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Jacobs stress testing_aug13_8-15-13_v4

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In this study we survey practices and supervisory expectations for stress testing (ST), in a credit risk framework for banking book exposures. We introduce and motivate ST; and discuss the function, supervisory requirements and expectations, credit risk parameters, interpretation results with respect to ST. This includes a typology of ST (uniform testing, risk factor sensitivities, scenario analysis; and historical, statistical and hypothetical scenarios) and procedures for con-ducting ST. We conclude with two simple and practical stress testing examples, one a ratings migration based approach, and the other a top-down ARIMA modeling approach.
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  • 1. Stress Testing Credit Risk Portfolios Michael Jacobs, Ph.D., CFA Senior Manager and Risk Advisor Enterprise Risk Services / Government and Regulatory Services Deloitte and Louche, LLP AUgust 2013 The views expressed herein are those of the author and do not necessarily represent the views of Deloitte and Touche LLP
  • 2. Outline • Introduction • The Function of Stress Testing • Supervisory Requirements and Expectations • The Credit Risk Parameters for Stress Testing • Interpretation of Stress Test Results • A Typology of Stress Tests – Uniform Testing – Risk Factor Sensitivities – Scenario Analysis • Historical Scenarios • Statistical Scenarios • Hypothetical Scenarios • Procedures for Conducting Stress Tests • Stress Testing Example: Ratings Based Approach • Stress Testing Example: ARIMA / Time Series Based Approach
  • 3. Introduction: Overview • Modern credit risk modeling (e.g., Merton, 1974) increasingly relies on advanced mathematical, statistical and numerical techniques to measure and manage risk in credit portfolios • This gives rise to model risk (OCC 2011-16) and the possibility of understating inherent dangers stemming from very rare yet plausible occurrences perhaps not in our reference data-sets • International supervisors have recognized the importance of stress testing credit risk in the Basel framework (BCBS, 2009) • It can and has been argued that the art and science of stress testing has lagged in the domain of credit, vs. other types of risk (e.g., market), and our objective is to help fill this vacuum • We aim to present classifications & established techniques that will help practitioners formulate robust credit risk stress tests
  • 4. Introduction: Motivation in the Financial Crisis* * Reproduced from: Inanoglu, H., Jacobs, Jr., M., and Robin Sickles, 2013 (March), Analyzing bank efficiency: Are “too-big-to- fail” banks efficient?, forthcoming Journal of Banking & Finance • Bank losses in the recent financial crisis exceed levels observed in recent history! • This illustrates the inherent limitations of backward looking models – we must anticipate risk Figure 1: Average Ratio of Total Charge-offs to Total Value of Loans for Top 50 Banks as of 4Q09 (Call Report Data 1984-2009) 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035
  • 5. Introduction: Motivation in the Imprecision of Value-at-Risk* Gaussian Copula Bootstrapped (Margins) Distribution of 99.97 Percentile VaR VaR99.7%=7.64e+8, q2.5%=6.26e+8, q97.5%=8.94e+8, CV=35.37% 99.97 Percentile Value-at-Risk for 5 Risk Types(Cr.,Mkt.,Ops.,Liqu.&IntRt.): Top 200 Banks (1984-2008) Density 5e+08 6e+08 7e+08 8e+08 9e+08 1e+09 0e+001e-092e-093e-094e-095e-096e-09 • Sampling variation in VaR inputs leads to huge confidence bounds for risk estimates (coefficient of variation =35.4%) • This is even assuming we have the correct model! *Inanoglu, H., and Jacobs, Jr., M., 2009, Models for risk aggregation and sensitivity analysis: An application to bank economic capital, The Journal of Risk and Financial Management 2, 118-189.
  • 6. An Evolving Regulatory Landscape: Continuum of New and Overlapping Requirements Regulatory supervisors have long advocated stress testing1 as an integral part of an overall risk management framework; however recent proposed guidance on capital planning and annual stress testing requirements formalizes stress testing as an integral component of determining capital adequacy SCAPBasel II CCAR / CapPR (Capital Plan Final Rule) & Disclosures? FASB Liquidity & IRR Disclosures FDIC/OCC ANNUAL STRESS TESTING 2012-16, 0004 ICAAP  The Supervisory Capital Assessment Program (“SCAP”) provided a granular view on supervisory expectations  CCAR formalized regulatory expectations and provided fairly prescriptive guidance associated with the role of stress testing and capital management, capital adequacy processes, and planning  The fundamental principles of the Basel III Internal Capital Adequacy Assessment Process (“ICAAP”) framework still remain and have been further supported by the recent capital planning and stress testing 7 capital principles/guidance  Model validation and independent review extend to all models used for risk measurement, stress testing, ICAAP or any models supporting the overall capital adequacy process models and should be supported by an overall model risk management framework. These components together highlight the need to consider an end to end view of capital adequacy to help provide clarity to internal and external stakeholders  Strong governance and risk management processes are further emphasized as cornerstones to effective capital management and planning  Guidelines for Capital Planning published June 7, 2012 by the Treasury/OCC/FDIC suggests all risks should be estimated, plus banks should calculate sensitivities, complete reverse stress tests and complete scenario analysis (idiosyncratic risk) MODEL VALIDATION 2011-7 or 12 DODD FRANK - ENHANCED PRUDENTIAL SUPERVISION (Proposed) 1 Enhanced Prudential Standards and Early Remediation Requirements for Covered Companies; Board of Governors of the Federal Reserve System (Board); & SR 2012-16 (6-7-2012)
  • 7. SR 2012-07’s Stress Test “Conceptual Process” Materiality Measures Qualitative Factors 5 Principles, Controls, Capital & Liq. Policies, and Procedures Credit/PPNR Loss Estimates & Assumptions Methodology Documentation Back Testing, Validation Balance Projections, Assets, Liabilities & Income & RWA Statements Ongoing Monitoring of Transparent, Repeatable & Auditable Process Strengths and Weaknesses of Risk Models RiskAppetite Governance Stress Test Results Capital Buffers for Uncertainty Risk Quantitative Factors
  • 8. 20+ Major Steps to Governance: For $10B to $50 Billion Banks Risk Identification & Measurement Ensure Integrity of Assessment Set & Assess Internal Adequacy Goals Related to Risk P1: Risk Identification & Measurement P2: Translate Risk Into Loss Estimate P3: Available Capital Resources P4: Impact of Loss and Resource Estimation on Capital Adequacy P5: Use Estimates to Make Key Capital Decisions P6: Internal Controls & Governance P7: Effective Board & Senior Management Oversight* 1. Risk measurement infrastructure identifies and assess all material risk 2. Risk models meet governance expectations and qualitative processes are transparent and repeatable 3. Leverage macroeconomic assumptions for capital planning and stress testing 4. Leverage risk measurement infrastructure to generate loss forecast 5. Loss forecasting sensitivity analysis 6. Clear definition of available capital composition and loss absorption capability 7. Effective resource forecasting process using assumptions consistent with loss forecasting 8. PPNR/other models meet governance expectations and qualitative processes are transparent and repeatable 9. Resource forecasting sensitivity analysis 10. Consistent and repeatable process to aggregate loss and resource estimates 11. Establish buffer for limitations and uncertainty 12. Analyze prospective capital measures that represent both leverage and risk 13. Assess capital adequacy vs. stated goals for the level and composition of capital 14. Capital policy guides key decisions: • Establish capital goals • Determining appropriate capital levels • Making decisions about capital actions • Maintaining capital contingency plans 15. ICAAP governance structure with defined roles and responsibilities 16. Robust internal controls with sufficient policy and process documentation 17. Sufficient model documentation, change control, validation and independent review 18. MIS to support quantitative tools with appropriate data governance 19. Sufficient audit testing 20. Appropriate reporting on key risks, impact loss/resource estimates on capital v. goals, and ICAAP weaknesses and uncertainty 21. Senior Management/Board make informed capital action recommendations and decisions 22. Documented approval of planned capital actions 23. ICAAP information used to inform other management and decision making processes $10-$50 B, similar to CCAR/CapPR” *Effective challenge and communication of limitations and uncertainty ICAAP:
  • 9. SR 2012-07 Stress Test “Governance End State”
  • 10. Consistent and transparent ICAAP, Capital, & Governance process with documented stress test models At the loan and transaction level, any higher risk assets can be isolated and the proper economic capital allocated, Assets or Geographic Regions with Risk Profiles beyond Risk Appetite Limits can be sold. Management (economic capital) and regulatory stress test and risk reports: Translate results into appropriate dynamic and static risk reports Result: Integration of Stress Test Results, Economic Capital, Concentration Management, New Loan Pricing all integrated into Business Line Processes and Results, including Capital Usage, and Product Level Pricing. Full process includes risk assessment and performance measurements. Process evaluates shareholder returns, rating agency ratings, and all regulatory requirements. Capital Policies level set expectations, roles & responsibilities, capital buffers and trigger levels, and required actions to preserve capital Types of scenarios: •Expected Losses for all Risks •~<1% Likely Unexpected Loss Views •Idiosyncratic Scenarios •Regulator-driven Scenarios •Reverse Stress Test • Risk Profile • Risk Tolerance and Buffers • Hightened Supervisory Review Response Levels • Concentrations: Uses of Capital by Product • Optimal Business Mix Profile Stress Testing Governance Oversight Capital Policy Scenario Development Business Mix, Risk Appetite & Concentration, New Business Profile Expected & Unexpected Losses @ Transaction Level Stress Results / Annual Budget Reporting Concentration, Uncertainty, & De-Risking Action Plans Integrated Capital & Liquidity, Concentration & Risk Appetite Process “Process End State”: Stress Test Results Integrated with Capital Planning, Economic Capital, Concentration Mgmt & Business Line Risk/Return Results
  • 11. Sample Credit Loss Modeling Framework for Stress TestingPortfolio Segment Loan / Pool Data Modeling Approach Key DependenciesPortfolio Segment C&I - Major Industries - Oil & Gas - Agriculture - etc. CRE - Construction - Income-Producing - Land Retail - Mortgage - HELOC - Credit Cards - Small Business - Other Macroeconomic and External Data - National - State-level - MSA-level - Unemployment - GDP Growth - HPI - T-Bill Rates - etc. - Property Prices - Land Prices - BBB Bond Spread - Stock Price Volatility Loan / Pool Data Loan Level - Ratings - EAD / Balances - Vintage - NAIC Code Loan Level - Ratings / LTV / DSCR - EAD / Balances - Collateral Type (Retail, Industrial, etc) Portfolio Level - Historical charge-offs - Further segmentation - Vintage/maturity - Legacy acquisition Modeling Approach Time Series Analysis - Predict quarterly changes in PD, LGD using footprint-specific state-level macro- factors (e.g. state-level Unemployment) and prior-period levels, for each industry segment Time Series Analysis - Predict quarterly changes in LTV and DSCR using state-level macro-factors and vended property price data - Defaults trigger charge-offs Time Series and Static Regression - Predict Charge-offs as function of macro factors, deposits, prior-period balances, FICO, OLTV, Vintage, Status - Choice of method depends on data quality and history length Footprint States - New York - Connecticut - New Jersey - etc. Key Dependencies - Valid PDs, LGDs, or charge-offs by Rating and by risk factor or industry segment - Rating history or reference data − Accurate LTVs and vintage − Reference property price data histories by region and for CLTV − Balance projections − Charge-off reference data across credit cycle by risk factor − Geography − Loan Type
  • 12. Key Success Factors for Stress-Test Modeling Engagements What’s Appropriate for the Bank Alignment with Business Knowing the Bank’s Story Using Intuitive Key Risk Drivers Getting Results Together Preparing for Challenges Knowledge and Tools Transfer •Do the proposed models fit yo •What loss and risk data do •Internal and external parties should see a model result and be able to understand •Modeling can be complex. Constant and ongoing communication •Driving ROI into Process, Concentration Management and Changing Risk Profile •Full ownership by the bank is the goal, with engagement in the business lines and process going forward •Model validation, documentatio n, model use, and the bank team, must be •The Models and the narrative in the Capital Methodologie s should be consistent and integrated
  • 13. Conceptual Issues in Stress Testing: Risk vs. Uncertainty • Knight (1921): uncertainty is when a probability distribution is unmeasurable or unknown, arguably a realistic scenario • Rely upon empirical data to estimate loss distributions, but this is complicated because of changing economic conditions • Popper (1945): situations of uncertainty closely associated & inherent to changes in knowledge & behavior (no historicism) • Shackle (1990): predictions reliable only for immediate future, as impact others’ choices after time has an appreciable effect • This role of human behavior in economic theory was a key impetus behind rational expectations & behavioral finance • Implication is that risk managers must be aware of model limitations & how an EC regime itself changes behavior • Although we face uncertainty, valuable to estimate loss distributions in that helps make explicit sources of uncertainty
  • 14. The Function of Stress Testing • A possible definition of stress testing (ST) is the investigation of unexpected loss (UL) under conditions outside our ordinary realm of experience (e.g., extreme events not in our data-sets) • Many reasons for conducting periodic ST are largely due to the relationship between UL and economic capital (EC) • EC is generally thought of as the difference between Value-at- Risk (VaR), or extreme loss at some confidence level (e.g., a high quantile of a loss distribution), and expected loss (EL) • This purpose for ST hinges on our definition of UL – while it is commonly thought that EC should cover this, in that UL may not only be unexpected but not credible as it is a statistical concept • Therefore some argue that results of an ST should be used for EC vs. UL, but this is rare, as we usually do not have probability distributions associated with stress events
  • 15. Function of Stress Testing: Expected vs. Unexpected Loss 0.01 0.02 0.03 0.04 20 40 60 80 Unexpected Losses Expected Losses “Body of the Distribution” “Tail of the Distribution” Probability Losses EL Economic Capital Vasicek distribution (theta = 0.01, rho = 0.06) Figure 1 VaR
  • 16. The Function of Stress Testing (continued) • ST can and commonly have been used to challenge the adequacy of regulatory (RC) or EC & derive a buffer for losses exceeding the VaR, especially for new products or portfolios • Another advantage to ST to determine capital is that it can easily aggregate different risk types (e.g., credit, market & operational), problematic under standard EC methodologies – E.g., different horizons and confidence levels for market vs. credit risk – Powerful dependencies between risk types in periods of stress • Quantification of ST appear and can be deployed several aspects of risk management with respect to extreme losses: – Risk buffers determined or tested – Risk capacity of a financial institution – Setting sub-portfolio limits, especially if low-default situation – Risk policy, tolerance and appetite
  • 17. Function of Stress Testing: The Risk Aggregation Problem -2 0 2 x 10 8 -5 0 5 x 10 8 -2 0 2 x 10 7 0 2 4 x 10 7 0 2 4 x 10 7 -2 0 2 x 10 8 -5 0 5 x 10 8 -2 0 2 x 10 7 0 2 4 x 10 7 Pairwise Scattergraph & Pearson Correlations of 5 Risk Types Top 200 Banks (Call Report Data 1984-2008) 0 2 4 x 10 7 Credit Liqu. Operat. Market Int.Rt. corr(cr,ops) = 0.6517 corr(mkt,liqu) = 0.1127 corr(int,liqu) = 0.1897 corr(cr,mkt) = 0.2241 corr(ops,liqu) = 0.1533 corr(mkt,int) = 0.2478 corr(cr,liqu) = 0.5343 corr(ops,int) = -0.1174 corr(ops,mkt) = 0.1989 corr(cr,int) = -0.1328 • Correlations amongst different risk types are in many cases large and cannot be ignored • As risks are modeled very different, it is challenging to aggregate these into an economic capital measure * Inanoglu, H., and Jacobs, Jr., M., 2009, Models for risk aggregation and sensitivity analysis: An application to bank economic capital, The Journal of Risk and Financial Management 2, 118-189.
  • 18. The Function of Stress Testing (continued) • Apart from risk measurement or quantification, ST can be a risk management tool in analyzing portfolio composition and resilience with respect to disturbances: – Identify potential uncertainties and locate the portfolio vulnerabilities – Analyze the effects of new complex structures and credit products – Guide discussion on unfavorable developments like crises and abnormal market conditions, which cannot be excluded – Help monitor important sub-portfolios exhibiting large exposures or extreme vulnerability to changes in the market – Derive some need for action to reduce the risk of extreme losses and hence economic capital, and mitigate the vulnerability to important risk relevant effects – Test the portfolio diversification by introducing (implicit) correlations – Question the bank’s attitude towards risk
  • 19. Supervisory Requirements and Expectations • ST appears in Basel II (BIS, 2006) framework under both Pillar I (minimum capital requirements) and Pillar 2 (the supervisory review process) with the aim of improving risk management • Every IRB bank has to conduct sound, significant and meaningful stress testing to assess the capital adequacy in a reasonably conservative way. – Major credit risk concentrations have to undergo periodic stress tests. – ST should be integrated in the internal capital adequacy process (i.e., risk management strategies to respond to the outcome of ST) • Banks shall ensure that they dispose of enough capital to meet the regulatory capital requirements even in the case of stress • Should identify possible future events / changes in economic conditions with potentially adverse effects on credit exposures & assess the ability of the bank to withstand such
  • 20. Supervisory Requirements and Expectations (continued) • A quantification of the impact on the parameters probability of default (PD), loss given default (LGD), exposure at default (EAD) as well as rating migrations is required • Special notes on how to implement these requirements include the use of scenarios including things like: – economic or industry downturn – market-risk events – liquidity shortage • Consider recession scenarios (worst-case not required) • Banks should use their own data for estimating rating migrations & integrate the insight of such for external ratings • Banks should build their stress testing also on the study of the impact of smaller deterioration in the credit environment
  • 21. Supervisory Requirements and Expectations: Regulatory Capital 0.00 0.05 0.10 0.15 0.00.20.40.60.8 Basel II Asymptotic Risk Factor Credit Risk Model for Risk Parameter Assumptions Credit Loss ProbabilityDensity EL-norm=0.40% EL-stress=0.90% CVaR-norm=6.78% CVaR-stress=15.79% Normal:PD=1%,LGD=40%,Rho=0.1 Stressed:PD=1.5%,LGD=60%,Rho=0.15 Stressed Capital Regulatory Capital • Shocking credit risk parameters can give us an idea of what kind of buffer we may need to add to an EC estimate
  • 22. Supervisory Requirements and Expectations (continued) • Though ST are mainly contained in Pillar 1, it is a fundamental part of Pillar 2, an important way of assessing capital adequacy • This ex
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