Transcript "An Empirical Study of Exposure at Default", Moody's KMV

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
•
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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 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
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 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”
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:



EADXt ,t,T = E t UTILX , |   T, Xt  E t AVAILX , |   T, Xt

• “Traditionally” estimated through an LEQ factor that is applied
to the current unused:
EAD Xt ,t,T  UTIL t  LEQ Xf ,t,T   AVAIL t  UTIL t 
t
LEQ
f
Xt ,t,T
 UTIL - UTIL t

 Et 
| τ  T, Xt 
 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
1
ˆ
Ti

LEQfX =

N X i=1  AVAIL Xt ,ti - UTIL Xt ,ti
i
i

Nx




Methodology: The Credit
Conversion Factor (CCF)
• An alternative approach estimates a credit conversion factor
(CCF) to be applied to the current outstanding (used amount):
EADXt ,t,T = UTILt ×CCFXf t ,t,T
• The CCF is simply the expected gross percent change in the
total outstanding:
f
Xt ,t,T
CCF
 AVAIL

 UTIL

= Et 
|   T, Xt  = E t 
|   T, Xt 
 UTILt

 UTIL t

• CCF can be estimated by averaging the observed percent
changes in outstandings:
1
fˆ
CCFX =
NX
NX

i=1
UTILX
TiD
,TiD
UTILXt ,ti
i
Methodology: The Exposure at Default
Factor (EADF) & Modeling of Dollar EAD
• Alternatively, dollar EAD may be factored into the product of
the current availability and an EAD factor:
EADXt ,t,T = AVAILt ×EADfXt ,t,T
• Where EADf is the expected gross change in the limit:
EAD
f
Xt ,t,T
 AVAIL

= Et 
|   T, Xt 
 AVAIL t

• May be estimated as the average of gross % limit changes:
1
EAD =
NX
fˆ
X
NX
AVAILX
 AVAIL
i=1
TiD
XXt
,TiD
,t
i i
• Most generally & least common, model dollar EAD as a function
of used / unused & covariates (Levonian, 2007) :



ˆ
EAD$  Yt   arg min E P  L EADYt  EAD$  Yt  


EAD$  Yt 
• Where Y=(X,AVAIL,UTIL,T,t), L(.) is a loss metric, and EP is
expectation with respect to physical (empirical) measure
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-ofcourt 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)
• Various $
exposure
measures:
EAD & ∆ to
default, drawn/
undrawn,
limits, “race to
default”
quantities
• LEQ (CCF &
EADF) 2 (3
• This conveys a sense of the extreme values observed here
types)
– 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
Table 1.1 - Summary Statistics on EAD Risk Measures
S&P and Moodys Rated Defaulted Borrowers Revolving Lines of Credits 1985-20071
Cnt
Exposure at Default
0
(EAD)
Dollar Change in Drawn
to EAD (DCDE)1
LEQ (Raw)
2
LEQ (Collared)
3
LEQ (Winsorized)4
CCF5
CCF (Winsorized)
EAD Factor6
EAD Factor (Winsorized)
Utilization6
Commitment7
Drawndown Rate8
Avg
530 133,140
Standard
Deviation Min
295,035
279,972
25th
Prcntl
5th Prcntl
158
2118
48,972
1582
63.72% 2759.66% -21000.00%
(3,177,300)
1582
1582
42.21%
16.80%
1,656
(3,177,300)
20,725
(2,056)
75th
Median Prcntl
116,234
508,232
4,250,000
4,250,000
231.76% 106250.00%
35.7617 1391.0651
0.00%
0.00%
-1165.74% -12.75%
33.28%
33.28%
87.64%
87.64%
100.00%
231.76%
0.3054
-1.9084
198.86%
198.86%
860.29% 704054.38%
855.66%
860.29%
95.96%
95.96%
152.86% 106250.00%
152.39%
152.86%
85.30% 111.11%
85.30% 111.11%
1587
1587
143.40% 2666.07%
70.76%
36.94%
0.37%
11.24%
0.37%
11.24%
42.46%
42.46%
0.00%
0.00%
14.00%
48.04%
217
217
40,000
80,000
0.39%
116.0538
275,400
87.64%
0.47%
26.29%
879
6.8444
36,617
0.47%
26.29%
32.85%
82.1857
7,514
1061.8% 20032.7%
190.4%
203.4%
383,442
7.5099
33.28%
1330
1330
45.85%
Kurtosis
-21000.00% -12.75%
0.00%
-1165.74%
1621 184,027
Skew
50,000
40.92%
210.38%
1621
95th Prcntl Max
70.67%
70.67%
74.27%
176,400
95.00%
570,000
100.00%
804.43%
100.00%
4,250,000
-1.5700
13.5038
32.9416 1145.3158
2.27
4.45
39.80
0.29
1584.89
-0.39
-0.06
-1.35
6.24
48.28
7.00%
-0.10%
-0.10%
-0.02%
0.01%
0.05%
0.41%
181.97%
23.17
561.82
88.50% 2791.11%
-96.07%
-96.07%
0.00%
0.00%
0.00%
66.67%
93650.00%
33.54
1125.34
163,029
0
0
5,557
26,463
76,900
260,000
3,090,000
8.41
107.87
329,695
0
0
13,082
34,099
82,300
396,500
4,250,000
7.79
73.49
Cutback Rate9
1126
Drawn10
Undrawn11
1621
71,576
773
112,450
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
0.0
0.004
Figure 1.1: Raw LEQ Factor (S&P and Moody's Rated Defaults 1985-2007)
-200
0
200
400
600
800
1000
EAD.Data.0$LEQ.Obs
0.0
0.10
0.25
Figure 1.2: W insorized LEQ Factor (S&P and Moody's Rated Defaults 1985-2007)
-10
-5
0
• Consistency with
common practice
• Numerical instability
of others ->
estimation problems
5
EAD.Data.0$LEQ.Obs.Wind
0
1
2
3
4
Figure 1.3: Collared LEQ Factor (S&P and Moody's Rated Defaults 1985-2007)
0.0
0.2
0.4
0.6
EAD.Data.0$LEQ.Obs.Coll
0.8
1.0
Empirical Results: Distributions of
EAD Risk Measures (continued)
• More stable than
LEQs
Figure 2.2: Winsorized CCF
• Natural floor at 0%
0.4
0.0015
0.6
Figure 2.1: Raw CCF
0.0
0.0
0.0005
0.2
• Choose Winsorized
measures
0
6000
4000
2000
0
4
2
6
8
EAD.Data.0$CCF.Obs.Wind
S&P and Moody's Rated Defaults 1985-2007
EAD.Data.0$CCF.Obs
S&P and Moody's Rated Defaults 1985-2007
Figure 2.4: Winsorized EADF
Figure 2.3: Raw EADF
1.5
• Multi-modality
(especially EADF)?
1.0
0.008
0.0
0.5
0.004
0.0
0
200
400
600
800
EAD.Data.0$EAD.Fact.Obs
S&P and Moody's Rated Defaults 1985-2007
1000
• As with LEQ,
estimation issues
with raw
0.0
0.5
1.0
EAD.Data.0$EAD.Fact.Obs.Wind
S&P and Moody's Rated Defaults 1985-2007
1.5
Empirical Results: Estimation
Regions of EAD Risk Measures
Table 3.2
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
• 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
• But this tendency to “quirky” values attenuated for worse rating and shorter
time-to-default
LEQ
Risk
Rating
Region
<0
=0
.(0,1)
=1
>1
Years-toDefau;t
Region
<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%
CCF
Risk
Rating
<0
Region
.(0,1)
=0
=1
>1
Years-toDefau;t
<0
=0
Region
.(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%
=1
>1
EADF
Risk
Rating
<0
Region
.(0,1)
=0
=1
>1
Years-toDefau;t
<0
=0
Region
.(0,1)
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%
Empirical Results: Summary
Statistics (Covariates)
•
•
•
Availability of
fin. ratios
limited vs.
instrument, cap
structure &
macro
Companies
highly levered,
unprofitable,
intangible,
negative cash
flow
Low LGDs (top
of the capital
structure)
Empirical Results: Distributions of
LEQ by Rating
Fig 3.2: Collared LEQ Factor (Ratings AAA-BBB)
0
0
1
1
2
2
3
3
4
5
4
Fig 3.1: Collared LEQ Factor (All Ratings)
0.0
0.2
0.4
0.6
0.8
1.0
0.0
EAD.Data.0$LEQ.Obs.Coll
0.2
0.4
0.6
0.8
1.0
EAD.Data.0$LEQ.Obs.Coll[EAD.Data.0$Rtg.Num.Obs == 1]
Fig 3.4: Collared LEQ Factor (Ratings B)
• But similar
bimodal shape
across all grades
0
0
1
1
2
2
3
3
4
Fig 3.3: Collared LEQ Factor (Ratings BB)
0.0
0.2
0.4
0.6
0.8
1.0
0.0
EAD.Data.0$LEQ.Obs.Coll[EAD.Data.0$Rtg.Num == 2]
0.2
0.4
0.6
0.8
1.0
EAD.Data.0$LEQ.Obs.Coll[EAD.Data.0$Rtg.Num == 3]
Fig 3.6: Collared LEQ Factor (Ratings C)
0
0
1
1
2
2
3
3
4
Fig 3.5: Collared LEQ Factor (Ratings CCC-CC)
0.0
0.2
0.4
0.6
• Clear shift of
probability mass
from 1 to zero as
grade worsens
0.8
EAD.Data.0$LEQ.Obs.Coll[EAD.Data.0$Rtg.Num == 4]
1.0
0.0
0.2
0.4
0.6
0.8
EAD.Data.0$LEQ.Obs.Coll[EAD.Data.0$Rtg.Num == 5]
1.0
Empirical Results: Distributions of
LEQ by Time-to-Default
Fig 34.2: Collared LEQ Factor (1 Year-to-Default)
0
0
1
1
2
2
3
3
4
4
Fig 4.1: Collared LEQ Factor (All Times-to-Default)
0.0
0.2
0.4
0.6
0.8
1.0
0.0
EAD.Data.0$LEQ.Obs.Coll
0.2
0.4
0.6
0.8
1.0
EAD.Data.0$LEQ.Obs.Coll[EAD.Data.0$TTD.Obs.Yr.1 == 1]
Fig 4.4: Collared LEQ Factor (3 Year-to-Default)
0
0.0
1
1.0
2
2.0
3
3.0
Fig 4.3: Collared LEQ Factor (2 Year-to-Default)
• Clear shift of
probability mass
from zero to 1 as
time-to-default
lengthens
0.0
0.2
0.4
0.6
0.8
1.0
0.0
EAD.Data.0$LEQ.Obs.Coll[EAD.Data.0$TTD.Obs.Yr.1 == 2]
0.2
0.4
0.6
0.8
1.0
EAD.Data.0$LEQ.Obs.Coll[EAD.Data.0$TTD.Obs.Yr.1 == 3]
Fig 4.6: Collared LEQ Factor (5 Year-to-Default)
0
0
1
1
2
2
3
3
Fig 4.5: Collared LEQ Factor (4 Year-to-Default)
0.0
0.2
0.4
0.6
0.8
EAD.Data.0$LEQ.Obs.Coll[EAD.Data.0$TTD.Obs.Yr.1 == 4]
1.0
0.0
0.2
0.4
0.6
0.8
EAD.Data.0$LEQ.Obs.Coll[EAD.Data.0$TTD.Obs.Yr.1 == 5]
1.0
• But similar
bimodal shape
across all TTDs
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
Count
Rating
<1
1
2
Time-to-Default (yrs)
3
4
5
>5
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
CCC-CC
84
102
61
30
16
8
0
301
C
NR
17
35
8
60
4
42
5
19
3
7
0
3
0
0
37
166
Total
263
526
369
215
128
78
3
1,582
Average
Risk
Rating
Time-to-Default (yrs)
3
<1
1
2
4
5
AAA-BBB
43.44%
64.56%
65.26%
84.93%
92.86%
84.58%
BB
27.82%
38.90%
42.13%
45.91%
43.91%
B
33.14%
41.51%
43.92%
42.60%
52.77%
CCC-CC
22.29%
32.97%
47.38%
54.80%
C
NR
9.91%
33.17%
28.21%
37.73%
9.71%
39.79%
Total
28.35%
40.81%
44.89%
>5
Total
0.00%
69.06%
42.35%
0.00%
40.79%
49.94%
14.00%
42.66%
55.05%
55.30%
0.00%
36.85%
47.64%
37.88%
25.67%
44.61%
0.00%
82.39%
0.00%
0.00%
20.22%
38.40%
47.79%
54.00%
52.05%
14.00%
42.21%
Standard Deviation
Risk
Rating
Time-to-Default (yrs)
3
<1
1
2
4
5
AAA-BBB
45.75%
38.08%
40.54%
27.94%
12.39%
19.09%
>5
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
NR
28.43%
46.50%
44.72%
43.02%
14.10%
41.09%
24.78%
40.79%
23.10%
41.57%
N/A
30.51%
N/A
N/A
32.34%
42.73%
Total
40.40%
40.58%
39.37%
40.12%
42.10%
40.48%
16.37%
40.92%
Total
• Similar table to this in
Araten et al (2001)
• Average LEQs
decrease (increase)
almost montonically in
worsening grade
(longer time-todefault)
• Results not as clearcut for either noncollared LEQ or CCF,
EADF
Empirical Results: EAD Risk
Measures vs. Rating
Figure 3: Average EAD Risk Measure by Rating Categories (S&P & Moody's Rated
Defaults 1985-2007)
• Generally a
decrease in
LEQ, CCF and
EADF with
worsening
grade
400.00%
350.00%
EAD Measure
300.00%
250.00%
200.00%
150.00%
100.00%
50.00%
0.00%
AAA-BBB
BB
B
Rating Group
CCC-CC
C
LEQ
CCF
EADF
• Does not hold
monotonically
for uncollared
LEQ or unWinsorized
CCF, EADF
Empirical Results: EAD Risk
Measures by Year of Observation
Table 4.1 - LEQ, CCF and EADF of Defaulted Instruments by
Observation Year (S&P and Moody's Rated Defaults 1985-2007)
Year
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
Total
Cnt of Avg of
1
LEQ
LEQ
1 29.17%
4 15.68%
7 27.14%
22 27.16%
59 36.12%
61 31.76%
34 34.08%
32 41.83%
33 43.46%
44 39.01%
43 42.09%
44 54.34%
89 47.81%
205 51.34%
237 45.79%
271 42.83%
184 37.85%
95 35.19%
59 37.20%
33 40.94%
22 40.26%
2
0.00%
1
0.00%
1,582
42.21%
Cnt of
CCF
1
4
7
21
52
59
34
31
32
42
39
38
71
162
195
204
150
86
53
27
19
2
1
Avg of
2
CCF
103.10%
103.63%
209.44%
203.18%
153.51%
167.52%
126.45%
185.09%
141.39%
199.40%
174.40%
218.06%
232.62%
242.20%
206.65%
194.02%
165.86%
151.30%
169.15%
168.12%
201.48%
88.07%
95.92%
1,330 190.42%
Cnt of
EADF
1
4
7
22
59
62
34
32
33
44
43
44
89
205
237
271
185
98
59
33
22
2
1
1,587
Avg of
3
5
EADF
Avg of Util
93.20%
90.40%
71.30%
77.02%
67.80%
68.79%
56.57%
57.51%
64.91%
55.53%
69.73%
62.31%
75.37%
72.32%
78.72%
62.68%
82.29%
65.59%
77.22%
57.34%
75.96%
55.91%
83.63%
46.95%
76.83%
40.05%
76.61%
38.78%
71.70%
45.80%
67.16%
44.39%
66.37%
49.34%
65.03%
53.80%
62.65%
55.01%
65.95%
44.81%
69.55%
46.24%
31.44%
56.76%
53.41%
55.68%
70.76%
48.64%
Mdy's
Spec
Grd Dflt
Rate
4.10%
4.97%
5.79%
4.89%
2.74%
6.58%
12.09%
7.32%
5.06%
2.80%
2.06%
3.01%
2.24%
2.98%
4.58%
6.80%
9.13%
11.01%
6.83%
4.77%
2.94%
2.28%
1.63%
5.17%
• 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?
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
Rated Defaults 1985-2007)
Year
Dflt
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
Total
Cnt of Avg of Cnt of Avg of
LEQ
LEQ1
CCF
CCF2
2 45.95%
10 110.59%
3 25.97%
16 180.88%
3
0.00%
11 277.41%
25 28.47%
79 119.56%
32 44.67%
127 160.69%
12 20.18%
59 238.46%
18 35.26%
79 124.55%
11 52.76%
65 150.90%
15 50.34%
74 177.61%
20 42.66%
73 169.87%
10 54.23%
47 224.12%
13 53.31%
43 218.91%
42 51.53%
135 167.20%
36 31.28%
157 179.93%
111 47.28%
741 230.71%
76 38.55%
380 210.54%
45 31.81%
260 166.22%
29 28.94%
164 157.30%
12 53.54%
67 221.29%
10 47.26%
51 250.14%
1
0.00%
10 74.79%
526
Mdy's
Cnt
Spec
Avg of Avg of Grd Dflt
of
EADF EADF3
Util5
Rate
4 82.52% 90.40%
5.79%
8 65.08% 77.02%
4.89%
6 71.92% 68.79%
2.74%
44 62.34% 57.51%
6.58%
66 67.33% 55.53% 12.09%
30 79.84% 62.31%
7.32%
51 70.62% 72.32%
5.06%
41 77.79% 62.68%
2.80%
45 75.02% 65.59%
2.06%
40 70.57% 57.34%
3.01%
29 83.15% 55.91%
2.24%
26 92.28% 46.95%
2.98%
90 75.25% 40.05%
4.58%
96 74.05% 38.78%
6.80%
312 74.97% 45.80%
9.13%
261 70.63% 44.39% 11.01%
203 66.91% 49.34%
6.83%
131 55.89% 53.80%
4.77%
54 80.94% 55.01%
2.94%
42 59.05% 44.81%
2.28%
8 21.30% 46.24%
1.63%
40.81% 2,648 190.42% 1,587
70.76%
56.76%
5.17%
• 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
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
Defaults 1985-2007)1
LEQ2
Cash /
Guarantees /
Other Highly
Inventories /
Receivables /
Other Current
Second Lien /
Real Estate /AllAssets / Oil & Gas
Capital Stock /
Inter-company
Debt
Plant, Property &
Equipment
Most Assets /
Intellectual
Property
Total Secured
Unsecured
Senior
Jun
Sub
Sub
Total
Senior
Cnt
28
7
0
35
Avg
17.7%
26.9%
N/A
19.6%
Cnt
212
42
13
267
Avg
32.6%
56.4%
46.1%
Cnt
719
229
96
Avg
38.0%
48.9%
44.3%
Cnt
54
17
0
Avg
51.9%
44.8%
N/A
Cnt
15
0
0
15
9
0
Avg
N/A
0.0%
N/A
53.9%
N/A
0.0%
Cnt
51
2
7
60
49
1
Avg
61.2%
98.7%
85.5%
Cnt
1079
297
116
Avg
37.7%
49.6%
54.0%
Cnt
62
26
2
Avg
53.1%
67.5%
44.9%
Cnt
1141
323
118
Total
Senior
EADF4
Jun
Sub
Sub
Total
5
0
29
28
7
0
35
77.4% 204.7%
N/A
99.4%
44.6%
86.3%
N/A
44.5%
8
230
212
42
13
267
37.0% 160.3% 255.4% 269.3% 178.6%
63.7%
86.3%
60.6%
67.1%
884
722
230
96
1048
41.0% 172.4% 220.9% 221.6% 185.8%
69.1%
72.0%
73.6%
70.2%
59
54
17
0
71
N/A 156.6%
84.4%
71.6%
N/A
81.3%
9
15
0
0
15
N/A 226.3%
65.7%
0.0%
N/A
65.7%
51
2
7
60
88.7% 112.5% 113.8%
92.4%
1044
71
24
CCF3
Jun
Sub
Sub
187
641
42
35
171
17
50.2% 150.8% 171.1%
65.2% 327.5% 429.8%
1492
0
5
55
N/A 335.4%
1082
298
116
1496
41.3% 173.0% 223.0% 260.2% 187.9%
69.1%
73.6%
74.6%
70.4%
64
63
26
2
91
57.1% 224.7% 292.0% 126.5% 240.0%
77.3%
75.7%
1145
324
47
229
0
1266
90
952
72
16
85
1
63.2% 76.54%
• 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
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
“intuitive” result?
(basis for some
• However, ample judgment applied in forming these
high level collateral groupings from lower level labels segmentations)
1582
999
245
86
1330
118
1587
Empirical Results: EAD Risk
Measures by Obligor Industry
Table 7.1.1 - LEQ, CCF and EADF of Defaulted Instruments and Obligors by
Industry (S&P and Moody's Rated Defaults 1985-2007)
Industry Group
Aerospace / Auto /
Capital Goods /
Equipment
Cnt
LEQ
Avg of Cnt of Avg of Cnt of Avg of
LEQ
CCF
CCF EADF EADF
Avg
of
Avg
Avg of
Rtg of Util Commit
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
6 50.0%
6 233.9%
6
67.2%
2.50 42.2%
233,267
1,582 42.2% 1,330 190.4% 1,587
70.8%
2.99 48.6%
181,118
Utilities
Total
• Difficult to discern an
explainable pattern
• Utilities, Tech, Energy &
Transportation above
average for LEQ
• 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
• More % bank, secured debt -> higher
EAD risk (monitoring/coordination story?)
• Countercyclical by speculative grade
default rate (by industry too, but weaker)
• Cash flow → +EAD risk for LEQ & EADF
(but weak & not in regressions)
• 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
•
•
Non-normality of EAD in general and collared LEQ factors in particular
(boundary bias)
OLS or even averaging across segments inappropriate or misleading
• 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)
Econometric Modeling of EAD:
Estimation Results (BLGLM Models)
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
2
LEQ
Partial
Effect
Utilization5
Commitment6
CCF
P-Value
-0.3508
2.53E-06
3.64E-05
0.0723
Partial
Effect
3
4
EADF
P-Value
-0.3881
6.52E-06
-0.0191
5.53E-07
Cutback Rate7
Drawn8
Undrawn
9
Time-to-Default10
3.27E-05
7.42E-03
2.20E-05
2.81E-06
0.0516
1.72E-05
0.3462
1.58E-06
Partial
Effect
P-Value
-1.74E-03
0.0658
7.45E-05
0.0441
0.0225 -2.08E-03
Rating 111
-0.1442
0.0426
-0.2440
0.1015
-0.0503
0.1267
11
-0.0681
6.20E-03
-0.1511
0.0835
-0.0093
0.3581
Rating 311
-0.0735
1.03E-05
-0.1895
3.70E-03
-0.0079
0.0634
Rating 411
-0.0502
2.08E-04
-0.1591
0.0977
-0.0135
0.0910
11
-0.0110
0.1003
-0.0277
0.2278
-0.0068
0.1195
-0.0515
0.0714
-0.1332
0.0276
-0.0922
0.0065
0.1154
2.63E-03
0.1855
0.0655
0.0463
0.1081
0.0600
0.0214
0.0483
0.0878
-0.0366
0.0251
-0.0264
0.0960
0.0265 -7.46E-05
0.0996
Rating 2
Rating 5
Leverage 1 - LTD/ MV 15
Leverage 2 - TD / BV 16
Size - log(Book Value)17
Tangibility - Intang/TA
18
Liquidity - Current Ratio
19
Profitabilty - Profit Margin
21
Colllateral Rank18
-6.59E-04
-0.1110
0.0230 -5.79E-04
0.0845
0.0306
3.07E-03
0.0816
0.0277
0.0111
0.1027
Debt Cushion19
-0.2801
5.18E-06
-0.5193
0.0122
-0.3073
7.34E-06
Speculative Default Rate20
-0.9336
0.0635
-0.0928
0.0960
-0.1766
5.03E-04
0.2854
5.61E-06
0.3859
0.0928
0.3868
8.09E-03
0.1115
2.65E-03
Percent Bank Debt21
Percent Secured Debt22
Degrees of Freedom
Likelihood Ratio P-Value
Pseudo R-Squared
Spearman Rank Correlation
MSE of Forecasted EAD
455
7.48E-12
0.2040
0.4670
2.74E+15
0.1830 -2.71E-03
457
1.66E-19
0.2336
0.5618
7.53E+15
456
7.62E-09
0.1611
0.4115
2.23E+17
• 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)
• Utilization the strongest factor but
only for LEQ and EADF
• Cutback Rate, Drawn and Undrawn
in only one model?
• Different measure of leverage (book
vs. market) in EADF model?
• Financials: larger, intangible, illiquid,
unprofitable → higher EAD risk
• CCF: best fit in-sample, but LEQ
forecasts $ EAD the best
• Estimates supports countercyclicality
Econometric Modeling of EAD: Outof-Sample & Out-of-Time Validation
Fig.7 - Densities of McFadden Pseudo R-Squareds for EAD Prediction
100,000 Repetitions Out-of-Sample and Out-of-Time 1995-2007
LEQ
CCF
EADF
5
Probability Density
4
Table 10 - Bootstrapped1 Out-of-Sample and Out-ofTime Classification and Predictive Accuracy Model
Comparison Analysis of EAD Risk Measures
• This shows
how in-sample
S&P and Moodys Rated Defaulted Borrowers Revolving Lines of
Credits (1985-2007)
results can be
Test Statistic Model
LEQ
CCF
EADF
misleading:
Median
0.1839
0.1684
0.1084
0.0255
0.0454
0.0260 massive
McFadden Standard Deviation
0.0826
0.0291
0.0329
Pseudo R- 5th Percentile
0.4151
0.5898
0.3042 divergence in
Squared 95th Percentile
Median
0.3461
0.4218
0.3078
Standard
Deviation
0.0676
0.0887
0.0642 performance
Spearman
5th Percentile
0.2021
0.2427
0.1790
Rank
0.4865
0.5997
0.4416 across runs
Correlation 95th Percentile
2
3
3
2
1
0
0.1
0.3
0.5
0.7
0.9
4
5
McFadden Pseudo R-Squared
Fig.8 - Densities of Spearman Rank Order Correlations for EAD Prediction
100,000 Repetitions Out-of-Sample and Out-of-Time 1995-2007
LEQ
CCF
EADF
5
Probability Density
4
3
2
1
0
0.1
0.3
0.5
Spearman Correlations
0.7
0.9
• 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
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)
• 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)
• A theoretical model, wherein the parameter restrictions or
functional forms could be subject to empirical falsification
• Joint estimation of EAD with PD or LGD risk measures