An Empirical Study of Exposure at Default

Michael Jacobs, Ph.D., CFA

Senior Financial Economist

Risk Analysis Division / Credit Risk Modeling

Moody’s KMV Credit Practitioner’s Conference

September 9, 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.

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

Background and MotivationWhy 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

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 modeling framework (structural or reduced form) understanding or predicting EAD?

We develop empirical methods potentially supporting EAD estimation in ALL of these senses

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

Review of the LiteratureLimited 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”

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)

Methodology: The Loan Equivalency Factor (LEQ)

• EAD: time t expected $ utilization (= availability) default time τ:

t ,t,Tt,t,T t t tEAD UTIL LEQ AVAIL UTILf

XX

t

f tt t,t,T

t t

UTIL - UTILLEQ E | τ T,

AVAIL - UTIL

XX

Dt iiD iTi

t i t ii i

N ,t,Tf̂

i=1 ,t ,t

UTIL - UTIL1

LEQ =N AVAIL - UTIL

x XX

XX X X

• “Traditionally” estimated through an LEQ factor that is applied to the current unused:

• 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”):

t ,t,T t , t t , tEAD = E UTIL | T, E AVAIL | T,

X X XX X

Methodology: The Credit Conversion Factor (CCF)

• An alternative approach estimates a credit conversion factor (CCF) to be applied to the current outstanding (used amount):

t t

f,t,T t ,t,TEAD = UT IL ×CCFX X

t

f,t,T t t t t

t t

AVAIL UTILCCF = E | T, = E | T,

UTIL UTIL

X X X

DD iTi

t ii

N ,Tf̂

i=1 ,t

UTIL1

CCF =N UTIL

X X

XX X

• The CCF is simply the expected gross percent change in the total outstanding:

• CCF can be estimated by averaging the observed percent changes in outstandings:

Methodology: The Exposure at Default Factor (EADF) & Modeling of Dollar EAD

t t

f,t,T t ,t,TEAD = AVAIL ×EADX X

• Alternatively, dollar EAD may be factored into the product of the current availability and an EAD factor:

• Most generally & least common, model dollar EAD as a function of used / unused & covariates (Levonian, 2007) :

• May be estimated as the average of gross % limit changes:

• Where Y=(X,AVAIL,UTIL,T,t), L(.) is a loss metric, and EP is expectation with respect to physical (empirical) measure

DTi

,tt ii

N ,Tf̂

i=1

AVAIL1

EAD =N AVAIL

Di

X

X

X

XX X

t

f,t,T t t

t

AVAILEAD = E | T,

AVAIL

X X

• Where EADf is the expected gross change in the limit:

$

$̂ $P

EAD

EAD arg min E L EAD EADt

t

t t Y

Y

Y Y

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)

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

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

Empirical Results: Summary Statistics (EAD Risk Measures)

• 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

Cnt AvgStandard Deviation Min 5th Prcntl

25th Prcntl Median

75th Prcntl 95th Prcntl Max Skew Kurtosis

Exposure at Default (EAD)0 530 133,140 295,035 158 1,656 20,725 50,000 116,234 508,232 4,250,000 7.5099 82.1857

Dollar Change in Drawn to EAD (DCDE)1 2118 48,972 279,972 (3,177,300) (3,177,300) (2,056) 7,514 36,617 275,400 4,250,000 6.8444 116.0538LEQ (Raw)2

1582 63.72% 2759.66% -21000.00% -21000.00% -12.75% 33.28% 87.64% 231.76% 106250.00% 35.7617 1391.0651LEQ (Collared)3

1582 42.21% 40.92% 0.00% 0.00% 0.00% 33.28% 87.64% 100.00% 100.00% 0.3054 -1.5700

LEQ (Winsorized)4 1582 16.80% 210.38% -1165.74% -1165.74% -12.75% 33.28% 87.64% 231.76% 804.43% -1.9084 13.5038CCF5

1330 1061.8% 20032.7% 0.47% 0.47% 85.30% 111.11% 198.86% 860.29% 704054.38% 32.9416 1145.3158

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 Factor6 1587 143.40% 2666.07% 0.37% 0.37% 42.46% 70.67% 95.96% 152.86% 106250.00% 39.80 1584.89

EAD Factor (Winsorized) 1587 70.76% 36.94% 11.24% 11.24% 42.46% 70.67% 95.96% 152.39% 152.86% 0.29 -0.39Utilization6

1621 45.85% 32.85% 0.00% 0.00% 14.00% 48.04% 74.27% 95.00% 100.00% -0.06 -1.35Commitment7 1621 184,027 383,442 217 217 40,000 80,000 176,400 570,000 4,250,000 6.24 48.28Drawndown Rate8

879 0.39% 7.00% -0.10% -0.10% -0.02% 0.01% 0.05% 0.41% 181.97% 23.17 561.82Cutback Rate9

1126 88.50% 2791.11% -96.07% -96.07% 0.00% 0.00% 0.00% 66.67% 93650.00% 33.54 1125.34Drawn10

1621 71,576 163,029 0 0 5,557 26,463 76,900 260,000 3,090,000 8.41 107.87Undrawn11

773 112,450 329,695 0 0 13,082 34,099 82,300 396,500 4,250,000 7.79 73.49

Table 1.1 - Summary Statistics on EAD Risk MeasuresS&P and Moodys Rated Defaulted Borrowers Revolving Lines of Credits 1985-20071

• Various $ exposure measures: EAD & ∆ to default, drawn/ undrawn, limits, “race to default” quantities

• LEQ (CCF & EADF) 2 (3 types)

Empirical Results: Distributions of EAD Risk Measures

• Raw LEQ distribution: akin to the return on an option?

• Collared LEQ: familiar “barbell” shape (like LGDs)

• Decide to go with collared measure• Consistency with

common practice

• Numerical instability of others -> estimation problems

-200 0 200 400 600 800 1000

0.0

0.0

04

Figure 1.1: Raw LEQ Factor (S&P and Moody's Rated Defaults 1985-2007)

EAD.Data.0$LEQ.Obs

-10 -5 0 5

0.0

0.1

00.

25

Figure 1.2: Winsorized LEQ Factor (S&P and Moody's Rated Defaults 1985-2007)

EAD.Data.0$LEQ.Obs.Wind

0.0 0.2 0.4 0.6 0.8 1.0

01

23

4

Figure 1.3: Collared LEQ Factor (S&P and Moody's Rated Defaults 1985-2007)

EAD.Data.0$LEQ.Obs.Coll

Empirical Results: Distributions of EAD Risk Measures (continued)

• More stable than LEQs • Natural floor at 0%

• Choose Winsorized measures• As with LEQ,

estimation issues with raw

• Multi-modality (especially EADF)?

0 2000 4000 6000

0.0

0.00

050.

0015

Figure 2.1: Raw CCF

S&P and Moody's Rated Defaults 1985-2007EAD.Data.0$CCF.Obs

0 2 4 6 80.

00.

20.

40.

6

Figure 2.2: Winsorized CCF

S&P and Moody's Rated Defaults 1985-2007EAD.Data.0$CCF.Obs.Wind

0 200 400 600 800 1000

0.0

0.00

40.

008

Figure 2.3: Raw EADF

S&P and Moody's Rated Defaults 1985-2007EAD.Data.0$EAD.Fact.Obs

0.0 0.5 1.0 1.5

0.0

0.5

1.0

1.5

Figure 2.4: Winsorized EADF

S&P and Moody's Rated Defaults 1985-2007EAD.Data.0$EAD.Fact.Obs.Wind

Empirical Results: Estimation Regions of EAD Risk Measures

• About 1/3 LEQs <= 0% → paydowns effectuated?• But 14% > 1 →

additional drawdowns?

• 34% CCFs < 1 → balance shrinkage?• But 56% > 1 →

inflation• 14% EADFs > 1 →

larger limits?• But 80 <1 →

lower limits

< 0 = 0 .(0,1) =1 >1 < 0 = 0 .(0,1) =1 >1

AAA-BBB 7.27% 1.82% 45.45% 16.36% 29.09% 1 30.42% 5.51% 45.44% 8.37% 10.27%

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%

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%

Total 28.63% 5.75% 45.26% 6.19% 14.16% Total 28.63% 5.75% 45.26% 6.19% 14.16%

< 0 = 0 .(0,1) =1 >1 < 0 = 0 .(0,1) =1 >1

AAA-BBB N/A N/A 11.43% 2.86% 85.71% 1 N/A N/A 33.76% 6.12% 57.17%

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%

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%

Total N/A N/A 34.14% 6.99% 56.32% Total N/A N/A 34.14% 6.99% 56.32%

< 0 = 0 .(0,1) =1 >1 < 0 = 0 .(0,1) =1 >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%

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%

CCF

Table 3.2Estimated 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

RegionRisk Rating

Region Years-to-Defau;t

LEQ

Years-to-Defau;t

Region

EADF

Years-to-Defau;t

RegionRisk Rating

Region

Risk Rating

Region

• But this tendency to “quirky” values attenuated for worse rating and shorter time-to-default

Empirical Results: Summary Statistics (Covariates)

• Availability of fin. ratios limited vs. instrument, cap structure & macro

Cnt Avg Std Dev Min 5th Prcntl25th Prcntl Median

75th Prcntl

95th Prcntl Max Skew Kurt

Time-to-Default 1616 1.7776 1.3167 -0.1644 -0.1644 0.7671 1.4986 2.7171 4.5671 6.4192 0.85 -0.07Rating 622 2.9873 0.8672 1.0000 1.0000 3.0000 3.0000 3.0000 4.0000 5.0000 -0.45 0.51Leverage 1 - LTD/ MV 537 0.7495 0.2188 0.0605 0.0605 0.6382 0.8190 0.9304 0.9878 1.0000 -1.06 0.26Leverage 2 - TD / BV 722 0.9735 0.3760 0.1785 0.1785 0.7608 0.9155 1.0618 1.6661 4.1119 2.49 11.77Size - log(Book Value) 725 2.7746 0.5077 0.4396 0.4396 2.4236 2.7588 3.0826 3.5195 5.0167 0.48 2.30Intangibility - Intangibles/Total Assets 474 0.3570 0.3669 0.0000 0.0000 0.0000 0.2593 0.6481 1.0834 1.3179 0.76 -0.53Liquidity - Current Ratio 685 1.5296 0.9900 0.0606 0.0606 0.9230 1.3977 1.9879 3.2472 12.5570 2.88 23.36Cash 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 8.55 157.51Profitabilty - Profit Margin 721 -20.23 354.98 -6735.49 -6735.49 -0.24 -0.05 0.00 0.04 0.81 -18.86 355.70Discounted Ultimate LGD 707 7.76% 29.76% -90.12% -90.12% -5.73% 0.00% 6.24% 77.62% 100.00% 1.07 1.85Market 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 -0.68Creditor Rank 1621 1.3967 0.7495 1.0000 1.0000 1.0000 1.0000 2.0000 3.0000 6.0000 2.38 6.80Colllateral Rank 1621 3.2529 1.4428 1.0000 1.0000 3.0000 3.0000 3.0000 8.0000 8.0000 2.16 4.64Debt Cushion 1621 25.70% 32.51% 0.00% 0.00% 0.00% 0.00% 52.00% 90.06% 99.48% 0.81 -0.84Speculative Grade Default Rate 1621 5.67% 2.92% 0.00% 0.00% 3.15% 6.03% 7.05% 11.39% 13.26% 0.44 -0.50Speculative 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 0.10Risk-Free Return 1621 0.40% 0.14% 0.06% 0.06% 0.35% 0.43% 0.50% 0.61% 0.72% -0.78 0.18Excess Equity Market Return 1621 0.52% 4.46% -10.76% -10.76% -0.46% 1.50% 3.41% 6.93% 8.00% -1.09 0.83Equity 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 0.40Equity 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 0.43Cumulative Abnormal Equity Return 525 -5.99% 66.63% -152.71% -152.71% -51.63% -6.96% 36.32% 117.66% 174.70% 0.31 -0.13Number of Creditor Classes 1621 2.3307 0.8228 1.0000 1.0000 2.0000 2.0000 3.0000 4.0000 6.0000 0.91 1.51Percent Secured Debt 1621 0.4776 0.3125 0.0000 0.0000 0.2354 0.4342 0.7004 1.0000 1.1382 0.32 -0.96Percent Subordinateded Debt 1621 0.2893 0.3328 0.0000 0.0000 0.0000 0.1329 0.5011 1.0000 1.1179 0.90 -0.51Percent 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

Table 1.2 - Summary Statistics: Borrower, Facility and Market CharacteristicsS&P and Moodys Rated Defaulted Borrowers Revolving Lines of Credits 1985-20071

• Companies highly levered, unprofitable, intangible, negative cash flow

• Low LGDs (top of the capital structure)

Empirical Results: Distributions of LEQ by Rating

• Clear shift of probability mass from 1 to zero as grade worsens

• But similar bimodal shape across all grades

0.0 0.2 0.4 0.6 0.8 1.0

01

23

4

Fig 3.1: Collared LEQ Factor (All Ratings)

EAD.Data.0$LEQ.Obs.Coll

0.0 0.2 0.4 0.6 0.8 1.0

01

23

45

Fig 3.2: Collared LEQ Factor (Ratings AAA-BBB)

EAD.Data.0$LEQ.Obs.Coll[EAD.Data.0$Rtg.Num.Obs == 1]

0.0 0.2 0.4 0.6 0.8 1.0

01

23

4

Fig 3.3: Collared LEQ Factor (Ratings BB)

EAD.Data.0$LEQ.Obs.Coll[EAD.Data.0$Rtg.Num == 2]

0.0 0.2 0.4 0.6 0.8 1.0

01

23

Fig 3.4: Collared LEQ Factor (Ratings B)

EAD.Data.0$LEQ.Obs.Coll[EAD.Data.0$Rtg.Num == 3]

0.0 0.2 0.4 0.6 0.8 1.0

01

23

4

Fig 3.5: Collared LEQ Factor (Ratings CCC-CC)

EAD.Data.0$LEQ.Obs.Coll[EAD.Data.0$Rtg.Num == 4]

0.0 0.2 0.4 0.6 0.8 1.0

01

23

Fig 3.6: Collared LEQ Factor (Ratings C)

EAD.Data.0$LEQ.Obs.Coll[EAD.Data.0$Rtg.Num == 5]

Empirical Results: Distributions of LEQ by Time-to-Default

• Clear shift of probability mass from zero to 1 as time-to-default lengthens

• But similar bimodal shape across all TTDs

0.0 0.2 0.4 0.6 0.8 1.0

01

23

4

Fig 4.1: Collared LEQ Factor (All Times-to-Default)

EAD.Data.0$LEQ.Obs.Coll

0.0 0.2 0.4 0.6 0.8 1.0

01

23

4

Fig 34.2: Collared LEQ Factor (1 Year-to-Default)

EAD.Data.0$LEQ.Obs.Coll[EAD.Data.0$TTD.Obs.Yr.1 == 1]

0.0 0.2 0.4 0.6 0.8 1.0

01

23

Fig 4.3: Collared LEQ Factor (2 Year-to-Default)

EAD.Data.0$LEQ.Obs.Coll[EAD.Data.0$TTD.Obs.Yr.1 == 2]

0.0 0.2 0.4 0.6 0.8 1.0

0.0

1.0

2.0

3.0

Fig 4.4: Collared LEQ Factor (3 Year-to-Default)

EAD.Data.0$LEQ.Obs.Coll[EAD.Data.0$TTD.Obs.Yr.1 == 3]

0.0 0.2 0.4 0.6 0.8 1.0

01

23

Fig 4.5: Collared LEQ Factor (4 Year-to-Default)

EAD.Data.0$LEQ.Obs.Coll[EAD.Data.0$TTD.Obs.Yr.1 == 4]

0.0 0.2 0.4 0.6 0.8 1.0

01

23

Fig 4.6: Collared LEQ Factor (5 Year-to-Default)

EAD.Data.0$LEQ.Obs.Coll[EAD.Data.0$TTD.Obs.Yr.1 == 5]

Empirical Results: LEQ vs. Rating & Time-to-Default Grids

• Similar table to this in Araten et al (2001)

• Average LEQs decrease (increase) almost montonically in worsening grade (longer time-to-default)

• Results not as clear-cut for either non-collared LEQ or CCF, EADF

<1 1 2 3 4 5 >5

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

CCC-CC 84 102 61 30 16 8 0 301

C 17 8 4 5 3 0 0 37NR 35 60 42 19 7 3 0 166

Total 263 526 369 215 128 78 3 1,582

<1 1 2 3 4 5 >5

AAA-BBB 43.44% 64.56% 65.26% 84.93% 92.86% 84.58% 0.00% 69.06%

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%

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%

<1 1 2 3 4 5 >5

AAA-BBB 45.75% 38.08% 40.54% 27.94% 12.39% 19.09% N/A 37.78%

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%

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%

Standard Deviation

Risk Rating

Time-to-Default (yrs)

Total

Average

Risk Rating

Time-to-Default (yrs)

Total

Rating

Time-to-Default (yrs)

Total

Table 2.1.1Estimated Collared Loan Equivalency Factors by Rating and Time-to-Default

S&P and Moodys Rated Defaulted Borrowers Revolving Lines of Credits 1985-2007Count

Empirical Results: EAD Risk Measures vs. Rating

• Generally a decrease in LEQ, CCF and EADF with worsening grade

• Does not hold monotonically for uncollared LEQ or un-Winsorized CCF, EADF

Figure 3: Average EAD Risk Measure by Rating Categories (S&P & Moody's Rated Defaults 1985-2007)

0.00%

50.00%

100.00%

150.00%

200.00%

250.00%

300.00%

350.00%

400.00%

AAA-BBB BB B CCC-CC C

Rating Group

EA

D M

ea

su

re

LEQ CCF EADF

Empirical Results: EAD Risk Measures by Year of Observation

• Where is the ”downturn EAD”?• How many banks look for it

• Define downturn as the default rate in the highest quintile • → DR > 6.8% (‘91-92,’01-03)

• A countercyclical effect can be seen (i.e., ↑ factors in mid-90s)• But 1st episode vs. 80s not so

clear (thin observations)

• Do we really expect higher EAD risk in downturns (but then what is the story here?)• Monitoring – “laxity” or ↑ cost

in good periods?

• Moral Hazard - incentives to overextend during expansion?

YearCnt of LEQ

Avg of LEQ1

Cnt of CCF

Avg of CCF2

Cnt of EADF

Avg of EADF3 Avg of Util5

Mdy's Spec

Grd Dflt Rate

1985 1 29.17% 1 103.10% 1 93.20% 90.40% 4.10%

1986 4 15.68% 4 103.63% 4 71.30% 77.02% 4.97%

1987 7 27.14% 7 209.44% 7 67.80% 68.79% 5.79%

1988 22 27.16% 21 203.18% 22 56.57% 57.51% 4.89%

1989 59 36.12% 52 153.51% 59 64.91% 55.53% 2.74%

1990 61 31.76% 59 167.52% 62 69.73% 62.31% 6.58%

1991 34 34.08% 34 126.45% 34 75.37% 72.32% 12.09%

1992 32 41.83% 31 185.09% 32 78.72% 62.68% 7.32%

1993 33 43.46% 32 141.39% 33 82.29% 65.59% 5.06%

1994 44 39.01% 42 199.40% 44 77.22% 57.34% 2.80%

1995 43 42.09% 39 174.40% 43 75.96% 55.91% 2.06%

1996 44 54.34% 38 218.06% 44 83.63% 46.95% 3.01%

1997 89 47.81% 71 232.62% 89 76.83% 40.05% 2.24%

1998 205 51.34% 162 242.20% 205 76.61% 38.78% 2.98%

1999 237 45.79% 195 206.65% 237 71.70% 45.80% 4.58%

2000 271 42.83% 204 194.02% 271 67.16% 44.39% 6.80%

2001 184 37.85% 150 165.86% 185 66.37% 49.34% 9.13%

2002 95 35.19% 86 151.30% 98 65.03% 53.80% 11.01%

2003 59 37.20% 53 169.15% 59 62.65% 55.01% 6.83%

2004 33 40.94% 27 168.12% 33 65.95% 44.81% 4.77%

2005 22 40.26% 19 201.48% 22 69.55% 46.24% 2.94%

2006 2 0.00% 2 88.07% 2 31.44% 56.76% 2.28%2007 1 0.00% 1 95.92% 1 53.41% 55.68% 1.63%

Total 1,582 42.21% 1,330 190.42% 1,587 70.76% 48.64% 5.17%

Table 4.1 - LEQ, CCF and EADF of Defaulted Instruments by Observation Year (S&P and Moody's Rated Defaults 1985-2007)

Empirical Results: EAD Risk Measures by Year of Default

• Grouping by default year and taking the observation 1-year back is akin to the “cohort approach” (CA) to EAD • Pure CA analogous to rating

agency default rate estimation • Same story here: still the cycle to

hard to detect in the “expected” direction• But why do people expect to

see this?• Evidence of countercyclicality

here, mainly from the 2nd downturn• EAD risk measures higher in

the benign mid-90’s

Year Dflt

Cnt of LEQ

Avg of LEQ1

Cnt of CCF

Avg of CCF2

Cnt of

EADFAvg of EADF3

Avg of Util5

Mdy's Spec

Grd Dflt Rate

1987 2 45.95% 10 110.59% 4 82.52% 90.40% 5.79%

1988 3 25.97% 16 180.88% 8 65.08% 77.02% 4.89%

1989 3 0.00% 11 277.41% 6 71.92% 68.79% 2.74%

1990 25 28.47% 79 119.56% 44 62.34% 57.51% 6.58%

1991 32 44.67% 127 160.69% 66 67.33% 55.53% 12.09%

1992 12 20.18% 59 238.46% 30 79.84% 62.31% 7.32%

1993 18 35.26% 79 124.55% 51 70.62% 72.32% 5.06%

1994 11 52.76% 65 150.90% 41 77.79% 62.68% 2.80%

1995 15 50.34% 74 177.61% 45 75.02% 65.59% 2.06%

1996 20 42.66% 73 169.87% 40 70.57% 57.34% 3.01%

1997 10 54.23% 47 224.12% 29 83.15% 55.91% 2.24%

1998 13 53.31% 43 218.91% 26 92.28% 46.95% 2.98%

1999 42 51.53% 135 167.20% 90 75.25% 40.05% 4.58%

2000 36 31.28% 157 179.93% 96 74.05% 38.78% 6.80%

2001 111 47.28% 741 230.71% 312 74.97% 45.80% 9.13%

2002 76 38.55% 380 210.54% 261 70.63% 44.39% 11.01%

2003 45 31.81% 260 166.22% 203 66.91% 49.34% 6.83%

2004 29 28.94% 164 157.30% 131 55.89% 53.80% 4.77%

2005 12 53.54% 67 221.29% 54 80.94% 55.01% 2.94%

2006 10 47.26% 51 250.14% 42 59.05% 44.81% 2.28%2007 1 0.00% 10 74.79% 8 21.30% 46.24% 1.63%

Total 526 40.81% 2,648 190.42% 1,587 70.76% 56.76% 5.17%

Table 5.1 - LEQ, CCF and EADF of Defaulted Instruments by Default Year and 1 Year Prior to Default (S&P and Moody's

Rated Defaults 1985-2007)

Empirical Results: EAD Risk Measures by Collateral & Seniority

• EAD risk is generally lower for better secured and more senior loans

• Mean LEQ 41% vs. 57% (39% vs. 51%) for secured vs. unsecured (senior vs. sub)

• Finally an “intuitive” result? (basis for some segmentations)

Senior SubJun Sub Total Senior Sub

Jun Sub Total Senior Sub

Jun Sub Total

Cnt 28 7 0 35 24 5 0 29 28 7 0 35

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%

Cnt 212 42 13 267 187 35 8 230 212 42 13 267

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%

Cnt 719 229 96 1044 641 171 72 884 722 230 96 1048

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%

Cnt 54 17 0 71 42 17 0 59 54 17 0 71

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%

Cnt 15 0 0 15 9 0 0 9 15 0 0 15

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%

Cnt 51 2 7 60 49 1 5 55 51 2 7 60

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%

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%

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%

Cnt 1141 323 118 1582 999 245 86 1330 1145 324 118 1587

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 Secured

Unsecured

Total Collateral

Capital Stock / Inter-company

Debt

Plant, Property & Equipment

Most Assets / Intellectual Property

Cash / Guarantees / Other Highly Inventories / Receivables / Other Current Second Lien /

Real Estate /All-Assets / Oil & Gas

Table 6.1.1 - EAD Risk Measures by Instrument and Major Collateral Types (S&P and Moody's Rated Defaults 1985-2007)1

LEQ2 CCF3 EADF4

• However, ample judgment applied in forming these high level collateral groupings from lower level labels

Empirical Results: EAD Risk Measures by Obligor Industry

• Difficult to discern an explainable pattern

• Utilities, Tech, Energy & Transportation above average for LEQ

Industry GroupCnt LEQ

Avg of LEQ

Cnt of CCF

Avg of CCF

Cnt of EADF

Avg of EADF

Avg of Rtg

Avg of Util

Avg of Commit

Aerospace / Auto / Capital Goods /

Equipment 225 40.1% 202 189.0% 227 68.5% 3.01 48.9% 120,843

Consumer / Service Sector 428 36.6% 374 186.3% 428 67.7% 3.02 48.2% 138,039

Energy / Natural Resources 162 47.7% 114 203.9% 162 74.0% 2.85 40.1% 304,305

Financial Institutions 11 45.3% 11 142.0% 11 72.2% 3.60 52.9% 33,722

Forest / Building Prodects / Homebuilders 40 29.0% 36 126.3% 40 64.3% 2.94 55.8% 114,421

Healthcare / Chemicals 149 38.5% 123 165.1% 150 69.5% 3.02 47.7% 168,155

High Technology / 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

Leisure Time / Media 167 46.1% 136 178.7% 167 72.2% 3.17 46.0% 150,574

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

Table 7.1.1 - LEQ, CCF and EADF of Defaulted Instruments and Obligors by Industry (S&P and Moody's Rated Defaults 1985-2007)

• Homebuilders & Consumer / Service below for LEQ• But rankings not

completely consistent across measures

• What could be the story? (e.g., tangibility & LGD)

Empirical Results: Correlations of EAD Risk Measures to Covariates

• Utilization strongest driver except in EADF

• TTD (rating) strongly + (-) → EAD risk

• Leverage, liquidity, profitability, tangibility (size) - (+) → EAD risk

• Better collateral rank, higher seniority, more debt cushion → lower EAD risk

• Countercyclical by speculative grade default rate (by industry too, but weaker)

• More % bank, secured debt -> higher EAD risk (monitoring/coordination story?)

• Cash flow → +EAD risk for LEQ & EADF (but weak & not in regressions)

LEQ CCF EADF

Utilization -33.50% -61.58% 1.03%

Commitment 2.51% -4.41% -6.88%

Drawndown Rate -4.38% -2.80% -2.76%

Cutback Rate 4.51% 1.52% 3.60%

Drawn -14.69% -18.58% -5.85%

Undrawn 9.54% 12.53% -5.08%

Time-to-Default 15.09% 18.14% 18.14%

Rating -17.80% -16.07% -11.28%

Leverage 1 - LTD/ MV -5.48% -10.20% 2.29%

Leverage 2 - TD / BV -6.62% 4.43% -5.48%

Size - log(Book Value) 17.80% 5.33% 7.37%

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 5.40% 1.96% 5.90%

Profitabilty - Profit Margin -7.77% -10.45% -4.53%

Discounted Ultimate LGD 10.02% 10.13% 9.29%

Market Implied LGD at Default 12.33% 16.48% 9.44%

Creditor Rank 7.06% 9.03% 2.00%

Colllateral Rank 15.94% 12.57% 11.85%

Debt Cushion -15.27% -10.35% -10.35%

Speculative Grade Default Rate -9.09% -9.53% -9.31%

Speculative Grade Default Rate - Industry -7.35% -7.36% -7.67%

Risk-Free Return 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%

Equity Market Value Factor (Fama-French) -1.58% -4.38% -4.63%

Cumulative Abnormal Equity Return -7.14% -9.38% -4.11%

Number of Creditor Classes 0.72% -2.51% -2.52%

Percent Secured Debt 17.35% 2.55% 14.67%

Percent Subordinateded Debt -4.10% -2.19% -4.38%

Percent Bank Debt 13.55% 8.50% 18.92%

Table 1.3 -Correlations of EAD Risk Measures to Database Attributes

S&P and Moodys Rated Defaulted Borrowers Revolving Lines

of Credits 1985-20071

• Equity markets – risk free rate & Fama French factors negative & small / weak

• Drawn (undrawn – ex EADF) + (-) EAD risk• CARs neg. corr but not in regressions

Econometric Modeling of EAD: Beta-Link Generalized Linear Model

• The distributional properties of EAD risk measures creates challenges in applying standard statistical techniques

• Here we borrow from the default prediction literature by adapting generalized linear models (GLMs) to the EAD setting

• Follow Mallick and Gelfand (Biometrika 1994) in which the link function is taken as a mixture of cumulative beta distributions vs. logistic

• We may always estimate the underlying parameters consistently and efficiently by maximizing the log-likelihood function (albeit numerically)

• Alternatives: robust / resistant statistics on raw LEQ, modeling of dollar EAD measures through quantile regression (Moral, 2006)

• Non-normality of EAD in general and collared LEQ factors in particular (boundary bias)

• OLS or even averaging across segments inappropriate or misleading

• See Maddalla (1981, 1983) for an introduction application to economics• Logistic regression in default prediction or PD modeling is a special case

• See Jacobs (2007) or Huang & Osterlee (2008) for applications to LGD

• Downside: computational overhead and interpretation of parameters

Econometric Modeling of EAD: Estimation Results (BLGLM Models)

• Estimates generally significant (but some p-values marginal), signs in line with univariate analysis & “good” fit

• Model selection process: alternating stepwise procedure applied judiciously (i.e., judgment again)

• Cutback Rate, Drawn and Undrawn in only one model?

• Different measure of leverage (book vs. market) in EADF model?

• CCF: best fit in-sample, but LEQ forecasts $ EAD the best

• Financials: larger, intangible, illiquid, unprofitable → higher EAD risk

• Utilization the strongest factor but only for LEQ and EADF

• Estimates supports countercyclicality

Partial Effect P-Value

Partial Effect P-Value

Partial Effect P-Value

Utilization5-0.3508 2.53E-06 -0.3881 6.52E-06

Commitment6 3.64E-05 0.0723Cutback Rate7

-1.74E-03 0.0658Drawn8

-0.0191 5.53E-07Undrawn9

3.27E-05 7.42E-03 2.20E-05 2.81E-06 7.45E-05 0.0441Time-to-Default10

0.0516 1.72E-05 0.3462 1.58E-06 0.0225 -2.08E-03Rating 111

-0.1442 0.0426 -0.2440 0.1015 -0.0503 0.1267Rating 211

-0.0681 6.20E-03 -0.1511 0.0835 -0.0093 0.3581Rating 311

-0.0735 1.03E-05 -0.1895 3.70E-03 -0.0079 0.0634Rating 411

-0.0502 2.08E-04 -0.1591 0.0977 -0.0135 0.0910Rating 511

-0.0110 0.1003 -0.0277 0.2278 -0.0068 0.1195Leverage 1 - LTD/ MV 15

-0.0515 0.0714 -0.1332 0.0276Leverage 2 - TD / BV 16

-0.0922 0.0065Size - log(Book Value)17

0.1154 2.63E-03 0.1855 0.0655 0.0463 0.1081Tangibility - Intang/TA18

0.0600 0.0214 0.0483 0.0878Liquidity - Current Ratio19

-0.0366 0.0251 -0.1110 0.0845 -0.0264 0.0960Profitabilty - Profit Margin21

-6.59E-04 0.0230 -5.79E-04 0.0265 -7.46E-05 0.0996Colllateral Rank18

0.0306 3.07E-03 0.0816 0.0277 0.0111 0.1027Debt Cushion19

-0.2801 5.18E-06 -0.5193 0.0122 -0.3073 7.34E-06Speculative Default Rate20

-0.9336 0.0635 -0.0928 0.0960 -0.1766 5.03E-04Percent Bank Debt21

0.2854 5.61E-06 0.3859 0.0928 0.3868 8.09E-03Percent Secured Debt22

0.1115 2.65E-03 0.1830 -2.71E-03

Degrees of FreedomLikelihood Ratio P-ValuePseudo R-SquaredSpearman Rank CorrelationMSE of Forecasted EAD 2.74E+15 7.53E+15 2.23E+17

0.4670 0.5618 0.41150.2040 0.2336 0.1611

Table 8 - Beta Link Generalized Linear Model Multiple Regression Models for EAD Risk Measures

S&P and Moodys Rated Defaulted Borrowers Revolving Lines of Credits (1985-2007)1

LEQ2 CCF3 EADF4

4567.48E-12 1.66E-19 7.62E-09

455 457

Econometric Modeling of EAD: Out-of-Sample & Out-of-Time Validation

• LEQ best by Pseudo R^2 (highest median, least dispersion)

• But hard to tell which is best by Spearman correlation (CCF/EADF higher/lower median but more/less dispersed)

• Non-normality of bootstrapped sampling distributions for statistics

• This shows how in-sample results can be misleading: massive divergence in performance across runs 0.1 0.3 0.5 0.7 0.9

McFadden Pseudo R-Squared

0

1

2

3

4

5

Pro

bab

ility

Den

sity

Fig.7 - Densities of McFadden Pseudo R-Squareds for EAD Prediction100,000 Repetitions Out-of-Sample and Out-of-Time 1995-2007

LEQCCFEADF

0.1 0.3 0.5 0.7 0.9

Spearman Correlations

0

1

2

3

4

5

Pro

babi

lity

De

nsity

Fig.8 - Densities of Spearman Rank Order Correlations for EAD Prediction100,000 Repetitions Out-of-Sample and Out-of-Time 1995-2007

LEQCCFEADF

Test Statistic Model LEQ3 CCF4 EADF5

Median 0.1839 0.1684 0.1084Standard Deviation 0.0255 0.0454 0.02605th Percentile 0.0826 0.0291 0.032995th Percentile 0.4151 0.5898 0.3042Median 0.3461 0.4218 0.3078Standard Deviation 0.0676 0.0887 0.06425th Percentile 0.2021 0.2427 0.179095th Percentile 0.4865 0.5997 0.4416

Table 10 - Bootstrapped1 Out-of-Sample and Out-of-Time Classification and Predictive Accuracy Model

Comparison Analysis of EAD Risk Measures S&P and Moodys Rated Defaulted Borrowers Revolving Lines of

Credits (1985-2007)2

McFadden Pseudo R-Squared

Spearman Rank

Correlation

Summary of Contributions and Major Findings

• Empirically investigated the determinants of, and built predictive econometric models for, measuring EAD risk

• Defined several metrics which in principle should all give the correct answer, but with different properties

• Built upon a limited practitioner literature, extending the prior empirical work of Araten et al (2001) and Asarnow et al (1995)

• Incorporate accounting, macro, capital structure, pre-default exposure determinants in addition to rating, utilization and tenor

• Various measures of EAD risk compared through a multiple regression model (BLGLM) & validated out-of-sample & -time

• “New Findings”: EAD risk found to increase (decrease) with company size, intangibility, % bank or secured debt (leverage, profitability, collateral quality, % debt cushion, seniority) & counter-cyclicality (i.e., elevated in expansions)

• CCF found to fit best in sample but LEQ measure found to forecast $ EAD best & best distribution of R2 out of sample

Directions for Future Research• Expand data-set (private companies, international) or type of

instruments (e.g., trade or financial letters of credit)

• Joint estimation of EAD with PD or LGD risk measures

• A theoretical model, wherein the parameter restrictions or functional forms could be subject to empirical falsification

• A more general framework to encompass all 3 measures of EAD risk (e.g., directly model dollar EAD)

• Alternatively, pursue econometric designs better capable of dealing with outliers (e.g., robust / resistant regression)