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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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 )