest U.K.-domiciled banking groups (HSBC, Barclays, RBS, Lloyds Banking Group, Standard Chartered); the largest foreign subsidiary with significant retail operations (Santander U.K.); and the largest building society (Nationwide). The stress test covers only banking operations within the United Kingdom. Banks with other significant businesses (e.g., insurance) that are separate companies, subject to separate regulations and that are effectively ring-fenced, may exclude those businesses from the stress test.

16. In order to measure the impact of stress in economic terms, an economic definition of capital adequacy should be used. Since all sample banks have adopted advanced Basel II standards, their economic profile is tested by calculating IRB capital requirements. As such, it is important to account for the point-in-time level of risk-weighted assets (RWAs), as well as changes in RWAs under stress in economic terms.

17. The test includes, as a minimum, credit risk and market risk. In order to allow for meaningful results, granular data should be used. Ideally, the tests are based on probabilities of default (PDs) and losses-given-default (LGDs) on a firm and/or portfolio level. In case this information is not available, other proxies such as provisions, NPLs and country-level LGDs may be referenced. Besides meaningful data on credit risk, data should include sectoral credit information, information on securities in the trading and banking book, and regulatory data on capital and capital adequacy.

A. Balance Sheet Growth

18. Firms’ balance sheets are assumed to be constant and to grow in line with nominal GDP. The growth rate assumption will also impact the forecast of losses and profits under various satellite models, which should be demonstrated. The assumption of a constant balance sheet falls in between the two extremes of static and dynamic balance sheets used in different stress tests—the FSA supervisory stress tests assume a dynamic balance sheet, while the planned EBA stress test assumes a static balance sheet (except for pre-agreed disposals).

19. Firms affected by stress are assumed to reduce asset growth through deleveraging or other means. Based on empirical evidence and expert judgment it is assumed that credit growth starts declining once firms reach a threshold of 2.5 percentage points above the minimum Tier 1 capital ratio applicable (e.g., 4.0 percent in 2011) over the forecast horizon. If a firm falls below the threshold, credit growth declines by twice the capital shortfall in percentage points. For instance, for a Tier 1 capital ratio of one percentage point below the regulatory minimum, credit growth declines by two percentage points. This adjustment is made in the same year the potential for deleveraging is assessed, and should shed light on potential deleveraging attempts by firms to cope with the capital shortfall during the same year (Figure 2).

Figure 2.
Figure 2.

Credit Growth Conditional on Tier 1 Ratio

(Example: Baseline scenario, year 1)

Citation: IMF Staff Country Reports 2011, 227; 10.5089/9781462335510.002.A002

20. Asset disposals are generally disallowed, and maturing exposures are assumed to be replaced:

  • Asset disposals (such as books in run-off or sales of non-core businesses) and acquisitions over time should not be considered, except where agreed with legally binding commitments under EU state aid rules (and consequent private contracts, e.g., LBG and RBS asset disposals and Santander U.K. acquisitions of selected RBS branch networks), consistent with EBA stress test assumptions.

  • Firms are also assumed to replace maturing exposures.

  • Any interim capital until end-2010 can be considered in calculations.

  • Firms in the Asset Protection Scheme (APS) should run stress tests on an APS vs. no-APS scenarios, and show the range of changes to solvency position.

B. Risk Measurement

21. Firms are expected to closely follow existing reporting standards, such that:

  • Probabilities of default (PDs) and losses-given-default (LGDs) are assumed to be “through-the-cycle”, but an appropriate way has to be found to run tests based on point-in-time risk parameters (such as through the scenario);

  • no feedback effect of firms’ lending on macro variables is assumed;

  • there is no change in the portfolio allocation to reduce RWAs; and

  • changes to firms’ lending standards and credit balance must be in accordance with changes in credit growth experienced during the last business cycle.

C. Dividend Payout Rule/Retained Income

22. The assessment of potential capital shortfall is made conditional on assumptions regarding the payout of dividends:

  • Dividend payouts are payable out of the previous year’s profit and, thus, cannot result in a drop below any of the minimum capital requirements.

  • Well-capitalized firms (i.e., firms that meet the minimum capital requirement and generate positive earnings after taxes) are assumed to pay out dividends only if they report profits.

  • Dividends are paid only by firms that satisfy all three measures of capital adequacy (total capital, Tier 1, and core Tier 1 capital ratios) and exhibit a leverage ratio of no less than three percent in a given year (after having created adequate provisions for impairment of assets and transfer of profits to staff benefits and statutory reserves).

23. The dividend pay-out rule is consistent with the maximum pay-out ratios defined under Basel III:26

  • The dividend payout ratio is defined as the percentage of “dividend payable in a year” to “net profit during the year”.

  • The maximum payout is capped at 40 percent of profits, in line with empirical evidence.

  • If the firm meets the minimum total capital ratio of 8.0 percent (after the envisaged dividend payout and, at the same time, exhibits sufficient Tier 1 and core Tier1 capitalization) but falls below the 10.5 percent threshold, it is considered capital-constrained and follows a schedule of fixed dividend payouts per Table 2, in anticipation of the full adoption of the “capital conservation buffer” of 2.5 percentage points as of January 1, 2019.

Table 2.

Payout Ratio Conditional on Capitalization under Stress

(In percent)

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D. Additional Elements Impacting Profits and Losses

Funding risk

24. The treatment of funding costs is explicit and avoids the simultaneity problem between contemporaneous losses and higher costs of capital. In each year, the impact of shocks to the firm’s balance sheet on the cost of funding (“funding rates”) should be estimated, and the effects on funding costs in the subsequent year are estimated (without taking into account the fact that losses themselves during the current year are attributable to higher funding costs).27

25. The estimation of the annual increase of funding costs is unaffected by possible balance sheet deleveraging:

  • Each year, funding costs are estimated—all short-term debt is funded at the new funding rate, but only the long-term debt due in each year is re-priced at the new rate. Based on this information, the change in the overall funding cost relative to the sample end-date (end-2010) can be derived. The short-term rate rises in proportion of the increase in long-term rate.

  • Against the background of rising competition for stable funding under adverse scenarios, the deposit rate moves in proportion to the change of funding costs paid by the bank, weighted by the levels of long- and short-term debt.28

26. A satellite model should be used to link short- and long-term funding costs (as a lagged term) to risk-weighted capital ratios (and/or leverage), loan loss provisions, funding gap and to simulate a non-linear effect with respect to default risk. If the firm’s existing approach does not meet this precondition, the following approaches to approximate the macro-financial linkages of short-term funding costs are suggested—one model based on historical inference (Appendix III, Option 1) as well as a refined approach of what has been done in the Global Financial Stability Report (GFSR), based on a reduced form estimation using an advanced contingent claims analysis (CCA) framework (Appendix III, Option 2). The cost of the short-term funding shock cannot be smaller than those provided under either method. In absence of a suitable model, the cost of long-term funding can be derived using expert judgment.

  • The first approach (“historical inference”) represents an aggregate funding risk model using country-level data to determine the relation between Moody’s KMV Expected Default Frequencies (EDFs) and (weighted-average) funding costs, i.e., taking into account the relative importance of different funding sources for specific countries as well as their costs (Option 1). The risk-based capital ratios for a series of rating grades are inferred from the Basel II capital model, by using the confidence level corresponding to the EDFs of banks. The method is heavily based on empirical data and determines changes in the cost of debt for the average banking sector. The idea is to determine the additional costs of underperformance of bank under stress resulting from funding.

  • The second approach (“advanced CCA”) provides an enhanced CCA-based projection of funding costs as a non-linear function of changes in asset values of individual banks, conditional on their leverage and liability structure (Option 2). Funding costs increase in response to a perceived erosion of asset values due to net loss in times of stress.29 The implied asset value of each bank is estimated using the Gram-Charlier extension to the conventional Merton (1974) option pricing formula based on equity market information. Then the change in the fair value credit spread is determined before and after a change to the asset value (as proxy for the marginal funding cost) for a given adverse scenario.

Valuation changes to fixed income holdings

27. The mark-to-market test of fixed income securities focuses on the projection of haircuts for holdings of both sovereign and bank debt. These haircuts will be applied to both the trading and banking books. Cash at central banks as well as repos or asset swaps where there is no economic interest in the security—for instance, instruments held against assets pledged to the BoE—are excluded. Moreover, haircuts will be applied only to non-AAA sovereigns.

Government debt holdings (sovereign risk)

28. For sovereign risk relating to both local and foreign government debt, firms are asked to adopt IMF estimates based on an assumed increase of sovereign distress consistent with market expectations, but does not entail a general shift in the yield curve (Table 3). We project the future yield-to-maturity (and associated haircut) based on changes in the market-implied default probability inferred from forward contracts on the country-specific sovereign credit default swap (CDS) spread, while excluding a common upward shift in yield curves (Appendix IV). The dynamics of monthly variations of expected default risk underpinning the changes of the sovereign CDS term structure between January 2009 and December 2010 are parametrically calibrated to inform estimates of default risk (and haircuts relative to end-2010) for each year of the forecast horizon. For the baseline, the median (50th percentile) is chosen. Haircuts under the adverse scenario take into account the volatility of market expectations of sovereign risk by assuming country-specific shocks at the 75th and 90th percentile of the probability distribution of default risk prior to the forecast horizon.

Table 3.

Debt Haircuts, as of December 31, 2010

(In percent)

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Bank debt holdings (banking sector risk)

29. The determination of haircuts for bank debt follows the assessment of sovereign risk. The recent crystallization of sovereign risk and its effects on government bond spreads has also been associated with rising spreads on bank debt. This has been reflected in a weakening in the implicit sovereign guarantee to banks, a lowering in the value of government bonds held by banks, and expected downgrades to banks following cuts to sovereign credit ratings. In all scenarios, the same haircuts are applied to firms’ holdings of bonds issued by other banks.

Remark: Excel spreadsheets for all funding and sovereign risk calculations are available upon request.

Valuation changes of net open positions due to foreign exchange (FX) shocks

30. Firms are asked to report separately the aggregate impact of FX shocks on net open positions in terms of a decline of the U.S. dollar, the euro and the Japanese yen vis-à-vis the pound sterling:

  • The shock for each currency should be based on two (four) standard deviations of the FX volatility during 2010 with respect to the mild and severe “double dip” scenario respectively.

  • Unexpected changes in FX rates translate into higher RWAs for market risk only and do not generate any knock-on effects on other elements of the stress test.

  • The shock should increase associated RWAs in 2011 (100 percent) and 2012 (50 percent) only.

V. Hurdle Rates: Basel III

31. Firms are required to assess solvency in accordance with recent changes of regulatory rules pursuant to agreements published by the Basel Committee on Banking Supervision (BCBS) in September and December 2010 (Figure 3). The recent changes include:

Figure 3.
Figure 3.

Overview of the Basel III Minimum Capital Requirements34

Citation: IMF Staff Country Reports 2011, 227; 10.5089/9781462335510.002.A002

  • higher in minimum capital requirement ratios, i.e., Tier 1 and common equity (core capital);

  • a more restrictive definition of eligible capital (“capital deductions”);

  • higher asset risk-weightings; and

  • the introduction of a maximum leverage ratio.30

32. Under this published schedule, firms will need to meet the following new minimum capital requirements in relation to RWAs as of January 1, 2013 (Table 4): 3.5 percent common equity/RWAs (up from 2.0 percent) and 4.5 percent Tier 1 capital/RWAs (up from 3.0 percent), in addition to the existing capital adequacy ratio (CAR) of 8.0 percent total capital/RWAs. These capital requirements are supplemented by a minimum Tier 1 leverage ratio of 3.0 percent.31 The regulatory adjustments (i.e., deductions and prudential filters), including amounts above the aggregate 15 percent limit for investments in financial institutions, mortgage servicing rights, and deferred tax assets from timing differences, are scheduled to begin on January 1, 2014.32

Table 4.

Capital Hurdle Rates

(In percent)

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33. The definition of capital at end-2010 should be consistent with the FSA guidelines, subject to phase-in, phase-out and grandfathering considerations:

  • The starting point for core Tier 1 and Tier 1 should be the official definitions as laid out in the FSA Handbook.33

  • For the phase-in of capital deductions, 20 percent (per annum) of core Tier 1 capital (such as deferred tax assets and minority interests that exceed the permissible limit) are deducted in 2014 and 2015. Firms must document deductions if the amount core Tier 1 to be phased out is less than 41.3 percent (which is the average value for large banks according to QIS-6).

  • For the phase-out of non-core Tier 1 and Tier 2 capital elements, it is the lower of either 10 percent (per annum) of the amount of capital to be phased-out or the amount of maturing capital maturing each year subject to phase out between 2013 and 2015.

  • Existing capital instruments are not grandfathered until they mature for the Tier in which they currently belong.

34. Higher RWAs, which will take effect as of January 1, 2011, should be taken into account with some form of expert judgment:

  • Changes in risk-weights for all risk types (credit, market and operational risk) increase equal to baseline nominal GDP growth (by accounting for business volume) throughout the forecast period.35 For credit and market risk, there should be an additional cumulative increase by at least 15.3 percent and 7.6 percent respectively between 2013 and 2015 per Table 5 (consistent with QIS-6 results for large banks). For the former, the minimum increase of RWAs applies to performing loans only.

  • Alternatively, firms may choose to estimate their own risk weights using available internal models (as of end-2010) while selecting minimum increases in risk weights only for certain sub-categories, such as securitization in the trading and/or banking book. Lower values for the changes in risk weights for credit and market risk need to be documented and approved by the FSA during the review process.

  • The risk-weights for credit risk are subsequently reduced by the RWAs of defaulted exposures, which should be approximated by taking 2.5 times the average RWAs for non-defaulted exposures (accounting for the fact that risk-weights for defaulted exposures were higher prior to default).

Table 5.

Risk-Weighted Assets

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excludes defaulted loans (which are subject to a separate treatment). Note: The change in RWA per year for each risk type and under each scenario is determined by the change in nominal GDP (except for selected risk-weights) and one-third of the impact of Basel III (for credit and market risk according to QIS-6) per year between 2013 and 2015 (based on the QIS-6 results). Firms can either adopt the catch-all change of minimum RWAs or choose to supplement own RWA models with minimum estimates of RWAs in certain subcategories of credit and market risk, such as counterparty credit risk (CCR), securitization in the banking book (Sec BB), stressed Value-at-Risk (sVaR), equity standard measurement method (SMM), and incremental risk charge and securitization in the trading book (IRC and Sec TB).

The impact of the FX shocks on market risk RWAs is estimated separately and added subsequently.

35. Firms should test the sensitivity of results to a voluntary capital buffer in anticipation of the graduated introduction of capital cushion for pro-cyclicality (“Capital Conservation Buffer”) past the forecast horizon. In order to account for the fact that banks have historically held more capital than needed, a (voluntary) capital buffer above the total capital (+2.5 percentage points), the Tier 1 capital ratio (+1.0 percentage point), and core Tier 1 capital (+1.0 percentage point) starting in 2011 are considered as a separate scenario.

36. This additional test using hurdle rates with capital buffers are for sensitivity check only. Firms will not be deemed to have actually “failed” if they do not meet those benchmarks and the results will not be published.

VI. Output

37. Firms assess capital adequacy under stress by reporting all capital measures for each year over the forecast horizon using the output template presented in Appendix V:

  • These metrics comprise (i) total capital; (ii) Tier 1 capital; and (iii) common equity capital.

  • Firms should also disclose the composition of capital in each period. In case of a capital shortfall, firms should show the calculated recapitalization needs.

  • Results are aggregated by the FSA and reported for each year of the forecast time horizon with some measure of dispersion, such as the inter-quartile range (IQR), i.e., between the 25th and the 75th percentile of the distribution of capital adequacy levels. This aggregation removes the possibility that individual firms can be identified.

  • The IMF will only publish results related to the stress test after consulting with the authorities and subject to the existing confidentiality agreement between the FSA and firms as well as IMF statutes that govern data confidentiality with national authorities.

38. Firms should report the major risk drivers (profitability, credit/trading losses, risk-weights). They should show the marginal impact of (i) including haircuts on sovereign and financial sector debt holdings; (ii) FX shocks to net open positions; (iii) capital phase-in/phase-out according to Basel III; and (iv) voluntary capital buffers.

39. Firms should document their estimation of important stress testing elements, such as funding costs, supervisory standards (risk-weightings), and macro-financial linkages (“satellite models” and/or expert judgment), and demonstrate their compliance with the IMF-provided minimum standards:

  • The FSA will engage, on an ongoing basis, with the stress testing efforts of firms to help ensure consistency of underpinning assumptions and suitability of models prior to the submission of the stress test results.

  • The results will also be sense-checked by the BoE and FSA against historical experience, other stress testing work by the firms, as well as by using results from a top-down version of the stress test exercise, processed using satellite models estimated based on aggregate data.

40. The proposed timeline for the completion of the bottom-up stress tests is presented in Appendix VI.

Appendix I. Summary of Scenarios, Key Assumptions and Hurdle Rates

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Appendix II. Other Macroeconomic Variables

Appendix Table 1.

Macroeconomic Projections from Simulated Shock to EU

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Note: Latin America (Brazil, Mexico, Colombia, Chile, Peru), Emerging Asia (China, India, Korea, Indonesia, Taiwan, Thailand, Malaysia, Hong Kong, Philippines, Singapore), and Remaining Countries (Russian, UK, Canada, Turkey, Australia, Argentina, South Africa, Venezuela, Sweden, Switzerland, Czech Republic, Denmark, Norway, Israel, Bulgaria, New Zealand, Estonia).
Appendix Table 2.

Macroeconomic Projections from Simulated Adverse Shock to EU and US interest rates

(applies to baseline and all adverse scenarios).

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Appendix III: Alternative Funding Risk Models

Option 1: Simple Empirical Estimation

Appendix Table 3.

Minimum Funding Cost: Empirical Estimation of Non-Linear Change

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Note: Funding cost exclude the cost of equity. The economic capital ratio includes a capital buffer above the hurdle rate of 2.5 percentage points.

Option 2: Contingent Claims Analysis (CCA)

The CCA-based projection of funding costs assumes that the average funding cost before the accrual of net losses during a given year is defined as spread s = –T-1 ln (1 – PGC/Be-rT), where the firm’s implied put option (using the Gram-Charlier extension) is defined as:


with “distance-to-default d1, skewness γ1T and kurtosis γ2T over maturity term T=1, standard normal density Φ(.), and debt service obligation (defined by the so-called “default barrier” Be-rT), which is the present value of outstanding debt. The asset volatility σA, is calculated as:


with bank equity volatility σE taken as the 3-month at-the-money implied volatility of the bank’s equity price. The value of implied assets A is determined from solving both equations above simultaneously.

The funding cost after the accrual of net losses is obtained by reducing the implied assets and increasing asset volatility accordingly. For a lower asset value A, asset volatility is adjusted utilizing the underlying asset dynamics of the Merton model, which yields the implied asset volatility under risk-neutrality:


where dDD=dDdAADdAA=μDr=(1Φ(d1))ADλσA=1Tln(1PBerT), with market value of debt D, and constant leverage Φ (d1). The new post-shock funding spread is then calculated as above.

Appendix IV: Sovereign Risk Model

The calculation of haircuts on fixed income holdings under different macro scenarios is based on an IMF-developed model for the valuation of sovereign debt using information from CDS markets. Sovereign bond prices for each year under each scenario are calculated using market expectations of default risk as reflected in forward rates on five-year sovereign CDS contracts. Five-year bonds are assumed to be representative of the maturities of banks’ bond holdings. Bonds for which market quotes from Bloomberg were available, with maturities between 4.5 and 6.5 were also included as in CEBS.

The standard pricing formula for coupon-bearing bonds is reconciled with the zero-coupon bond pricing formula


with the cumulative probability of default (PD) and loss given default (LGD), in order to project bond prices contingent on changes in idiosyncratic risk (irrespective of changes in the term structure of yields). Since the sample bonds carry regular coupon payments, the cash flow pricing formula


of the bond b in year t and time to maturity T-t is stripped of coupon payments c (with payout frequency n) and set equal to the quasi-zero coupon price at the last observable sample date after controlling for changes in market valuation over the course of 2010 in excess of baseline expectations of each country-specific yield-to-maturity according to CEBS. Thus, one can write


where rt is the yield in each year, f is the face value and the idiosyncratic risk is represented by the five-year cash CDS spread sCDS,j = –ln (1 – LGD × PD (t))/T of country j. Note that the actual end-2010 YTM refers to the observed YTM on December 31, 2010. The equation above is then solved for the risk-free rate rf at end-2010 (before the first forecast year) by maximum likelihood.

For all bonds of each sample country, the future prices Pb,t,j up to five years are calculated by applying the probability distribution of the forward five-year sovereign CDS spread F(sCDS,j)t to the zero-coupon pricing formula Pb,t,j = exp ((–rtT + F (sCDS,j)t/10,000)t) in order to inform estimates of default risk (and haircuts relative to end-2010) for each year of the forecast horizon. This is done for several bonds of each sample country (with a residual maturity T of about five years).

More specifically, the dynamics of monthly variations of expected default risk reflected in the forward rates on CDS spreads F(sCDS,j)t between January 2009 and December 2010 are parametrically calibrated as a generalized extreme value distribution with point estimates, x^t,a=μ^j+σ^j/ξ^j((ln(a))ξj1),where 1+ξj(xμj)/σj>0, scale parameter σj>0, location parameter µj, and shape parameter ξj = 0.5.36 The higher the absolute value of shape parameter, the larger the weight of the tail and the slower the speed at which the tail approaches its limit.37 For the baseline, the median (50th percentile) for x^t,a=0.5 is chosen. Since haircuts under the adverse scenario should reflect the volatility of market expectations, country-specific shocks to F(sCDS,j)t are assumed at the 75th percentile (for the mild “double dip” scenario and the slow growth scenario (“adverse i”), and 90th percentile (for the severe “double dip” scenario (“adverse 2”) of the probability distribution. Thus, for each year over the forecast horizon there are three bond prices {Pb,t,jbaseline; Pb,t,jbaseline1; Pb,t,jbaseline2} based on three different forward CDS rates {F(sCDS,j)tbaseline; F(sCDS,j)tbaseline1; F(sCDS,j)tbaseline2}.

Corresponding haircuts were calculated for each bond from changes in bond prices relative to the base year 20i0, using the following specification


where Pb,0 is the bond price in the base year.38

The haircut h for each sovereign j is calculated as an issuance size-weighted average of individual projected haircuts applied to a k-number of bonds outstanding,39 so that


where ΔPb,t,j is the haircut on bond b, and Amtb is the outstanding amount of bond b issued by country j. These haircuts should then be applied to banks’ sovereign bond exposures to countries40 j ϵ J held in both the banking and trading books as of end-2010. The sovereign bond losses or changes in valuation in each year t over the forecast horizon are calculated as ΣjJht,j×exposure0,j,based on a bank’s total exposure to country j at end-2010. Sovereign exposure gains, should they materialize, are ignored for stress test purposes.

Appendix V. Solvency Stress Tests: Desired Output

Appendix Table 4.

Suggested Output Template for Reporting by Firms to FSA

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Appendix Table 5.

Suggested Output Template for Reporting by FSA to IMF

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Appendix VI. Proposed Timeline for Completion of Solvency Stress Test

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Prepared by Andy Jobst (IMF/MCM).


One recent example where this was attempted is the CEBS stress testing exercise.


These shocks are scaled up (e.g. doubled) for the more severe “double dip recession” scenario, and spread over longer time horizon, for the “slow growth” scenario.


Benchmarks for the sensitivity of credit losses to macroeconomic variables are the stress tests conducted by the European authorities (CEBS in 2010 and EBA in 2011) as well as past system-wide stress tests conducted by the FSA.


For the large banks, a model using net interest income was referred to.


While empirical evidence suggests that there is a very weak relation between the trading result and macroeconomic conditions, it is assumed that unfavorable trading results coincide with macroeconomic shocks—a scenario that was observed for many U.K. banks during the crisis.


In that context, institutions are expected to demonstrate a clear link between their risk appetite, their business strategy, and their capital planning relative to the outcome of difference macro scenarios. In particular, institutions should assess and be able to demonstrate (by credible management actions, plans and other concrete steps, including changes in business strategy, reinforcing the capital base and/or other contingency plans) their ability to remain above regulatory minimum capital requirements during a stress that is consistent with their stated risk appetite.


Under Basel III, the maximum pay-out rules are defined based on core Tier 1 capitalization rather than based on total capitalization.


The macro-scenarios affect any liquidity stress test only insofar as any changes in funding costs will be consistent with assumptions applied to the solvency test.


Assumptions of funding cost in liquidity stress tests should be aligned with the stress parameters affecting the solvency condition of banks on a best effort basis.


We account for revenues but not the extent to which these losses themselves have been attributable to higher funding cost.


The changes in minimum capital requirements also have to be taken into account for counterparty risk and market risk considerations.


In particular, the regulatory adjustments will begin at 20 percent of the required deductions from common equity on January 1, 2014 and 40 percent on January 1, 2015. During this transition period, the remainder not deducted from common equity will continue to be subject to existing national treatments.


Basel Committee for Banking Supervision, 2010, “Results of the Comprehensive Quantitative Impact Study,” BCBS Publication No. 186 (December).


The upper tails of most (conventional) limit distributions (weakly) converge to this parametric specification of asymptotic behavior, irrespective of the original distribution of observed maxima (unlike parametric VaR models).


All raw moments are estimated by means of the Linear Combinations of Ratios of Spacings (LRS) estimator.


Note that the haircut estimation is not fully accurate, because in each year over the projected time horizon, the projected yield to maturity is imposed on an unchanged set of bonds. This implies no new government issuance (and time-invariant coupon), which overstates the actual haircut (unlike in cases when the sample of bonds changes and the remaining maturity is kept constant over the projected time period).


Haircuts cannot take negative values when price appreciation occurs between years (e.g., in response to “safe haven flows”).


Austria, Belgium, France, Germany, Greece, Ireland, Italy, Luxembourg, The Netherlands, Portugal, Spain, Sweden, Switzerland, UK, and the United States.

United Kingdom: Stress Testing the Banking Sector Technical Note
Author: International Monetary Fund