W.Mussil / CRM 2001 - February 1st, 2001
Credit Risk Modellingand Analysis in Practice
DI Walter MUSSIL
Bank Austria AG
CRM 2001
Vienna, February 1st, 2001
Abbreviated Handout Version
W.Mussil / CRM 2001 - February 1st, 2001
Overview
- Basic concepts
- Level 1: The rating model
- Level 2: The portfolio model
- Sidestep: Using simulation models - Parameter effects
- Portfolio management
W.Mussil / CRM 2001 - February 1st, 2001
Basic concepts: Risk vs. Return
TO APPLY RAROC ACROSS THE CREDIT BOOK WE NEED TO KNOW THE PARAMETERS
+ Margin
Expected Loss
- Cost
+ Capital Benefit
= Profit before tax
Economic capital
-
= RAROC
Analysis of
portfoliodefaulted
Severity
Loan Equivalency Loss
given default
of economicParameters
capital (UL)
Lossparameter
Expected
Projects Measures Risk Parameters RAROC-Calculation
Grading Corp.
Expected DefaultFrequency
Correlations &Concentrations
Grading Intl.
Project, CRE,Leveraged
PortfolioModel
Grading SME
W.Mussil / CRM 2001 - February 1st, 2001
Level 1 - The rating model: Major steps
1) Analysis of portfolio / Requirements
2) Building of model
3) Implementation / Institutionalization
W.Mussil / CRM 2001 - February 1st, 2001
Level 1 - The rating model: Requirements
- Analysis of portfolio structure
- Determine level of detail / seperate modelling
DomesticDeveloped Markets
Emerging Markets
Eastern Europe
Private x xSME x xCorporates x x x xLeveragedFinancialsProject & R. EstateCountries x
Clie
nt
Region
xxx
W.Mussil / CRM 2001 - February 1st, 2001
Level 1 - The rating model: Building of model
Raw financialcompany data
Defaultprobability
Calibration
Internal rating
Weighting
The short way: calibrating the old model
W.Mussil / CRM 2001 - February 1st, 2001
0.01
0.10
1
10
100
EDF
RatingR1 R2 R3 R4 R5
Level 1 - The rating model: Building of model
But: Usually large overlaps can be observed
W.Mussil / CRM 2001 - February 1st, 2001
Level 1 - The rating model: Building of model
Defaultprobability
Calibration
Internal rating
Raw financialcompany data
QualitativeFactors
Warningsignals
Weighting
Transformation
Building a new model
W.Mussil / CRM 2001 - February 1st, 2001
DATA-COLLECTION
SINGLE-FACTOR
ANALYSIS
FACTOR-COMBINATIONS
(CORRELATIONS)
WEIGHTINGand TEST
CALIBRATION
- Customer Data- External Data- Rating-Agencies
- Selection / Definition- Analysis of discriminatory power
-> Short list
- Elimination of highlycorrelated factors
-> opt.combination
- Determination of factor weightings
- Test
- Calibration tomaster scale
Level 1 - The rating model: Building process
The necessary steps for building a statistical rating model are:
W.Mussil / CRM 2001 - February 1st, 2001
Level 1 - The rating model: Theory
[1..K]kRfP kkk ∈∀= )(
)(~
kPfP =
)( iPi Pfp =
- Determine transformation function for each ratio
- Calibrate to get default probabilities for each company i
- Find optimal parametrization for the sample space
with Rk financial / economic ratioK total number of ratios
W.Mussil / CRM 2001 - February 1st, 2001
Level 1-The rating model: Practice
0
5
10
15
20
25
30
0.02
0.07
0.12
0.17
0.22
0.27
0.31
0.36
0.41
0.46
0.51
0.56
0.60
0.65
0.70
0.75
0.80
0.85
0.89
0.94
0.99
0
0.2
0.4
0.6
0.8
1Ratio distribution
Transformed ratio vs. defaults
# of
obs
erva
tions
defa
ult p
roba
bilit
y in
%
cum
. pro
babi
lity
0.37
0.40
0.43
0.46
0.48
0.51
0.54
0.57
0.60
0.63
0.66
0.69
0.72
0.75
0.78
0.80
0.83
0.86
0.89
0.92
0.95
Bucket-EDF
+1 StdDev
Fit
W.Mussil / CRM 2001 - February 1st, 2001
STATISTICAL ANALYSIS:
Measure predictive power of single factors
Identify optimal weights for combining highly predictive and economically important factors (multi-linearregressions)
Compare various models withhigh discriminatory power,according to economic criteria
EXPERT DISCUSSIONS:
- Accounting Experts- Research Group- Risk Management- External benchmarks - Experience
. . . SINCE THERE EXISTS LIMITED DATA, EXPERT DISCUSSIONS PLAY AN ESSENTIAL ROLE
Level 1 - The rating model: Building processThe rating system should be the result of a combination ofstatistical analysis and expert discussions ...
W.Mussil / CRM 2001 - February 1st, 2001
DATA-COLLECTION
STATISTICALANALYSIS
40%
Level 1 - The rating model: Time consumption
Building several rating models has shown a common profile:
EXPERTDISCUSSIONS /
BENCHMARKING
30%
30%
W.Mussil / CRM 2001 - February 1st, 2001
Level 1 - The rating model: Implementation
A) Building of IT-application:- centralized data warehouse in uniform format- modular system
- usage throughout the whole bank
B) Definition of "Rating Rules" (guideline)
C) Installation of rating-process
Time Horizon: 7 - 9 months
W.Mussil / CRM 2001 - February 1st, 2001
Level 2 - The portfolio model: Major steps
1) Specification of portfolio-model
2) Data collection
3) Parametrization
4) Prototype for reconciliation and structuring
5) Implementation and reporting
W.Mussil / CRM 2001 - February 1st, 2001
MODELSPEZIFICATION
DATACOLLECTION
20%
Level 2 - The portfolio model: Time consumption
Data collection and parametrization are the most important steps
EXPERTDISCUSSIONS
40%
10%
PARAMETRIZATION 30%
W.Mussil / CRM 2001 - February 1st, 2001
Level 2 - The portfolio model: The process
Portfoliodata
Rawcorporate
data
ClusterCreditqualityunify
Stat.analysis
Modelparameters
(Correlations)
Macroeconomicdata
Scenarios
Simulationengine
- Default model- NPV model
Lossdistribution
W.Mussil / CRM 2001 - February 1st, 2001
Level 2 - The portfolio model: Theory part 1
{ }ttp ii ≤= τPr)(
( )ii p1−=χ
- Start with the unconditional default probability of obligor i ...
... and transform it into an unconditional credit quality
- A change in orthogonal economic factor returns mj results in a change in credit quality ...
... which leads to a conditional default probability for each scenario
, with τi time of default
∑
∑−=
⋅+⋅==
2
1
1
]1,0[~,;)())(|(
iji
ii
M
jjiji Niidmtmtmt
βσ
εεσβδ
{ }
⋅−=≤= ∑
i
iiii
tmtmttmtp
σβχ
τ )()(|Pr))(|(
Φ
Φ
W.Mussil / CRM 2001 - February 1st, 2001
Level 2 - The portfolio model: Clustering
Comp 1
Comp 2
Comp n
.
.
.
.
.
.
.
.
Time serie for each company
Cluster 1
Cluster 2
Cluster m
.
.
.
.
C_1
C_2
C_m
Time serie for each cluster
Transformation
Grouping
- Grouping companies into clusters reduces complexity dramatically
W.Mussil / CRM 2001 - February 1st, 2001
Level 2 - The portfolio model: Macroeconomic factors
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Dec
-91
Jun-
92
Dec
-92
Jun-
93
Dec
-93
Jun-
94
Dec
-94
Jun-
95
Dec
-95
Jun-
96
Dec
-96
Jun-
97
Dec
-97
Actual
Predicted
Change in Credit Quality
Clusters responded well to the macro-economy
W.Mussil / CRM 2001 - February 1st, 2001
Level 2 - The portfolio model: Theory part 2
( ) ( ) ( )[ ])(1)()( tmtmXtmLGD iii η−⋅=- After modelling default probabilities we need to focus on exposure
with Xi conditional exposure of obligor iηi conditional recovery rate
- Now we can calculate conditional loss distributions for each obligor resp. for the whole portfolio
Full monte carlo simulation leads finally to the portfolio loss distribution
{ } )()(|Pr || xLyLmyLossx mimii −=<<{ } )()(|Pr || xLyLmyLossx mPFmPFPF −=<<
with θ(m) pdf of scenarios
{ } { }∫ <<=<<m
PFPF mdmyLossxyLossx )(|PrPr θ
W.Mussil / CRM 2001 - February 1st, 2001
Level 2 - The portfolio model: Simulation Framework
INPUTDATA
CLIENT /CLUSTERCHARACTERISTICS
• Exposure• Colleterals• Margin• Rating
• Factorweights
FACTOR-CORRELATIONS
MONTE-CARLO SIMULATION
SZENARIO 1PORTFOLIO-REACTION
T O SZENARIO
DEquityDFX
DUnemp
==••=
-20%+5%
+2%
SZENARIO 2
SZENARIO 3
•
•
SZENARIO N*
DEquityDFX
DUnemp
==••=
+15%+0.5%
-0.5%
% C hange in Value, % Losses
Probability Density
•
••
Probability Density
% C hange in Value, % Losses
The loss distribution is generated with a Monte-Carlo-Simulation of theunderlying macro factors
5.00%0.00%-5.00%-10.00%
SIMULATED LOSS- &NPV-DISTRIBUTION
%NPV-Change, % Loss
Probability
Loss
NPV
W.Mussil / CRM 2001 - February 1st, 2001
Sidestep - Using simulation models
To determine complete loss distribution:
- Usually calculation of 10.000s scenarios necessary (even with sophisticated sampling techniques)
⇒ compared to analytical solutions a little more time consuming
But: - Calculation can easily be "distributed"- Results are much more transparent- Illiquid portfolios can be modelled- Much higher flexibility
W.Mussil / CRM 2001 - February 1st, 2001
Sidestep - Using simulation models
Using intranet-technology increases speed enormously...
Client 1 Virtual parallel computing
Client 4
Client 3
Client 2
Server 2
C1
C4
C2
C3
Server 1
W.Mussil / CRM 2001 - February 1st, 2001
Sidestep - Using simulation models
- A Client-Server-Client concept coordinates calculations throughout the whole network
Client 1
Client 4
Client 3
Client 2
Server 2
C1
C4
C2
C3
Server 1
W.Mussil / CRM 2001 - February 1st, 2001
Sidestep - Using simulation models
Each scenario leads to a conditional expected and unexpected loss
W.Mussil / CRM 2001 - February 1st, 2001
Level 2 - The portfolio model: Loss Distribution
To determine the discrete loss distribution all scenarios are aggregated
ELULUL
Economic capital 99,9..% cumulative loss distribution
Aggregated Loss Distribution
0%
1%
2%
3%
4%
5%
6%
Pro
babi
lity
Loss
W.Mussil / CRM 2001 - February 1st, 2001
Level 2 - The portfolio model: Sensitivity Analysis
Dramatic changes in macro-economic factors can result in extremelyhigh losses.
Conditional Loss x.x%Probability 0.25% (1x all 400 years)
Loss
S&P +xx%Trade-weighted EURO +xx%Raw materials index -xx%EURO ST-IR +x,x% absolut
W.Mussil / CRM 2001 - February 1st, 2001
Parameter effects: EDF
Sample calculations help to point out influences of parametrization...
0,0%
0,2%
0,4%
0,6%
0,8%
1,0%
1,2%
1,4%
1,6%
0% 1% 2% 3% 4% 5% 6% 7%
EDF -10%
EDF +10%base case
EL UL Capital AA1,49% 0,82% 6,08%1,66% 0,88% 6,39%1,83% 0,93% 6,66%
Sample portfolio size: 300 Mrd ATS
W.Mussil / CRM 2001 - February 1st, 2001
Parameter effects: Correlation vs. stochastic severity
Changes in correlation also have high impact on UL and capital ...
avg rho asset UL AA -10% rel.chg 17% 0,83% 5,85%base case 19% 0,88% 6,39% +10% rel.chg 21% 0,93% 6,93%high level 50% 2,68% 26,63%even higher level 80% 4,03% 42,65%
σSEV UL AA
0% 0,880% 6,39%30% 0,882% 6,39%50% 0,885% 6,41%
... but modelling volatility of severity has only small effects
W.Mussil / CRM 2001 - February 1st, 2001
Portfolio Management: RAROC I
xx%
xx%
xx%
xx%
Ind A
Ind B
Ind C
Ind E
Ind D
Ind L
Ind KInd JInd HInd GInd F Ind I
RAROC
Economic Capital (ATS bn)
Analysis of different industry-segments shows us clearly the loss leaders.
W.Mussil / CRM 2001 - February 1st, 2001
Portfolio Management: RAROC II
xx%
xx%
xx%
Capital (ATS bn)
RAROC %
R1 R2 R3 R4 R5 RATING
Risk adjusted profitability looks similar across and within rating classes.
W.Mussil / CRM 2001 - February 1st, 2001
Portfolio Management: Risk contributions
Systematic analysis of risk contributions helps to find concetrations andto optimize the portfolio
1
2
3
4
5
6
7
8
9
101 2 3 4 5 6 7 8 9 10
INDUSTR
REGI
ON
1
2
3
4
5
6
7
8
9
101 2 3 4 5 6 7 8 9 10
INDUSTRY
REGI
ON
ECONOMIC CAPITAL
High capital consumptionLow capital consumption
1
2
3
4
5
6
7
8
9
101 2 3 4 5 6 7 8 9 10
INDUSTR
REGI
ON
1
2
3
4
5
6
7
8
9
101 2 3 4 5 6 7 8 9 10
INDUSTRY
REGI
ON
RAROC
Low RAROCHigh RAROC
W.Mussil / CRM 2001 - February 1st, 2001
Portfolio Management: A „real“ sample picture
Sample snapshot of BA - credit risk portfolio application
W.Mussil / CRM 2001 - February 1st, 2001
A sample calculation illustrates the impact of concentration on capital requirements
Portfolio Management: Risk concentration
4,0%
4,5%
5,0%
5,5%
6,0%
6,5%
7,0%
0,33% 0,11% 0,03% 0,01%
Avg Size in % Exp
Cap
ital i
n %
Exp
AA
A
BBB
Avg size % exp AA A BBB
0,111% 1.415 1.210 1.0840,033% 1.402 1.184 1.0710,011% 1.393 1.166 1.071
Economic capital in million Euro
0,333% 1.476 1.275 1.140
Portfolio size: 22 bn Euro
W.Mussil / CRM 2001 - February 1st, 2001
0,01% 0,03% 0,1% 0,3%1% 3%
0%
1%
10%
0x%
1x%
2x%
3x%
4x%
5x%
Margin
% Exposure
EDF
To reach the same level of RAROC concentration effects need to beconsidered in pricing
Portfolio Management: Pricing
W.Mussil / CRM 2001 - February 1st, 2001
The modelling circle: Possible steps
PORTFOLIOOPTIMIZATION
DATA QUALITY
CALCULATION-TOOL
REPORTING
Clean information
More detailed resultsResults on transactionlevel
Demand for more detailed information
BALANCE BETWEEN
• Model complexity• Accuracy• Computational efficiency• Tractability• Transparency• Expenses
W.Mussil / CRM 2001 - February 1st, 2001
Concluding remarks
Rating Models- Usually one year period for complete re-rating- Risk mitigation / transfer
Portfolio Models- Homogenity in clusters- Benchmarks / use of analogues- Don‘t trust the stats blindly
And generally...- New BIZ requires high flexibility in models- Right balance between theory and practice