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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  • E.g., fair vs. loaded die (or die w/unknown # sides) Popper: emphasized that growth of knowledge & freedom implies cannot perfectly predict the course of history (refutation of historicism)-e.g., statement that $ is ineveitably going to depreciate if the U.S. does not control its debt is refutable but not valid
  • Vasicek distribution with theta = 0.01 (PD or EL) & rho (corr) = 0.06
  • Mlt LGD: avail only for mark debt, subj to ill/swings inv sent; W.O. / ult LGD: takes many years to get data, the B II std for many banks (esp middle mkt or priv debt portfolios), probl in meas (need all mat costs-coll costs, dir + indir)Diff WO prac -> banks see diff d-LGD behavior in diff portf (also
  • Mlt LGD: avail only for mark debt, subj to ill/swings inv sent; W.O. / ult LGD: takes many years to get data, the B II std for many banks (esp middle mkt or priv debt portfolios), probl in meas (need all mat costs-coll costs, dir + indir)Diff WO prac -> banks see diff d-LGD behavior in diff portf (also
  • Mlt LGD: avail only for mark debt, subj to ill/swings inv sent; W.O. / ult LGD: takes many years to get data, the B II std for many banks (esp middle mkt or priv debt portfolios), probl in meas (need all mat costs-coll costs, dir + indir)Diff WO prac -> banks see diff d-LGD behavior in diff portf (also
  • Dflt Rate Serv d.b. – mkt LGD, MURD: ult LGD
  • Dflt Rate Serv d.b. – mkt LGD, MURD: ult LGD
  • Dflt Rate Serv d.b. – mkt LGD, MURD: ult LGD
  • Facility ultimate LGD de(in)creasing in creditor rank, collateral quality, tranche thickness (time-to-maturity,EAD,ultimate obligor LGD, market LGD)Firm ultimate LGD de(in)creasing in leverage, liquidity, cash flow, size, profitability,industry utility/profit,time-between defaults,% secured or bank debt,CARs, prepack,S&P return, investment grade at origination (intangibility,Tobin’s Q, industry tech, # creditor classes, obligor market LGD, bankruptcy filing,recession period,Moody’s default rate)
  • Typically borr going into dflt will try to draw down on credit lines as liqu or alt funding dries upDer. WWE ex.: 1. cross-FX swap with weaker curr CP: more likely to dflt just when curr weakens & bank is in the $ 2. CDS purch prot & insurer is deter same time as the ref entityAs either borr deteriorates or in downturn, EAD risk may become lower as banks cut lines
  • Looked at dflt rev in Moody’s MURD database & traced exposure back in fin filings (10Q &10K reports)Similar to JPMC (2001) study, added a few variables, and tried alt meas EAD risk to LEQ factorCaveat: onlt defaults up to early 2009, somewhat sens to the part meas, r^2 still low given # var’s ,judg calls in reading fin statements
  • May be direct inp (RMM) or der obl inf (SM)We want our est not to refl things out of contr obl –e.g., trans&conv event for country freezes outflowsEg coll matters: AIG tripped received govt loan to post coll & avoided dflt – is this real or not?Dflt def: ag (bankrupt,ren debt, missed payment-they claim basically B2), B2 (bank det unl to pay or obl 90dpd any mat obs-now typically same as nonaccr, but some diff do exist)PIT: PD refl curr sit->obl quickly upgr/downgr & DRs by rating same acr cycle, TTC: stable ratings but DRs fluctuateScrcrd sys:popular because don’t rely on extensive internal default data (esp. for low dflt portf.)Stat mdls: more prev in rtl due to much dflt data
  • May be direct inp (RMM) or der obl inf (SM)We want our est not to refl things out of contr obl –e.g., trans&conv event for country freezes outflowsEg coll matters: AIG tripped received govt loan to post coll & avoided dflt – is this real or not?Dflt def: ag (bankrupt,ren debt, missed payment-they claim basically B2), B2 (bank det unl to pay or obl 90dpd any mat obs-now typically same as nonaccr, but some diff do exist)PIT: PD refl curr sit->obl quickly upgr/downgr & DRs by rating same acr cycle, TTC: stable ratings but DRs fluctuateScrcrd sys:popular because don’t rely on extensive internal default data (esp. for low dflt portf.)Stat mdls: more prev in rtl due to much dflt data
  • May be direct inp (RMM) or der obl inf (SM)We want our est not to refl things out of contr obl –e.g., trans&conv event for country freezes outflowsEg coll matters: AIG tripped received govt loan to post coll & avoided dflt – is this real or not?Dflt def: ag (bankrupt,ren debt, missed payment-they claim basically B2), B2 (bank det unl to pay or obl 90dpd any mat obs-now typically same as nonaccr, but some diff do exist)PIT: PD refl curr sit->obl quickly upgr/downgr & DRs by rating same acr cycle, TTC: stable ratings but DRs fluctuateScrcrd sys:popular because don’t rely on extensive internal default data (esp. for low dflt portf.)Stat mdls: more prev in rtl due to much dflt data
  • May be direct inp (RMM) or der obl inf (SM)We want our est not to refl things out of contr obl –e.g., trans&conv event for country freezes outflowsEg coll matters: AIG tripped received govt loan to post coll & avoided dflt – is this real or not?Dflt def: ag (bankrupt,ren debt, missed payment-they claim basically B2), B2 (bank det unl to pay or obl 90dpd any mat obs-now typically same as nonaccr, but some diff do exist)PIT: PD refl curr sit->obl quickly upgr/downgr & DRs by rating same acr cycle, TTC: stable ratings but DRs fluctuateScrcrd sys:popular because don’t rely on extensive internal default data (esp. for low dflt portf.)Stat mdls: more prev in rtl due to much dflt data
  • A competitor to the well-known KMV model – the structural EDF based on Merton (1973)Refs: van Deventer & Imai book (2003), academic paper Chava & Jarrow RF 2004, Hosmer & Lemeshow (2000) bk log regrJust as diff classes of EC mdl, same for the drivers (and as PD is driver of EC, PD has its own drivers)Allows different expl var’s/mdls for diff hor
  • Contag.: phen that it is not only gen ec that makes firms default, but 2nd order feedback eff (eg, real est./subpr crsis-dflt->suply overhang & neg wealth eff->depr ec cond further->more defaults)E.g., high frequ equ price (daily, weekly) corr can show small corr betw cycl & oncycl ind, but longer term (quart, ann) loss data can show high dep->need to analyze sens of estm to thisEg, incr lev & PD->decr value equ, which is consis with decr asset vol (equ is call opt); emp evid Gordy and HeitfeldL (2002)Eg, data sources: losses, equities, CDS
  • Jacobs, Michael. (2010) “Modeling the Time Varying Dynamics of Correlations: Applications for Forecasting and Risk Management,” (with Ahmet Karagozoglu). Working Paper. Estimates over longer moving windows are smoother overall, but shorter window estimates can look to be zero over shorter time periodsCorr can go from very negative to very pos from one time period to another – structural breaksDifferent sectors can have very diff avg corr to the broader market-implic for div
  • Case of strured prod (tranche of RMBS) this is an order of magn more sens
  • For example, an increase in price of resources such as oil or energy can have a negative impact on PDs in the automobile or any other industry consuming lots of energy, but it could have a positive impact on the PDs in the country trading these resources
  • For example, for a bank focusing on real estate, GDP, employment rate, inflation rate, spending capacity in the countries, it is acting in, will be of more relevance than the oil price, exchange rates, etc.
  • Jacobs Str Tst Crdt Prtfl Risk Mar2012 3 22 12 V20 Nomacr

    1. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 23. The Credit Risk Parameters forStress Testing: LGD (continued)
    24. 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 Investment Grade at Origination -0.2382 -0.0720 7.45E-03 4.81E-03 macroeconomy, equity market / CARsCredit Quality / Principal at Default 8.99E-03 1.14E-03 (seniority, collateral quality, debt Market Cumulative Abnormal Returns -0.2753 1.76E-04 Ultimate LGD - Obligor 0.5643 7.82E-06 LGD at Default - Obligor 0.1906 4.05E-04 LGD at Default - Instrument 0.2146 1.18E-14 cushion) Legal Prepackaged Bankruptcy -0.0406 5.38E-03 Bankruptcy Filing 0.1429 5.00E-03 1989-1991 Recession 0.0678 0.0474 • Feedback from ultimate obligor LGD Macro 2000-2002 Recession 0.1074 0.0103 Moodys Speculative Default Rate 0.0726 1.72E-04 S&P 500 Return Number of Observations In-Smpl Out-Smpl 568 114 -0.1392 In-Smpl 568 2.88E-04 Out-Smpl 114 to the facility level & at both level Diagnostics Log-Likelihood Pseudo R-Squared Hoshmer-Lemeshow 1.72E-10 9.60E-08 0.6997 0.4115 0.6119 0.3345 1.72E-10 0.5822 0.5204 9.60E-08 0.4744 0.3907 ultimate LGD depends upon market Area under ROC Curve 0.8936 0.7653 0.8983 0.7860 Kolmogorov-Smirnov 1.12E-07 4.89E-06 1.42E-07 6.87E-06 *Jacobs, Jr., M., and Karagozoglu, A, 2011, Modeling ultimate loss given default on corporate debt, The Journal of Fixed Income, 21:1 (Summer), 6-20.
    25. 25. The Credit Risk Parameters for Stress Testing: EAD• EAD: an estimate of the dollar amount of exposure on an instrument if there is a counterparty / obligor default over some horizon• Typically, a borrower going into default will try to draw down on credit lines as liquidity or alternative funding dries up• Correlation between EAD & PD for derivatives exposure: wrong way exposure (WWE) problem: higher exposure & more default risk• Derivative WWE examples – A cross-FX swap with weaker a currency counterparty: more likely to default just when currency weakens & banks are in the money – A bank purchases credit protection through a CDS & the insurer is deteriorating at the same time as the reference entity• Although Basel II stipulates “margin of conservatism” for EAD, in the case of loans greater monitoring->negative correlation with PD• As either borrower deteriorates or in downturn conditions, EAD risk may actually become lower as banks cut lines
    26. 26. The Credit Risk Parameters forStress Testing: EAD (continued) • For traditional credit products depends on loan size, redemption schedule, covenants, bank monitoring, borrower distress, pricing • Case of unfunded commitments (e.g., revolvers): EAD anywhere from 0% to 100% of line limit (term loans typically just face value)• Typically banks estimate EAD by a loan equivalency quotient (LEQ): fraction of unused drawn down in default over total current availability: O - Ot EADXt ,t,T = Ot + LEQXf ,t,T × Lt - Ot Ot + E t | T , Xt × Lt - Ot t Lt - Ot• Where O: outstanding, L: limit, t: current time, τ: time of default, T: horizon, X: vector of risk factors , Et (.) mathematical expectation
    27. 27. EAD Example for Credit Models: Jacobs (2010) Study Table 6 - Generalized Linear Model Multiple • EAD risk increasing in time-to- Regression Model for EAD Risk (LEQ Factor) - default; loan undrawn or limit Moodys Rated Defaulted Revolvers (1985-2009) Coeff. P-Value amount; firm size or intangibility; %Utilization: Used Amount / Limit (%) -0.3508 2.53E-06Total Commitment: Line Limit ($) 3.64E-05 0.0723 bank or secured debtUndraw n: "Headroom" on line ($)Time-to-Default (years) 3.27E-05 0.0516 7.42E-03 1.72E-05 • EAD risk decreasing in PD ( worseRating 1: BB (base = AAA-BBB) -0.1442 0.0426 obligor rating or aggregate defaultRating 2: B -0.0681 6.20E-03Rating 3: CCC-CC -0.0735 1.03E-05 rate); firm leverage or profitability;Rating 4: CCC -0.0502 2.08E-04 loan collateral quality or debtLev erage: L.T.Debt / M.V. Equity -0.0515 0.0714Size: Book Value (logarithm) 0.1154 2.63E-03 cushionI ntangibility: I ntangible / Total Assets 0.0600 0.0214 Table 5 1Liquidity: Current Cssets / Current Liabilities -0.0366 0.0251 Estimated LEF by Rating and Time-to-DefaultProfitabilty: Net I ncome / Net Sales -6.59E-04 0.0230 Moodys Rated Defaulted Borrowers Revolvers 1985-2009Colllateral Rank: Higher -> Low er Quality 0.0306 3.07E-03 Risk Time-to-Default (yrs)Debt Cushion: % Debt Below the Loan -0.2801 5.18E-06 Rating 1 2 3 4 5 >5 TotalAggregate Speculativ e Grade Default Rate -0.9336 0.0635 AAA-BBB 64.56% 65.26% 84.93% 92.86% 84.58% 0.00% 69.06%Percent Bank Debt in the Capital Structure 0.2854 5.61E-06 BB 38.90% 42.13% 45.91% 43.91% 42.35% 0.00% 40.79%Percent Secured Debt in the Capital Structure 0.1115 2.65E-03 B 41.51% 43.92% 42.60% 52.77% 49.94% 14.00% 42.66%Degrees of Freedom 455 CCC-CC 32.97% 47.38% 54.80% 55.05% 55.30% 0.00% 36.85%Likelihood Ratio P-Value 7.48E-12 C 28.21% 9.71% 47.64% 25.67% 0.00% 0.00% 20.22%Pseudo R-Squared 0.2040 Total 40.81% 44.89% 47.79% 54.00% 52.05% 14.00% 42.21%Spearman Rank Correlation 0.4670 *Jacobs Jr., M., 2010, An empirical study of exposure at default,MSE of Forecasted EAD 2.74E+15 The Journal of Advanced Studies in Finance, Volume 1, Number 1
    28. 28. The Credit Risk Parameters for Stress Testing: PD• In ST the PD risk parameter is the most common of the three that risk managers prefer to shock• PD varies for two principal reasons – Obligors may be rated differently due to changes in risk factors that determine the PD grade (e.g., increased leverage, decreased cash flow) – Realized default rates upon which PD estimates with respect to a given rating may change (e.g., economic downturn leads to more defaults)• This gives rise to two design options for integration of PDs into ST: altering either the assignment of rating or associated PDs – Re-grading has the advantage that it admits the inclusion of transitions to non-performing loans – As varying PDs corresponds to a rating change, up-grades are possible• Possibilities of variance & sensitivity of the input for the rating process should be investigated to get a first estimate
    29. 29. The Credit Risk Parameters for Stress Testing: PD (continued)• ST should incorporate expert opinion on rating methodology in addition analysis of hard reference data for transition & default• Altering PDs associated with ratings could originate in the variation of systematic risk drivers, an important theme in ST• A common approach is as a 1st step to estimate the volatility of PDs in ST of regulatory capital, with differential systematic & idiosyncratic risk on PD deviations as 2nd step enhancement• An analysis of the transition structure for rating grades might also be used to determine PDs under stress conditions• An advantage (disadvantage) of modifying PDs via rating assignment is greater diversity change type (absence of a modified assignment to performing & non-performing portfolio)
    30. 30. PD Estimation for Credit Models: Rating Agency Data• Credit rating agencies have a long history in providing estimates of firms’ creditworthiness• Information about firms’ creditworthiness has historically been difficult to obtain• In general, agency ratings rank order firms’ likelihood of default over the next five years• However, it is common to take average default rates by ratings as PD estimates• The figure shows that agency ratings reflect market segmentations
    31. 31. PD Estimation: Rating AgencyData – Migration & Default Rates• Migration matrices Moodys Letter Rating Migration Rates (1970-2010)* Panel 1: One-Year Average Rates Default summarize the average From/To: AA AA AA A BBB BB B CCC CC-C WR 87.395% 8.626% 0.602% 0.010% 0.027% 0.002% 0.002% 0.000% 3.336% 0.000% Rates rates of transition AA A BBB 0.971% 85.616% 7.966% 0.359% 0.045% 0.018% 0.008% 0.001% 4.996% 0.020% 0.062% 2.689% 86.763% 5.271% 0.488% 0.109% 0.032% 0.004% 4.528% 0.054% 0.043% 0.184% 4.525% 84.517% 4.112% 0.775% 0.173% 0.019% 5.475% 0.176% between rating BB B 0.008% 0.056% 0.370% 5.644% 75.759% 7.239% 0.533% 0.080% 9.208% 1.104% 0.010% 0.034% 0.126% 0.338% 4.762% 73.524% 5.767% 0.665% 10.544% 4.230% CCC 0.000% 0.021% 0.021% 0.142% 0.463% 8.263% 60.088% 4.104% 12.176% 14.721% categories CC-C 0.000% 0.000% 0.000% 0.000% 0.324% 2.374% 8.880% 36.270% 16.701% 35.451% Panel 2: Five-Year Average Rates• The default rates in the Default From/To: AA AA A BBB BB B CCC CC-C WR Rates AA 54.130% 24.062% 5.209% 0.357% 0.253% 0.038% 0.038% 0.000% 15.832% 0.081% final column are often AA A BBB 3.243% 50.038% 21.225% 3.220% 0.521% 0.150% 0.030% 0.012% 21.374% 0.186% 0.202% 8.545% 52.504% 14.337% 2.617% 0.831% 0.143% 0.023% 20.247% 0.551% 0.231% 1.132% 13.513% 46.508% 8.794% 2.827% 0.517% 0.083% 24.763% 1.631% taken as PD estimates BB B 0.043% 0.181% 2.325% 12.105% 26.621% 10.741% 1.286% 0.129% 38.668% 7.900% 0.038% 0.062% 0.295% 1.828% 6.931% 22.064% 4.665% 0.677% 43.918% 19.523% CCC 0.000% 0.000% 0.028% 0.759% 2.065% 7.138% 8.234% 1.034% 44.365% 36.378% for obligor rated CC-C 0.000% 0.000% 0.000% 0.000% 0.208% 2.033% 1.940% 2.633% 44.352% 48.833% * Source: Moodys Investor Service, Default Report: Corporate Default and Recovery Rates (1920-2010), 17 Mar 2011 similarly to the agency ratings• Default rates are increasing for worse ratings & as the time horizons increase
    32. 32. PD Estimation: Rating Agency Data – Default Rates*• Default rates tend to Moodys Average Annual Issuer Weighted Corporate Default Rates by Moodys Average Annual Issuer Weighted Corporate Default Rates by Year: Investment Grade Year: Speculative Grade 1.200 120.000 rise in downturns and 1.000 0.800 100.000 80.000 are higher for Default Rate (%) Default Rate (%) Aaa Ba Aa 60.000 B 0.600 A Caa-C speculative than 0.400 Baa All Inv. Grade 40.000 All Spec. Grade investment grade 0.200 20.000 0.000 ratings in most years 0.000• Investment grade default rates are very All Inv. All Aaa Aa A Baa Grade Spec. 0.15 Ba B Caa-C Grade Mean 0.0000 0.0405 0.0493 0.2065 0.0928 6 Mean 1.2532 5.2809 24.0224 4.7098 Median 0.0000 0.0000 0.0000 0.0000 0.0000 Median 1.0020 4.5550 20.0000 3.5950 volatile and zero in St Dev 0.0000 0.1516 0.1089 0.3198 0.1420 St Dev 1.1982 3.8827 19.7715 2.9758 Probability Density Probability Density Min 0.0000 0.0000 0.0000 0.0000 0.0000 Min 0.0000 0.0000 0.0000 0.9590 Max 0.0000 0.6180 0.4560 1.0960 0.4610 Max 4.8920 15.4700 100.0000 13.1370 0.10 many years, with an 4 extremely skewed 0.05 2 distribution 0 0.0 0.1 0.2 0.3 Investment Grade Default Rates 0.4 0.5 0.00 0 4 8 Spec.Grade.Default.Rates 12 16*Reproduced with permission from: Moody’s Investor Services / Credit Policy, Special Comment: Corporate Default an and RecoveryRates 1970-2010, 2 -28-11.
    33. 33. PD Estimation: Rating Agency Data – Performance of Ratings• Issuers downgraded to the B1 level as early as five years prior to default, B3 among issuers that defaulted in 2010• Cumulative accuracy profile (CAP) curve for 2010 bows towards the northwest corner more than the one for the 1983-2010 period, which suggests recent rating performance better than the historical average• 1-year accuracy ratio (AR) is positively correlated with the credit cycle, less so at 5 years
    34. 34. PD Estimation for Credit Models: Kamakura Public Firm Model*• This vendor provides a suite of PD models (structural, reduced-form & hybrid) all based upon logistic regression techniques• Similar to credit scoring models in retail: directly estimate PD using historical data on defaults and observable explanatory variables• Kamakura Default Probability (KDP) estimate of PD: 1 – X: explanatory variables P Yi ,t 1| X i ,t K – α,β: coefficient estimates 1 exp X i j,t, – Y: default indicator (=1,0 if default,survive) j 1 j – i,j,t,τ: indexes firm, variable, calendar time, time horizon• “Leading” Jarrow-Chava model: based on 1990-2010 actual defaults all listed companies N. America (1,764,230 obs. & 2,064 defaults)• Variables included in the final model: • Accounting: net income, cash, total assets & liabilities, number of shares • Macro: 1 mo. LIBOR, VIX, MIT CRE, 10 govt. bond yld, GDP, unemployment rate, oil price • 3 stock price-related: firm & market indices, firm percentile rank • 2 other variables: industry sector & month of the year*Reproduced with permission from: Kamakura Corporation (Donald van Deventer), Kamakura Pubic Firm Model: Technical Document,September, 2011.
    35. 35. PD Estimation for Credit Models:Kamakura Public Firm Model (cont.) • Area Under the Receiver * Operating Curve (AUROC) : measure rank ordering power of models to distinguish default risk at different horizon & models decent but reduced form dominates structural model • Comparison of predicted PD vs. actual default rate measures accuracy of models: broadly consistent with history & RFM performs better than SFM • Issues & supervisory concerns with this: overfitting (“kitchen sink” modeling) and concerns about out- sample-performance *Reproduced with permission from: Kamakura Corporation (Donald van Deventer), Kamakura Pubic Firm Model: Technical Document, September, 2011.
    36. 36. PD Estimation for Credit Models: Bayesian Model*• Jacobs & Kiefer (2010): Bayesian 1 (Binomial – rating agencies), 2 (Basel II ASRF) & 3-parameter extension (Generalized Linear Mixed Models) models• Combines default rates for Moody’s Ba rated credits 1999-2009 in conjunction with an expert elicited prior distribution for PD• Coherent incorporation of expert information (formal elicitation & fitting of a prior) with limited data & in line with supervisory validation expectations• A secondary advantage is access to efficient computational methods such as Markov Chain Monte Carlo (MCMC)• Evidence that expert information can result in a reasonable posterior distribution of the PD given limited data information• Findings: Basel 2 asset value correlations may be mispecified (too high) & systematic factor mildly (positively) autocorrelated Markov Chain Monte Carlo Estimation: 1 ,2 and 3 Parameter Models Default (Moodys Ba Rated Default Rates 1999-2009) Stressed 95% 95% 95% Stressed Minimum Regulatory Credible Credible Credible Acceptance Regulatory Regulatory Capital *Jacobs Jr., M., and N. M. Kiefer (2010) “The E(θ|R) σθ Interval E(ρ|R) σρ Interval E(τ|R) στ Interval Rate Capital (θ)1 Capital2 Markup Bayesian Approach to Default Risk: A1 Parameter (0.00662,Model 0.00977 0.00174 0.0134) 0.245 6.53% 5.29% 23.49% Guide,” (with.) in Ed.: Klaus Boecker,2 Parameter (0.00732, (0.0435, Rethinking Risk Measurement and ReportingModel 0.0105 0.00175 0.0140) 0.0770 0.0194 0.119) 0.228 6.72% 5.55% 21.06% (Risk Books, London)..3 Parameter (0.0069, (0.043, (-0.006,Model 0.0100 0.00176 0.0139) 0.0812 0.0185 0.132) 0.162 0.0732 0.293) 0.239 6.69% 5.38% 24.52%1 - Using the 95th percentile of the posterior distribution of PD, an LGD of 40%, and asset value correlation of 20% and unit EAD in the supervisory formula2 - The same as the above but using the mean of the posterior distribution of PD
    37. 37. PD Estimation for CreditModels: Bayesian Model (cont.) Smoothed Prior Density for Theta 80 60 Density 40 20 0 0.000 0.005 0.010 0.015 0.020 0.025 0.030  • Ba default rate 0.9%, both prior & posterior centered at 1%, 95% credible interval = (0.7%, 1.4%) • Prior on rho a diffuse beta distribution centered at typical Basel 2 value 20%, posterior mean 8.2%, 95%CI = (4%,13%), • Prior on tau uniform centered at 0%, posterior mean 16.2%, 95% CI (-.01%, 29.2%)
    38. 38. The Credit Risk Parameters for Stress Testing: Correlations• Correlations of creditworthiness between counterparties critical to credit models but hard to estimate & results sensitive to it• The 1st source is the state of the economy, but extent & timing of the rise in default rates varies by industry & geography• Also depends upon degree to which firms are diversified across activities (often proxied for by size: larger->less correlation)• Contagion: apart from the broader economy, default itself implies more defaults (interdependencies), which can worsen the economy• Time horizon over which correlations are measured matters – shorter (longer) can imply see little (much) dependence between sectors• Some credit models have asset correlation decrease in PD (Basel II), but weak evidence for this & not intuitive->need economic source
    39. 39. The Credit Risk Parameters forStress Testing: Correlations (cont.)• May use various types of data having sufficient history, but beware of structural change & time variation (cyclicality- increases in downturn)• PD, LGD & EAD variations might not be sufficient in ST design: we need parameters modeling portfolio effects (i.e.,correlations) between the loans or the common dependence on risk drivers• Analysis of historical credit risk crises reveal that correlations & risk concentration exhibit huge deviations in these episodes• Basis for widely used portfolio models (e.g., CreditMetrics) used by banks for estimating the credit VaR are provided by factor models to present systematic risk affecting the loans• In such models it makes sense to stress strength of the factor dependence & their variations in ST with portfolio models

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