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Jacobs Str Tst Crdt Prtfl Risk Mar2012 3 22 12 V20 Nomacr

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Modern credit risk modeling (e.g., Merton, 1974) increasingly relies on advanced mathematical, statistical and numerical echniques to measure and manage risk in redit portfolios This gives rise to model risk (OCC 2011-16) and the possibility of nderstating nherent dangers stemming from very rare yet plausible occurrencs perhaps not in our eference 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
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  • 1. Stress Testing Credit Risk Portfolios Michael Jacobs, Ph.D., CFA Senior Financial Economist Credit Risk Analysis Division U.S. Office of the Comptroller of the Currency Risk / Incisive Media Training, March 2012 The views expressed herein are those of the author and do not necessarily represent the views of the Office of the Comptroller of the Currency or the Department of the Treasury.
  • 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• A Simple Stress Testing Example
  • 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 occurrencs 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* losses in • Bank Figure 3: Average Ratio of Total Charge-offs to Total Value of Loans for Top 50 Banks as of 4Q09 the recent 0.035 (Call Report Data 1984-2009) financial crisis exceed levels 0.03 observed in 0.025 recent history! 0.02 • This illustrates 0.015 the inherent limitations of 0.01 backward 0.005 looking 0 models – we must 84 1 85 1 86 0 87 0 87 1 88 1 89 0 90 0 90 1 91 1 92 0 93 0 93 1 94 1 95 0 96 0 96 1 97 1 98 0 99 0 99 1 00 1 01 0 02 0 02 1 03 1 04 0 05 0 05 1 06 1 07 0 08 0 08 1 09 1 30 19 033 19 123 19 093 19 063 19 033 19 123 19 093 19 063 19 033 19 123 19 093 19 063 19 033 19 123 19 093 19 063 19 033 19 123 19 093 19 063 19 033 20 123 20 093 20 063 20 033 20 123 20 093 20 063 20 033 20 123 20 093 20 063 20 033 20 123 09 84 19 anticipate risk* Reproduced from: Inanoglu, H., Jacobs, Jr., M., and Robin Sickles, 2010 (July), Analyzing bank efficiency: Are “too-big-to-fail” banks efficient?, forthcoming in the Journal of Efficiency
  • 5. Introduction: Motivation in the Imprecision of Value-at-Risk* Gaussian Copula Bootstrapped (Margins) Distribution of 99.97 Percentile VaR • Sampling variation in 6e-09 VaR inputs leads to huge 5e-09 confidence 4e-09 bounds for risk estimatesDensity 3e-09 (coefficient of variation 2e-09 =35.4%) 1e-09 • This is even 0e+00 assuming we 5e+08 6e+08 7e+08 8e+08 9e+08 1e+09 have the 99.97 Percentile Value-at-Risk for 5 Risk Types(Cr.,Mkt.,Ops.,Liqu.&IntRt.): Top 200 Banks (1984-2008) correct model VaR99.7%=7.64e+8, q2.5%=6.26e+8, q97.5%=8.94e+8, CV=35.37% * 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. 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
  • 7. 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
  • 8. Function of Stress Testing:Expected vs. Unexpected Loss Figure 1 Vasicek 80 distribution (theta = 0.01, rho = 0.06) Expected Economic Capital Losses 60Probability 40 Unexpected Losses 20 EL “Tail of the VaR 99.95% “Body of the Distribution” Distribution” Losses 0.01 0.02 0.03 0.04
  • 9. 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
  • 10. Function of Stress Testing: The Risk Aggregation Problem • Correlations Pairwise Scattergraph & Pearson Correlations of 5 Risk Types 7 x 10 Top 200 Banks (Call Report Data 1984-2008) 4 Credit amongst different 2 0 x 10 7 risk types are in 4 Operat. many cases large 2 corr(cr,ops) = 0.6517 and cannot be 0 x 10 7 ignored 2 0 corr(cr,mkt) corr(ops,mkt) Market • As risks are = 0.2241 = 0.1989 -2 x 10 8 modeled very 5 corr(mkt,liqu) Liqu. different, it is corr(cr,liqu) corr(ops,liqu) 0 8 = 0.5343 = 0.1533 = 0.1127 challenging to -5 x 10 2 aggregate these Int.Rt. 0 corr(cr,int) = -0.1328 corr(ops,int) = -0.1174 corr(mkt,int) = 0.2478 corr(int,liqu) = 0.1897 into an economic -2 capital measure 0 2 4 0 2 4 -2 0 2 -5 0 5 -2 0 2 7 7 7 8 8 x 10 x 10 x 10 x 10 x 10* 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.
  • 11. 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
  • 12. 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
  • 13. 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
  • 14. Supervisory Requirements and Expectations: Regulatory Capital Basel II Asymptotic Risk Factor Credit Risk Model for Risk Parameter Assumptions Normal:PD=1%,LGD=40%,Rho=0.1 EL-norm=0.40% Stressed:PD=1.5%,LGD=60%,Rho=0.15 0.8 Regulatory Capital EL-stress=0.90% 0.6 CVaR-norm=6.78%Probability Density CVaR-stress=15.79% 0.4 Stressed Capital 0.2 0.0 0.00 0.05 0.10 0.15 Credit Loss • Shocking credit risk parameters can give us an idea of what kind of buffer we may need to add to an EC estimate
  • 15. 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 explains the non-prescriptiveness for ST as Pillar 2 recognizes that banks are competent to assess and measure their credit risk appropriately• This also implies that ST should focus on EC as well as regulatory capital, as these represent the supervisory and bank internal views on portfolio credit risk• ST has been addressed by regulators or central banks beyond the Basel II framework, regarding the stability of the financial system, in published supplements (including now Basel III)• ST should consider extreme deviations from normal situations & hence involve unrealistic yet still plausible scenarios (i.e. situations with low probability of occurrence)
  • 16. Supervisory Requirements and Expectations (continued)• ST should also consider joint events which are plausible but which may not yet been observed in reference data-sets• Financial institutions should also use ST to become aware of their risk profile and to challenge their business plans, target portfolios, risk politics, etc.• ST should not only be addressed to check the capital adequacy, but also used to determine & question credit limits• ST should not be treated only as an amendment to the VaR evaluations for credit portfolios, but as a complimentary method, which contrasts the purely statistical approach of VaR- methods by including causally determined considerations for unexpected losses – In particular, it can be used to specify extreme losses in a qualitative and quantitative way
  • 17. The Credit Risk Parameters for Stress Testing (continued)• A key aspect of ST mechanics in Basel II or EC is examining the sensitivity to variation in risk parameters• In the case of RC the risk parameters in the ST exercise are given by the PD, LGD, EAD and Correlation• PD has played a more prominent role since conditional upon obligor default LGD & EAD tend to be adapted to malign environments & the stress scenarios are more limited• EAD may exhibit some sensitivity to certain exogenous factors like FX rates, we would expect such to be in the usual estimate• LGD ranges are largely dependent upon the quantification technique (e.g., the discount rate used for post default cash flows) which should be disentangled from the economic regime – For most types of lending it is thought that collateral values should be key & incorporate sufficient conservatism naturally, but that varies
  • 18. The Credit Risk Parameters for Stress Testing: LGD• LGD: estimate of the amount a bank loses if a counterparty defaults (expected PV of economic loss / EAD or 1 minus the recovery rate)• Depends on claim seniority, collateral, legal jurisdiction, condition of defaulted firm or capital structure, bank practice, type of exposure• Measured LGDs depend on default definition: broader (distressed exchange/reneg.) vs. narrow (bankruptcy,liquidation)->lower/higher• Market vs. workout LGD: prices of defaulted debt shortly after default vs. realized discounted ultimate recoveries up to resolution• LGDs on individual instruments tends to be either very high (sub or unsecured debt) or very low (secured bonds or loans) - “bimodal”• Downturn LGD: intuition & evidence that should be elevated in economic downturns – but mixed evidence & role of bank practice• Note differences across different types of lending (e.g., enterprise value & debt markets is particular large corporate) Discounted RecoveriesLGD=1- EAD 1 RecoveryRate Discounted Direct & Indirect Workout Costs
  • 19. The Credit Risk Parameters forStress Testing: LGD (continued) • Contractual features: Employees, Trade Creditors, Lawyers more senior and secured instruments do better. Bank Loans Banks • Absolute Priority Rule: S some violations (but E usually small) Senior Secured N • More senior instruments I tend to be better secured. O Senior Unsecured R Bondholders • Debt cushion as distinct I from position in the Senior Subordinated T capital structure. Y Junior Subordinated • High LGD for senior debt with little sub-debt? Preferred Shares • Proportion of bank debt Shareholders • The “Grim Reaper” story Common Shares • Enterprise value 19
  • 20. The Credit Risk Parameters for Stress Testing: LGD (continued) • Bankruptcies (65.2%) have higher LGDs than out-of-court settlements (55.8%) • Firms reorganized (emerged or acquired) have lower LGDs (43.9%) than firms liquidated (68.9%)*Diagram reproduced from: Jacobs, M., et al., 2011, Understanding and predicting the resolution of financial distress, ForthcomingJournal of Portfolio Management (March,2012), page 31. 518 defaulted S&P/Moody’s rated firms 1985-2004.
  • 21. The Credit Risk Parameters for Stress Testing: LGD (continued) • Distributions of Distribution of Moodys Market LGD: All Seniorities (count=4400,mean=59.1%) Distribution of Moodys Market LGD: Senior Bank Loans (count=54,mean=16.7%) 2.5 1.5 * 2.0 Moody’s Defaulted 1.0 1.5 Density Density 1.0 0.5 Bonds & Loan 0.5 0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 LGD Distribution of Moodys Market LGD: Senior Secured Bonds (count=1022,mean=46.7%) LGD Distribution of Moodys Market LGD: Senior Unsecured Bonds (count=2215,mean=60.0%) LGD (DRS 2.0 Database 1970- 1.5 1.5 1.0 Density Density 2010) 1.0 0.5 0.5 • Lower the quality 0.0 0.0 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 LGD LGD of collateral, the Distribution of Moodys Market LGD: Senior Subordinated Bonds (count=600,mean=67.9%) Distribution of Moodys Market LGD: Junior Subordinated Bonds (count=509,mean=74.6%) 2.5 1.5 2.0 higher the LGD 1.5 1.0 Density Density 1.0 0.5 • Lower ranking of 0.5 0.0 0.0 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 the creditor class, LGD LGD Table 2 - Ultimate Loss-Given-Default1 by Seniority Ranks and Collateral Types Reproduced with permission: (Moodys Ultimate Recovery Database 1987-2010)2 Senior Senior Junior the higher the LGD Senior Secured Unsecured Subordinated Subordinated Subordinated Moody’s, URD, Release 10-15- 10. Bank Loans Bonds Bonds Bonds Bonds Bonds Total Instrument • And higher Collateral Type Cash & Highly Liquid Collateral Count Average Count Average Count Average Count Average Count Average Count Average Count Average 32 -0.4% 7 8.7% 7 8.7% 1 0.0% 0 N/A 0 N/A 40 1.2% seniority debt tends to haveMajor Collateral Inventory & Accounts Receivable 173 3.6% 0 N/A 7 6.9% 0 N/A 0 N/A 0 N/A 180 3.8% Category All Assets, 1st Lien & Capital Stock 1199 18.8% 242 24.7% 242 24.7% 1 14.0% 2 30.8% 0 N/A 1444 19.8% Plant, Property & Equipment 2nd Lien Intangible or Illiquid Collateral 67 65 1 12.4% 41.2% 0.0% 245 75 5 49.6% 37.5% 72.2% 245 75 5 49.6% 37.5% 72.2% 2 4 0 39.6% 59.0% N/A 0 5 0 N/A 50.6% N/A 0 1 0 N/A 60.0% N/A 314 150 6 41.6% 40.3% 60.2% better collateral Total Secured Total Unsecured 1537 129 17.4% 43.1% 581 0 36.8% N/A 0 1147 N/A 51.4% 8 451 41.2% 70.8% 7 358 44.9% 71.7% 1 64 60.0% 80.8% 2134 2149 22.9% 59.2% * Reproduced with permision: Total Collateral 1666 19.4% 581 36.8% 1147 51.4% 459 70.3% 365 71.2% 65 80.5% 4283 41.1% Moody’s Analytics.Default Rate1 - Par minus the settlement value of instruments received in resolution of default as a percent of par.2 - 4283 defaulted and resolved instruments as of 8-9-10 Service Database, 10-15-10.
  • 22. The Credit Risk Parameters forStress Testing: LGD (continued)• Downturns: 1973-74, 1981-82, 1990-91, 2001-02, 2008-09• As noted previously, commonly accepted that LGD is higher during economic downturns when default rates are elevated• Lower collateral values• Greater supply of distressed debt• The cycle is evident in time series, but note all the noise * Reproduced with permission: Moody’s Analytics. Default Rate Service Database, Release Date 10-15-10.
  • 23. The Credit Risk Parameters forStress Testing: LGD (continued)
  • 24. The Credit Risk Parameters for Stress Testing: LGD (continued) • Jacobs & Karagozoglu (2011)* study Table 3 of Jacobs & Karagozoglu (2010): Simultaneous Equation Modeling of Discounted Instrument & Oligor LGD: Full Information Maximum Likelihood Estimation (Moodys URD 1985–2009) ultimate LGD in Moody’s URD at the Category Instrument Obligor Partial Partial Variable Effect P-Value Effect P-Value Debt to Equity Ratio (Market) Book Value -0.0903 -0.0814 2.55E-03 0.0174 loan & firm level simultaneously Financial Tobins Q 0.0729 8.73E-03 Intangibles Ratio Working Capital / Total Assets Operating Cash Flow 0.0978 -0.1347 -8.31E-03 7.02E-03 4.54E-03 0.0193 • Empirically models notion that recovery on a loan is akin to a collar Industry Profit Margin - Industry -0.0917 1.20E-03 Industry - Utility -0.1506 8.18E-03 option on the firm/enterprise level Industry - Technology 0.0608 2.03E-03 Senior Secured 0.0432 0.0482 Senior Unsecured 0.0725 3.11E-03 Contractual Senior Subordinated 0.2266 1.21E-03 Junior Subordinated Collateral Rank Percent Debt Above 0.1088 0.1504 0.1241 0.0303 4.26E-12 3.84E-03 recovery Percent Debt Below -0.2930 7.65E-06 • Firm (loan) LGD depends on fin ratios, Time Time Between Defaults -0.1853 7.40E-04 Time-to-Maturity 0.0255 0.0084 capital structure, industry state,Structure Number of Creditor Classes 0.0975 1.20E-03 Capital Percent Secured Debt -0.1403 7.56E-03 Percent Bank Debt Invest
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