United Kingdom
Stress Testing the Banking Sector Technical Note
Author:
International Monetary Fund
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Publication Date:
03 Aug 2011
eISBN:
9781462335510
Language:
English
Keywords:
ISCR; CR; Tier 1; capital ratio; nominal GDP; holding; bullet; capital; credit risk; rule; cash flow; central bank; Basel III; BU result; liquidity profile; sample bank
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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.

Abstract

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. Introduction1

1. The U.K. FSAP stress testing exercise takes place following a period of unrivalled turbulence and consolidation in the history of the country’s financial sector. U.K. banks vary significantly in terms of their business models, risk management systems and geographic footprint and were accordingly affected differently by the crisis (Figure 1). Some large, systemically important banks were among those that felt the full brunt of the financial turmoil, and the U.K. authorities had to take decisive policy actions to restore stability to the financial system. The financial system is in the process of recovering but fragilities exist. The extent of its complexity and interconnectedness suggests that that it remains widely exposed to stresses originating domestically and elsewhere in the world, while being a potential conduit of shocks both locally and to the global financial system.

Figure 1.
Figure 1.

Major U.K. Banks: Differentiated Business and Geographic Models

(In percent of individual banks’ revenues)

Citation: IMF Staff Country Reports 2011, 227; 10.5089/9781462335510.002.A001

Sources: Bloomberg; individual bank reports; and IMF staff calculations.

2. Although conditions in the financial sector have improved significantly, vulnerabilities remain and new risks loom.2 U.K. banks are continuing to de-risk their balance sheets, but the diversity across individual banks means that they continue to be exposed to different risks (Figure 2). For instance, retail-focused institutions are likely to be more vulnerable if the recovery of the U.K. economy remains weak for a prolonged period of time, unemployment rises sharply and the real estate sector comes under further pressure or if debt affordability were to be negatively affected by a sustained tightening in monetary policy in light of continuing upside surprises on inflation. Meanwhile, institutions that are more reliant on wholesale funding are more at risk in and are susceptible to disruptions from internal and external pressures—notably, those arising from the direct and indirect impact from the realization of sovereign risks from vulnerable EU countries—which could impair access and/or drive up the cost of funding (Figure 3).

Figure 2.
Figure 2.

U.K. Banks: Breakdown of Assets and Risk-Weighted Assets

(In trillions of pound sterling)

Citation: IMF Staff Country Reports 2011, 227; 10.5089/9781462335510.002.A001

Source: BoE.
Figure 3.
Figure 3.

United Kingdom: Liquidity in the Banking System

Citation: IMF Staff Country Reports 2011, 227; 10.5089/9781462335510.002.A001

Sources: BoE; FSA calculations; CB Richard Ellis; De Montfort University; Dealogic DCM Analysis; financial statements of major U.K. banks; ICB; Office of National Statistics; and IMF staff calculations.

3. The financial crisis brought about a sharp deterioration in the United Kingdom’s public finances and fiscal space to further support the financial system is limited. Specific measures taken by the authorities have included acting as a lender of last resort to some banks; introducing exceptional liquidity support through the Special Liquidity Scheme; providing additional funding support through the Credit Guarantee Scheme; and creating the Asset Protection Scheme to provide participating institutions with protection against future credit losses. Additionally, the government injected a cumulative £70 billion of capital into several banks. As a result, the direct cost of fiscal support by the U.K. government to the financial sector relative to GDP is one of the largest in the EU to date (Table 1. With gross general government debt currently at around 79 percent of GDP and expected to peak at 87 percent of GDP in 2013, there is limited fiscal space to accommodate any further substantial shocks to the financial system.

Table 1.

Selected Advanced Economies: Recovery of Outlays and Net Cost of Financial Sector Support 1/

(Latest available date; in percent of 2010 GDP unless otherwise indicated)

article image
Source: Fiscal Monitor, IMF. Note: Fiscal outlays of the central government. In addition, some countries may have supported financial institutions via fiscal outlays at the subnational level or through other public sector institutions. For example, in Germany, capital injections from the Laender and KfW (development bank) amount to 1.1 percent of GDP; in Belgium, financial sector support from regional government amount to 1.6 percent of GDP.

Cumulative since the beginning of the crisis; latest available data, ranging between end-December 2010 and end-March 2011.

Direct support does not include asset purchases by the National Asset Management Agency, as these are not financed directly through the general government but with government-guaranteed bonds.

Direct support includes an estimated amount of €240 billion (9½ percent of GDP) for asset purchases.

4. The U.K. authorities have been very supportive of the FSAP mission undertaking comprehensive and stringent stress tests of the banking sector. Both solvency and liquidity stress tests were conducted (Figure 4). The stress test analysis is based on end-2010 audited financial data of the key institutions in the U.K. financial system, as well as the macroeconomic projections and financial market information available at that time. The 6 largest U.K. banks plus the biggest building society (hereafter “seven major U.K. banks”), accounting for 71 percent of total banking assets, are included in the solvency stress tests; 16 financial institutions, covering those 7 major banks, other building societies, 1 cooperative bank and foreign investment bank subsidiaries, totaling more than 80 percent the total assets in their respective categories, are captured in the liquidity stress tests (Table 2). The FSAP’s close collaboration with the authorities and banks means that granular supervisory information as well as banks’ own internal data and are also used in the tests, in addition to publicly available information.

Figure 4.
Figure 4.

Overview of the U.K. FSAP Update Stress Testing Exercise

Citation: IMF Staff Country Reports 2011, 227; 10.5089/9781462335510.002.A001

Table 2.

United Kingdom: Composition of the Banking System and Banks Included in the FSAP Update Stress Testing Exercise

article image
Sources: FSA; and BoE. Note: The core stress test sample, whose constituent members are marked “*,” represents 71.1 percent of banking sector assets and 89 percent of loans and advances to customers. “O” denotes financial institutions included in the stress test sample; “X” denotes those which are excluded. The BoE’s RAMSI uses Santander Group data.

Non-trading book.

5. The objective of the FSAP stress testing exercise is to assess the capital adequacy and the stability of funding of the U.K. banking sector by exploring system-wide vulnerabilities under adverse macroeconomic conditions. The solvency tests consist of BU stress tests run by the seven major banks and separate TD tests undertaken by the U.K. authorities and the FSAP team. The FSA aggregated the BU results received from individual banks, which were then reconciled by the FSAP team with those generated by the BoE’s Risk Assessment Model for Systemic Institutions (RAMSI) and the FSAP team’s Systemic Contingent Claims Analysis (CCA) model. The liquidity stress tests consist of TD tests of sixteen institutions which were conducted by the U.K. authorities, using supervisory data and applying parameters specified by the FSAP team. Basel III standards are applied in both solvency and liquidity tests; the results are also compared against the FSA’s interim supervisory framework requirements.

6. Key risks over both the short and medium term are incorporated into the design of the stress tests. More specifically, the U.K. financial system’s general vulnerabilities to shocks triggered by specific risk factors, as discussed above, upcoming regulatory reforms, as well as the behavioral changes of banks are examined. Where relevant, the recapitalization needs are estimated. It should be noted, however, that FSAP stress tests are for surveillance purposes, with a medium-term focus. The tests typically involve very severe stress scenarios to assess the overall resilience of the financial system, but may be less prescriptive than supervisory stress tests given resource and time considerations. The results provide a basis for policy discussions with the authorities, but do not require management action by banks.

7. Admittedly, the implementation of stress tests is conceptually challenging. For the U.K. banks, the assessment of vulnerabilities is not straightforward given the diversity of business models and global activities of the largest banks. Some of the presented findings are derived from valuation models that are subject to varying degrees of estimation uncertainty and assumptions, and these need to be taken into account when drawing policy conclusions. The key limitations are acknowledged and reflected as caveats in the relevant sections.

8. Overall, the solvency analysis shows that the largest U.K. banks have solid capital buffers that have reduced solvency concerns to a very low-probability confluence of adverse macroeconomic developments. Comprehensive BU stress tests by banks reveal adequate levels of capitalization even under severe macroeconomic stresses, with all banks passing the relevant Basel III and FSA hurdle rates under all adverse scenarios. The BoE RAMSI results show similar broad trends in terms of the overall solvency of the banking system in each scenario. Correspondingly, the forward-looking Systemic CCA model—which reflects market perceptions of each bank’s risk profile and its contribution to the likelihood of joint distress—confirms that markets remain broadly comfortable with the capital adequacy of the seven major banks against the prescribed shocks, relative to both the Basel III and FSA capital requirements, and that only extreme tail-risk events could potentially give rise to capital shortfall in the system.

9. At the same time, liquidity risks could potentially compromise the restoration of financial sector soundness. Although banks have made progress in moving away from less stable wholesale funding and towards deposit and secured term financing, the phasing-out of public sector support schemes and sizeable debt rollover over the next year leave many banks vulnerable to disruptions in funding markets. TD tests comprising reverse stress tests and proxies for the proposed liquidity measures under Basel III indicate that the banking system would be able to withstand moderately severe cash flow shocks.

10. Nonetheless, any realization of very low probability extreme tail risk events could still pose significant challenges. A situation where multiple banks concurrently experience a dramatic escalation of losses in a severe double-dip recession could result in a capital shortfall within the banking system, of up to 1.8 percent of GDP. Bottom-up stress tests show credit shocks to be the key risk driver for banks, while sustained disruptions to wholesale funding markets (funding liquidity risk), coupled with a persistent decline in asset values (market liquidity risk), could expose vulnerabilities at six-month maturities and longer. Given the rising risks in vulnerable EU countries since the cut-off date for the FSAP stress tests, U.K. banks’ exposures to the private sector in those countries and to core European banks could potentially lead to liquidity and solvency concerns (see discussion below). Further, market uncertainty over the ongoing deliberations by the Independent Commission on Banking (ICB), which could result in the ring-fencing of banking groups’ operations, may unsettle funding markets for banks.

11. This Technical Note is structured as follows. Section II presents the different components of the FSAP’s solvency stress tests, analyzes the results of the BU tests and cross-validates with the findings of the TD tests. The findings of the liquidity stress testing exercise are covered in Section III, followed by the conclusion and discussion on policy implications of the findings, in Section IV.

II. Solvency Stress Tests

12. Solvency stress tests based on banks’ end-2010 audited financial results are undertaken in this FSAP exercise. The objective is to determine the capacity of the banking sector to absorb any realization of key macro-financial risks, which would result in downside deviations from a defined baseline scenario. It should be emphasized that the stress tests are necessarily based on economic and market conditions as at the end of 2010, given the cut-off date of the exercise, and do not take into account recent developments in the international sphere.

13. The three-pronged approach to stress testing consists of:

  • BU stress tests conducted by individual banks based on guidelines provided by the FSAP team, drawn up in collaboration with the U.K. authorities (Attachment). The institutions involved in this exercise are the six largest U.K. banks, Barclays, HSBC, LBG, RBS, Santander U.K. and SCB, plus the largest building society, Nationwide.

  • Cross-validation of BU results through TD stress tests using the BoE’s RAMSI. The banks included in this sample are Barclays, HSBC, LBG, RBS, Santander Group.

  • Cross-validation of BU results by the FSAP team through TD stress tests using structural approach, the Systemic CCA framework. The banks included in this sample are Barclays, HSBC, LBG, RBS, Santander U.K., SCB and Nationwide.

14. Three types of growth trends and four macro scenarios, including three adverse ones based on different magnitudes of deviation of GDP from a baseline, are examined (Figure 5):

Figure 5.
Figure 5.

Overview of the U.K. FSAP Update Stress Test Scenarios

Citation: IMF Staff Country Reports 2011, 227; 10.5089/9781462335510.002.A001

Sources: BoE; FSA; and IMF staff calculations.

  • The baseline, which is specified as the IMF’s WEO baseline projections.

  • Two “double-dip recession” scenarios comprising:

    • (i) One standard deviation shock to real GDP growth from the baseline growth trend over the first two years of 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 in output and rising employment over two years (“mild double-dip recession” or “DD mild”).3

    • (ii) Two standard deviations of the same, consistent with the FSA’s 2011 anchor scenario (“severe double-dip recession” or “DD severe”).

  • A prolonged slow growth—i.e., severe and long-term—scenario with a cumulative negative deviation of about 7.5 percentage points from baseline growth, 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 (“prolonged slow growth” or “SG”).

15. Macro projections and guidelines on selected parameters are consistently applied across the different approaches as much as possible:

  • Based on the growth scenarios, related key macro and financial variables are projected, using the FSA’s macro models, for input into the solvency stress tests, namely, inflation, unemployment, residential and commercial real estate prices, short and long-term interest rates and equity prices (Figure 5).

  • Prescriptive assumptions covering areas such as (i) risk factors (loss rates, profitability, fixed income holdings, exchange rates, taxes, debt haircuts, funding costs) account for credit, market and operational risks, while trading book stresses take into account exposures from any breakdown in hedged positions; (ii), behavioral adjustments (balance sheet growth, dividend payout, credit growth, asset disposal, capital raising); and (iii) regulatory changes (capital requirements, risk-weighted assets, definition of capital) are also provided for all three approaches (Appendix I).

  • However, some elements have been excluded, such as on-going de-risking of balance sheets through restructuring—which is reflected in a gradual decrease of risk-weighted assets (RWAs)—and potential risks from restructured loans that no longer meet contractual covenants. Potential mitigating factors such as contingent capital arrangements and bail-in provisions are also not considered.

16. Solvency is assessed in accordance with recent changes in regulations published by the Basel Committee on Banking Supervision (BCBS) in September and December 2010 (“Basel III”) and compared against the FSA’s requirements under its Interim Capital Regime. Thus, the hurdle rates applied in the FSAP stress tests follow the graduated schedule of Basel III (Table 3); since the conservation buffer will come into effect only after the end of the stress test horizon, it is not directly relevant for this exercise. The post-stress capital requirements under the FSA’s Interim Capital Regime of 4 percent for common equity Tier 1 capital ratio and 6–7 percent for Tier 1 capital are juxtaposed against the results to determine banks’ ability to meet the supervisor’s requirements.

Table 3.

Overview of the Basel II and III Minimum Capital Requirements

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Source: Basel Committee for Banking Supervision. Currently Basel II. Transition to Basel III.

A. Bottom-Up Solvency Stress Tests

17. The BU stress tests involving the seven major banks form the core element of the analytical framework for solvency risk. The exercise was administered jointly with the FSA, with banks conducting the stress tests using their own internal models. Detailed guidelines on assumptions were drawn up by the FSAP team in collaboration with the FSA and in consultation with the banks themselves and applied (Attachment). These guidelines contain key assumptions relating to the calibration and estimation of important risk drivers, which are necessary to ensure a robust and credible exercise. All banks in the sample have undergone, are or will be undergoing the FSA’s supervisory stress tests under the Internal Capital Adequacy Assessment Process (ICAAP), which provides further opportunity for cross-validation by supervisors.4 The definition of capital as at end-2010 for the purposes of the BU stress testing exercise follows the FSA guidelines per the interim supervisory framework, which differ in parts from those defined by Basel III (Appendix II).

18. Each bank submitted a “report card” of the outcome to the FSA, which subsequently aggregated these results and provided them to the FSAP team on an anonymized basis for further analysis. The analysis estimates changes in potential losses as well as post-shock RWAs and, where applicable, the recapitalization needs of a particular bank (Figures 6–8). The team also met with the risk management team from each bank to discuss the nuances of the results.

Figure 6.
Figure 6.

Distribution of Core Tier 1 Capital Ratios from the U.K. FSAP Update Bottom-Up Stress Tests, 2011–15

(In percent)

Citation: IMF Staff Country Reports 2011, 227; 10.5089/9781462335510.002.A001

Sources: FSA; major U.K. banks; and IMF staff calculations.
Figure 7.
Figure 7.

Distribution of Tier 1 Capital Ratios from the U.K. FSAP Update Bottom-Up Stress Tests, 2011–15

(In percent)

Citation: IMF Staff Country Reports 2011, 227; 10.5089/9781462335510.002.A001

Sources: FSA; major U.K. banks; and IMF staff calculations.
Figure 8.
Figure 8.

United Kingdom: Distribution of Total Capital Ratios from the U.K. FSAP Update Bottom-Up Stress Tests, 2011–15

(In percent)

Citation: IMF Staff Country Reports 2011, 227; 10.5089/9781462335510.002.A001

Sources: FSA; major U.K. banks; and IMF staff calculations.

19. The results essentially show that banks hold robust capital positions and would remain well-capitalized and largely profitable under all three adverse scenarios:

  • Capital ratios stay above the respective minimum regulatory requirements.

    • The weighted-average capital ratios (total capital, Tier 1 capital and core Tier 1 capital) for the seven banks exceed the Basel III minima by at least 6 percentage points at any time over the stress test horizon (and the FSA Interim Capital Regime requirements by at least 4 percentage points).

    • The weighted-average core Tier 1 capital ratio for the aggregated sample stays at or above 8.8 percent (severe double-dip scenario) throughout the stress-test horizon and the average leverage ratio never drops below 4.6 percent.

    • The weighted-average core Tier 1 capital ratio for the aggregated sample stays at or above 8.8 percent (severe double-dip scenario) throughout the stress-test horizon and the average leverage ratio never drops below 4.6 percent.

    • On an individual basis, the lowest capital ratios are typically observed in 2013. Under the severe double-dip scenario, the median core Tier 1 ratio drops to 7.6 percent, largely attributable to high credit losses during the first two years of the stress test horizon. During the same year, the median Tier 1 and total capital ratios are 9.3 and 12.2 percent, respectively.

    • Even if voluntary capital buffers of 2.5 percentage points above the total capital ratio and one percentage point above the core Tier 1 and Tier 1 capital ratios are incorporated in the hurdle rates, the potential shortfall in total capital would not exceed £2.1 billion (0.1 percent of GDP) under the severe double-dip scenario.

  • The severe double-dip scenario, which is consistent with the FSA’s 2011 anchor scenario, has turned out to be the most stringent. The prolonged slow growth scenario does not have as negative an impact as initially anticipated—an outcome that banks attribute to the relatively benign unemployment profile associated with that scenario. Indeed, the impact of prolonged slow growth on all capital components generally appears more benign than that of the mild double-dip recession.

  • The diverse operations of the major banks, both across business lines and in terms of their geographic footprints mean that each is exposed to a different set of risks. Almost all banks are most affected by the severe double-dip recession scenario, but the extent of the impact of the other two adverse scenarios appears to depend on their business focus, with retail banks more affected by the mild double-dip recession, while banks with investment banking operations appear more susceptible to the prolonged slow growth scenario. Nonetheless all banks appear to have sufficient capital to absorb the prescribed shocks.

  • Aggregated information on common risk drivers suggests that the resilience exhibited—which could be aided by considerable creditor forbearance at some banks—may mask some vulnerabilities. Persistently high credit losses during a recession represent the main risk.5 Not surprisingly, retail-focused banks would be hardest hit by any sharp economic downturn. Separately, exchange rate shocks on major currencies and higher risk weights on securitization and counterparty risk exposures under revised regulatory standards are the main contributors to the increase in RWAs for market risk.

  • The sovereign exposures of the major banks do not appear to represent a major source of risk, unless stresses lead to severe disruptions in wholesale funding markets (see below). In general, banks appear to have significantly reduced their banking book exposures to non-AAA rated sovereign and bank debt by end-2010, leaving their trading books to absorb any potential further haircuts. Under the severe double dip scenario, average potential losses amount to the equivalent of 0.07 percent of 2010 GDP (£1 billion) over the stress test horizon, with 2011 losses alone amounting to an equivalent of 0.2 percent of 2010 GDP (£2.9 billion)—around 20 percent of the exposure from the previous year’s debt holding.

20. Overall, the results confirm the significant recapitalization efforts and the de-risking of balance sheets by banks. The latter observation is consistent with the FSAP’s own quantitative analysis (see below). However, a possible cumulative increase in RWAs of more than 30 percent over the stress test horizon under each scenario suggests that there may be room for further de-risking of balance sheets, a process that is continuing at present. Discussions with banks on their reverse stress tests reveal that a combination of severe adverse events (e.g., persistently high unemployment, stagflation, rising interest rates, sovereign defaults, geopolitical risks) could lead to solvency concerns. Banks are required to formally incorporate reverse stress tests in the next round of the ICAAP.

B. Top-Down Solvency Stress Tests

The BoE’s RAMSI

21. RAMSI is used to generate stress estimates for assessing the systemic risk of the five largest U.K. banks, using end-2010 financial data. The model provides a quantitative framework for assessing how shocks transmit through balance sheets (Box 1). It incorporates network interactions and feedback effects arising from both the asset and liability sides of the balance sheets of banks.

22. RAMSI’s satellite models are initially used to generate idiosyncratic variables from the macro-financial variables derived from the FSA’s macro models (Figure 9). The model has at its center a detailed description of each banks’ balance sheet and profit and loss account and uses a set of inter-connected modules to analyze banks’ dynamic response to a change in macro-financial conditions. Projections of interest income, non-interest income, trading income, operating expenses and credit losses are used as inputs to estimate shocks to capital in RAMSI and as inputs to satellite models underpinning the Systemic CCA stress tests (Figure 10).

Figure 9.
Figure 9.

Estimation of Satellite Models in the U.K. FSAP Update Stress Testing Exercise

Citation: IMF Staff Country Reports 2011, 227; 10.5089/9781462335510.002.A001

Figure 10.
Figure 10.

Application of Satellite Output in the RAMSI and the Systemic CCA Stress Tests

Citation: IMF Staff Country Reports 2011, 227; 10.5089/9781462335510.002.A001

23. The stress test results obtained under the RAMSI framework suggest that the largest U.K. banks are resilient even against severe stress (Figures 11–13):

Figure 11.
Figure 11.

Distribution of Core Tier 1 Capital Ratios from the BoE RAMSI Top-Down Stress Tests for the U.K. FSAP Update, 2011–15

(In percent)

Citation: IMF Staff Country Reports 2011, 227; 10.5089/9781462335510.002.A001

Sources: BoE; and IMF staff calculations.
Figure 12.
Figure 12.

United Kingdom: Distribution of Tier 1 Capital Ratios from the BoE RAMSI Top-Down Stress Tests for the U.K. FSAP update, 2011–15

(In percent)

Citation: IMF Staff Country Reports 2011, 227; 10.5089/9781462335510.002.A001

Sources: BoE; and IMF staff calculations.
Figure 13.
Figure 13.

United Kingdom: Distribution of Total Capital Ratios from the BoE RAMSI Top-Down Stress Tests for the U.K. FSAP Update, 2011–15

(In percent)

Citation: IMF Staff Country Reports 2011, 227; 10.5089/9781462335510.002.A001

Sources: BoE; and IMF staff calculations.

  • The cyclical treatment of projected trading income and a sluggish increase in credit losses are the key risk drivers. The largest impact appears to be on banks with the most diversified business models.

  • Although all banks pass the capital hurdle rates under all scenarios, two banks experience a substantial impact on capital in the severe double-dip scenario. Core Tier 1 ratios diverge by as much as 6.2 percentage points from the corresponding baseline scenario, but remain at least 6 percentage points above the relevant hurdle rates.

  • In contrast to the BU stress test results, shocks to sovereign and bank debt appear to have greater impact on capital adequacy. When the FSAP’s debt haircut methodology is applied to bank holdings of non-AAA rated sovereign and bank debt on both the banking and trading books of banks, potential aggregate capital losses of up to a maximum equivalent to 1.8 percent of 2010 GDP (£26 billion) in sovereign and bank debt are estimated under the severe double-dip scenario, in 2011. The combined impact on core Tier 1 capital would be 10 percent, translating to almost a one percentage point decline in the core Tier 1 ratio, still well above the relevant hurdle rates. Over the five-year stress test horizon, the realization of risks to sovereign and bank debt could have an impact averaging the equivalent of 1.7 percent of 2010 GDP (almost £25 billion).

  • The impact of the prolonged slow growth scenario on the banking system appears similar to that of the mild double-dip recession. The distribution by bank differs somewhat between the two, but the median result above the relevant hurdle rates shows a generally consistent trend for each capital ratio.

Overview of the BoE’s RAMSI 1/

RAMSI is a model of the major banks in the U.K. financial system. The model has at its centre a detailed description of each bank’s balance sheet and profit and loss account, and uses a set of interconnected modules to analyze banks’ dynamic response to a change in macro-financial conditions. The framework also incorporates a network model that captures second-round “contagion” risk stemming from interbank exposures, on both the asset and liability side, and from the interaction between balance sheets and asset prices. 2/

RAMSI produces projections for key banking sector variables conditional on projections for the macro-financial environment. RAMSI can generate its own macro-financial projections using a medium-scale Vector Auto-regression,3/ or RAMSI can use macro-financial inputs from another source. For the FSAP, for example, the baseline conditioning paths were taken from the October WEO. A set of independent modules is then used to map these projections into bank-specific profit and loss numbers, focusing on five key headline items: net interest income, credit losses, non-interest income excluding trading income, net trading income and operating expenses. In addition, an asset pricing model is used to estimate any changes in the market value of banks’ exposures triggered by changes in equity prices or market interest rates.

These modules are largely based on reduced-form econometric equations. For instance, credit losses are estimated using a system of regressions that link write-off rates on broad asset classes (e.g., domestic mortgages) to a set of empirically relevant macro indicators (e.g., unemployment and house prices). The main exceptions are the net interest income and market value calculations, which rely on a calibrated asset pricing model that incorporates a simple no-arbitrage condition.4/ A key feature of the model is that the spreads on banks’ exposures relative to risk-free (government) yields are endogenous and will generally change in response to a macroeconomic shock; as credit losses rise, for example, banks increase the spread on risky lending to corporates and households.

Risk factors and profit and loss numbers are simulated on a quarterly basis, but RAMSI can be run over an arbitrary forecasting horizon because it takes account of the reinvestment of profits between quarters. Box Figure 1 gives a stylized overview of how the reinvestment model is linked to the P&L projections, and illustrates the key behavioral assumption behind the model.5/

Box Figure 1.
Box Figure 1.

Investment and Balance Sheet Dynamics in RAMSI

Citation: IMF Staff Country Reports 2011, 227; 10.5089/9781462335510.002.A001

At the beginning of each quarter, each bank’s income statement is simulated based on the estimated impact of the chosen macro-financial scenario. Profits are split between tax, dividends and potential retained earnings. Three cases can then arise. If the bank makes a loss, its capital buffer is eroded and the balance sheet shrinks. The process continues until the bank manages to make a profit or breaches the regulatory capital buffer. If the bank’s earnings are positive but, given the state of the balance sheet, not sufficient to achieve an exogenously set capital ratio target, the bank retains the earnings entirely to boost capital and only purchases zero-risk weight assets (to ensure the balance sheet balances). It continues to do this in later periods until the target capital ratio is met. Finally, if earnings and existing capital are sufficient to exceed the target, the bank expands its assets to hit the target, holding constant the distribution of assets at the start of the projection.

The upper arrow in the diagram highlights that income in the following period depends on the updated values of assets and liabilities given the flows in the previous period, and given macro-financial conditions at that point. The reinvestment model thus generates a complex feedback loop where the size and composition of the balance sheets is allowed to change dynamically over time. Modeling the reinvestment process is necessary to achieve internal stock-flow consistency. It also implies that banks in RAMSI are not completely passive, although their responses to exogenous shocks are dictated by simple behavioral rules rather than an explicit forward-looking optimization.

1/ Prepared by BoE staff. 2/ Alessandri et al. (2009) discuss the structure of the prototype model; Aikman et al. (2009) focus on liquidity feedbacks. 3/ The model includes 26 domestic and foreign macro-financial variables, including short and long-term government interest rates, equity prices, house prices and commercial property values, output and unemployment, and income gearing. The VAR is estimated using Bayesian methods, and it can be used to generate joint point-wise forecasts or distributions for these indicators, either unconditionally or subject to a predefined path for a subset of the variables, as is typical in stress testing. 4/ Details and applications can be found in Alessandri and Drehmann (2010) and Drehmann et al. (2010). 5/ The diagram abstracts for simplicity from external shocks and network externalities.

The IMF’s market-based systemic solvency model

24. A second approach to TD stress testing using the Systemic CCA model is undertaken to estimate systemic solvency risk. The Systemic CCA framework accounts for the dependence among individual banks in estimating the joint market-implied potential losses under systemic distress assumptions in order to estimate the resulting shortfall (Box 2). Under this approach, the banking sector is essentially viewed as a portfolio of individual potential losses, specified as implicit put options with individual risk parameters, whose joint exposure to common risk factors can be accounted for by including their dependence structure (since conventional bivariate correlation is ill-suited for systemic risk analysis when extreme events occur jointly and in a non-linear fashion)

25. The interdependencies, which proved critical during the crisis, are analyzed using a forward-looking, market data-based framework. Data from January 2005 to March 2011 are used to estimate the central case (median) market-implied potential capital losses as well as the losses during extreme market stresses at a statistical probability of 5 percent or less (expressed as “tail risk”).6 The estimates are then used to determine individual contributions to systemic risk.

Historical shock estimates

26. An examination of the historical estimates suggest that only a few banks generated the bulk of systemic risk during the crisis (Table 4):

Table 4.

United Kingdom: Individual Contributions of Large Banks to Systemic Risk during the Crisis—Market-Implied Joint Capital Losses

(Average per time period, in percent of joint capital shortfall)

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Source: IMF staff calculations.

Each bank’s percentage share is based on its time-varying contribution to the multivariate density of potential losses at the 50th (median) and 95th percentiles. The multivariate probability distribution is generated from univariate marginals (based on generalized extreme value assumption) and a time-varying dependence structure.

  • At the time, the escalation of joint solvency stresses was mostly attributable to banks that required government support.

  • The contributions of individual banks to both the median and extreme market-implied joint capital loss amounts are consistent with the BU stress test results insofar as the concentration of solvency risks in some banks creates a skewed dispersion.

  • The estimated percentage share of systemic risk in different periods of the crisis reveals that at the apex of the credit crisis, the concentration of risks increased beyond the previous average, with the median contribution of under 10 percent of joint capital losses—far below the expected median share of 14.3 percent for the sample of seven banks in a uniform distribution.

  • There has been significant de-risking of banks’ balance sheets since late-2008.

27. The historical estimates of the joint capital losses are used for stress testing. By modeling how macroeconomic conditions and bank-specific income and loss elements (net interest income, fee income, trading income, operating expenses, and credit losses) have influenced the changes in the financial institutions’ market-implied potential losses—as measured by monthly implicit put option values based on an “elevated” default barrier—it is possible to link a particular macroeconomic path (and associated financial sector performance) to potential losses in the future. Alternatively, it is possible to adjust the implied assets of each sample bank by projected profitability in order to determine changes in the put option value underpinning the level of market-implied potential losses. The amount by which the capital losses fall below the defined “distress barrier” represents the potential capital shortfall.

28. Two different methods are thus adopted to model the macro-financial linkages affecting individual potential losses that determine joint capital shortfall under the Systemic CCA approach. Using projections on individual bank performance generated by RAMSI, two types of satellite models are applied for the specification of the macro-financial linkages of any capital shortfall, based on the implied Basel III Tier 1 capital hurdle rates (and compared against the FSA’s Interim Capital Regime requirements). For each model, the individually estimated capital loss is aggregated using the Systemic CCA framework with a five-year sliding window and monthly updates over the forecast horizon:

  • In the first model (“IMF satellite model”), the historical sensitivity of the market-implied capital loss is estimated from several macroeconomic variables7 (short-term interest rate [+], long-term interest rate [-], real GDP [-], and unemployment [+]) and bank-specific variables (net interest income [+], operating profit before taxes [-], credit losses [+], leverage [+], and funding gap [+]) using a dynamic panel regression specification.

  • In the second model (“structural model”), the value of implied assets of each bank as at end-2010 is adjusted by forecasts of operating profit and credit losses generated in the RAMSI model in order to derive a revised put option value (after re-estimating implied asset volatility), which determines the market-implied capital loss.

Central case tail risks

29. The central case results under Systemic CCA could be considered analogous to those obtained under the BU and RAMSI tests; consistent with those approaches, the Systemic CCA findings are that any impact from the realization of systemic solvency risks would be limited even in a severe recession. After taking into account further declines in the market value of sovereign and bank debt held by the major banks, we find that the joint potential capital loss would be contained under all adverse scenarios and that there would be no capital shortfall (Figure 14 and Table 5):

Figure 14.
Figure 14.

Systemic CCA Estimates of the Market-Implied Joint Capital Losses from the U.K. FSAP Update Top-Down Stress Tests, Historical and Potential (with IMF Satellite Model)

(In billions of pound Sterling)

Citation: IMF Staff Country Reports 2011, 227; 10.5089/9781462335510.002.A001

Source: IMF staff calculations.
Table 5.

Systemic CCA Estimates of the Market-Implied Joint Potential Capital Loss and Resulting Shortfall from the U.K. FSAP Update Top-Down Stress Tests, 2011–15

(Average over time period, in billions of pound sterling unless stated otherwise)

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Source: IMF staff calculations. Note: The estimations show the joint capital requirements for maintaining the market value of Tier 1 capital, with a gradual increase of the hurdle rate from 2013 onwards consistent with the Basel III proposal as at December 2010.

The IMF satellite model uses a set of macroeconomic variables (short-term interest rates, long-term interest rates, real GDP growth, and unemployment) as well as income elements specific to each bank (operating profit, net interest income) to project potential losses generated by the CCA methodology.

As an alternative, projected operating profit based on RAMSI model results is integrated in the CCA framework by adjusting implied bank assets, which increase potential losses via an option pricing approach. The treatment of losses from haircuts on holdings of sovereign and bank debt differs between both satellite model approaches. In the case of the former, these losses are calculated each year and added to the estimated overall potential losses. In contrast, for the alternative satellite model, losses from these debt holdings are subtracted from the RAMSI-model projected operating profit each quarter.

The tail risk at the 95th percentile represents the average probability density beyond the 95th percentile as a threshold level.

  • Overall, both satellite models yield similar and consistent results despite their rather different specifications. They suggest robustness of estimates under either a panel regression approach or a structural approach via updates of model parameters using forecast changes in profitability.

  • Consistent with the findings in the other two stress test approaches, the severe double-dip recession scenario has the biggest impact on the banking system. The impact of the mild double-dip and prolonged slow growth scenarios are almost similar. The banking system remains solvent in all cases.

  • Existing capital buffers are sufficient to absorb the realization of central case (median) joint solvency risks. Under baseline conditions, potential joint solvency pressures from the realization of slowing profitability, moderate credit losses and risks to sovereign bank debt holdings would be relatively benign, resulting in joint potential capital losses averaging the equivalent of 0.03 percent of 2010 GDP (£0.4 billion) over 2011–15. In the event that the severe double-dip scenario were to be realized, capital losses could amount up to an average 0.12 percent of 2010 GDP (£1.8 billion) over the next five years. The resulting capital balance would remain comfortably above the “distress barrier” under the Basel III capital hurdle rates, and there would be no resulting shortfall. (There would also be no shortfall under the FSA’s Interim Capital Regime requirements.)

  • As a comparison, perfect correlation of solvency risks across sample banks, as implied by the sum of individual potential losses without taking into account dependence across institutions, could result in larger capital losses albeit still above the required capital adequacy levels. In this case, average capital losses could amount up to 1.1 percent of 2010 GDP (£15.6 billion) over the next five years under the severe double-dip scenario with haircuts to sovereign and bank debt, or as low as 0.1 percent of 2010 GDP (£1.6 billion) under the corresponding baseline scenario (Table 6).

Table 6.

Systemic CCA Estimates of the Market-Implied Total Potential Capital Loss from the U.K. FSAP Update Top-Down Stress Tests, 2011–15

(Average over time period, in billions of pound sterling unless stated otherwise)

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Source: IMF staff calculations. Note: The estimation shows joint capital shortfall below market-implied Tier 1 capital, with a gradual increase of the hurdle rate from 2013 onwards consistent with the Basel III proposal as of December 2010.

The IMF satellite model uses a set of macroeconomic variables (short-term interest rates, long-term interest rates, real GDP growth, and unemployment) as well as income elements specific to each bank (operating profit, net interest income) to project potential losses generated by the CCA methodology.

As an alternative, projected operating profit based on RAMSI model results is integrated in the CCA framework by adjusting implied bank assets, which increase potential losses via an option pricing approach. The treatment of losses from haircuts on holdings of sovereign and bank debt differs between both satellite model approaches. In the case of the former, these losses are calculated each year and added to the estimated overall potential losses. In contrast, for the alternative satellite model, losses from these debt holdings are subtracted from the RAMSI-model projected operating profit each quarter.

“Tail of the tail” risks

30. Although much reduced since the crisis, potential challenges exist from the realization of a very low probability extreme tail risk of multiple banks experiencing a dramatic escalation of losses amid a rapidly deteriorating macroeconomic environment. The Systemic CCA model has the added advantage of estimating a distribution of the potential impact from shocks. Thus, we are able to estimate the outcome of a 5 percent “tail of the tail” risk event (at a very high statistical confidence level beyond the 95th percentile) under this method. Under the adverse scenarios, the market-implied capital shortfall would be significantly higher, likely as a result of significantly lower profitability in conjunction with a sharp deterioration in asset quality and weaker fee-based income:

  • The extreme tail risk of assumed macro shocks could erode current capital levels to below the distress barrier, resulting in a capital shortfall in the system. A 2 percent probability of a severe double-dip recession scenario beyond the 95th percentile (i.e., a 0.1 percent probability event) could result in average joint capital losses of up to 3.4 percent of 2010 GDP (£50 billion), albeit still well below the peaks seen during the crisis (Figure 14). Under this scenario, an average capital shortfall of between 1.3–1.6 percent of 2010 GDP could materialize relative to the Basel III Tier 1 hurdle rates (and 1.6–1.8 percent of 2010 GDP relative to the FSA Interim Capital Regime Tier 1 requirements). At the extreme tail, the prolonged slow growth scenario could yield average joint capital losses of up to 2 percent of GDP (£29 billion), which translates to an average shortfall of up to 0.4 percent of 2010 GDP (£6.3 billion).

  • Depending on the timing and adversity of macroeconomic conditions as well as the evolution of sovereign risk affecting banks’ government and bank debt holdings, capital losses could range widely over the five-year horizon. Estimates suggest that potential losses could range between zero (baseline, double-dip mild and double-dip severe without debt haircuts, from 2013 onwards) to an equivalent of between 6.4–7.1 percent of 2010 GDP (double-dip severe with sovereign and bank debt haircuts in 2011), or £94–104 billion, potentially resulting in an estimated capital shortfall of between 4.4–5.0 percent of GDP, or £63–73 billion, relative to Basel III Tier 1 capital hurdles (and 4.9–5.6 percent of GDP relative to FSA Interim Capital Regime requirements).

31. An important caveat to the haircuts applied to banks’ debt holdings of all non-AAA rated sovereigns and banks in those countries is that their severity and dynamics are informed by the forward term structure of 5-year sovereign credit default swap (CDS) spreads as at end-2010 (Attachment). Since then, the sovereign CDS spreads for select debtor countries of U.K. banks have increased commensurately with the rising risks to the economic outlook (Figure 15), which are not reflected in the haircuts given the cut-off point for the stress tests. This means that U.K. banks could be affected by additional losses—well beyond the prescribed haircuts projected as at end-2010—in the event that shocks lead to extreme stresses in the private sector in those countries or in core European banks to which they have large exposures.

Figure 15.
Figure 15.

Selected EU Countries: CDS Spreads

(In basis points)

Citation: IMF Staff Country Reports 2011, 227; 10.5089/9781462335510.002.A001

Source: Markit.

Overview of the Systemic CCA Framework

The Systemic CCA framework can be decomposed into two sequential estimation steps. First, the market-implied potential losses (and associated change in existing capital levels) are estimated for each sample bank using an advanced form of CCA. Then, these individual estimates are aggregated in a multivariate set-up in order to derivate estimates of joint potential losses and changes in capital levels.

In order to understand individual risk exposures in times of stress, first, CCA is applied to construct risk-adjusted (economic) balance sheets of financial institutions (Appendix IV). In its basic concept, CCA quantifies default risk on the assumption that owners of corporate equity in leveraged firms hold a call option on the firm value after outstanding liabilities have been paid off.1/ So, corporate bond holders effectively write a European put option to equity owners, who hold a residual claim on the firm’s asset value in non-default states of the world. More specifically, CCA applies this concept to determine the risk-adjusted balance sheet of firms whose assets are stochastic and may be above or below promised payments on debt. When there is a chance of default, the repayment of debt is considered “risky”—to the extent that it is not guaranteed in the event of default. Higher uncertainty about changes in future asset value, relative to the default barrier, increases default risk which occurs when assets decline below the barrier.

In this framework, market-implied potential losses associated with outstanding liabilities can be valued as an implicit put option in the form of a credit spread above the risk-free rate that compensates investors for holding risky debt. The put option value is determined by the duration of the total debt claim, the leverage of the firm, and the volatility of its asset value.2/ The put option was modeled based on a jump diffusion process (Appendix IV) to achieve robust and reliable estimation results in light of empirical shortcomings of the commonly used in the underpinning Merton (1974) model.3/ This approach is an alternative to other proposed extensions aimed at imposing more realistic assumptions, such as the introduction of stationary leverage ratios (Collin-Dufresne and Goldstein, 2001) and stochastic interest rates (Longstaff and Schwartz, 1995).4/

The CCA-generated, market-implied potential losses of individual banks can be transposed into estimates of market-implied potential capital shortfall and generalized to estimates of average and extreme system-wide solvency risk (“joint capital shortfall”). In order to establish greater comparability with balance sheet-based analysis of capital adequacy, the market-implied capital shortfall is estimated as the marginal change of the put option value after a graduated percentage point increase of the total debt claim in each year of the forecast horizon, in line with Tier 1 capital requirements under the current Basel III proposal (so that the “default barrier” becomes a “distress barrier”). So in each case, capital shortfall is derived as the marginal increase of potential losses below a default barrier that includes a capital level commensurate to the minimum Tier 1 capital ratio (which is viewed as proxy for the market-implied capital level).5/ Then the Systemic CCA approach (Gray and Jobst, 2010 and forthcoming; Gray and others, 2010; see Appendix V) is applied to derive point estimates6/ of the market-implied joint capital shortfall from the multivariate density of each bank’s individual marginal distribution of market-implied capital shortfalls (if any) and their dependence structure among all sample banks.

This approach can also be used to quantify the contribution of banks to systemic (solvency) risk (at different levels of statistical confidence) as measured by the market-implied joint capital shortfall. The joint capital shortfall can be written as a linear combination of individual shortfall amounts of banks, whose relative weights (in the weighted sum) are given by the second order cross-partial derivatives of the inverse of the joint probability density function to changes in both the dependence function and individual capital shortfalls. Thus, the contribution can be derived as the partial derivative of the multivariate density to changes in the relative weight of the univariate marginal distribution of individual capital shortfall and its impact on the dependence function (of all capital shortfalls of sample banks) at the specified percentile.

1/ Shareholders also have the option to default if their firm’s asset value (“reference asset”) falls below the present value of the notional amount of outstanding debt (“strike price”) owed to bondholders at maturity. Bond holders receive a put option premium in the form of a credit spread above the risk-free rate in return for holding risky corporate debt (and bearing the potential loss) due to the limited liability of equity owners. 2/ The value of the put option is subject three principles: (i) the values of liabilities (equity and debt) are derived from assets; (ii) liabilities have different priority (i.e., senior and junior claims); and (iii) assets follow a stochastic process. 3/ The Merton model has shown to consistently under-predict spreads (Jones and others, 1984; Ogden, 1987; Lyden and Saranti, 2000), with more recent studies pointing to considerable pricing errors due to its simplistic nature (Eom and others, 2004). 4/ Incorporating early default (Black and Cox, 1976) does not represent a useful extension in this context given the short estimation and forecasting time window used for the CCA analysis. 5/ The market value of equity is considered equivalent to core capital since CCA does not specify reported capital tiers but implicitly assumes that any potential loss first affects the most junior claims on bank assets (i.e., common equity). However, cross-sectional differences in the quality of capital will affect changes in valuation, which affects the accuracy of individual estimates of market-implied capital shortfall. Limited availability of market data on two banks in the FSAP stress tests means that additional calculations for the estimation of market-implied potential losses and capital shortfall on an individual basis are necessary. Since Santander U.K. and Nationwide are not listed companies, the implied asset values and asset volatilities underpinning the CCA model have to be derived via peer group analysis and historical balance sheet data. Implied assets for Nationwide are derived from quarterly reported total assets, scaled by the median ratio between the individual option-derived implied asset value (Appendix IV, Box 1) and quarterly reported total assets over the five sample banks with available equity prices. Its historical asset volatility (estimated via a simple GARCH(1,1) specification using total assets is estimated at quarterly frequency and interpolated for daily values by using the dynamics from the median asset volatility of sample banks. For Santander, the implied asset values of the parent company are re-scaled using balance sheet data for the U.K. operations of the bank in order to obtain the implied assets of Santander U.K. Similarly, the implied asset volatility is obtained after adjusting for the non-linear relationship between assets and asset volatility. 6/ Since point estimates of systemic risk are derived from a time-varying multivariate distribution, it is more comprehensive than the current exposition of both CoVaR (Adrian and Brunnermeier, 2008) and Marginal Expected Shortfall (MES) (Acharya and others, 2009) (as well as extensions thereof, such as Huang and others, 2009).

C. Reconciliation of Bottom-Up with Top-Down Solvency Stress Test Results

32. The RAMSI TD stress test results are broadly consistent with the aggregated BU findings. The trends for core Tier 1 and Tier 1 capital ratios, for the baseline and all three adverse scenarios, are broadly similar (Figures 16–18):

Figure 16.
Figure 16.

Weighted-Average Core Tier 1 Capital Ratios from the U.K. FSAP Update Bottom-Up and BoE RAMSI Top-Down Stress Tests, 2011–15

(In percentage points) 1/

Citation: IMF Staff Country Reports 2011, 227; 10.5089/9781462335510.002.A001

Sources: BoE; FSA; individual banks; and IMF staff calculations.1/ The definitions of capital are as follows: For the BU exercise, the starting point is in line with FSA definitions as laid out in the FSA Handbook and the definition in the FSA’s Interim Capital Regime; for the RAMSI, the Basel II-consistent definition of capital is used.
Figure 17.
Figure 17.

Tier 1 Capital Ratios from the U.K. FSAP Update Bottom-Up and BoE RAMSI Top-Down Stress Tests, 2011–15

(In percentage points)

Citation: IMF Staff Country Reports 2011, 227; 10.5089/9781462335510.002.A001

Sources: BoE; FSA; individual banks; and IMF staff calculations.
Figure 18.
Figure 18.

Total Capital Ratios from the U.K. FSAP Update Bottom-Up and BoE RAMSI Top-Down Stress Tests, 2011–15

(In percentage points)

Citation: IMF Staff Country Reports 2011, 227; 10.5089/9781462335510.002.A001

Sources: BoE; FSA; individual banks; and IMF staff calculations.

  • The contrast between the RAMSI and BU results is partly driven by the differences in the baseline estimates. The RAMSI baseline is stronger than the BU baseline, largely due to the difference in the two approaches taken with regards to the growth of banks’ RWAs: The BU tests assume higher asset growth than RAMSI, thus pushing the capital ratios down, with the effect becoming more marked in the latter years of the stress test horizon.

  • Higher sovereign and bank debt haircuts account for the larger reduction in capital ratios in the RAMSI results, relative to the BU ones. The impact is greater in the severe double dip and prolonged slow growth scenarios; the magnitude of these differences is reduced when the haircuts are excluded.

33. Differences in the two sets of results are likely attributable to several factors:

  • Sample banks. The BU tests are undertaken by the seven major U.K. banks; the RAMSI tests include five major banks (and Santander Group instead of Santander U.K.).

  • Assumptions. Unavoidable differences in the stress test assumptions (Appendix I).

  • Model design. The aggregate BU results are not derived from a specific model.

  • Timeliness of exposure data. RAMSI assumes banks’ sovereign debt exposures are unchanged from the 2010 CEBS stress test disclosures, whereas the BU tests use more up-to-date exposure data.

  • Definition of and assumptions on capital and RWAs. RAMSI uses the Basel II definition of capital and RWAs, and assumes fixed risk weights for the baseline and stress projections.8 This would result in higher capital adequacy ratios compared to banks’ BU results, which are based on the FSA’s Interim Capital Regime definitions and assumes that changes in risk weights increase at the same rate as baseline nominal GDP growth throughout the period,

  • Definition of exposures. RAMSI applies haircuts to banks’ gross exposures, whereas banks implement the BU tests using their own risk management systems’ exposure data that would have incorporated any hedged or netted positions.

  • Trading book positions. Although both the RAMSI and BU stress tests apply haircuts to both banking and trading book positions, banks may have taken into account their marked-to-market losses as at end-2010 in applying the trading book haircuts.

34. The Systemic CCA results provide support for the findings of the BU and RAMSI stress tests. The median shortfall amounts estimated by the Systemic CCA method suggest that markets are broadly comfortable that the current levels of capitalization of the major banks would be adequate to withstand the prescribed shocks. In all three stress testing approaches, the double-dip recession has proven to be the toughest shock scenario.

III. Liquidity Stress Tests

35. A suite of TD liquidity stress tests are carried out in order to assess the short-term resilience of large financial institutions with respect to sudden, sizeable withdrawals of funding (liabilities). These liquidity tests focus on implied cash flow calculations and applied proxies for the proposed Basel III measures of liquidity risk, within the following parameters:

  • The tests are conducted by the authorities using the spreadsheet-based tool provided by the FSAP team. The FSA’s Liquidity Reporting Profile (LRP) data as at end-2010, for 16 large financial institutions consisting of the seven major banks (from the solvency stress test sample), building societies (including one cooperative bank) and five subsidiaries of foreign investment banks, are used in the exercise. The institutions are selected in collaboration with the U.K. authorities on the basis of supervisory remit.

  • The liquidity stress tests are run separately from the solvency risk analysis.

  • Outflow shocks are applied to a range of liabilities, including deposits, wholesale funding and intergroup funding, while haircuts to assets include investment and trading securities, derivatives and secured assets. Eligible securities could either be sold on secondary markets or used as collateral for normal access to central bank liquidity.

  • The static nature of the tests and the assumption that all banks face escalating liquidity risk at the same time means that any estimated liquidity shortfall should be interpreted in terms of a general vulnerability to the particular assumptions rather than it being representative of an actual liquidity need.

  • Where possible, the FSAP results are juxtaposed against the FSA’s results for comparison purposes, to highlight the importance of the assumptions used (Appendix III).

36. The proposed liquidity tests comprise outflows of funding (liabilities) even as haircuts are being applied to assets on the balance sheet. Specifically:

  • Two implied cash flow tests simulate a gradual outflow of funding over five consecutive days, and over a 30-day time horizon in keeping with a reverse stress test rationale. The analysis provides an assessment of the overall resilience of the system to a withdrawal of deposits and the run-off of wholesale funding. The aggregate outcome for European banks in the December 2010 quantitative impact study (QIS-6) is used as a proxy for cash flow assumptions.

    • article image
      Two separate and additional specifications are also examined for each test: (i) customer deposits are assumed to be unaffected;9 (ii) intergroup funding is assumed to be available.

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      For simplicity of application, aggregate, rather than daily, flows data are used; the contractual nature of wholesale funding is ignored.

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      A bank is considered illiquid once deposits and wholesale funding are run down.

  • The severity of the 30-day test exceeds the FSA’s current supervisory requirements. The assumption of more than 40 percent outflows of deposits and wholesale funding for the 30-day test is considered a very severe one, worse than those experienced by Northern Rock during the crisis.10 This 30-day test is aimed at gauging the magnitude of shocks required to cause severe distress, using a reverse stress testing rationale, rather than at providing projections under scenarios. The objective is to reflect a series of assumptions that generate extremely severe liquidity risk scenarios. It does not take into account the following mitigating considerations:

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      Offsetting contractual capital inflows from maturing wholesale lending.

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      Possible central bank support via the BoE’s discount window.

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      The likely positive effect on depositor confidence of having the Financial Services Compensation Scheme (FSCS) in place.11

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      A likely compensating outcome for the system as a whole, such as the reallocation of deposits within the banking sector when banks do not experience funding shocks simultaneously (and assuming that deposits largely remain in the banking system).

  • Additional analysis is conducted using the proposed Basel III liquidity risk measures. The LCR, which measures the sufficiency of the stock of high quality liquid assets to meet short-term liquidity needs under a specified acute stress scenario. The NSFR, which measures the amount of longer-term, stable sources of funding employed relative to the liquidity profiles of the assets funded and the potential for contingent calls on funding liquidity arising from off-balance sheet commitments and obligations, are derived to inform insights into the quality of liquid assets and the maturity profile and stability of funding. Given the tentative nature of these proposed measures, the FSAP team’s interpretation of the proposed Basel III liquidity risk measures are applied, and referred to as quasi-measures. The FSAP’s assumptions regarding contractual maturities and liquidity risk have been adopted on a best effort basis and reconciled with the FSA’s own interpretation and assumptions, which differ somewhat. The results are juxtaposed against the FSA’s for completeness:

    • For the quasi-LCR, the minimum parameters for the outflow of stable and less stable deposits are selected for the FSAP tests. Other assumptions include: (i) the share of high quality liquid assets needed to satisfy margin calls (10 percent); (ii) the change in the market value of derivatives (20 percent); (iii) the share of asset-backed securities maturing within the next 30 days (10 percent); (iv) the share of undrawn but committed liabilities that are withdrawn (50 percent); and (v) the share of assets that is reinvested (80 percent). An LCR ratio of unity or greater suggests sufficient high-quality liquidity.

    • For the quasi-NSFR, the FSAP’s assumptions underpinning the definition of available sources of funding are very conservative and are defined in line with the final Basel III publication as of December 2010 (BCBS, 2010) and recent Fund staff analysis on systemic liquidity risk published in the April 2011 issue of the Global Financial Stability Report (IMF, 2011). Stable funding is defined by an NSFR ratio of unity or greater.

37. The results indicate that the banking system would be resilient against short-lived shocks to funding but may be vulnerable to more prolonged disruptions to funding access:

  • Implied 5-day cash flow tests (Table 7). The banking system would largely be able to support a short-lived shock to cash flows

    • The aggregate shortfall would equal 0.03 percent of assets included in the test.

    • If deposits are assumed to remain stable, banks would generate sufficient cash inflows from asset sales to offset outflows.

    • If intra-group lending is assumed to be readily available, the shortfall would be equivalent to around 0.03 percent of assets for the sample of 16 banks and 0.04 percent for the seven major banks.

    • Overall, the results suggest that retail deposits are a much more important source of funding for the banking system, and that intra-group funding does not play a big role for the foreign subsidiaries in the sample.

  • Implied 30-day cash flow tests (Table 7). Despite the extreme severity of the test, the overall liquidity shortfall remains largely contained under more severe cash outflows over 30 days, where deposit outflows and run-offs of liabilities are doubled.12

    • Although more banks would be affected—as would be expected—with an aggregate shortfall equal to under 6 percent of assets used in the liquidity calculations for the sample of 16 banks (an average shortfall of 0.4 percent of assets) and about 6.6 percent of assets under consideration for the seven major banks (an average shortfall of 1 percent of assets), significant increases in the liquidity shortfall remain concentrated in a very few institutions.

    • Retail deposits remain the key source of funding for banks that survive the 30-day test

    • These results are reflective of the relative importance of the maturity gap (i.e., a high portion of short-term deposits and a focus on medium and long-term lending, which applies to the retail-focused commercial banks and building societies in the sample) as well as the share of wholesale funding (which is high for some of the larger banks)

    • By comparison, the FSA’s 30-day survival test shows that all seven major banks would have had sufficient liquidity to sustain the prescribed shocks, while four banks out of the total sample of 16 would have come up short.

  • Quasi-LCR test (Table 8). All 16 banks pass the FSAP’s quasi-LCR test, indicating a sufficient degree of highly liquid assets to withstand short-lived shocks to cash flows. Under the FSA’s assumptions, with numerous banks—accounting about 85 percent of assets in the sample of sixteen banks and about 93 percent of assets of the seven major banks—falling below unity, largely concentrated in the 0.55–0.75 range.

  • Quasi-NSFR (Table 8). In the FSAP test, the indicator falls below unity for banks accounting for more than 95 percent of assets in each sample. In both samples, banks accounting for some 50–60 percent of assets have NSFRs falling in the 0.50–0.75 range, suggesting insufficiently stable sources of funding in the system. The concentration is different for the FSA’s corresponding test, with banks accounting for around 90 percent of assets in the sample of 16 banks and 100 percent of all seven major banks clustered in the 0.75–1.00 range.

  • Maturity mismatch. The maturity mismatch in banks’ liquidity profiles support the quasi-NSFR findings. In the 6–12 months maturity bucket, assets that are mismatched amount to about 70 percent of the total assets of all banks in the sample, and the proportion goes up to around 90 percent in the 12-plus months maturity bucket. For some banks, this vulnerability would be amplified by concentrations of sizeable reliance on wholesale funding.

Table 7.

U.K. FSAP Update Liquidity Stress Tests: 5- and 30-Day Implied Cash Flow Analysis

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Sources: FSA; and IMF staff calculations.

The cumulative outflow is weighted across different types of deposits and sources of wholesale funding, whose relative magnitude differs across sample banks. Note that the implied cash flow analysis applies outflow assumptions to aggregate values of funding maturities of up to one month irrespective of callability. The FSA does not complete tests that are directly comparable to these results. However, the survival day metric monitored by the FSA to assess vulnerabilities to wholesale funding is broadly similar to the 30-day test.

Table 8.

U.K. FSAP Update Liquidity Stress Tests: Quasi-Basel III and Maturity Mismatch Analysis

(In percent of total sample assets included in the liquidity tests)

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Sources: FSA; and IMF staff calculations.

The maturity mismatch of each bank is calculated as the difference of the value of assets and liabilities in each of six “maturity buckets” determined by their tenor and callability, i.e., (i) on demand, (ii) up to one month, (iii) between one month and three months, (iv) between three months and six months, (v) between six months and twelve months, and (v) greater than 12 months. For a given “maturity bucket”, the total assets of all banks that exhibit mismatch are added and divided by the total assets of all banks in the sample. The differences between the FSAP and FSA assumptions lie largely in the interpretation of the proposed Basel III measures.

38. The overall results suggest that the banking system would be able to withstand moderately severe cash flow shocks, without the need for access to central bank liquidity. However, intensification of market stresses, amplified by the considerable interconnectedness of the United Kingdom to the global financial system is an important concern. Sustained disruptions to wholesale funding markets—possibly due to the realization of sovereign risks in the EU and potentially exacerbated by market uncertainty about the outcome of current deliberations by the ICB—affecting repo markets and counterparty risk assessments, coupled with a persistent decline in asset values, could expose vulnerabilities if individual banks lose access to their funding sources.

IV. Summary and Policy Implications

39. The U.K. banking system appears to be adequately capitalized against adverse shocks and banks are well-placed to meet the Basel III solvency requirements. It is evident that the significant recapitalization of the U.K. banking sector, in tandem with the de-risking of balance sheets, has been critical in boosting the solvency of the system. Both the BU stress test results by banks as well as the cross-validation TD tests by the BoE indicate that the capital adequacy of the aggregate banking system as at end-2010 would comfortably pass the Basel III (and FSA Interim Capital Regime) hurdle rates under the defined shock scenarios; the capital adequacy of individual banks varies, but all would be able to absorb the shocks clear the hurdle rates as well. The FSAP’s own TD tests suggest that markets also consider banks to be sufficiently capitalized against the prescribed shocks.

40. While banks have continued to improve their funding profiles, significant work is still required to reduce liquidity risk in the system. The liquidity stress tests, comprising reverse stress tests and proxies for the proposed liquidity measures under Basel III, assess the resilience of the banking system to a loss in funding and market access (including the closure of long-term and short-term funding markets and higher funding costs), as well as haircuts in the realization of liquid assets. The results indicate that the banking system would have sufficient liquid assets to withstand short-lived cash flow stresses (without taking into account access to central bank liquidity), but that significant maturity mismatch exist in banks’ liquidity profiles at the six-month maturity mark and beyond.

41. It is imperative that complacency does not set in and that the restructuring and de-risking of banks’ balance sheets continue. The asset quality of institutions may be at risk in the event of a severe double-dip recession or if the recovery of the U.K. economy is drawn out, especially if lender forbearance is also masking the true extent of risks in residential and commercial real estate lending. Any significant escalation in stresses under these scenarios resulting in the realization of extreme tail risks could and potentially push joint potential capital losses below the distress barrier, resulting in a capital shortfall relative to the Basel III (and FSA) hurdle rates. The deterioration in the outlook for vulnerable EU sovereigns since the cut-off date for the stress tests represents a potentially significant concern for solvency and liquidity risks in the U.K. banking system, while the as yet unknown outcome of current regulatory deliberations on the banking sector adds to the uncertainty. Banks’ funding sources are not yet sufficiently stable, and they remain vulnerable to sustained disruptions to funding markets.

42. Overall, the stress test results confirm the supervisory focus to require banks to build up capital and liquidity buffers both in terms of institution-specific requirements as well as industry-wide standards. U.K. banks are subject to the Basel III capital requirements, including trading book capital charges, according to the agreed gradual phase-in schedule, in order to balance the potential adverse implications on lending, while the core Tier 1 and Tier 1 capital requirements of the FSA’s interim supervisory framework were implemented during the crisis in anticipation of the Basel III proposals. The authorities have also decided to implement liquidity requirements ahead of the phase-in schedule agreed internationally. While the solvency and liquidity regulations are more stringent than in other major jurisdictions presently, they appropriately reflect the authorities’ response to the specific structure and vulnerabilities of the U.K. financial system presently and the lessons learned from the crisis.

Appendix I. Key Assumptions Applied in the U.K. FSAP Update Solvency Stress Tests Relative to the European Banking Authority (EBA) and FSA Supervisory Stress Tests

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Prepared by: BoE; FSA; and IMF staff.

The FSA’s stress testing framework for major UK banking groups involves a bottom up stress test by individual banking groups based on a designated macroeconomic scenario covering a 5 year horizon. Banks’ results reflect each banking groups own methodologies and assumptions. In parallel, the FSA undertakes its own stress testing using banks’ data applying internally approved methodologies as well as expert judgmental overlays to bank results.

Appendix II. Comparison of Capital Definitions—Basel, EBA, FSA and U.K. FSAP Update

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Prepared by: FSA

Appendix III. Parameters Applied in the U.K. FSAP Update Liquidity Stres Tests

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Sources: FSA; and IMF staff.

Appendix IV. The Contingent Claims Analysis Approach: Standard Definition

43. CCA is used to construct risk-adjusted balance sheets, based on three principles. The principles are: (i) the values of liabilities (equity and debt) are derived from assets; (ii) liabilities have different priority (i.e., senior and junior claims); and, (iii) assets follow a stochastic process. Assets (for example, present value of income flows, and proceeds from assets sales) are stochastic and over a horizon period may be above or below promised payments on debt which constitute a default barrier. Uncertain changes in future asset value, relative to the default barrier, are the driver of default risk which occurs when assets decline below the barrier. When there is a chance of default, the repayment of debt is considered “risky,” to the extent that it is not guaranteed in the event of default (risky debt = risk-free debt minus guarantee against default). The guarantee can be held by the debt holder, in which case it can be thought of as the expected loss from possible default or by a third party guarantor, such as the government.

44. In the first structural specification, commonly referred to as the Black-Scholes-Merton (BSM) framework (or short “Merton model”) of capital structure-based option pricing theory (OPT), total value of firm assets follows a stochastic process may fall below the value of outstanding liabilities.13 Thus, the asset value A(t) at time t describes a continuous asset process so that the physical probability distribution of the end-of-period value is:

A ( T − t ) ∼ A ( t ) exp ⁡ { ( r A + σ A 2 / 2 ) ( T − t ) + σ A T − t z }

for time to maturity T-t. More specifically, A(t) is equal to the sum of its equity market value, E(t), and its risky debt, D(t), so that A(t) = E(t) + D(t). Default occurs if A(t) is insufficient to meet the amount of debt owed to creditors at maturity, which constitute the bankruptcy level (“default threshold” or “distress barrier”). The equity value E(t) is the value of an implicit call option on the assets, with an exercise price equal to default barrier. It can be computed as the value of a call option E(t)=A(t)Φ(d1)−Be−r(T−t)Φ(d2), with d1=[ln(A(t)/B)+(r+σA2/2)(T−t)](σAT−t)−1, d2=d1−σAT−t, asset return volatilityσA, and the cumulative probability Φ(.) of the standard normal density function. Both the asset, A(t), and asset volatility, σA, are valued after the dividend payouts. The value of risky debt is equal to default-free debt minus the present value of expected loss due to default,

D ( t ) = B e − r ( T − t ) − P E ( t ) .

45. Thus, the present value of market-implied potential losses associated with outstanding liabilities can be valued as an implicit put option, which is calculated with the default threshold B as strike price on the asset value A(t) of each institution. Thus, the present value of market-implied potential loss can be computed as:

P E ( t ) = B e − r ( T − t ) Φ ( − d 2 ) − A ( t ) Φ ( − d 1 )

over time horizon T–t at risk-free discount rate r, subject to the duration of debt claims, the leverage of the firm, and asset volatility. Note that the above option pricing method for PE(t) does not incorporate skewness, kurtosis, and stochastic volatility, which can account for implied volatility smiles of equity prices. Since the implicit put option PE(t) can be decomposed into the PD and LGD,

P E = Φ ( − d 2 ) ( 1 − Φ ( − d 1 ) Φ ( − d 2 ) A ( t ) B e − r T ) B e − r ( T − t ) = P D × L G D ,

there is no need to introduce potential inaccuracy of assuming a certain LGD. As a consequence of the assumptions on the underlying asset price process, this would imply the risk-neutral probability distribution (or state price density, SPD) of A(t) is a log-normal density:

f t * ( A ( T ) ) = e − r t , T − t T − t ∂ 2 E ( t ) ∂ B 2 | B = A ( T ) = 1 A ( T ) 2 π σ 2 ( T − t ) exp ⁡ [ − [ l n ( A ( T ) / A ( t ) ) − ( r t , T − t − σ 2 / 2 ) ( T − t ) ] 2 2 σ 2 ( T − t ) ]

with mean (r−σA2/2)(T−t)and variance σA2(T−t) for ln(A(T)/A(t)), where rt,T-t and f*(.) denote the risk-free interest rate and the risk-neutral probability density function (or SPD) at time t, with risk measures:

Δ = d e f ∂ E ( t ) ∂ A ( t ) = Φ ( d 1 )  and   Γ = d e f ∂ 2 E ( t ) ∂ A ( t ) 2 = Φ ( d 1 ) A ( t ) σ T − t .

46. In this analysis, the Merton model is refined without altering the analytical form by means of the closed-form Gram-Charlier model of Backus and others (2004), which allows for kurtosis and skewness in returns and does not require market option prices to implement, but is constructed using the same diffusion process for asset prices.14 The above option pricing method, however, does not incorporate skewness and kurtosis, which can account for implied volatility smiles of equity prices. Thus, the Merton model is enhanced - without altering the analytical form by means of a jump diffusion that follows a standard Poisson process, where λ is the average number of jumps per unit time. The jump size follows a log-normal distribution with average jump size m and the volatility v of the jump size.15 Hence, the price of a European put option can be written as

P E ( t ) = Σ k = 0 ∞ exp ⁡ ( − m λ t ) ( m λ t ) k k ! B e − r ( T − t ) Φ ( − d 2 ) − A ( t ) Φ ( − d 1 )

with distance to default d1=(ln⁡(A(t)/B)+(rA+σA2/2)(T−t))/σT−t and d2=d1−σAT−t.16 The kth term in this series corresponds to the scenario where k jumps occur over a 120-day rolling window. Asset volatility σAk=σA2+kv2/t and the revised risk-free interest rate rk=r–λ(m–1)+kln(m)/t are updated accordingly.

47. Since the Merton model also contains empirical irregularities that can influence the estimation of implied assets (which also affects the calibration of implied asset volatility), the SPD of implied asset values is estimated from equity option prices without any assumptions on the underlying diffusion process (Box 1 below). Using equity option prices, we can derive the risk-neutral probability distribution of the underlying asset price at the maturity date of the options. We determine the implied asset value as the expectation over the empirical SPD by adapting the Breeden and Litzenberger (1978) method, together with a semi-parametric specification of the Black-Scholes option pricing formula (Aït-Sahalia and Lo, 1998). More specifically, this approach uses the second derivative of the call pricing function (on European options) with respect to the strike price (rather than option prices as identifying conditions). Estimates are based on option contracts with identical time to maturity, assuming a continuum of strike prices. Since available strike prices are always discretely spaced on a finite range around the actual price of the underlying asset, interpolation of the call pricing function inside this range and extrapolation outside this range are performed by means nonparametric (local polynomial) regression of the implied volatility surface (Rookley, 1997).

48. The implied asset value is estimated directly from option prices (in tandem with an option pricing approach that takes into account higher moments of the underlying asset diffusion process). This avoids the calibration error of using two-equations-two unknowns in the traditional Merton model in solving both implied asset value and asset volatility simultaneously. Thus, asset volatility can be derived from:

σ A 2 + k v 2 / t = E ( t ) A ( t ) Φ ( d 1 ) σ E .

17

Estimation of the Empirical SPD

Breeden and Litzenberger (1978) show Arrow-Debreu prices can be replicated via the concept of the butterfly spread on European call options. This spread entails selling two call options at strike price K and buying two call options with adjacent strike prices K- = K–ΔK and K+ = K+ΔK respectively, with the stepsize ΔK between the two call strikes. If the terminal underlying asset value A(T) = K then the payoff Z(.) of 1/ΔK of such butterfly spreads at time T–τ (and time to maturity τ) is defined as

Z ( A ( T ) , K ; Δ K ) = P r i c e ( A ( T − τ ) , τ , K ; Δ K ) | τ = 0 = u 1 − u 2 Δ K | A ( T ) = K , τ = 0 = 1 ,

with

u 1 = C ( A ( T − τ ) , τ , K + Δ K ) − C ( A ( T − τ ) , τ , K )

and

u 2 = C ( A ( T − τ ) , τ , K ) − C ( A ( T − τ ) , τ , K − Δ K ) .

C(A,τ,K) denotes the price of a European call option with an underlying asset price A, a time to maturity τ and a strike price K. As ΔK→0, Price(A(T–τ),τ,K;ΔK) of the position value of the butterfly spread becomes an Arrow-Debreu security paying 1 if A(T) = K and zero in other states. If A(T)ε+ is continuous, however, we obtain a security price

lim Δ K → 0 ( Pr ⁡ i c e ( A ( t ) , τ , K ; Δ K ) Δ K ) | K = A ( T ) = f * ( A ( T ) ) e − r t , τ ,

where rt,τ and f*(.) denote the risk-free interest rate and the risk-neutral probability density function (or SPD) at time t. On a continuum of states K at infinitely small ΔK a complete state pricing function can be defined. Moreover, as ΔK→0, this price

lim Δ K → 0 ( P r i c e ( A ( t ) , τ , K ; Δ K ) Δ K ) = lim Δ K → 0 u 1 − u 2 ( Δ K ) 2 = ∂ 2 C t ( . ) ∂ K 2

will tend to the second derivative of the call pricing function with respect to the strike price evaluated at K, provided that C (.) is twice differentiable. Thus, we can write

∂ 2 C t ( . ) ∂ K 2 | K = A ( T ) = f t * ( A ( T ) ) e − r t , τ ⁢ τ

across all states, which yields the SPD

f t * ( A ( T ) ) = e − r t , τ τ ∂ 2 C t ( . ) ∂ K 2 | K = A ( T )

under no-arbitrage conditions and without assumptions on the underlying asset dynamics. Preferences are not restricted since no-arbitrage conditions only assume risk-neutrality with respect to the underlying asset. The only requirements for this method are that markets are perfect, i.e., there are no transactions costs or restrictions on sales, and agents are able to borrow at the risk-free interest rate.

Appendix V. The Systemic CCA Methodology: Calculating the Systemic Worst-Case Scenario Using Multivariate Extreme Value Distribution

49. The Systemic CCA framework is predicated on the quantification of the systemic financial sector risk (Gray and Jobst, 2010; Gray and Jobst, forthcoming). It is applied in this context to generate a multivariate extreme value distribution (MGEV) that formally captures the potential of tail realizations of market-implied joint potential losses. The analysis of dependence is completed independently from the analysis of marginal distributions, and, thus, differs from the classical approach, where multivariate analysis is performed jointly for marginal distributions and their dependence structure by considering the complete variance-covariance matrix, such as the MGARCH approach.

50. We first define a non-parametric dependence function of individual potential losses. We then combine this dependence measure with the marginal distributions of these individual potential losses, which are assumed to be generalized extreme value (GEV). These marginal distributions estimated via the Linear Ratio of Spacings (LRS) method, which identifies possible limiting laws of asymptotic tail behavior of normalized extremes (Coles and others, 1999; Poon and others, 2003; Stephenson, 2003; Jobst, 2007). The dependence function is estimated iteratively on a unit simplex that optimizes the coincidence of multiple series of cross-classified random variables – similar to a Chi-statistic that measures the statistical likelihood of observed values to differ from their expected distribution. More specifically, we first specify the asymptotic tail behavior of the vector-valued series Xi,j≡Pi,j=(P1n,...,Pmn) of potential losses (i.e., put option values) of an m number of financial sector entities j as the limiting law of an n-sequence of normalized maxima (over rolling window estimation period of τ=120 days and daily updating), so that the jth univariate marginal

y j = y j ( x ) = ( 1 + ξ j ( x − μ j ) / σ j ) + − 1 / ξ j   ( for   ⁢     j = 1 , ... , m )

lies in the domain of attraction of the generalized extreme value (GEV) distribution, where 1+ξj(x−μj)/σj>0, scale parameter σj>0 location parameter µj, and shape parameter ξj. 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.

51. Second, the multivariate dependence structure of joint tail risk of potential losses is derived non-parametrically as the convex function:

A ( ω ) = min ⁡ ( 1 , max ⁡ { n { Σ i = 1 n ∧ j = 1 m y i , j / y ^ • j ω j } − 1 , ω , 1 − ω } )

over the same estimation window, where y^•j=Σi=1nyi,j/n and 0≤max(ω1,...,ωm–1)≤A(ωj)≤1, for all 0≤ωj≤1. subject to the optimization of the (m-1)-dimensional unit simplex

S m = { ( ω 1 , ... , ω m − 1 ) ∈ + n : ω j ≥ 0 , 1 ≤ j ≤ m − 1 ; Σ j = 1 m − 1 ω j ≤ 1 ⁢     and ⁢   ⁢   ω m = 1 − Σ j = 1 m − 1 ω j } .

52. Finally, after estimation of the marginal distributions and the dependence structure over the a rolling window of τ number of days, we obtain the multivariate distribution:

G t , ξ ^ , μ ^ , σ ^ ( X ) = exp ⁡ { − ( Σ j = 1 m y j ) A ( ω ) }

at time tτ+1, using the maximum likelihood estimation θ^MLE=arg⁡ θmax⁡Πi=1ng(x;θ)

53. We then obtain the Expected Shortfall (ES) (or conditional Value-at-Risk (VaR)) as the probability-weighted residual density beyond a pre-specified statistical confidence level (say, a=0.95) of maximum losses, where point estimate of joint potential losses is defined as: 18

x ^ t , a = G t , ξ ^ , μ ^ , σ ^ − 1 ( a ) = μ ^ j + σ ^ j / ξ ^ j ( ( − ln ⁡ ( a ) A ( ω ) ) − ξ ^ j ⁢   − 1 ) .

ES defines the average estimated value z of the aggregate potential losses over estimation days τ in excess of the statistical confidence limit. Thus, we can write ES at time t as

E S t , τ , a = − E [ Z τ | Z τ ≥ G t − 1 ( a ) = V a R t , a ]

at a threshold quantile value

V a R t , τ , a = sup ⁡ { G t − 1 ( • ) | Pr ⁡ [ z τ > G t − 1 ( • ) ] ≥ a = 0.95 } ⋅

ES can also be written as a linear combination of individual ES values, where the relative weights (in the weighted sum) are given by the second order cross-partial derivatives of the inverse of the joint probability density function Gt–1(a) to changes in both the dependence function and the individual marginal severity of expected loses. Thus, by re-writing ESt,τ,a above, we obtain the sample ES

E S t , τ , a = − Σ j m M C j , τ , a E [ z j , τ | z m , τ ≥ G t − 1 ( a ) = V a R t , q a ] ,

where the relative weight of institution j is defined as the marginal contribution

M C j , τ , a = ∂ 2 G t − 1 ( a ) ∂ y j , a ∂ A − 1 ( ω )  s. t . Σ i m M C j , τ , a = 1  and   M C j , τ , a z i , τ ≤ z m , τ

to expected shortfall

E S t , ℓ , a = − Σ j m ψ j , ℓ , a E [ z j , ℓ | z m , ℓ ≥ G t − 1 ( a ) V a R t , q a ] ,

attributable to the joint effect of both the marginal distribution yj,a and the change of the dependence function absent A(.) institution j.

Attachment. Guidelines for the U.K. FSAP Update Bottom-Up Solvency Stress Tests by Banks

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1

Prepared by Andreas Jobst and Li Lian Ong, with research assistance from Suchitra Kumarapathy (all IMF/MCM). The FSAP team would like to express its deep gratitude to counterparts at the Financial Services Authority (FSA) and the Bank of England (BoE) for their cooperation and close collaboration in facilitating this comprehensive stress testing exercise; staff at Her Majesty’s Treasury (HMT) for their constructive input throughout the process; and management and the stress testing teams at Barclays, HongKong and Shanghai Banking Corporation (HSBC), Nationwide, Lloyds Banking Group (LBG), Royal Bank of Scotland (RBS), Santander U.K. and Standard Chartered Bank (SCB) for their participation.

2

The Risk Assessment Matrix in the Financial System Stability Assessment details the risks, their estimated probability of occurrence and impact.

3

Based on the volatility of the two-year growth rate over 30 years as calculated by the FSA.

4

For the very high impact banks, supervisory review by the FSA, including rigorous capital stress testing, is undertaken annually. Smaller banks are obliged to submit their ICAAP results to the FSA each year, incorporating the results of their stress testing; the FSA is more likely to review these institutions on a longer cycle.

5

See also FSAP Technical Note, “Vulnerabilities of Household and Corporate Balance Sheets and Risks for the Financial Sector.”

6

Two types of satellite models have been applied in order to determine the sensitivity of financial sector performance to changes in macroeconomic conditions. Under first approach forecasts of operating profit and credit losses generated in the RAMSI model are incorporated in the structural valuation approach that underpins the Systemic CCA approach.

7

The “+/-” signs indicate whether the selected variable exhibit a positive/negative regression coefficient. The statistical significance of model variables was restricted to no more than 10 percent.

8

Under RAMSI, banks are assumed to increase capital through retained earnings until they achieve challenging core Tier 1 capital ratio targets that are set using Basel III definitions and then translated back into Basel II terms.

9

The level of outflows of liabilities and the liquidity of assets under stress was set in accordance with empirical evidence, assumptions used in other FSAPs and upcoming regulatory changes.

10

The implied cash flow analysis applies outflow assumptions to aggregate values of funding maturities of up to one month irrespective of callability.

11

The scope of FSCS deposit insurance has been expanded from £2000 plus 90 percent of the next £30,000 to the maximum of £85,000 per customer, which covers around 80 percent of retail deposits in the system; speed of pay-out has also improved.

12

The stress testing framework does not use daily cash flows for wholesale funding maturities but aggregates funding maturities of up to one month irrespective of callability. It is assumed that a proportion of such wholesale funding, which is otherwise contractual in nature, is withdrawn under the 5-day and 30-day cash flow test. This simplified assumption may overstate actual outflows unless daily cash inflows and outflows are matched and equally distributed over one month.

13

See Black and Scholes (1973) and Merton (1973, 1974).

14

Further refinements of this model would include various simulation approaches at the expense of losing analytical tractability. The ad hoc model of Dumas, Fleming, and Whaley (1998) is designed to accommodate the implied volatility smile and is easy to implement, but requires a large number of market option prices. The pricing models by Heston (1993) and Heston and Nandi (2000) allow for stochastic volatility, but the parameters driving these models can be difficult to estimate. Many other models have been proposed, to incorporate stochastic volatility, jumps, and stochastic interest rates. Bakshi and others (1997), however, suggest that most of the improvement in pricing comes from introducing stochastic volatility. Introducing jumps in asset prices leads to small improvements in the accuracy of option prices. Other option pricing models include those based on copulas, Levy processes, neural networks, GARCH models, and non-parametric methods. Finally, the binomial tree proposed by Cox, Ross and Rubinstein (1979) spurned the development of lattices, which are discrete-time models that can be used to price any type of option—European or American, plain-vanilla or exotic.

15

All parameters are calibrated over the entire sample period of five years.

16

The advantage of the GC model is that it is only slightly more complicated to implement than the Merton model because only two additional parameters—skewness and kurtosis—need to be estimated. The disadvantage is that it is assumes that these parameters are constant.

17

The two-equations-two-unknowns approach is based on Jones and others (1984), which was subsequently extended by Ronn and Verma (1986) to a single equation to solve two simultaneous equations for asset value and volatility as two unknowns. Duan (1994), however, shows that the volatility relationship between implied assets and equity is redundant if equity volatility is stochastic. An alternative estimation technique for asset volatility introduces a maximum likelihood approach (Ericsson and Reneby, 2004 and 2005) which generates good prediction results.

18

Expected shortfall (ES) is an improvement over VaR, which, in addition to being a pure frequency measure, is “incoherent”, i.e., it violates several axioms of convexity, homogeneity, and sub-additivity found in coherent risk measures. For example, sub-additivity, which is a mathematical way to say that diversification leads to less risk, is not satisfied by VaR.

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:

P G C = B e − r T ( 1 − Φ ( d 1 − σ A ) ) + A t ( Φ ( d 1 ) + Φ ( d 1 ) σ A ( γ 1 T 3 ! ( 2 σ A − d 1 T ) − γ 2 T 4 ! ( 1 − d 1 2 + 3 d 1 σ A − 3 σ A 2 ) ) − 1 ) ,

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:

σ A = σ E [ 1 − B e − r T A Φ ( d 1 − σ A T ) Φ ( d 1 ) ] ,

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:

P = B e − r T exp ⁡ ( ( 1 − Φ ( d 1 ) ) A D λ σ A ( − T ) ) ⇔ σ A = P B e − r T ( − D λ A ( 1 − Φ ( − d 1 − σ A T ) ) T ) ,

where dDD=dDdAADdAA=μD−r=(1−Φ(d1))ADλσA=−1Tln⁡(1−PBe−rT), 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

P B = exp ⁡ ( − r T T ) ( 1 − L G D × P D ( T ) ) ,

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

P b , T − t = Π k = 1 T − t c ( 1 + r t ) ( T − t ) / n + f ( 1 + r t ) T − t

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

P b , T − t = f ( 1 + r t ) T − t = exp ⁡ ( ( − r f t + ( Y T M e n d − 2010 , b a s e l i n e − Y T M e n d − 2010 , a c t u a l ) + S C D S 10 , 000 ) ( T − t ) ) ,

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))⁡−ξj−1),where 1+ξj(x−μj)/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

Δ P b , t , j = ( P b , t , j / P b , 0 , j − 1 ) × 100 ,

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

h t , j = max ⁡ ( Σ b = 1 k Δ P b , t , j   ×   A m t b , j ( Σ b = 1 k A m t b , j ) − 1 , 0 ) ,

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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20

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

21

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.

22

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.

23

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

24

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.

25

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.

26

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

27

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.

28

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.

29

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

31

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

32

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.

35

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

36

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).

37

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

38

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).

39

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

40

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

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Cover IMF Staff Country Reports
United Kingdom: Stress Testing the Banking Sector Technical Note
Author:
International Monetary Fund
Volume/Issue:
Volume 2011: Issue 227
Publisher:
International Monetary Fund
ISBN:
9781462335510
ISSN:
1934-7685
Pages:
126
DOI:
https://doi.org/10.5089/9781462335510.002
  • Figure 1.
    View in gallery
    Figure 1.

    Major U.K. Banks: Differentiated Business and Geographic Models

    (In percent of individual banks’ revenues)

  • Figure 2.
    View in gallery
    Figure 2.

    U.K. Banks: Breakdown of Assets and Risk-Weighted Assets

    (In trillions of pound sterling)

  • Figure 3.
    View in gallery
    Figure 3.

    United Kingdom: Liquidity in the Banking System

  • Figure 4.
    View in gallery
    Figure 4.

    Overview of the U.K. FSAP Update Stress Testing Exercise

  • Figure 5.
    View in gallery
    Figure 5.

    Overview of the U.K. FSAP Update Stress Test Scenarios

  • Figure 6.
    View in gallery
    Figure 6.

    Distribution of Core Tier 1 Capital Ratios from the U.K. FSAP Update Bottom-Up Stress Tests, 2011–15

    (In percent)

  • Figure 7.
    View in gallery
    Figure 7.

    Distribution of Tier 1 Capital Ratios from the U.K. FSAP Update Bottom-Up Stress Tests, 2011–15

    (In percent)

  • Figure 8.
    View in gallery
    Figure 8.

    United Kingdom: Distribution of Total Capital Ratios from the U.K. FSAP Update Bottom-Up Stress Tests, 2011–15

    (In percent)

  • Figure 9.
    View in gallery
    Figure 9.

    Estimation of Satellite Models in the U.K. FSAP Update Stress Testing Exercise

  • Figure 10.
    View in gallery
    Figure 10.

    Application of Satellite Output in the RAMSI and the Systemic CCA Stress Tests

  • Figure 11.
    View in gallery
    Figure 11.

    Distribution of Core Tier 1 Capital Ratios from the BoE RAMSI Top-Down Stress Tests for the U.K. FSAP Update, 2011–15

    (In percent)

  • Figure 12.
    View in gallery
    Figure 12.

    United Kingdom: Distribution of Tier 1 Capital Ratios from the BoE RAMSI Top-Down Stress Tests for the U.K. FSAP update, 2011–15

    (In percent)

  • Figure 13.
    View in gallery
    Figure 13.

    United Kingdom: Distribution of Total Capital Ratios from the BoE RAMSI Top-Down Stress Tests for the U.K. FSAP Update, 2011–15

    (In percent)

  • Box Figure 1.
    View in gallery
    Box Figure 1.

    Investment and Balance Sheet Dynamics in RAMSI

  • Figure 14.
    View in gallery
    Figure 14.

    Systemic CCA Estimates of the Market-Implied Joint Capital Losses from the U.K. FSAP Update Top-Down Stress Tests, Historical and Potential (with IMF Satellite Model)

    (In billions of pound Sterling)

  • Figure 15.
    View in gallery
    Figure 15.

    Selected EU Countries: CDS Spreads

    (In basis points)

  • Figure 16.
    View in gallery
    Figure 16.

    Weighted-Average Core Tier 1 Capital Ratios from the U.K. FSAP Update Bottom-Up and BoE RAMSI Top-Down Stress Tests, 2011–15

    (In percentage points) 1/

  • Figure 17.
    View in gallery
    Figure 17.

    Tier 1 Capital Ratios from the U.K. FSAP Update Bottom-Up and BoE RAMSI Top-Down Stress Tests, 2011–15

    (In percentage points)

  • Figure 18.
    View in gallery
    Figure 18.

    Total Capital Ratios from the U.K. FSAP Update Bottom-Up and BoE RAMSI Top-Down Stress Tests, 2011–15

    (In percentage points)

Figure 1.

Major U.K. Banks: Differentiated Business and Geographic Models

(In percent of individual banks’ revenues)
Figure 2.

U.K. Banks: Breakdown of Assets and Risk-Weighted Assets

(In trillions of pound sterling)
Figure 3.

United Kingdom: Liquidity in the Banking System
Figure 4.

Overview of the U.K. FSAP Update Stress Testing Exercise
Figure 5.

Overview of the U.K. FSAP Update Stress Test Scenarios
Figure 6.

Distribution of Core Tier 1 Capital Ratios from the U.K. FSAP Update Bottom-Up Stress Tests, 2011–15

(In percent)
Figure 7.

Distribution of Tier 1 Capital Ratios from the U.K. FSAP Update Bottom-Up Stress Tests, 2011–15

(In percent)
Figure 8.

United Kingdom: Distribution of Total Capital Ratios from the U.K. FSAP Update Bottom-Up Stress Tests, 2011–15

(In percent)
Figure 9.

Estimation of Satellite Models in the U.K. FSAP Update Stress Testing Exercise
Figure 10.

Application of Satellite Output in the RAMSI and the Systemic CCA Stress Tests
Figure 11.

Distribution of Core Tier 1 Capital Ratios from the BoE RAMSI Top-Down Stress Tests for the U.K. FSAP Update, 2011–15

(In percent)
Figure 12.

United Kingdom: Distribution of Tier 1 Capital Ratios from the BoE RAMSI Top-Down Stress Tests for the U.K. FSAP update, 2011–15

(In percent)
Figure 13.

United Kingdom: Distribution of Total Capital Ratios from the BoE RAMSI Top-Down Stress Tests for the U.K. FSAP Update, 2011–15

(In percent)
Box Figure 1.

Investment and Balance Sheet Dynamics in RAMSI
Figure 14.

Systemic CCA Estimates of the Market-Implied Joint Capital Losses from the U.K. FSAP Update Top-Down Stress Tests, Historical and Potential (with IMF Satellite Model)

(In billions of pound Sterling)
Figure 15.

Selected EU Countries: CDS Spreads

(In basis points)
Figure 16.

Weighted-Average Core Tier 1 Capital Ratios from the U.K. FSAP Update Bottom-Up and BoE RAMSI Top-Down Stress Tests, 2011–15

(In percentage points) 1/
Figure 17.

Tier 1 Capital Ratios from the U.K. FSAP Update Bottom-Up and BoE RAMSI Top-Down Stress Tests, 2011–15

(In percentage points)
Figure 18.

Total Capital Ratios from the U.K. FSAP Update Bottom-Up and BoE RAMSI Top-Down Stress Tests, 2011–15

(In percentage points)