Convergence of Credit Capital
Models
ISDA Seminar-July 18, 2006
IACPM ISDA Study Objectives
• For a hypothetical, large corporate portfolio with all
data elements specified evaluate the degree of
convergence of economic capital estimates across
commercially available models and across internal
models as implemented by financial institutions
– Provide benchmarks to participating firms of
methodologies for capital estimation and allocation
as practiced by peers
– Use results to demonstrate to regulators the
degree to which regulatory capital can be
estimated using banks internal models
2
Summary Conclusions
• Economic capital models employed by
firms can for the most part be shown to
converge in their estimates of portfoliolevel capital requirements, given the
same data assumptions.
• Where differences arise, a road map of
the modeling assumptions can be used
to reconcile these differences.
3
Project Overview
• Mini-survey to determine modeling practices
• Development of a representative portfolio of
transactions with pre-specified risk
parameters
– Separating out modeling approaches vs. data
assumptions
• Phase 1:Analysis of overall levels of portfolio
capital
• Phase 2: Sensitivity analysis
• Phase 3: Allocation to individual exposures
4
Project Structure
•
•
•
•
Joint venture between IACPM and ISDA
28 financial institutions participated
Steering Committee for governance
Consultant (Rutter Associates) for
confidentiality, tabulation of results, and
running two vendor models
• Project results published in February
2006 after a two-year period
5
Models and mini survey results
• Participants were using three vended models
– Moody’s KMV Portfolio Manager (PM)
– RiskMetrics Group CreditManager (CM)
– Credit Suisse CreditRisk+ (CR+).
• and internally-developed models
• Of the 28 participants
– 12 obtain eco capital directly from vended models
– 6 obtain eco capital from internal models using the
output from vended models
– 8 obtain eco capital from internally-developed models
that are similar to vended models
– 2 obtain eco capital from internally-developed models
that are significantly different from the vended models
6
Test Portfolio
• 3,000 obligors 2 term loans each → $100 billion portfolio
• Obligors
– 61 M-KMV industries (643 NAICS industry codes)
– 7 countries
– 8 whole-grade rating buckets
• Term Loans:
– Principal: $1MM to $1,250MM
– Tenor: 6 months to 7 years
– LGD: 22% to 58%
• Correlation(R2): 10% to 65%.
• Contractual spreads: Chosen such that initial MTM value
of exposures is approximately par
7
Portfolio exposure by industry
ISDA/IIF Industry Name
Automobiles
Banking and Finance
Broadcasting & media
Chemicals
Construction & building mat
Electronics
Energy
Entertainment
Food
General
Health care & Pharmaceuticals
Hotels
Insurance
Machinery
Manufacturing
Metals Mining
Oil & gas - refining & marketi
Paper & forest products
Publishing
Technology
Telecommunications
Textiles
Transportation
Utilities
Total
No.
Avg Exp Avg R
Expos. ($000s) Obligors ($000s)
Count
7,985,000
64 124,766
11,331,000
179
63,302
3,745,000
32 117,031
4,095,000
108
37,917
3,685,000
125
29,480
1,933,000
95
20,347
4,667,000
127
36,748
979,000
163
6,006
2,138,000
170
12,576
4,943,000
201
24,592
1,049,000
103
10,184
1,221,000
122
10,008
2,946,000
133
22,150
2,895,000
194
14,923
5,684,000
151
37,642
2,960,000
64
46,250
7,715,000
112
68,884
3,669,000
133
27,586
2,459,000
128
19,211
5,377,000
135
39,830
9,350,000
112
83,482
575,000
44
13,068
4,439,000
135
32,881
4,160,000
170
24,471
100,000,000
3,000
33,333
8
by
30%
21%
24%
25%
15%
21%
26%
13%
14%
13%
11%
14%
28%
19%
16%
25%
23%
19%
14%
22%
28%
14%
20%
27%
20%
Avg R by $
Exposure
49.0%
45.7%
36.3%
35.7%
33.7%
38.1%
36.6%
15.3%
19.2%
26.4%
19.8%
18.3%
38.0%
36.0%
48.4%
32.8%
37.6%
34.1%
22.0%
35.9%
41.5%
15.2%
39.9%
41.9%
37.9%
Portfolio credit quality
Number Alpha
Total Exp
No.
Rating
Rating ($000s)
Obligors
1
AAA
3,332,000
87
2
AA
6,640,000
213
3
A
20,667,000
568
4
BBB
38,862,000
1192
5
BB
20,513,000
637
6
B
7,259,000
190
7
CCC
1,843,000
79
8
CC
884,000
34
Total
100,000,000
3,000
Exposure weighted Average
4.00
Simple Average
4.05
9
LGD exposure distribution
LGD Exposure Distribution
12,000,000
10,000,000
Exposure
8,000,000
6,000,000
4,000,000
2,000,000
0
0.22
0.24
0.26
0.28
0.3
0.32
0.34
0.36
0.38
0.4
LGD
0.42
0.44
10
0.46
0.48
0.5
0.52
0.54
0.56
0.58
Exposure distribution
Exposure ($000s)
1,000
2,000
5,000
10,000
15,000
25,000
50,000
75,000
100,000
150,000
200,000
250,000
500,000
750,000
1,000,000
1,250,000
Number
382
509
660
421
236
262
239
102
33
39
35
17
46
8
7
4
Total
11
Total Exp ($000s)
382,000
1,018,000
3,300,000
4,210,000
3,540,000
6,550,000
11,950,000
7,650,000
3,300,000
5,850,000
7,000,000
4,250,000
23,000,000
6,000,000
7,000,000
5,000,000
100,000,000
Project Phases
1. Compare aggregate eco capital
– “Default Only” and “Mark-to-Market”
modes
– “Base” and “Production” settings
2. Compare changes in aggregate economic
capital associated with changes in data
assumptions and risk parameters
3. Compare economic capital attributed to a
selection of individual transactions and
cohorts
12
Phase 1 – Default Only Mode
• Initial model results seem to produce very different
estimates
Default Mode (maturities capped at 1 yr)
Expected Loss
Eco Capital
(99.90% Conf Level
PM and Similar Models
790
4,420
CM and Similar Models
566
3,817
CR+ and Similar Models
564
3,387
Basel II (caps, floor, min .03 bps)
607
3,345
• Expected Loss differences greatest for poor quality
exposures whose coupons were highest (were priced
at par)
13
Phase 1 – Default only mode
• However, the difference results from the way the models treat
the 3-, 6-, 9- and 12-month interest payments if default is
simulated to have occurred at the one-year horizon.
– PM: Obligor defaults on all coupons; all coupons that were
owed between time zero and horizon are included in EAD.
– CM and CR+: Obligor pays all of the coupons; loss is limited
to principal
• If PM is run with CM/CR+ assumptions (no coupons)
Default Mode (Maturity capped at 1 year)
Expected
Loss
Eco Capital
PM with spreads and risk-free rate set to zero
563
3,791
CM
562
3,533
CR+
564
3,662
14
Phase 1 – Mark-to-Market mode
Also showed significant differences in estimates
MTM mode (full maturities)
Expected
Loss
Eco Capital
PM and Similar Models
790
5,618
CM and Similar Models
761
4,823
Basel II (caps, floors, min 1
yr maturity, ,03 bps)
607
4208
Leading to further evaluation of treatment of coupons
and correlations
15
Coupon and correlation analysis
Spreads, Coupons & RiskFree Rates SET EQUAL TO
ZERO
Industries
61
Industries
One Industry
“Unassigned”
61 Industries
One Industry
“Unassigned”
Countries
7
Countries
One country
(“US”)
7 Countries
One country
(“US”)
DEFAULT ONLY MODE
EL Difference*
34%
34%
0%
0%
Eco Cap Difference*
25%
20%
3%
-1%
EL Difference*
8%
8%
-34%
-34%
Eco Cap Difference *
25%
19%
19%
12%
MARK TO MARKET MODE
*Uses PM values as base (PM-CM)/PM
16
Further analysis of MTM differences
• Application of LGD to principal and
coupons also arises in MTM mode.
• Point in Time at which Eco Capital is
reported
• PM: Time zero.
• CM: Horizon
• Remaining differences result from varying
assumptions regarding matching EDF term
structure to transition matrices, valuation at
horizon
17
Phase 2-sensitivity analysis (DO/MTM)
PM &
similar
models
CM &
similar
models
CR+ &
similar
models
Basel II
Segment Portfolio into IG and NIG
10% / 7%
16% / 12%
14% / NA
No Chg
Chg all countries to US
46% / 43%
20% / 19%
5% / NA
No Chg
Chg all industries to “Unassigned”
9% / 7%
32% / 32%
1% / NA
No Chg
Chg all to “US” and “Unassigned”
87% / 80%
77% / 76%
8% / NA
No Chg
Increase 1 Telecom
from 5MM to 1,005MM
0.1% / 0.4%
0.1% / 0.2%
0% / NA
0.2% / 0.4%
from 5MM to 5,005MM
1.2% / 2.6%
1.7% / 9.1%
6% / NA
0.8% / 2.2%
8% / 6%
8% / 6%
8% / NA
6% / 6%
Increase all LGDs by 20%
16% / 15%
17% / 15%
20% / NA
20% / 20%
Increase all R2 by 20%
15% / 15%
15% / 14%
15% / NA
No Chg
Increase all PDs by 20%
18
Phase 3- allocation to transactions
• 23 participants provided risk contributions for 8
individual exposures and 2 cohorts
• Participants asked to characterize their risk
contributions:
– Mode: “Default Only” or “Mark-to-Market”
– Type of Risk Contribution: “Standard-deviation-based”
risk contribution or “Tail-based” risk contribution
– Use of risk contribution: Performance measurement or
Pricing
• As expected, risk contributions exhibited
significant dispersion.
19
Summary
• Credit capital models in use by major financial
institutions can be shown to converge in overall level
of results
• Differences can be traced to assumptions regarding
lost coupons, correlations, and in MTM mode (vs.
DO) term structure and horizon valuation
assumptions
• Sensitivity analysis shows generally consistent
results (Basel lI proformas by construction invariant
to portfolio composition)
• Allocations to individual exposures reflects varied
purposes of these measures and different
approaches to risk management
20