LGD Quantification

1. LGD Quantification Michael Jacobs, Ph.D., CFA Senior Financial Economist – Credit Risk Analysis Division Office of the Comptroller of the Currency IRB Training for Wholesale Exposures September 2010

2. Objectives • LGD in the Final Rule (FR) • LGD and Regulatory Capital • Measurement of LGD: Reference Data • Estimation of LGD • Downturn LGD • LGD Mapping and Application • LGD Validation • Key Takeaways

3. Definition of LGD • Loss given default (LGD), for either an individual wholesale exposure or a loss-severity grade of such exposures is the greatest of: • Zero; • or ELGD, which is empirically based best estimate of the long-run default-weighted average economic loss per dollar of EAD, if the obligor (or typical obligor in the loss-severity segment) were to default within a one-year horizon over a mix of economic conditions, including economic downturn conditions; • or Downturn LGD, which is empirically based best estimate of the economic loss per dollar of EAD, if the obligor (or typical obligor in the loss-severity) segment were to default within a one-year horizon during economic downturn conditions. • Mathematically, we can write this as simply:

4. LGD: Importance to Regulatory Capital • LGD is important because the capital requirement K (and thus risk weighted asset-RWA) is proportional to LGD, but not to PD. For example: • A one percent decrease in LGD results in a one percent drop in capital requirements and RWA. • A one percent decrease in PD results in less than one percent drop in capital requirements and RWA.

5. LGD in Advanced IRB: Further Discussion • The bank must be able to identify any material adverse correlations between drivers of default and LGD, and incorporate such identified correlations into the quantification of LGD. • Reference data must include only obligations that have defaulted according to the FR and exposures should be grouped according to factors likely to be important in predicting loss severity rates. • Several key issues around LGD need to be addressed in taking this approach: • How is LGD defined and measured? • What drives differences in LGD? • How can banks model or estimate LGD?

6. Measurement of LGD: Basic Concepts • The definition of loss used in estimating LGD is rate of economic loss (not accounting loss) on the loan expected to occur if the obligor were to default within one year. • LGD is a facility phenomenon. • Includes all material credit related losses: accrued but unpaid interest or fees, and all material direct and indirect costs of workout and collections. • Incorporates the mark-to-market loss of value of a defaulted exposure and collateral. • Equivalent expression that define of LGD: • Total Economic Loss / Exposure-at-Default • Sometimes defined as:LGD = 1 – Recovery Rate • Recovery Rate = Total Economic Recovery / Exposure-at -Default

7. Measurement of LGD: Definition of Default • A default is considered to have occurred with regard to a particular obligor when particular events takes place. • Default is an obligor phenomenon. • Banks must use the default definition in the Final Rule. • LGD must be based on the definition of default as per the Final Rule (FR), which states that a bank’s wholesale obligor is in default if for any exposure of the bank to the obligor: • The bank considers the obligor unlikely to pay its credit obligations in full, without recourse to actions like realizing collateral; or • The obligor is past due more than 90 days on any material credit obligation to the bank.

8. Definition of Default (cont.) • Example: Suppose a bank uses the following default definition for its large-corporate portfolio: • Non-accrual. • Charge-off. • Bankruptcy. • Major down-grade. • Is the bank’s definition of default likely to result in higher or lower capital requirement, compared to the Final Rule definition of default? And is this in compliance with the FR? • Are they capturing all the 90dpd? (do those go into NA as per policy?) • Bankruptcies: are they tracking out-out-of court settlements (e.g., distressed restructurings where the bank incurs a loss?) • How about accruing substandards? • Is the bank tracking loan sales at a steep loss?

9. Months 0 42 24 6 18 30 12 Ultimate Resolution Initial Workout Period Later Recovery Period Measurement of LGD: Stylized Timeline REC1 EAD C/O1 C/O2 REC2 Book Value of Loan = $0 Default • Losses and recoveries are tracked from default to ultimate resolution. • Resolution is defined as the time of the final cash flow realization. • The mechanism of resolution may be in- or out-of court (e.g., Chapter 11 or a distressed exchange) and the outcome may include emergence, acquisition or liquidation.

10. Realized Loss Severity Calculation • Example: A defaulted exposure to a middle market borrower • $10M EAD (including net accrued but unpaid interest and fees) • $5M charged-off 6 & 9 months after default - zero cash flow • $2M is extended in a post-default extension of credit 1 yr. after - negative cash flow (positive cost) • $8M recovered at resolution in 2 years (includes repayment of DIP) - positive cash flow (negative cost) • There is a 1% or $0.1M allocation of direct & indirect workout costs - assume incurred at resolution in 2 yrs. • Cash-flows are discounted 15% (= 5% risk-free rate + 10% risk premium) – assume covers lost interest / fees

11. Measurement of LGD: Economic Loss • Economic loss is a broader concept than accounting loss, it includes all material credit-related losses on the exposure: • Accrued but unpaid interest or fees. • Losses on the sale of repossessed collateral. • Direct and an appropriate allocation of indirect workout costs. • Pre-default reductions in exposures. • Post-default extension of credit. • Material negative fair value adjustment of principal on the exposure for credit-related reasons (held-for-sale portfolio.) • Net present value (NPV) of all cash flows as of default date.

12. Measurement of LGD: Economic Loss (cont.) • Examples of workout costs for commercial loans: • Direct workout costs: • Lost interest & fees. • Violations of Absolute Priority Rule (APR) in court. • Losses on sale of collateral. • Indirect workout costs: • Corporate overhead (salaries, legal, administrative, etc) • Note: No allocation from operational risk • E.g., failing to perfect a lien on collateral. • A separate component of the Basel II framework.

13. Measurement of LGD: Discount Rates • Time dimension to LGD: discounted recoveries must reflect the riskiness of recoveries. • Higher rate -> lower discounted recoveries -> higher LGD • Which discount rate used to discount cash flows after default? • Empirical evidence: sensitive to facility variables. • Candidates are: • Constant punitive rate. • Risk-free (Treasury) rate. • Contractual coupon rate. • Bank’s hurdle rate (WACC.) • Another high-risk/high-return rate (e.g., high yield index.) • Rating agency study approaches: • “Market Implied” LGD (price 30-45 days after default.) • Ultimate recovery discounted by contractual coupon rate.

14. Measurement of LGD: Discount Rates (continued) • The annualized yield on holding defaulted loans from default to resolution is 32.2% - suggests that a risk adjustment to the LGD discount may be in order!

15. LGD Reference Data • Must be based on at least 7 years of loss severity data of sufficient quality over a mix of economic conditions including economic downturn conditions. • Can be internal or external data - most banks rely on both for wholesale exposures (but depends on type of portfolio.) • Data be relevant to the bank’s actual wholesale exposures and banks need to document this through the mapping process. • Reference data must be comprehensively reviewed at least annually to determine its relevance to the bank’s exposures, quality to support estimation and consistency with the FR definition of default.

16. LGD Reference Data (cont.) • Treatment of “outlier” values. • Reference data may contain individual observations that are negative or greater than 100%: • LGD>100% -> loss was more than the EAD (e.g., post default extension of credit.) • LGD<0% -> loss was negative (e.g., appreciation of collateral values.) • Caution about excluding either kind of observations but extra diligence is required for negative loss observations to ensure economic loss is being measured. • Plausible, but judgment determines true outliers. • Diligence required to determine if loss (or gain) measured is really the consequence of the default.

17. LGD Reference Data (cont.) • Common data limitations: • Lack of the amount & timing of recoveries, direct & indirect costs. • Obligor instead of loan-level recoveries due to pooling of defaulted loans & systems issues. • Particular problem if relying on accounting data. • Manual reconciliation of data from different systems: exposure, accounting, booking, loss systems, and model databases. • Lack of data from period of economic downturn conditions. • Lack of historical data to support new products (e.g., covenant light & pay-in-kind or PIK loans.) • Low default portfolios (e.g., highly rated counterparties.) • Common remedies for data limitations: • Economic losses determined at obligor or family level • Estimation at LGD “segment level” (e.g., secured vs. unsecured) & applied to the defaulted loans in a segment • Broad averages used to allocate expenses • Costs and recoveries discounting can use an average length of recovery horizon for a pool of similar exposures

18. LGD Reference Data (cont.) • Workout LGD: based on observed or estimated (properly discounted) cash flows from the workout or collections process • Encompasses most material losses, direct and indirect. • Closest to the IRB notion • Often available to banks, but hard to gather • “Ultimate LGD” proxy – discounted value of securities received in settlement of bankruptcy (e.g., Moody’s URD) • Market LGD: observed from market prices of defaulted bonds or marketable loans soon after default • May use if have marketable loans or a portfolio that can be mapped to such • E.g., bonds or syndicated loans

19. Measurement of LGD: Ultimate vs. Market • Ultimate LGD (discounted market values of settlement instruments) - can be viewed as a proxy for workout LGD • Typically get back a bundle of different securities inn exchange from a defaulted instrument • Market (trading price at default) LGD is typically greater • Discounted for risk implicitly by the market • Problem of excess volatility due to illiquidity, swings in risk aversions and sentiment • Market over-penalizing or irrational exuberance?

20. Distribution of Ultimate LGD: MURD Database (1987-2010) 0.5 1.0 0.0 LGD Distribution of Market LGD: MURD Database (1987-2010) 0.0 0.5 1.0 LGD Ultimate vs. Market LGD (cont.) • Market LGD on average 5% greater than ultimate • Distribution of market LGD has more (less) 100% (0%) LGDs

21. Bimodality of the LGD Distribution • A dominant feature of LGD is that you either loose a lot (around 80%) or loose a little (around 20%.) • Appreciation vs. depreciation in collateral or enterprise values in the workout process? • Possible to loose more (less) than 100% (0%), but these may not be measured properly and get clumped together • Hence averages can be very misleading, but this depends upon how you look at the data: • More “normal” if aggregate facilities to obligor level. • Single modes at 80%/20% if look at senior bank loans/subordinated debt separately. • But modes still there for senior unsecured Loss-Given-Default

22. Distribution of Moody’s Market LGD: Defaulted Bonds and Loans (1970-2010) 0.6 0.8 1.0 0.4 0.0 0.2 LGD Bimodality of the LGD Distribution (cont.)

23. Banks Employees, Trade Creditors, Lawyers Bank Loans Senior Secured Bondholders Senior Unsecured Senior Subordinated Junior Subordinated Preferred Shares Shareholders SENIORITY Common Shares Determinants of LGD: Capital Structure • Contractual features: more senior and secured instruments do better. • Absolute Priority Rule: some violations (but usually small.) • More senior instruments tend to be better secured. • Debt cushion as distinct from position in the capital structure. • High LGD for senior debt with little sub-debt? • Proportion of bank debt in the mix. • The “Grim Reaper” story • Enterprise value

24. Distributions of Moody’s Defaulted Bonds & Loan LGD (DRS Database 1970-2010 ) All Seniorities (count = 4400, mean = 59.1%) Senior Bank Loans (count = 54, mean = 16.7%) 0.4 0.2 0.4 0.6 1.0 0.6 1.0 0.0 0.2 0.8 -0.2 0.0 0.8 LGD LGD Senior Secured Bonds (count = 1022, mean = 46.7%) Senior Unsecured Bonds (count = 2215, mean = 60.0%) 1.2 0.8 -0.2 1.0 0.6 0.4 0.0 1.2 1.2 0.4 0.4 0.2 0.0 0.0 0.2 0.2 0.6 0.6 -0.2 -0.2 0.8 0.8 1.0 1.0 LGD LGD LGD Junior Subordinated Bonds (count = 509, mean = 74.6%) Senior Subordinated Bonds (count = 600, mean = 67.9%) 1.2 -0.2 0.8 1.0 0.4 0.0 0.2 0.6 LGD Determinants of LGD: Recovery by Seniority

25. LGD by Seniority Class and Collateral Type • The lower the quality of collateral, the higher the LGD • The lower ranking of the creditor class, the higher the LGD • And higher seniority debt tends to have better collateral

26. LGD by Seniority Class and Debt Cushion • Debt cushion: it is best to have less debt above & more debt below • But better to be the entire than in the middle of the capital structure • Higher seniorities tend to be higher in the capital stucture than lower seniorities

27. Determinants of LGD: Other Factors • Obligor characteristics: profit margin, debt concentration, stock return, internal control environment, etc. • Matters for more instrument LGD at default vs. ultimate. • But indirectly matters since important for ultimate obligor LGD . • No enterprise value -> 100% LGD even if at the top of the capital structure. • Industry characteristics seem to matter • Certain industries (utilities) yield higher recoveries than others (small retailers, telecom.) • Why? Tangible assets, defensive, regulation. • Industry distress (Acharya et al, 2005):“fire sale” hypothesis • Region due to differential legal environment (i.e., creditor vs. debtor friendly countries.) • Resolution process: Chapter 11 bankruptcy vs. out-of-court restructuring.

28. Determinants of LGD: Other Factors (continued) • Industry: Utilities and Sovereign much lower LGD • Region: UK and Western Europe much higher LGD • Resolution process: Chapter 11 higher LGD than out-of-court restructuring

29. Determinants of LGD: Resolution Process and Outcome of Default* • 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%) LGD=65.2% LGD=63.1% LGD=68.9% LGD=55.8% *Diagram reproduced from: Jacobs, M., Karagozoglu, A., and Layish, D., 2008, Understanding and predicting the resolution of financial distress, Working paper, page 31. 518 defaulted S&P/Moody’s rated firms 1985-2004.

30. Distribution of Moody’s Market LGD: Economic Expansions Time Series of Moody’s Market LGD Count = 1514, Mean = 52.4% Distribution of Moody’s Market LGD: Economic Downturns Count = 2886, Mean = 62.6% LGD and the Business Cycle: 1970-2010 • 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

31. LGD and the Business Cycle (cont.) • However, there is evidence that facilities may respond differently to the effect of the business cycle depending on security. • Unsecured LGD tends to track the business cycle. • Secured instruments tend to enjoy a degree of insulation. • The degree to which secured facilities may be to some extent protected from cyclical effects depends upon: • Quality of collateral. • Liquid market -> less likely to incur a loss in selling. • Cash collateral -> hold up value in downturn. • Position in the capital structure. • More senior of greater debt cushion -> less likely collateral will disappear or loose value

32. Downturn LGD • Economic downturn conditions for an exposure are generally conditions in which the aggregate default rates for the exposure’s subcategory in its national jurisdiction are significantly higher than average. • The process for measuring this phenomenon must appropriately identify and assess the impact of downturn economic conditions and incorporate this into the quantification of LGD. • If banks are unable to identify downturn LGD in their data, this calls for further research into whether data is relevant, the segmentation is robust, etc.

33. Downturn LGD as a Function of Expected LGD 1.0 0.8 Downturn LGD 0.6 0.4 0.2 Internal Mapping for Downturn LGD Supervisory Mapping for Downturn LGD 45 Degree Line 0.0 0.2 0.4 0.6 0.0 0.8 1.0 ELGD The Regulatory Stress Mapping • This is a highly stylized hypothetical internal mapping 45O

34. Estimation of LGD: Introduction • Many banks employ rather crude segmentations. • Collateral type: cash, receivables, equipment, PPE, etc. • Seniority rank: senior secured vs. unsecured, subordinated. • Product type: term loans, revolvers, bonds, preferred stock. • Obligor type: corporates, financials, sovereigns. • Some banks have developed further segmentations using risk drivers for LGD, but this is still relatively rare. • E.g., LTV or coverage, levels of collateral monitoring . • If so, based predominantly on expert judgment (e.g., non-statistical decision trees or “scorecards”.)

35. Estimation of LGD: Introduction (cont.) • Few banks in the U.S. have developed loan-level LGD estimates based on a structural approach to LGD components. The “cutting edge” is: • For smaller business or middle market, modeling balance sheets and liquidation values. • For large-corporates, modeling bankruptcy resolution and enterprise value. • However, note that there are questions about the validity of the “enterprise value” concept in this context. • Note that the FR allows for the use of vendor models for LGD estimation. • However, there are challenges in documentation and validation here.

36. Estimation of LGD: The LRDWA • The long-run default-weighted average loss rate given default(LRDWA)means simply the arithmetic average of all LGD observations in the reference data-set. • This weighs more heavily downturn having more defaults Where there are N total defaults, i stands for the facility. • LRDWA is the best statistical estimate of average LGD if we are looking at segments homogenous with respect to recovery risk. • This is equivalent to weighted average of annual average LGD rates, where the weights are the annual number of defaults. • This is called the default-weighted average – DWA

37. Average LGD Exercise* * Moody’s DRS Market LGD (rounded values for LGD & counts scaled by 10)

38. Average LGD Exercise* (continued) • But how does this compare to the “straight average” across 10 years of annual LGDs (and why)? * Moody’s DRS Market LGD (rounded values for LGD & counts scaled by 10)

39. Estimation of LGD: Example of a Regression Model and Downturn LGD • A model based upon internal LGD data with 3 indicator variable factors (if “true” get a value of 1, otherwise 0) • Eg, senior (subordinated) loan having liquid (illiquid) collateral and greater (less) than 50% debt cushion has ELGDs: • ELGDlow recovery risk = 0.80-0.25X1-0.20X1-0.15X1=0.20 • ELGDhigh recovery risk = 0.80-0.25X0-0.20X0-0.15X0=0.80

40. Estimation of LGD: Example of a Regression Model and Downturn LGD (continued) • Downturn LGD has one more factor: the difference between a stressed & overall default rate • If the difference between long-run and stressed default rate is 0.05, then there is an add-on of 0.15: • DLGDlow recovery risk = 0.80-0.25X1-0.20X1-0.15X1+3X0.05=0.35 • DLGDhigh recovery risk = 0.80-0.25X0-0.20X0-0.15X0+3X0.05=0.95

41. LGD Estimation: Vendor Models • The importance of these is that the FR allows the use of vendor models in the absence of adequate. • Currently only S&P and MKMV model LGD • S&P LossStats™ • Calculates distribution of LGD conditional on current economic state and facility characteristics • Data restricted solely to public bankruptcies 1988-2009 • “Maximum Expected Utility” approach • Statistical model can handle bimodality • MKMV LossCalc™ • ~3000 defaults from large corporate segment • Must be large enough to have issued debt or large syndicated loans • Issue amount: $700K - $100mm

42. LGD Estimation: Public Data Sources • Bank consortia: Fitch/Algo, RMA, MKMV (CRD) • But issues of data quality and normalization • Moody’s Corporate Default Risk Service (DRS) • Debt rated by Moody’s, 1970 to present • Moody’s Ultimate LGD database. • Complete capital structures on ~ 4000 (800) defaulted (Ch. 11 + out-of court) firms 1985 to 2009 • Altman defaulted debt data • Focus on the high yield sector • LPC/Fitch/Algorithmics Loan Loss data base • Prices on 3500 defaults since 1993 in syndicated loan market

43. LGD Mapping • We ask the question: is the reference data representative of the bank’s current exposures? • E.g., consistency with underwriting practices and work-out strategies • This amount to the set of questions regarding differences in any of the following: • Borrower characteristics • Underwriting standards • Products • Risk profile of portfolios • Definition of default • Definition of loss

44. LGD Mapping (cont.) • A particular concern is observations eliminated from reference data – at the end of the day, we have to ask if there is bias in what remains • There is an important role for RAD here • Why might this happen? – a claim that the data is not relevant or somehow invalid. E.g., • Loan sales or exited business lines • Incomplete or inaccurate data eliminate din the course of routine cleansing • E.g., a large bank has exited a set of SME exposures having very high losses, and the LGD in its remaining data appears very low. • Note the tradeoff between paucity of data & relevance

45. LGD Application • LGD estimates are applied together with other parameters (PD, EAD, M) to the current portfolio to calculate regulatory capital. • At minimum, the bank must mechanically attach the correct LGD estimates to exposures • Example: LGD is assigned according to collateral type at origination. However, as there are changes to the collateral, this is not captured in the Basel system, so that the wrong LGD is being applied. • Adjustments to LGD estimates may be necessary to account for issues in reference data, estimation or mapping • E.g., LGDs underestimated due to mild downturn in reference data or different (more lenient) default definition • What would be an appropriate adjustment here?

46. LGD Application (cont.) • It is important that such adjustments conservative enough to account for data limitations or other weakness in the process • Insufficient analysis to support downturn LGD • Questions about the quality or quantity of reference data • Example of an adjustment in the application stage of LGD quantification • A bank adjusts its LGD estimate for 1st lien corporate loans from 40% to 35%, citing the bank’s plan to reduce credit lines, more closely monitor collateral and covenants, and re-price loans to generate more income • Is this adjustment justified? • What if the bank has recently implemented the planned actions?

47. LGD Validation Illustrative Validation Questions on LGD Quantification

48. LGD Validation – Example • A bank has developed a decision tree to assign exposures to LGD buckets according to seniority, collateral type & debt cushion for its loan portfolio • Due to lack of internal data, the bank uses a data-set of recoveries from one of the agencies, in conjunction with expert judgment • The validation consists of comparing model LGDs to actual LGDs in the reference data-set • Bank concludes that LGD model is fit-for-purpose: • Predictive accuracy: model LGDs “adequately” match actual numerically (although mean squared error – MSE – is high) • Discriminatory power: higher model LGDs are associated with higher actuals (CAP curve & Accuracy Ratio = 70%) • The override rate (17%) is “within tolerance” (but highest in difficult segments - financial services, junk grade) • The model is biased but in overall conservatively (i.e., high model error rate but on the “right” side) • …

49. Figure 1: Decision Tree for Mapping Risk Factors to LGD Grades* LGD Validation – Example (continued) • 1st lien senior with liquid collateral -> LGD=10% • Core collateral & > 50% debt cushion -> LGD=20% • Any collateral or > 20% debt cushion -> LGD=40% • Core collateral & < 20% debt cushion -> LGD=50% • Senior unsecured & > 50% debt cushion -> LGD=50% • Senior unsecured & < 50% debt cushion-> LGD=60% • 2nd lien senior secured any collateral -> LGD=75% • Senior subordinated any collateral -> LGD=75%

50. Figure 2: Model vs. Actual LGDs LGD Validation – Example (continued) • Average LGDs increasing in bucket: basic requirement (but are these differences statistically meaningful?) • Model LGD tracks actual LGD, but in most buckets averages are much lower • Increasingly so for better LGD segments (loans)