An Empirical Study of
          Exposure at Default
                 Michael Jacobs, Ph.D., CFA
                  Senior F...
Outline
•   Background and Motivation
•   Introduction and Conclusions
•   Review of the Literature
•   Basel Requirements...
Background and Motivation
Why the special interest in understanding risk of
  committed revolving (unfunded) credit facili...
Formulation of the Research
Problem: What Exactly is EAD?
• Basel II definition: “A Bank’s best estimate of the amount dra...
Introduction and Conclusions
• Empirical study of EAD for the large corporate defaulted (i.e.,
  Chapter 11 & distress) un...
Review of the Literature
Limited previous work, but some well-regarded benchmarks
• The “classics”: Asarnow & Marker (1995...
Advanced IRB Requirements
• Within the Basel II framework EAD is a bank’s expected gross
  dollar exposure to a facility u...
Methodology: The Loan
         Equivalency Factor (LEQ)
• EAD: time t expected $ utilization (= availability) default time...
Methodology: The Credit
         Conversion Factor (CCF)
• An alternative approach estimates a credit conversion factor
  ...
Methodology: The Exposure at Default
           Factor (EADF)
• Alternatively, dollar EAD may be factored into the product...
Methodology:
                Modeling of Dollar EAD
• Most generally & least common, model dollar EAD as a function
  of u...
Methodology: A Quantile
            Regression Model for LEQ
•   Collect all the covariates into Yt with function g(.) (LE...
Measurement Issues
• The process is saturated with judgment & labor intensive (importance
  of documentation, automation &...
Empirical Results: Data Description
• Starting point: Moody’s Ultimate LGD Database™ (“MULGD”)
   •   February 2008 releas...
Empirical Results: Data
          Description (continued)
• MULGD has information on all classes of debt in the capital
  ...
Empirical Results: Summary
             Statistics (EAD Risk Measures)
                                                   ...
Empirical Results: Distributions of
          EAD Risk Measures
                                                          ...
Empirical Results: Distributions of
 EAD Risk Measures (continued)
                                                       ...
Empirical Results: Estimation
           Regions of EAD Risk Measures
                                                  Ta...
Empirical Results: Summary
                     Statistics (Covariates)
                          Table 1.2 - Summary Stat...
Empirical Results: Distributions of
          LEQ by Rating
     Fig 3.1: Collared LEQ Factor (All Ratings)               ...
Empirical Results: Distributions of
     LEQ by Time-to-Default
Fig 4.1: Collared LEQ Factor (All Times-to-Default)       ...
Empirical Results: LEQ vs. Rating
           & Time-to-Default Grids      Table 2.1.1
         Estimated Collared Loan Equ...
Empirical Results: EAD Risk
                             Measures vs. Rating
                        Figure 3: Average EAD...
Empirical Results: LEQ vs. Rating
     & Time-to-Default Plot
   Figure 5: 3-Dimensional Scatterplot of LEQ vs. Time-to-De...
Empirical Results: EAD Risk
   Measures by Year of Observation
  Table 4.1 - LEQ, CCF and EADF of Defaulted Instruments by...
Empirical Results: EAD Risk
                Measures by Year of Default
Table 5.1 - LEQ, CCF and EADF of Defaulted Instrum...
Empirical Results: EAD Risk
                Measures by Year of Default
Table 5.1 - LEQ, CCF and EADF of Defaulted Instrum...
Empirical Results: EAD Risk
 Measures by Collateral & Seniority
Table 6.1.1 - EAD Risk Measures by Instrument and Major Co...
Empirical Results: EAD Risk
               Measures by Obligor Industry
                                                  ...
Empirical Results: LEQ by Obligor
  Industry and Annual Default Rates
Table 7.1 - LEQ and Moody's Specultive Grade Default...
Empirical Results: Correlations of
     EAD Risk Measures to Covariates
  Table 1.3 -Correlations of EAD Risk Measures to ...
Empirical Results: Correlations of
EAD Risk Measures to Covariates
                Figure 6: Multipanel Pairwise Scatterpl...
Econometric Modeling of EAD:
Beta-Link Generalized Linear Model
•   The distributional properties of EAD risk measures cre...
Econometric Modeling of EAD:
           Beta-Link GLM (continued)
•     Denote the ith observation of some EAD risk measur...
An Empirical Study of Exposure at Default
An Empirical Study of Exposure at Default
An Empirical Study of Exposure at Default
An Empirical Study of Exposure at Default
An Empirical Study of Exposure at Default
An Empirical Study of Exposure at Default
Upcoming SlideShare
Loading in …5
×

An Empirical Study of Exposure at Default

1,185 views

Published on

Published in: Economy & Finance, Technology
0 Comments
1 Like
Statistics
Notes
  • Be the first to comment

No Downloads
Views
Total views
1,185
On SlideShare
0
From Embeds
0
Number of Embeds
36
Actions
Shares
0
Downloads
54
Comments
0
Likes
1
Embeds 0
No embeds

No notes for slide

An Empirical Study of Exposure at Default

  1. 1. An Empirical Study of Exposure at Default Michael Jacobs, Ph.D., CFA Senior Financial Economist Credit Risk Analysis Division Office of the Comptroller of the Currency December, 2008 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 • Background and Motivation • Introduction and Conclusions • Review of the Literature • Basel Requirements • Methodology • Measurement Issues • Empirical Results • Econometric Model & Out-of-Sample Validation • Summary and Future Directions
  3. 3. Background and Motivation Why the special interest in understanding risk of committed revolving (unfunded) credit facilities? • Unique structural characteristics / complexities (optionality) and risk factors (adverse selection) • Represents a large exposure to the banking system and historically high risk / return tradeoff • Basel II requirements: Banks must empirically support assumptions on expected drawdowns given default • Relatively unstudied as compared with other aspects of credit risk (capital, PD, LGD, etc.) • Arises in many contexts / products (e.g., credit cards, market risk: trading CPC exposure, LCs) But focus here is on “standard”, “traditional” revolvers for U.S. large-corporates
  4. 4. Formulation of the Research Problem: What Exactly is EAD? • Basel II definition: “A Bank’s best estimate of the amount drawn down upon on a revolving credit upon default in a year”? • Historical observation of a drawn (or fraction of previously undrawn) amount on a default in a reference data-set? • A random variable (or distribution) of future $ drawn (or % fraction of undrawn) amounts conditional upon default? • A feature of the EAD distribution (e.g., measure of central tendency or high quantile)? • The distributional properties of this feature (if we are modeling parameter uncertainty)? • A form of modeling framework (structural or reduced form) understanding or predicting EAD? We develop empirical methods potentially supporting EAD estimation in ALL of these senses
  5. 5. Introduction and Conclusions • Empirical study of EAD for the large corporate defaulted (i.e., Chapter 11 & distress) universe (U.S., 1985-2007) • Builds upon previous practitioner literature and current practices in the industry • References issues in risk management and supervisory requirements (Basel II Advanced IRB) • Application of advanced statistical methods (beta-link GLM) • Highlights issues in measurement and data interpretation • Exploration of alternative measures of EAD risk • Confirms some previous findings: increased EAD risk with better rating, lower utilization or longer time-to-default • “New” findings: EAD risk found to increase (decrease) with company size, intangibility,% bank or secured debt (leverage, profitability, collateral quality, percent debt cushion), and • Counter-cyclicality: evidence that EAD risk is elevated during economic expansion periods
  6. 6. Review of the Literature Limited previous work, but some well-regarded benchmarks • The “classics”: Asarnow & Marker (1995 - ”The Citi Study”), Araten & Jacobs (2001 - “The Chase Study”) – Still the standard in methodology & concept • Multiple unpublished studies by financial institutions previously & in more recently preparation for Basel II – Much variation in degree to which differs from the above • Recent works in the academic & especially the supervisory / academic community (including this) – Moral* (2006): alternative frameworks for estimating EAD (optimal in regulatory sense, i.e. LEQ > 0, reg. capital not under-estimated) – Sufi (RFS, 2008): usage of credit lines in a corporate finance perspective (↑ historical profitability→more credit,revolvers=80% of all financing U.S.) – Jimenez et at (S.F. FRB, 2008): empirical EAD study for Spanish credit register data (defaulted firms -> higher usage up to 5 yrs. to default) – Loukoianova, Neftci & Sharma (J of Der., 2007): arbitrage-free valuation framework for contingent credit claims *In “The Basel II Risk Parameters: Estimation, Validation, and Stress Testing”
  7. 7. Advanced IRB Requirements • Within the Basel II framework EAD is a bank’s expected gross dollar exposure to a facility upon the borrower’s default – EAD is meant to reflect the capital at risk • The general ledger balance is appropriate for fixed exposures, like bullet and term loans (see Paragraph 134) – But provides an allowance for allocated transfer risk reserve if the exposure is held available-for-sale • In the case of variable exposures, like revolving commitments and lines of credit exposures, this is not appropriate: banks must estimate the EAD for each exposure in the portfolio – But the guidance is not prescriptive about how to form this estimate – Ideally use internal historical experience relevant to the current portfolio • Note that there is no downward adjustment for amortization or expected prepayments – EAD is floored at current outstanding – At odds with empirical evidence (Banks seeing evidence ort paydowns) – Implications for properties of estimators (i.e., LEQ>0 or EAD>drawn)
  8. 8. Methodology: The Loan Equivalency Factor (LEQ) • EAD: time t expected $ utilization (= availability) default time τ: ( ) ( ) EAD Xt ,t,T = E t UTIL Xτ ,τ | τ ≤ T, X t = E t AVAIL Xτ ,τ | τ ≤ T, X t • “Traditionally” estimated through an LEQ factor that is applied to the current unused: EAD Xt ,t,T = UTIL t + LEQ X ,t,T × ( AVAIL t − UTIL t ) f t ⎛ UTILτ - UTIL t ⎞ = Et ⎜ | τ ≤ T, X t ⎟ f LEQ X t ,t,T ⎝ AVAIL t - UTIL t ⎠ • The LEQ factor conditional on a vector of features X can be estimated by observations of changes in utilization over unused to default (typically averaging over “homogenous segments”): ⎛ UTIL X D ,TiD - UTIL Xti ,ti ⎞ Nx 1 ⎜ ⎟ ∑ ˆ LEQfX = Ti N X i=1 ⎜ AVAIL Xt ,ti - UTIL Xt ,ti ⎟ ⎝ ⎠ i i
  9. 9. Methodology: The Credit Conversion Factor (CCF) • An alternative approach estimates a credit conversion factor (CCF) to be applied to the current outstanding (used amount): f EAD Xt ,t,T = UT IL t ×CCFXt ,t,T • The CCF is simply the expected gross percent change in the total outstanding: ⎛ AVAILτ ⎞ ⎛ UTILτ ⎞ | τ ≤ T, X t ⎟ = E t ⎜ | τ ≤ T, X t ⎟ f CCF = Et ⎜ X t ,t,T ⎝ UTIL t ⎝ UTIL t ⎠ ⎠ • CCF can be estimated by averaging the observed gross percent changes in outstandings: UTIL X NX ,TiD 1 ∑ ˆ TiD f CCF =X NX UTIL Xt ,ti i=1 i
  10. 10. Methodology: The Exposure at Default Factor (EADF) • Alternatively, dollar EAD may be factored into the product of the current availability and an EAD factor: EAD Xt ,t,T = AVAIL t × EADfXt ,t,T • Where EADf is the expected gross change in the limit: ⎛ AVAILτ ⎞ | τ ≤ T, X t ⎟ f EAD = Et ⎜ X t ,t,T ⎝ AVAIL t ⎠ • May be estimated as the average of gross % limit changes: AVAIL X NX ,TiD 1 ∑ ˆ TiD f EAD = X NX AVAIL XX i=1 t i ,t i
  11. 11. Methodology: Modeling of Dollar EAD • Most generally & least common, model dollar EAD as a function of used / unused & covariates (Levonian, 2007) • Restrictions upon parameter estimates could shed light upon the optimality of LEQ vs. CCF vs. EADF • We can set this up in a decision-theoretic framework as follows: { )} • ( EAD$ ( Yt ) = arg min E P ⎡ L EAD Yt − EAD$ ( Yt ) ⎤ ˆ ⎣ ⎦ EAD$ ( Yt ) • Where Y=(X,AVAIL,UTIL,T,t), L(.) is a loss metric, and EP is expectation with respect to physical (empirical) measure
  12. 12. Methodology: A Quantile Regression Model for LEQ • Collect all the covariates into Yt with function g(.) (LEQ, CCF or EADF) & seek to minimize a loss function L(.) of the forecast error (Moral,2006): { } g * ( Yt ) = arg min EP ⎡ L ( EAD t,T − g ( Yt ) ) ⎤ ⎣ ⎦ g(Y ) t • Moral (2006) proposes the deviation in the quantile of a regulatory capital metric, which gives rise to an asymmetric loss function of the form: iff x ≥ 0 ⎧ax L ( x) = ⎨ b>a iff x < 0 ⎩ bx • Assuming that PD and LGD are independent & casting the problem in terms of LEQ estimation, we obtain the problem: { } LEQ* ( Yt ) = arg min EP ⎡ L ( EAD t,T − LEQ ( Yt ) × [ AVAILt − UTILt ]) ⎤ ⎣ ⎦ LEQ ( Y ) t • The solution to this is equivalent to a quantile regression estimator (Koenker and Bassett, 1978) of the dollar change in usage to default EADT,t-UTILt on the risk drivers Yt (the “QLEQ” estimator): 1 a LEQ* ( Yt ) = Q EAD t,T − UTILt , × a + b Yt AVAILt − UTILt P* • Key property: this estimator on raw data constrained such that 0<LEQ<1 is optimal also on censored data having this property (i.e., no collaring needed)
  13. 13. Measurement Issues • The process is saturated with judgment & labor intensive (importance of documentation, automation & double checking work) • Data on outstandings and limits extracted from SEC filings: Lack of consistent reporting & timing issues (the Basel 1-Year horizon?) • Unit of observation: is it the same facility? – Amendments to loan agreements (“stringing together”) over time – Combining facilities for a given obligor • Need of a sampling scheme: generally at 1-year anniversaries, rating changes, amendments or “significant” changes in exposure – Avoid duplicative observations • Data cleansing: elimination of clearly erroneous data points vs. modifying estimates (capping / flooring, Winsorization) – When are extreme values deemed valid observations? – Treatment of outliers and “non-credible” observations • Repeat defaults of companies (“Chapter 22s”): look at spacing – Determine if it is really a distinct instance of default • Ratings: split between S&P & Moody’s? – Take to worst rating (conservativism)
  14. 14. Empirical Results: Data Description • Starting point: Moody’s Ultimate LGD Database™ (“MULGD”) • February 2008 release • Comprehensive database of defaults (bankruptcies and out-of- court settlements) • Broad definition of default (“quasi-Basel”) • Largely representative of the U.S. large corporate loss experience • Most obligors have rated instruments (S&P or Moody’s) at some point prior to default • Merged with various public sources of information • www.bankruptcydata.com, Edgar SEC filing, LEXIS/NEXIS, Bloomberg, Compustat and CRSP • 3,886 defaulted instruments from 1985-2007 for 683 borrowers • Revolving credits subset: 496 obligors, 530 defaults and 544 facilities
  15. 15. Empirical Results: Data Description (continued) • MULGD has information on all classes of debt in the capital structure at the time of default, including revolvers – Exceptions: trade payables & other off-balance sheet obligations • Observations detailed by: – Instrument characteristics: debt type, seniority ranking, debt above / below, collateral type – Obligor / Capital Structure: Industry, proportion bank / secured debt – Defaults: amounts (EAD,AI), default type, coupon, dates / durations – Resolution types : emergence from bankruptcy, Chapter 7 liquidation, acquisition or out-of-court settlement • Recovery / LGD measures: prices of pre-petition (or received in settlement) instruments at emergence or restructuring – Sub-set 1: prices of traded debt or equity at default (30-45 day avg.) – Sub-set 2: revolving loans with limits in 10K and 10Q reports
  16. 16. Empirical Results: Summary Statistics (EAD Risk Measures) • Various $ Table 1.1 - Summary Statistics on EAD Risk Measures S&P and Moodys Rated Defaulted Borrowers Revolving Lines of Credits 1985-2007 exposure Standard 25th 75th measures: EAD Cnt Average Deviation Minimum 5th Prcntl Prcntl Median Prcntl 95th Prcntl Maximum Skew Kurtosis & ∆ to default, Exposure at Default (EAD) 530 133,140 295,035 158 1,656 20,725 50,000 116,234 508,232 4,250,000 7.5099 82.1857 Dollar Change in Drawn to EAD (DCDE) drawn/ undrawn, 2118 48,972 279,972 (3,177,300) (3,177,300) (2,056) 7,514 36,617 275,400 4,250,000 6.8444 116.0538 LEQ (Raw) 1582 63.72% 2759.66% -21000.00% -21000.00% -12.75% 33.28% 87.64% 231.76% 106250.00% 35.7617 1391.0651 3 LEQ (Collared) 1582 42.21% 40.92% 0.00% 0.00% 0.00% 33.28% 87.64% 100.00% 100.00% 0.3054 -1.5700 limits, “race to LEQ (Winsorized) 1582 16.80% 210.38% -1165.74% -1165.74% -12.75% 33.28% 87.64% 231.76% 804.43% -1.9084 13.5038 CCF 1330 1061.8% 20032.7% 0.47% 0.47% 85.30% 111.11% 198.86% 860.29% 704054.38% 32.9416 1145.3158 default” CCF (Winsorized) 1330 190.4% 203.4% 26.29% 26.29% 85.30% 111.11% 198.86% 855.66% 860.29% 2.27 4.45 EAD Factor 1587 143.40% 2666.07% 0.37% 0.37% 42.46% 70.67% 95.96% 152.86% 106250.00% 39.80 1584.89 quantities, EAD Factor (Winsorized) 1587 70.76% 36.94% 11.24% 11.24% 42.46% 70.67% 95.96% 152.39% 152.86% 0.29 -0.39 Utilization 1621 45.85% 32.85% 0.00% 0.00% 14.00% 48.04% 74.27% 95.00% 100.00% -0.06 -1.35 Commitment 1621 184,027 383,442 217 217 40,000 80,000 176,400 570,000 4,250,000 6.24 48.28 • LEQ (CCF & Drawndown Rate 879 0.39% 7.00% -0.10% -0.10% -0.02% 0.01% 0.05% 0.41% 181.97% 23.17 561.82 Cutback Rate 1126 88.50% 2791.11% -96.07% -96.07% 0.00% 0.00% 0.00% 66.67% 93650.00% 33.54 1125.34 EADF) 2 (3 Drawn 1621 71,576 163,029 0 0 5,557 26,463 76,900 260,000 3,090,000 8.41 107.87 Undrawn 773 112,450 329,695 0 0 13,082 34,099 82,300 396,500 4,250,000 7.79 73.49 types) • This conveys a sense of the extreme values observed here – LEQ ranges in [-210,106], CCF (EADF) max at 704 (106) – Shows that you need to understand extremes & the entire distribution • Mean collared LEQ factor 42.2% in “ballpark” with benchmarks – Median 33.3% OK but mean 16.1% raw seems too low – Raw CCF, EADF better (natural flooring) but decide to Winsorize
  17. 17. Empirical Results: Distributions of EAD Risk Measures • Raw LEQ distribution: Figure 1.1: Raw LEQ Factor (S&P and Moody's Rated Defaults 1985-2007) akin to the return on 0.004 an option? • Collared LEQ: familiar 0.0 -200 0 200 400 600 800 1000 “barbell” shape (like EAD.Data.0$LEQ.Obs LGDs) Figure 1.2: W insorized LEQ Factor (S&P and Moody's Rated Defaults 1985-2007) 0.25 • Decide to go with collared measure 0.10 0.0 • Consistency with -10 -5 0 5 EAD.Data.0$LEQ.Obs.Wind common practice Figure 1.3: Collared LEQ Factor (S&P and Moody's Rated Defaults 1985-2007) • Numerical instability 4 of others -> 3 2 estimation problems 1 0 0.0 0.2 0.4 0.6 0.8 1.0 EAD.Data.0$LEQ.Obs.Coll
  18. 18. Empirical Results: Distributions of EAD Risk Measures (continued) • More stable than Figure 2.1: Raw CCF Figure 2.2: Winsorized CCF LEQs 0.6 0.0015 • Natural floor at 0% 0.4 • Choose Winsorized 0.2 0.0005 measures 0.0 0.0 • As with LEQ, 0 2000 4000 6000 0 2 4 6 8 estimation issues EAD.Data.0$CCF.Obs EAD.Data.0$CCF.Obs.Wind S&P and Moody's Rated Defaults 1985-2007 S&P and Moody's Rated Defaults 1985-2007 with raw Figure 2.3: Raw EADF Figure 2.4: Winsorized EADF • Multi-modality 1.5 0.008 (especially EADF)? 1.0 0.004 0.5 0.0 0.0 0 200 400 600 800 1000 0.0 0.5 1.0 1.5 EAD.Data.0$EAD.Fact.Obs EAD.Data.0$EAD.Fact.Obs.Wind S&P and Moody's Rated Defaults 1985-2007 S&P and Moody's Rated Defaults 1985-2007
  19. 19. Empirical Results: Estimation Regions of EAD Risk Measures Table 3.2 • About 1/3 LEQs Estimated Regions of LEQ, CCF and EAD Factors by Rating and Time-to-Default S&P and Moodys Rated Defaulted Borrowers Revolving Lines of Credits 1985-2007 <= 0% → LEQ Region Region Risk Years-to- paydowns <0 =0 .(0,1) =1 >1 <0 =0 .(0,1) =1 >1 Rating Defau;t AAA-BBB 7.27% 1.82% 45.45% 16.36% 29.09% 1 30.42% 5.51% 45.44% 8.37% 10.27% effectuated BB 32.00% 3.43% 52.00% 1.71% 10.86% 2 28.73% 0.81% 51.22% 5.15% 14.09% B 27.49% 4.04% 50.32% 4.67% 13.49% 3 26.98% 0.47% 49.30% 5.12% 18.14% • But 14% > 1 CCC-CC 33.89% 9.30% 36.54% 6.31% 13.95% 4 21.09% 0.78% 48.44% 4.69% 25.00% C 27.03% 18.92% 45.95% 2.70% 5.41% 5 16.67% 0.00% 52.56% 3.85% 26.92% → additional Total 28.63% 5.75% 45.26% 6.19% 14.16% Total 28.63% 5.75% 45.26% 6.19% 14.16% CCF drawdowns? Region Region Risk Years-to- <0 =0 .(0,1) =1 >1 <0 =0 .(0,1) =1 >1 Rating Defau;t AAA-BBB N/A N/A 11.43% 2.86% 85.71% 1 N/A N/A 33.76% 6.12% 57.17% • 34% CCFs < 1 → BB N/A N/A 38.36% 4.79% 56.85% 2 N/A N/A 35.45% 1.00% 61.87% B N/A N/A 33.69% 5.10% 61.21% 3 N/A N/A 34.94% 0.60% 62.65% balance shrinkage CCC-CC N/A N/A 41.53% 11.29% 47.18% 4 N/A N/A 29.03% 2.15% 66.67% C N/A N/A 30.30% 21.21% 48.48% 5 N/A N/A 31.71% 0.00% 65.85% • But 56% > 1 Total N/A N/A 34.14% 6.99% 56.32% Total N/A N/A 34.14% 6.99% 56.32% EADF → inflation? Region Region Risk Years-to- <0 =0 .(0,1) =1 >1 <0 =0 .(0,1) =1 >1 Rating Defau;t • 14% EADFs > 1 AAA-BBB N/A N/A 54.55% 16.36% 29.09% 1 N/A N/A 84.15% 6.04% 9.81% BB N/A N/A 86.93% 2.27% 10.80% 2 N/A N/A 81.40% 8.35% 10.25% B N/A N/A 81.74% 4.79% 13.48% 3 N/A N/A 80.81% 5.14% 14.05% • Larger limits? CCC-CC N/A N/A 79.93% 6.25% 13.82% 4 N/A N/A 76.74% 5.12% 18.14% C N/A N/A 91.89% 2.70% 5.41% 5 N/A N/A 69.77% 5.43% 24.81% Total N/A N/A 79.58% 6.30% 14.11% Total N/A N/A 79.58% 6.30% 14.11% • But this tendency to quirky values attenuated for worse rating and shorter time-to-default
  20. 20. Empirical Results: Summary Statistics (Covariates) Table 1.2 - Summary Statistics: Borrower, Facility and Market Characteristics • Availability of S&P and Moodys Rated Defaulted Borrowers Revolving Lines of Credits 1985-20071 fin. ratios 25th 75th 95th Cnt Avg Std Dev Min 5th Prcntl Prcntl Median Prcntl Prcntl Max Skew Kurt limited vs. Time-to-Default 1616 1.7776 1.3167 -0.1644 -0.1644 0.7671 1.4986 2.7171 4.5671 6.4192 0.85 -0.07 Rating 622 2.9873 0.8672 1.0000 1.0000 3.0000 3.0000 3.0000 4.0000 5.0000 -0.45 0.51 instrument, cap Leverage 1 - LTD/ MV 537 0.7495 0.2188 0.0605 0.0605 0.6382 0.8190 0.9304 0.9878 1.0000 -1.06 0.26 Leverage 2 - TD / BV 722 0.9735 0.3760 0.1785 0.1785 0.7608 0.9155 1.0618 1.6661 4.1119 2.49 11.77 structure & Size - log(Book Value) 725 2.7746 0.5077 0.4396 0.4396 2.4236 2.7588 3.0826 3.5195 5.0167 0.48 2.30 Intangibility - Intangibles/Total Assets 474 0.3570 0.3669 0.0000 0.0000 0.0000 0.2593 0.6481 1.0834 1.3179 0.76 -0.53 macro Liquidity - Current Ratio 685 1.5296 0.9900 0.0606 0.0606 0.9230 1.3977 1.9879 3.2472 12.5570 2.88 23.36 Cash Flow - Free Cash Flow/ Total Aseets 672 -2.36 100.03 -434.16 -434.16 -0.16 0.02 3.58 28.49 1739.52 8.55 157.51 • Companies Profitabilty - Profit Margin 721 -20.23 354.98 -6735.49 -6735.49 -0.24 -0.05 0.00 0.04 0.81 -18.86 355.70 Discounted Ultimate LGD 707 7.76% 29.76% -90.12% -90.12% -5.73% 0.00% 6.24% 77.62% 100.00% 1.07 1.85 highly levered, Market Implied LGD at Default 175 31.16% 23.48% -3.72% -3.72% 10.25% 28.00% 49.63% 74.22% 90.00% 0.51 -0.68 Creditor Rank 1621 1.3967 0.7495 1.0000 1.0000 1.0000 1.0000 2.0000 3.0000 6.0000 2.38 6.80 unprofitable, Colllateral Rank 1621 3.2529 1.4428 1.0000 1.0000 3.0000 3.0000 3.0000 8.0000 8.0000 2.16 4.64 Debt Cushion 1621 25.70% 32.51% 0.00% 0.00% 0.00% 0.00% 52.00% 90.06% 99.48% 0.81 -0.84 intangible, Speculative Grade Default Rate 1621 5.67% 2.92% 0.00% 0.00% 3.15% 6.03% 7.05% 11.39% 13.26% 0.44 -0.50 Speculative Grade Default Rate - Industry 1621 5.90% 4.12% 0.00% 0.00% 2.96% 5.08% 7.95% 14.14% 20.00% 0.78 0.10 negative cash Risk-Free Return 1621 0.40% 0.14% 0.06% 0.06% 0.35% 0.43% 0.50% 0.61% 0.72% -0.78 0.18 Excess Equity Market Return 1621 0.52% 4.46% -10.76% -10.76% -0.46% 1.50% 3.41% 6.93% 8.00% -1.09 0.83 flow Equity Market Size Factor (Fama-French) 1621 0.26% 2.76% -5.74% -5.74% -1.64% 0.44% 1.52% 5.84% 8.43% 0.34 0.40 Equity Market Value Factor (Fama-French) 1621 2.08% 4.59% -5.68% -5.68% -0.74% 1.67% 4.23% 12.52% 13.80% 0.58 0.43 • Low LGDs (top Cumulative Abnormal Equity Return 525 -5.99% 66.63% -152.71% -152.71% -51.63% -6.96% 36.32% 117.66% 174.70% 0.31 -0.13 Number of Creditor Classes 1621 2.3307 0.8228 1.0000 1.0000 2.0000 2.0000 3.0000 4.0000 6.0000 0.91 1.51 of the capital Percent Secured Debt 1621 0.4776 0.3125 0.0000 0.0000 0.2354 0.4342 0.7004 1.0000 1.1382 0.32 -0.96 Percent Subordinateded Debt 1621 0.2893 0.3328 0.0000 0.0000 0.0000 0.1329 0.5011 1.0000 1.1179 0.90 -0.51 structure) Percent Bank Debt 1621 0.4481 0.2898 0.0000 0.0000 0.2220 0.4117 0.6260 1.0000 1.1382 0.50 -0.66
  21. 21. Empirical Results: Distributions of LEQ by Rating Fig 3.1: Collared LEQ Factor (All Ratings) Fig 3.2: Collared LEQ Factor (Ratings AAA-BBB) • Clear shift of 4 5 probability mass 4 3 3 2 from 1 to zero as 2 1 1 grade worsens 0 0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 EAD.Data.0$LEQ.Obs.Coll EAD.Data.0$LEQ.Obs.Coll[EAD.Data.0$Rtg.Num.Obs == 1] Fig 3.3: Collared LEQ Factor (Ratings BB) Fig 3.4: Collared LEQ Factor (Ratings B) • But similar 4 3 bimodal shape 3 2 2 across all grades 1 1 0 0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 EAD.Data.0$LEQ.Obs.Coll[EAD.Data.0$Rtg.Num == 2] EAD.Data.0$LEQ.Obs.Coll[EAD.Data.0$Rtg.Num == 3] Fig 3.5: Collared LEQ Factor (Ratings CCC-CC) Fig 3.6: Collared LEQ Factor (Ratings C) 4 3 3 2 2 1 1 0 0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 EAD.Data.0$LEQ.Obs.Coll[EAD.Data.0$Rtg.Num == 4] EAD.Data.0$LEQ.Obs.Coll[EAD.Data.0$Rtg.Num == 5]
  22. 22. Empirical Results: Distributions of LEQ by Time-to-Default Fig 4.1: Collared LEQ Factor (All Times-to-Default) Fig 34.2: Collared LEQ Factor (1 Year-to-Default) • Clear shift of 4 4 probability mass 3 3 2 2 from zero to 1 as 1 1 time-to-default 0 0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 lengthens EAD.Data.0$LEQ.Obs.Coll EAD.Data.0$LEQ.Obs.Coll[EAD.Data.0$TTD.Obs.Yr.1 == 1] Fig 4.3: Collared LEQ Factor (2 Year-to-Default) Fig 4.4: Collared LEQ Factor (3 Year-to-Default) 3.0 3 • But similar 2.0 2 1.0 bimodal shape 1 0.0 0 across all TTDs 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 EAD.Data.0$LEQ.Obs.Coll[EAD.Data.0$TTD.Obs.Yr.1 == 2] EAD.Data.0$LEQ.Obs.Coll[EAD.Data.0$TTD.Obs.Yr.1 == 3] Fig 4.5: Collared LEQ Factor (4 Year-to-Default) Fig 4.6: Collared LEQ Factor (5 Year-to-Default) 3 3 2 2 1 1 0 0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 EAD.Data.0$LEQ.Obs.Coll[EAD.Data.0$TTD.Obs.Yr.1 == 4] EAD.Data.0$LEQ.Obs.Coll[EAD.Data.0$TTD.Obs.Yr.1 == 5]
  23. 23. Empirical Results: LEQ vs. Rating & Time-to-Default Grids Table 2.1.1 Estimated Collared Loan Equivalency Factors by Rating and Time-to-Default S&P and Moodys Rated Defaulted Borrowers Revolving Lines of Credits 1985-2007 • Similar table to this in Count Time-to-Default (yrs) Araten et al (2001) <1 1 2 3 4 5 >5 Rating Total AAA-BBB 11 43 25 17 10 4 0 110 BB 13 59 43 29 16 15 0 175 B 103 254 194 115 76 48 3 793 • Average LEQs CCC-CC 84 102 61 30 16 8 0 301 C 17 8 4 5 3 0 0 37 decrease (increase) NR 35 60 42 19 7 3 0 166 263 526 369 215 128 78 3 1,582 Total almost montonically in Average Time-to-Default (yrs) Risk worsening grade <1 1 2 3 4 5 >5 Rating Total AAA-BBB 43.44% 64.56% 65.26% 84.93% 92.86% 84.58% 0.00% 69.06% (longer time-to- BB 27.82% 38.90% 42.13% 45.91% 43.91% 42.35% 0.00% 40.79% B 33.14% 41.51% 43.92% 42.60% 52.77% 49.94% 14.00% 42.66% default) CCC-CC 22.29% 32.97% 47.38% 54.80% 55.05% 55.30% 0.00% 36.85% C 9.91% 28.21% 9.71% 47.64% 25.67% 0.00% 0.00% 20.22% NR 33.17% 37.73% 39.79% 37.88% 44.61% 82.39% 0.00% 38.40% Total 28.35% 40.81% 44.89% 47.79% 54.00% 52.05% 14.00% 42.21% • Results not as clear- Standard Deviation Time-to-Default (yrs) Risk cut for either non- <1 1 2 3 4 5 >5 Rating Total AAA-BBB 45.75% 38.08% 40.54% 27.94% 12.39% 19.09% N/A 37.78% collared LEQ or CCF, BB 38.00% 39.32% 41.45% 42.87% 44.64% 38.14% N/A 40.42% B 40.97% 39.61% 37.79% 38.43% 42.18% 40.63% 16.37% 39.67% EADF CCC-CC 37.58% 39.91% 40.05% 41.41% 44.04% 48.67% N/A 41.37% C 28.43% 44.72% 14.10% 24.78% 23.10% N/A N/A 32.34% NR 46.50% 43.02% 41.09% 40.79% 41.57% 30.51% N/A 42.73% Total 40.40% 40.58% 39.37% 40.12% 42.10% 40.48% 16.37% 40.92%
  24. 24. Empirical Results: EAD Risk Measures vs. Rating Figure 3: Average EAD Risk Measure by Rating Categories (S&P & Moody's Rated • Generally a Defaults 1985-2007) decrease in 400.00% LEQ, CCF and 350.00% EADF with worsening 300.00% grade 250.00% EAD Measure 200.00% • Does not hold 150.00% monotonically 100.00% for uncollared 50.00% LEQ or un- Winsorized 0.00% AAA-BBB BB B CCC-CC C CCF, EADF Rating Group LEQ CCF EADF
  25. 25. Empirical Results: LEQ vs. Rating & Time-to-Default Plot Figure 5: 3-Dimensional Scatterplot of LEQ vs. Time-to-Defaault & Rating • It is very hard to discern a pattern looked at this way • If anything, LEQs look uniformly distributed in LEQ each bucket Rating TTD S&P & Moody's Rated Defaults 1985-2007
  26. 26. Empirical Results: EAD Risk Measures by Year of Observation Table 4.1 - LEQ, CCF and EADF of Defaulted Instruments by • Where is the ”downturn EAD”? Observation Year (S&P and Moody's Rated Defaults 1985-2007) Mdy's • How many banks look for it Spec Cnt of Avg of Avg of Avg of Cnt of Cnt of Grd Dflt • Define downturn as the default 1 2 3 5 LEQ LEQ CCF CCF EADF EADF Avg of Util Rate Year 1 29.17% 1 103.10% 1 93.20% 90.40% 4.10% 1985 rate in the highest quintile 4 15.68% 4 103.63% 4 71.30% 77.02% 4.97% 1986 7 27.14% 7 209.44% 7 67.80% 68.79% 5.79% 1987 • → DR > 6.8% (‘91-92,’01-03) 22 27.16% 21 203.18% 22 56.57% 57.51% 4.89% 1988 59 36.12% 52 153.51% 59 64.91% 55.53% 2.74% 1989 • A countercyclical effect can be 61 31.76% 59 167.52% 62 69.73% 62.31% 6.58% 1990 34 34.08% 34 126.45% 34 75.37% 72.32% 12.09% 1991 seen (i.e., ↑ factors in mid-90s) 32 41.83% 31 185.09% 32 78.72% 62.68% 7.32% 1992 33 43.46% 32 141.39% 33 82.29% 65.59% 5.06% 1993 • But 1st episode vs. 80s not so 44 39.01% 42 199.40% 44 77.22% 57.34% 2.80% 1994 clear (thin observations) 43 42.09% 39 174.40% 43 75.96% 55.91% 2.06% 1995 44 54.34% 38 218.06% 44 83.63% 46.95% 3.01% 1996 • Do we really expect higher EAD 89 47.81% 71 232.62% 89 76.83% 40.05% 2.24% 1997 205 51.34% 162 242.20% 205 76.61% 38.78% 2.98% 1998 risk in downturns (but then what 237 45.79% 195 206.65% 237 71.70% 45.80% 4.58% 1999 271 42.83% 204 194.02% 271 67.16% 44.39% 6.80% 2000 is the story here?) 184 37.85% 150 165.86% 185 66.37% 49.34% 9.13% 2001 95 35.19% 86 151.30% 98 65.03% 53.80% 11.01% 2002 • Monitoring – “laxity” or ↑ cost 59 37.20% 53 169.15% 59 62.65% 55.01% 6.83% 2003 in good periods? 33 40.94% 27 168.12% 33 65.95% 44.81% 4.77% 2004 22 40.26% 19 201.48% 22 69.55% 46.24% 2.94% 2005 • Moral Hazard - incentives to 2 0.00% 2 88.07% 2 31.44% 56.76% 2.28% 2006 1 0.00% 1 95.92% 1 53.41% 55.68% 1.63% 2007 overextend during expansion? 1,582 42.21% 1,330 190.42% 1,587 70.76% 48.64% 5.17% Total
  27. 27. Empirical Results: EAD Risk Measures by Year of Default Table 5.1 - LEQ, CCF and EADF of Defaulted Instruments by Default Year and 1 Year Prior to Default (S&P and Moody's • Grouping by default year and Rated Defaults 1985-2007) taking the observation 1-year Mdy's Cnt Spec back is akin to the “cohort Cnt of Avg of Cnt of Avg of Avg of Avg of Grd Dflt Year of 1 2 3 5 Dflt LEQ LEQ CCF CCF EADF EADF Util Rate approach” to EAD 2 45.95% 10 110.59% 4 82.52% 90.40% 5.79% 1987 3 25.97% 16 180.88% 8 65.08% 77.02% 4.89% 1988 • Same story here: still the cycle to 3 0.00% 11 277.41% 6 71.92% 68.79% 2.74% 1989 hard to detect in the expected 25 28.47% 79 119.56% 44 62.34% 57.51% 6.58% 1990 32 44.67% 127 160.69% 66 67.33% 55.53% 12.09% 1991 direction 12 20.18% 59 238.46% 30 79.84% 62.31% 7.32% 1992 18 35.26% 79 124.55% 51 70.62% 72.32% 5.06% 1993 • Again, a some evidence of 11 52.76% 65 150.90% 41 77.79% 62.68% 2.80% 1994 15 50.34% 74 177.61% 45 75.02% 65.59% 2.06% 1995 countercyclicality here, but it is 20 42.66% 73 169.87% 40 70.57% 57.34% 3.01% 1996 10 54.23% 47 224.12% 29 83.15% 55.91% 2.24% faint 1997 13 53.31% 43 218.91% 26 92.28% 46.95% 2.98% 1998 42 51.53% 135 167.20% 90 75.25% 40.05% 4.58% • Now utilization is not that much 1999 36 31.28% 157 179.93% 96 74.05% 38.78% 6.80% 2000 higher in the downturns vs. by 111 47.28% 741 230.71% 312 74.97% 45.80% 9.13% 2001 76 38.55% 380 210.54% 261 70.63% 44.39% 11.01% 2002 observation year for all years 45 31.81% 260 166.22% 203 66.91% 49.34% 6.83% 2003 29 28.94% 164 157.30% 131 55.89% 53.80% 4.77% 2004 12 53.54% 67 221.29% 54 80.94% 55.01% 2.94% 2005 10 47.26% 51 250.14% 42 59.05% 44.81% 2.28% 2006 1 0.00% 10 74.79% 8 21.30% 46.24% 1.63% 2007 526 40.81% 2,648 190.42% 1,587 70.76% 56.76% 5.17% Total
  28. 28. Empirical Results: EAD Risk Measures by Year of Default Table 5.1 - LEQ, CCF and EADF of Defaulted Instruments by • Grouping by default year and Default Year and 1 Year Prior to Default (S&P and Moody's Rated Defaults 1985-2007) taking the observation 1-year back Mdy's is akin to the “cohort approach” Cnt Spec Cnt of Avg of Cnt of Avg of Avg of Avg of Grd Dflt Year of (CA) to EAD 1 2 3 5 Dflt LEQ LEQ CCF CCF EADF EADF Util Rate 2 45.95% 10 110.59% 4 82.52% 90.40% 5.79% 1987 • Pure CA analogous to rating 3 25.97% 16 180.88% 8 65.08% 77.02% 4.89% 1988 3 0.00% 11 277.41% 6 71.92% 68.79% 2.74% 1989 agency default rate estimation 25 28.47% 79 119.56% 44 62.34% 57.51% 6.58% 1990 32 44.67% 127 160.69% 66 67.33% 55.53% 12.09% 1991 • Same story here: still the cycle to 12 20.18% 59 238.46% 30 79.84% 62.31% 7.32% 1992 18 35.26% 79 124.55% 51 70.62% 72.32% 5.06% 1993 hard to detect in the “expected” 11 52.76% 65 150.90% 41 77.79% 62.68% 2.80% 1994 direction 15 50.34% 74 177.61% 45 75.02% 65.59% 2.06% 1995 20 42.66% 73 169.87% 40 70.57% 57.34% 3.01% 1996 • But why do people expect to 10 54.23% 47 224.12% 29 83.15% 55.91% 2.24% 1997 13 53.31% 43 218.91% 26 92.28% 46.95% 2.98% 1998 see this? 42 51.53% 135 167.20% 90 75.25% 40.05% 4.58% 1999 36 31.28% 157 179.93% 96 74.05% 38.78% 6.80% 2000 • Evidence of countercyclicality 111 47.28% 741 230.71% 312 74.97% 45.80% 9.13% 2001 76 38.55% 380 210.54% 261 70.63% 44.39% 11.01% 2002 here, mainly from the 2nd 45 31.81% 260 166.22% 203 66.91% 49.34% 6.83% 2003 downturn 29 28.94% 164 157.30% 131 55.89% 53.80% 4.77% 2004 12 53.54% 67 221.29% 54 80.94% 55.01% 2.94% 2005 • EAD risk measures higher in 10 47.26% 51 250.14% 42 59.05% 44.81% 2.28% 2006 1 0.00% 10 74.79% 8 21.30% 46.24% 1.63% 2007 the benign mid-90’s 526 40.81% 2,648 190.42% 1,587 70.76% 56.76% 5.17% Total
  29. 29. Empirical Results: EAD Risk Measures by Collateral & Seniority Table 6.1.1 - EAD Risk Measures by Instrument and Major Collateral Types (S&P and Moody's Rated • EAD risk is 1 Defaults 1985-2007) 2 3 4 LEQ CCF EADF generally lower Jun Jun Jun Senior Sub Sub Total Senior Sub Sub Total Senior Sub Sub Total for better Cash / Cnt 28 7 0 35 24 5 0 29 28 7 0 35 Guarantees / secured and Avg 17.7% 26.9% N/A 19.6% 77.4% 204.7% N/A 99.4% 44.6% 86.3% N/A 44.5% Other Highly Inventories / Cnt 212 42 13 267 187 35 8 230 212 42 13 267 more senior Receivables / Avg 32.6% 56.4% 46.1% 37.0% 160.3% 255.4% 269.3% 178.6% 63.7% 86.3% 60.6% 67.1% Other Current Second Lien / loans Cnt 719 229 96 1044 641 171 72 884 722 230 96 1048 Real Estate /All- Avg 38.0% 48.9% 44.3% 41.0% 172.4% 220.9% 221.6% 185.8% 69.1% 72.0% 73.6% 70.2% Assets / Oil & Gas • Mean LEQ 41% Capital Stock / Cnt 54 17 0 71 42 17 0 59 54 17 0 71 Inter-company Avg 51.9% 44.8% N/A 50.2% 150.8% 171.1% N/A 156.6% 84.4% 71.6% N/A 81.3% vs. 57% (39% Debt Cnt 15 0 0 15 9 0 0 9 15 0 0 15 Plant, Property & vs. 51%) for Avg N/A 0.0% N/A 53.9% N/A 0.0% N/A 226.3% 65.7% 0.0% N/A 65.7% Equipment Most Assets / secured vs. Cnt 51 2 7 60 49 1 5 55 51 2 7 60 Intellectual Avg 61.2% 98.7% 85.5% 65.2% 327.5% 429.8% N/A 335.4% 88.7% 112.5% 113.8% 92.4% Property unsecured Cnt 1079 297 116 1492 952 229 85 1266 1082 298 116 1496 Avg 37.7% 49.6% 54.0% 41.3% 173.0% 223.0% 260.2% 187.9% 69.1% 73.6% 74.6% 70.4% (senior vs. sub) Total Secured Cnt 62 26 2 90 47 16 1 64 63 26 2 91 Avg 53.1% 67.5% 44.9% 57.1% 224.7% 292.0% 126.5% 240.0% 77.3% 75.7% 63.2% 76.54% Unsecured • Finally an Cnt 1141 323 118 1582 999 245 86 1330 1145 324 118 1587 “intuitive” result? Avg 39.2% 51.0% 47.0% 42.2% 177.5% 227.6% 234.9% 190.4% 69.5% 73.8% 74.4% 70.8% Total Collateral (basis for some • However, ample judgment applied in forming these high level collateral groupings from lower level labels segmentations)
  30. 30. Empirical Results: EAD Risk Measures by Obligor Industry • Difficult to discern an Table 7.1.1 - LEQ, CCF and EADF of Defaulted Instruments and Obligors by Industry (S&P and Moody's Rated Defaults 1985-2007) explainable pattern Avg Cnt Avg of Cnt of Avg of Cnt of Avg of of Avg Avg of • Utilities, Tech, Energy & LEQ LEQ CCF CCF EADF EADF Rtg of Util Commit Industry Group Aerospace / Auto / Transportation above Capital Goods / Equipment 225 40.1% 202 189.0% 227 68.5% 3.01 48.9% 120,843 average for LEQ Consumer / Service Sector 428 36.6% 374 186.3% 428 67.7% 3.02 48.2% 138,039 • Homebuilders & Consumer Energy / Natural Resources 162 47.7% 114 203.9% 162 74.0% 2.85 40.1% 304,305 / Service below for LEQ Financial Institutions 11 45.3% 11 142.0% 11 72.2% 3.60 52.9% 33,722 Forest / Building Prodects / • But rankings not Homebuilders 40 29.0% 36 126.3% 40 64.3% 2.94 55.8% 114,421 completely consistent Healthcare / Chemicals 149 38.5% 123 165.1% 150 69.5% 3.02 47.7% 168,155 High Technology / across measures Telecommunications 213 49.3% 146 199.9% 213 75.5% 2.93 37.6% 276,191 Insurance and Real Estate 17 36.0% 17 119.0% 17 92.8% 3.13 82.8% 137,190 • What could be the story? Leisure Time / Media 167 46.1% 136 178.7% 167 72.2% 3.17 46.0% 150,574 (e.g., tangibility & LGD) Transportation 164 47.9% 131 215.5% 166 71.4% 2.86 42.2% 203,296 Utilities 6 50.0% 6 233.9% 6 67.2% 2.50 42.2% 233,267 Total 1,582 42.2% 1,330 190.4% 1,587 70.8% 2.99 48.6% 181,118
  31. 31. Empirical Results: LEQ by Obligor Industry and Annual Default Rates Table 7.1 - LEQ and Moody's Specultive Grade Default Rates of Defaulted Instruments and Obligors by Observation Year and Major Industry Category (S&P and Moody's Rated Defaults 1985-2007) Aerospace / Auto / High Capital Consumer / Energy / Forest / Building Technology / Goods / Service Natural Financial Prodects / Healthcare / Telecommuni Insurance and Leisure Time / Equipment Sector Resources Institutions Homebuilders Chemicals cations Real Estate Media Transportation Utilities All Industries Mdy's Mdy's Mdy's Mdy's Mdy's Mdy's Mdy's Mdy's Mdy's Mdy's Spec Spec Spec Spec Mdy's Spec Spec Spec Spec Mdy's Spec Spec Grd Grd Grd Grd Spec Grd Grd Grd Grd Spec Grd Grd Avg. Dflt Avg. Dflt Avg. Dflt Avg. Dflt Avg. Grd Dflt Avg. Dflt Avg. Dflt Avg. Dflt Avg. Dflt Avg. Grd Dflt Avg. Dflt Avg. Dflt LEQ Rate LEQ Rate LEQ Rate LEQ Rate LEQ Rate LEQ Rate LEQ Rate LEQ Rate LEQ Rate LEQ Rate LEQ Rate LEQ Rate 1985 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 29.2% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 29.2% 0.0% 1986 0.0% 0.0% 31.4% 2.9% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 2.9% 0.0% 0.0% 0.0% 0.0% 0.0% 8.7% 0.0% 0.0% 0.0% 0.0% 15.7% 4.3% 1987 0.0% 0.0% 77.9% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 6.4% 0.0% 0.0% 10.7% 3.7% 0.0% 0.0% 25.3% 3.2% 0.0% 0.0% 0.0% 0.0% 27.1% 3.3% 1988 33.3% 4.0% 23.3% 1.8% 0.0% 0.0% 0.0% 0.0% 0.0% 4.0% 0.0% 1.8% 34.9% 4.4% 0.0% 0.0% 18.4% 6.6% 84.0% 0.0% 0.0% 0.0% 27.2% 3.5% 1989 28.6% 3.6% 25.1% 1.9% 0.0% 0.0% 0.0% 0.0% 25.0% 4.4% 39.6% 3.3% 53.1% 0.8% 27.3% 2.8% 46.9% 11.0% 76.6% 5.1% 0.0% 0.0% 36.1% 3.7% 1990 25.8% 6.0% 40.8% 6.8% 95.3% 6.1% 100.0% 8.9% 0.0% 5.3% 0.0% 7.5% 39.4% 4.6% 0.0% 6.7% 7.9% 18.1% 49.1% 5.4% 100.0% 6.1% 31.8% 7.4% 1991 25.0% 13.1% 22.1% 11.8% 0.0% 3.3% 86.6% 12.1% 0.0% 11.6% 0.0% 10.2% 69.6% 5.4% 69.0% 11.9% 0.0% 17.1% 0.0% 0.0% 50.0% 6.1% 34.1% 10.7% 1992 58.8% 5.2% 43.2% 8.9% 0.0% 7.7% 0.0% 5.8% 0.0% 3.5% 0.0% 6.4% 70.3% 3.7% 0.0% 0.0% 33.3% 9.4% 0.0% 0.0% 0.0% 0.0% 41.8% 7.0% 1993 81.0% 3.1% 26.8% 11.9% 54.7% 4.5% 0.0% 4.1% 0.0% 3.6% 0.0% 13.9% 51.4% 1.1% 100.0% 4.1% 100.0% 11.1% 25.0% 0.0% 100.0% 4.8% 43.5% 6.5% 1994 0.0% 0.0% 44.7% 2.4% 36.8% 0.0% 5.3% 2.7% 0.0% 0.0% 47.0% 1.4% 21.6% 1.7% 14.5% 3.0% 50.4% 6.1% 0.0% 0.0% 0.0% 0.0% 39.0% 2.5% 1995 0.0% 0.0% 45.4% 1.3% 33.3% 2.5% 0.0% 1.3% 0.0% 0.0% 0.0% 0.0% 41.6% 1.8% 0.0% 2.4% 61.2% 2.6% 5.7% 5.1% 0.0% 0.0% 42.1% 2.0% 1996 75.9% 1.7% 39.4% 6.5% 64.6% 2.1% 0.0% 0.0% 42.5% 1.2% 0.0% 0.0% 58.5% 1.1% 0.0% 0.0% 75.0% 3.4% 83.0% 6.3% 0.0% 0.0% 54.3% 4.5% 1997 42.2% 1.8% 37.5% 1.5% 46.6% 0.3% 0.0% 0.0% 38.9% 1.5% 56.8% 1.1% 56.9% 2.6% 100.0% 2.7% 33.7% 5.3% 64.9% 3.1% 0.0% 0.0% 47.8% 2.0% 1998 49.2% 2.3% 44.9% 2.6% 65.6% 1.4% 47.1% 2.8% 65.5% 2.6% 39.7% 3.1% 52.2% 1.2% 100.0% 0.0% 52.7% 3.3% 52.8% 2.8% 0.0% 0.0% 51.3% 2.4% 1999 44.4% 3.5% 37.0% 4.3% 49.8% 7.4% 0.0% 3.6% 31.3% 3.5% 50.1% 4.0% 47.0% 3.9% 0.0% 0.0% 48.1% 7.1% 53.2% 6.0% 0.0% 0.0% 45.8% 4.9% 2000 47.3% 7.5% 32.2% 7.8% 46.6% 10.6% 0.0% 0.0% 54.5% 8.7% 43.3% 7.5% 54.1% 5.0% 4.2% 7.0% 41.7% 9.4% 38.4% 5.7% 0.0% 4.6% 42.8% 7.4% 2001 32.8% 11.4% 29.0% 12.6% 46.0% 3.4% 0.0% 0.0% 29.5% 11.8% 28.1% 12.7% 45.2% 9.4% 0.0% 0.0% 52.2% 11.1% 38.6% 4.9% 0.0% 4.1% 37.9% 9.5% 2002 16.4% 13.1% 38.1% 10.3% 23.1% 0.5% 0.0% 0.0% 75.6% 12.7% 32.6% 10.5% 46.6% 17.1% 0.0% 0.0% 76.6% 8.4% 26.2% 8.8% 0.0% 0.0% 35.2% 10.5% 2003 26.9% 5.9% 36.8% 4.8% 26.5% 3.0% 0.0% 0.0% 64.1% 5.4% 22.8% 5.1% 63.4% 12.0% 0.0% 0.0% 42.7% 2.6% 50.9% 16.7% 0.0% 0.0% 37.2% 6.8% 2004 0.0% 5.9% 39.7% 6.7% 23.3% 0.0% 0.0% 0.0% 0.0% 6.6% 26.7% 7.0% 55.0% 7.2% 0.0% 0.0% 65.4% 1.6% 57.1% 1.3% 0.0% 0.0% 40.9% 4.7% 2005 9.8% 3.4% 46.3% 6.6% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 13.6% 6.5% 16.7% 2.4% 0.0% 0.0% 0.0% 2.2% 100.0% 9.4% 0.0% 0.0% 40.3% 6.1% 2006 0.0% 0.0% 0.0% 3.7% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 3.7% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 3.7% 2007 0.0% 0.0% 0.0% 3.6% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 3.6% Total 40.1% 6.4% 36.6% 6.1% 47.7% 4.4% 45.3% 7.1% 29.0% 5.6% 38.5% 5.7% 49.3% 5.7% 36.0% 4.5% 46.1% 7.1% 47.9% 5.3% 50.0% 5.3% 42.2% 5.9%
  32. 32. Empirical Results: Correlations of EAD Risk Measures to Covariates Table 1.3 -Correlations of EAD Risk Measures to Database • Utilization strongest driver except in EADF Attributes S&P and Moodys Rated Defaulted Borrowers Revolving Lines 1 • TTD (rating) strongly + (-) → EAD risk of Credits 1985-2007 LEQ CCF EADF Utilization -33.50% -61.58% 1.03% • Leverage, liquidity, profitability, Commitment 2.51% -4.41% -6.88% -4.38% -2.80% -2.76% Drawndown Rate tangibility (size) - (+) → EAD risk 4.51% 1.52% 3.60% Cutback Rate Drawn -14.69% -18.58% -5.85% • Better collateral rank, higher seniority, Undrawn 9.54% 12.53% -5.08% Time-to-Default 15.09% 18.14% 18.14% more debt cushion → lower EAD risk Rating -17.80% -16.07% -11.28% -5.48% -10.20% 2.29% Leverage 1 - LTD/ MV • More % bank, secured debt -> higher -6.62% 4.43% -5.48% Leverage 2 - TD / BV Size - log(Book Value) 17.80% 5.33% 7.37% EAD risk (monitoring/coordination story?) Intangibility - Intangibles/Total Assets 12.61% 3.68% 3.68% Liquidity - Current Ratio -9.18% -8.79% -8.95% Cash Flow - Free Cash Flow/ Total Aseets • Countercyclical by speculative grade 5.40% 1.96% 5.90% -7.77% -10.45% -4.53% Profitabilty - Profit Margin 10.02% 10.13% 9.29% Discounted Ultimate LGD default rate (by industry too, but weaker) Market Implied LGD at Default 12.33% 16.48% 9.44% Creditor Rank 7.06% 9.03% 2.00% • Cash flow → +EAD risk for LEQ & EADF Colllateral Rank 15.94% 12.57% 11.85% Debt Cushion -15.27% -10.35% -10.35% (but weak & not in regressions) -9.09% -9.53% -9.31% Speculative Grade Default Rate -7.35% -7.36% -7.67% Speculative Grade Default Rate - Industry Risk-Free Return • Equity markets – risk free rate & Fama 0.10% 2.67% 0.72% Excess Equity Market Return 4.22% 5.85% 3.05% Equity Market Size Factor (Fama-French) -1.22% 0.39% -2.06% French factors negative & small / weak Equity Market Value Factor (Fama-French) -1.58% -4.38% -4.63% -7.14% -9.38% -4.11% Cumulative Abnormal Equity Return • Drawn (undrawn – ex EADF) + (-) EAD risk 0.72% -2.51% -2.52% Number of Creditor Classes Percent Secured Debt 17.35% 2.55% 14.67% • CARs neg. corr but not in regressions Percent Subordinateded Debt -4.10% -2.19% -4.38% 13.55% 8.50% 18.92% Percent Bank Debt
  33. 33. Empirical Results: Correlations of EAD Risk Measures to Covariates Figure 6: Multipanel Pairwise Scatterplot of Key EAD Variables • Another disappointing 4 3 4 3 graph – not easy to Lev.LR.1.Obs 2 1 look at 1 2 8 5 6 7 8 7 6 5 Coll.Obs 4 3 2 1 2 3 4 1 1 .0 0 .6 0 .8 1 .0 • It is hard to see what 0 .8 0 .6 Util.Obs 0 .4 is going on with 0 .2 0 .0 0 .2 0 .4 0 .0 5 3 4 5 these variables (i.e., 4 Rtg.Num.Obs 3 3 the dependency 2 1 2 3 1 3 4 5 6 6 structure) 5 4 TTD.Obs 3 3 2 1 0 0 1 2 3 1 .0 0 .6 0 .8 1 .0 0 .8 0 .6 LEQ.Obs.Coll 0 .4 0 .2 0 .0 0 .2 0 .4 0 .0 S&P & Moody's Rated Defaults 1985-2007
  34. 34. Econometric Modeling of EAD: Beta-Link Generalized Linear Model • The distributional properties of EAD risk measures creates challenges in applying standard statistical techniques • Non-normality of EAD in general and collared LEQ factors in particular (boundary bias) • OLS inappropriate or even averaging across segments • Here we borrow from the default prediction literature by adapting generalized linear models (GLMs) to the EAD setting • See Maddalla (1981, 1983) for an introduction application to economics • Logistic regression in default prediction or PD modeling is a special case • Follow Mallick and Gelfand (Biometrika 1994) in which the link function is taken as a mixture of cumulative beta distributions vs. logistic • See Jacobs (2007) or Huang & Osterlee (2008) for applications to LGD • We may always estimate the underlying parameters consistently and efficiently by maximizing the log-likelihood function (albeit numerically) • Downside: computational overhead and interpretation of parameters • Alternatives: robust / resistant statistics on raw LEQ, modeling of dollar EAD measures through quantile regression (Moral, 2006)
  35. 35. Econometric Modeling of EAD: Beta-Link GLM (continued) • Denote the ith observation of some EAD risk measure by εi in some limited domain (l,u), a vector of covariates xi, and a smooth, invertible function m() that links linear function of xi to the conditional expectation EP(εi|xi ): u η = βT xi = m−1 ( μ ) EP [ε i | xi ] = μ = p ( ε i | xi ) yi dυ ( ε i ) = m (η ) ∫ l • In this framework, the distribution of εi resides in the exponential family, membership in which implies a probability distribution function of the form: ⎛ ζ ⎞ ⎤ τ, γ are smooth functions, ⎡ Ai p ( ε i | xi , β, Ai , ζ ) = exp ⎢ {ε iθ ( xi | β ) − γ ( xi | β )} + τ ⎜ ε i , ⎟ ⎥ A is a prior weight, ζ is a ⎢ζ ⎝ Ai ⎠ ⎥ i ⎣ ⎦ scale parameter • The location function θ(.) is related to the linear predictor according to: ( ) θ ( xi | β ) = (γ ') −1 ( μ ( xi ) ) = (γ ') −1 m ( βT xi )

×