Commercial Banking - Goethe

Transcrição

Schwerpunkt Finanzen
Johann Wolfgang Goethe Universität, Frankfurt (Main)
Prof. Dr. Mark Wahrenburg
und Dr. Peter Raupach
Commercial Banking
4-stündige Vorlesung mit Übung im SS 2002
© Commercial Banking
The last decade has seen an increase in the demand and
possibilities for credit risk management
Driving forces:
Impact:
New methods for credit risk
measurement
Rating systems
Evolving market for credit risk
Credit derivatives and securitization
Bank regulation (Basle II)
(mainly) Rating systems
Shareholder-value management in
banks requires risk assessment
Credit portfolio management
Credit portfolio management
RAROC / EVA Tools
Purpose and objectives
Rating systems
Purpose
Learn how the credit risk of individual obligations can
be measured through ratings
Objectives
Understand dimensions of credit losses
Understand differences between rating systems
Learn how to implement particular rating systems
Learn how ratings are used in the Basle II proposal
Expected credit loss (from default) is default probability × loss
given default × exposure at default
Dimensions of credit risk
Which losses will you
suffer on average?
What is the likelihood that a
borrower becomes insolvent?
Expected loss
=
EL
=
Probability of default
=
PD
X
What is your exposure to
the borrower in case
of insolvency?
Exposure at default
=
EAD
X
How much of your nominal
exposure will be lost
in case of insolvency?
Loss given default
=
LGD
Verwendungsbereiche von Rating
• Aufsichtsbehörden / Eigenkapitalregulierung
– Basel
– National bank regulators
• Securitization
– Bewertung von Collateralized Loan Obligations
• Strategisches Management
– ROE/EVA
– Entry/Exit Entscheidung
• Kreditmanagement
– Vorprüfung von Kreditanträgen
– Kreditvergabeentscheidung (ja/nein)
– Marking to Market des Kreditportfolios
– Überwachung von Engagements (work-out)
– Bildung von EWBs
– Pricing / Konditionstafeln
– Incentive compensation
The dimensions of credit risk need to be exactly defined
When is loss given default measured?
– initiation / end of bankruptcy procedures
– emergence of: liquidation, settlement, completion of restructuring)
What constitutes a default?
– missed payments
– distressed exchanges
– bankruptcy
What probability of default shall be measured?
– time horizon (usually 1 year)
– point in time perspective or rating through the cycle
Basle II proposes a definition of default based on four criteria
Basle 2 definition of default event:
(a) It is determined that the obligor is unlikely to pay its debt obligations
(principal, interest, or fees) in full.
(b) A credit loss event associated with any obligation of the obligor, such as a
charge-off, specific provision, or distressed restructuring involving the
forgiveness or postponement of principal, interest, or fees.
(c) The obligor is past due more than 90 days on any credit obligation
(d) The obligor has filed for bankruptcy or similar protection from creditors.
Measuring default probability through-the-cycle abstracts
from the current position in the credit cycle
Permanent
deterioration of
credit quality
Credit quality
under neutral
conditions
Credit quality
under neutral
conditions
Current position
in cycle
no rating
change
rating
change
no rating
change
Because of its medium term perspective, a through-the-cycle
approach may contain valuable information
Consider investing in a 10-year corporate bond
You plan to sell the bond in one year
Question:
One year default probability sufficient for assessing the risk of your position?
Answer:
No. If the bond has not defaulted, the price in one year depends on the
default probabilities prevailing in one year.
Ideally, you have a complete term-structure of default probabilities.
A long term average (rating through-the-cycle) is useful
Rating systems can distinguish between long-term and shortterm risk, and between issue and issuer risk
Issuer rating: an assessment of an obligor’s overall financial capacity to pay
its financial obligations
Issue rating: creditworthiness of an obligor with respect to a specific financial
obligation
Short-term rating (pertaining to obligations with an original maturity of no more
than 365 days)
Long-term rating: covers all obligations
S&P rating
grades
High credit quality
Low credit quality
Long-term
rating
Short-term
rating
AAA
AA
A
BBB
BB
B
CCC
A-1
A-2
A-3
B
C
Rating modifyers allow better differentiaton of risk
High credit quality
Investment grade
Non-investment
grade
Low credit quality
Rating
category
Rating modifiers
(+, flat, -)
AAA
AA
A
BBB
BB
B
CCC
AAA
AA+, AA, AAA+, A, ABBB+, BBB, BBBBB+, BB, BBB+, B, BCCC
Rating may also be continuous, e.g. equal to the estimated default probability
Bank often map their internal Rating system to
external ratings
Internal
Grade
S&P
1 year EDF Equivalent
AAA - A
Moody's
Equivalent
Group
Aaa - A2
Investment grades
-
0.01-0.07%
1
0.08%
A-
A3
2
0.12%
BBB+
Baa1
3
0.18%
BBB
Baa2
4
0.27%
BBB-
5
0.41%
BB+
6
0.61%
BB+
7
0.91%
BB
8
1.37%
9
2.05%
10
3.08%
11
4.61%
B
B1
12
6.92%
B-
B2
13
10.38%
CCC
B3
BBB+
14
CC, C
15
D
Baa3
Active business grades
Ba1
Ba2
Ba3
High yield grades
Watchlist
Defaulted
Default probabilities for a rating grade can be derived
from historical default frequencies for issuers of that
grade
Rating
AAA
AA
A
BBB
BB
B
CCC
Percentage defaulted after year
2
3
4
5
0.00
0.05
0.11
0.17
0.02
0.07
0.15
0.27
0.12
0.21
0.36
0.56
0.54
0.85
1.52
2.19
3.4
6.32
9.38
12.38
12.36 19.03 24.28 31.66
33.52 41.13 47.43 54.25
1
0.00
0.00
0.04
0.24
1.01
5.45
23.69
10
1.00
0.96
2.06
5.03
23.69
42.24
60.91
less observations available
* Quelle: S&P, 1981-1998.
As with default probabilities, probabilities for rating
migrations can be estimated with historical data
S&P transition matrix (1981-1998)
Rating at year end (%)
Initial
Rating
AAA
AA
A
BBB
BB
B
CCC
AAA
AA
A
BBB
BB
B
CCC
D
91.94
0.64
0.07
0.04
0.04
0.00
0.19
7.46
91.79
2.27
0.27
0.10
0.10
0.00
0.48
6.76
91.68
5.56
0.61
0.28
0.37
0.08
0.60
5.12
87.87
7.75
0.46
0.75
0.04
0.06
0.56
4.83
81.48
6.95
2.43
0.00
0.12
0.25
1.02
7.90
82.80
12.13
0.00
0.03
0.01
0.17
1.11
3.96
60.44
0.00
0.00
0.04
0.24
1.01
5.45
23.69
Rating systems differ in the concept of credit loss they employ
Through-the-cycle expected loss
– Moody’s ratings
Through-the-cycle probability of default
– Standard & Poor’s ratings
– Fitch IBCA ratings
Point in time probability of default
– Internal ratings of banks (typically)
– KMV (KealhoferMcQuownVasicek)
– Moody’s Riskcalc (default probabilities for private firms)
Rating systems differ in the way they aggregate information
There are various ways of deriving ratings from information about credit quality
Methods for weighting
individual indicators
Indicators of
credit quality:
- leverage
- profitability
- management
- stock price
- ...
Judgmental / expert system
Theoretical reasoning
Statistical analysis
(Discriminant Analysis,
Logistic Regression,
Neural Networks, ...)
Hybrid
Rating
Grundlage jeden Ratings: Vergleich von „gut“ und
„schlecht“
Gesunde Unternehmen
Ausfallsample
Kunde Merkmale
EWB- Merkmale
Fall
A
B C...
X
A
1
1
2
2
3
3
.
.
.
.
.
.
N
K
B C...
X
Vergleich der
Ausprägungen
ZIEL IST DIE ERMITTLUNG DER INDIVIDUELLEN TRENNSCHÄRFE VON
KENNGRÖSSEN
They are other reasons whey ratings can differ
Incentives faced by raters
– are raters paid by borrowers? (solicited / unsolicited ratings)
– are raters involved in credit approval or other business with the borrower?
– it the rater “betting his money” on his rating?
– could a rating revision signal bad quality of the initial rating?
Frequency of rating revisions
Type of information that enters the rating process
– public information
– personal interviews / private information
– analysts information
Indicators of default probabilities: retail clients
Information obtained through loan request
– occupation
– salary
– marital status, children
– assets and liabilities
– age, sex, education
– domicile (ZIP-code)
Information from checking account
– length and amount of overdrafts
– pays bills in time
– spending behavior
General information
– regional unemployment rate
– observed trends in default frequency of customer segment
Indicators of default probabilities: corporate clients
Firm-specific accounting information
– profit margins
– interest rate coverage
– leverage
– sales
Other firm-specific information
– forecasts of earnings, sales etc.
– management quality
– competitive position
Financial market variables
– stock and bond prices (of borrower or comparable firms)
– stock price volatility
Macroeconomic variables
– profitability in industry
– interest rate level, term structure of interest rates
The most important financial indicators are profitability and
leverage
Median financial ratios for S&P rating categories
EBIT interest coverage
Free oper. Cash flow / total debt
Return on capital
Operating income / Sales
Total debt / total capital
Total sales (bil $)
AAA
18
55
28
29
27
21
AA
11
25
23
21
36
13
A
7
16
20
18
40
5
Source: S&P Special Report, September 20, 2000
Qualitative Credit Risk Assesment: Stepwi
1. Bilanzanalyse
2. Qualität der Rechnungslegung
3. Management Qualität & Soft
Factors
4. Industrie-Rating
5. Tier Position innerhalb Industrie
6. Länderisiko
7. Garantien dritter Parteien
8. Vertragsstruktur
9. Sicherheiten
BBB
4
7
14
15
47
2
BB
2
2
12
15
61
0.8
B
1
-5
7
11
75
0.4
1. Bilanzanalyse
• Qualität, Liquidationswert der Aktiva
– Korrektur um Eigentumsvorbehalte und andere vorrangige
Rechte Dritter
• Profitabilität
– ordentliche / außerordentliche Erträge
– Kapitalrentabilität
• Cash Flow/ EBITDA
– Operating Cash Flow / Fremdkapital
– Schuldendienstkapazität (z.B. EBITDA/Zinsen p.a.)
• Liquidität
– kurzfr. Vermögen/ kurzfr. FK
• Leverage (Verschuldungsgrad)
Unternehmensanalyse ff.
• Zyklizität/Schwankungen von Earnings / Cash Flows
• Zugang zu Kapitalmärkten
• Private Reserven der Gesellschafter/ Zugang zu
Hausbankfinanzierung
• Marktkapitalisierung, book-to-market-Verhältnis
Benchmarking von Bilanzkennziffern gegen S&P-Daten
S&P Medianwerte Industrial Comp. AAA
EBIT / Zinszahlung
16
EBITDA / Zinszahlung
20
Vorsteuer Gesamtkapitalrentabilität
77
Operating Income / Sales
24
Langfristiges FK / Gesamtes FK
13
FK / Gesamtkapital
23
AA
11
15
30
19
22
29
A
6
8
19
16
32
39
BBB
4
6
8
15
43
47
BB
2
4
2
15
54
56
Quelle: S&P Corporate Ratings Criteria, 1998
2. Qualität der Rechnungslegung / Berichterstattung
• Pünktlichkeit
• Vollständigkeit
• Plausibilität von Angaben
• Identität von Wirtschaftsprüfer / Aufsichtsrat etc.
B
1
2
1
13
66
69
3. Soft Factors
• Beobachtbare Kontobewegungen
• Risiken: Umwelt / Schadenersatzklagen...
• Ausbildung / Erfahrung des Management Teams
• Risikomanagementprozess des Unternehmens
• Plausibilität / Stringenz der Unternehmensplanung
4. Industrie-Rating
• Wachstumstrends
• Kapazitätsauslastung
• Profitabilitätstrends
• Innovationsintensität
• Regulierung
• Konjunkturabhängigkeit
• Wettbewerbsintensität
5. Tier Position innerhalb der Industrie
• Marktanteil
• Strategie (Kostenführer / Technologieführer,
Nischenplayer...)
• Ausnutzung von Skaleneffekten
• Homogenität der Produkte und Wettbewerbsintensität
6. Länderrisiko
• Anleihespread über US-Treasuries
• Hermes-Exportbürgschaftspreise
• Länder-Risikoanalyse mit Zahlungsbilanz-, Makrodaten
etc.
7. Garantien dritter Parteien
• Implizite / explizite Garantie durch Konzernmutter
• Bürgschaften von Gesellschaftern, „Friends & Relatives“
• offenstehende Kreditlinien anderer Banken
8. Kreditvertragsstruktur
• Vorzeitige Kündigungsrechte durch Bank
• Vorzeitige Fälligkeit bei „material adverse change“
• Schutz vor Reichtumsverschiebungen durch
Gewinnausschüttungen / vorrangiges Fremdkapital
9. Sicherheiten
• Bewertung und Wertschwankungsrisiko
• Korrelation von Wertschwankung und Kreditwürdigkeit
• Durchsetzbarkeit der Ansprüche / Verwertbarkeit
– kollidierende Ansprüche
– Vollstreckungssperre im Insolvenzverfahren
Statistical methods use historical data to derive optimal weights
for credit quality indicators
Observations on past credit losses are coded into a variable y
(0= no default, 1= no default)
Set up functional relationship between y and variables x1, x2,...xN
y= f(x1, x2,...xN)
Estimation of functional relationship f (.) based on some optimality criterion
– minimize squared prediction error [ y - f(x1, x2,...xN)]²
– maximum likelihood
– minimize probability of misclassification
Statistical Models require good data feeds for calibration
Data basis of several systems
Fitzpatrick
Beaver
Altman
Lev
Wilcox
Deakin
Edmister
Blum
Taffler
Libby
Diamond
Altman, Haldeman and Narayanan
Marais
Dambolena and Khoury
Ohlson
Taffler
El Hennawy and Morris
Moyer
Taffler
Zmijewski
Zavgren
Casey and Bartczak
Peel and Peel
Barniv and Raveh
Boothe and Hutchninson
Gupta, Rao, and Bagchi
Kease and McGuiness
Keasey, McGuiness and Short
Shumway
Moody’s RiskCalc Public Firm
Moody’s RiskCalc Private Firm
Median
Year
Defaults
Non-Defaults
(32)
19
19
(67)
79
79
(68)
33
33
(71)
37
37
(71)
52
52
(72)
32
32
(72)
42
42
(74)
115
115
(74)
23
45
(75)
30
30
(76)
75
75
(77)
53
58
(79)
38
53
(80)
23
23
(80)
105
2,000
(82, 83)
46
46
(83a)
22
22
(84)
35
35
(84)
22
49
(84)
40
800
(85)
45
45
(85)
60
230
(88)
35
44
(89)
58
142
(89)
33
33
(90)
60
60
(90)
43
43
(90)
40
40
(96)
300
1,822
(00)
1,406
13,041
(00)
1,621
23,089
40
45
Logitanalyse zur Schätzung der Ausfallwahrscheinlichkeit
• Modell:
Z = ß1 x1 + ß2 x2 + ... + ε ("Score" )
1
(logistische Funktion)
1 + e −Z
ß : zu schätzendeRegressionskoeffizienten
p(def ) =
P(def)
1
x : Faktorausprägungen
• Dateninput: Sample von Krediten mit Outcome (p = 1 oder 0)
• Modellschätzung: Suche ß‘s, die Prognosegüte maximieren
• Output: p(def) für gegebene Faktorausprägungen
• Probleme:
– Wahl einer repräsentativen Stichprobe für
Modellkalibrierung
– Konstanz der Parameter im Zeitablauf unterstellt
Auswahl der Faktoren
Z
Diskriminanzanalyse
Z = ß1 x1 + ß2 x2 + ... + ε ("Score" )
Wahrscheinlichkeit
Sample: Kein Konkurs
Sample: Konkurs
Z
Z*
Schlechte Kredite akzeptiert (Typ 1 Fehler)
Gute Kredite abgelehnt (Typ 2 Fehler)
Ziel: Suche ß‘s, die (mit Stabw normierten) Gruppenmittelwert-Abstand maximieren.
Output: 1. Z* (⇒ Klassenzuordnung)
2. Wahrscheinlichkeit einer Fehlklassifikation (aus Z-Z*)
Relationship between credit risk indicators and default
probability is often non-linear
Leverage (%)
Median leverage (total debt / total capital) for S&P rating grades compared with
historical default probabilities for the respective grades
80
70
60
50
40
30
20
10
0
0%
1%
2%
3%
4%
Default probability
5%
6%
Rating systems should allow for non-linearities in the relation
between credit risk and credit risk indicators
The scoring method (widely used in banks) uses a linear combination of credit
risk indicators xi with weights bi
Credit risk score =
Σi bi xi
(The scoring method does not produce default probabilities since
score is not constrained to lie between 0 and 1)
The probit regression is one method for nonlinear estimation:
1,0
y=Φ[bi xi]
0,8
Φ= cumulative normal
0,6
distribution function
0,4
0,2
0,0
x
An aside: standardized rating procedures are not
necessarily based on statistical procedures for weighting
credit risk indicators
Many banks use scoring methods for their ratings
Often, the weights have been set judgmentally
⇒ The rating is standardized but not based on a statistical optimization of the
weights (e.g. using discriminant analysis)
Example: Moodys Rating-System RiscCalc
• Anspruch: Transparentes Benchmarksystem schaffen
Æ nur „hard data“ verwendet
Æ nur Bilanzdaten gehen ein
Ziele:
• Verständlichkeit
• Statistische Power
• Trennschärfe (Unterscheidung)
• Kalibrierung an PODs
• Empirisch validierbar
Schritt 1: Transformation der Inputvariablen
Schritt 2: Schätzung eines multivariaten Probitmodels
y = prob(default) = Φ{ f ( x, B)}
Φ(x)
1
x
f ( x, B ) = B0 + T1 ( x1 ) B1 + T2 ( x2 ) B2 + ... + T10 ( x10 ) B10
Schritt 3: Anpassung des Modells an empirische
Ausfallwahrscheinlichkeiten
Results: Input variables of Moody’s RiskCalc
Accounting Variable
Weight
Profitability
Capital Structure
Liquidity
Size
Sales Growth
Trading Accounts
23%
21%
19%
14%
12%
12%
Source: Moody‘s (2000): RiskCalc private model: Moody‘s default model for private firms
Option pricint theory can be used to derive default probabilities
( Merton model)
Firm is solvent, if value of assets > value of liabilities
Firm is insolvent otherwise
Default probability is the probability that the value of total assets falls below
the value of liabilities
This probability can be determined if we know
– the current asset value
– the distribution of future asset value changes
– the value of liabilities
To estimate the distance to default we need assumptions about
the evolution of the asset value
Assume: firm’s debt consists only of a 1 year zero bond
asset value is
distributed lognormally
Possible paths
Market value in t0
1+µ
Equity
Assets
Liabilities
probability
of default
Pay Offs of Debt and Equity in the Merton Model
Value of Debt =
Value of Assets
./. Value of Put
Wert FK in T
or:
Value of Zerobond
./. Value of Call
D
Value of Equity =
Value of Call
D
Wert der Aktiva in T
Valuation of risky debt with the Merton-Model
BT
F
Ausfallbedrohtes FK + Put-Option = risikoloses FK
B0
PT
+
P0
=
Fe-rT
VT
F
P0 = −N (−d1 )V0 + Fe−rT N (−d2 ) (Black/Scholes Formel)
ln(V0 / F ) + (r +1/ 2σ 2 )T
d1 =
; d2 = d1 − σ T
σ T
Berechnung des fairen Spreads von ausfallbedrohtem FK
im Merton Modell
• Yield to maturity des ausfallbedrohten FK (yT):
B0e yT T = F
⇒ yT = − ln( B0 / F ) / T
⇒ yT = − ln ( Fe− rT − P0 ) / F  / T
einsetzen von P0 :
1

V

π T = yT − r = − ln  N (d2 ) + −0rT N (−d1 )
T 
Fe

Faire Spreads und Laufzeit nach Merton-Modell (illustr.)
yT
Volatilität hoch
Volatilität gering
T
An implementation of the Merton model is the KMV
CreditMonitor
For listed firms: stock market prices & volatility used
Use data of comparable firms
Rely on empirical observation that firms typically default if
Asset Value < Short-term Debt + α × Long-term Debt = Default Point
(α: industry-specific)
Use distance to default (DD) as sole default risk indicator
DD =
Asset Value - Default Point
σ Asset Value
Transform DD into default probability
using an empirical fit
(instead of lognormal distribution)
PD
DD
KMV ratings often react faster to crises
Default probability of US company Acme metals according to KMV and S&P
Bankkruptcy
on 29.9.98
Default probability in %
20
15
10
5
0
Okt
95
Jan
96
Apr
96
Jul
96
Okt
96
Jan
97
Apr
97
According to S&P Rating
Jul
97
Okt
97
Jan
98
Apr
98
Jul
98
KMV EDF
Difficulties in applying the Merton model
Often, only book values available, not market values of equity and debt
lagged and incomplete accounting information
lognormal distribution assumption may be wrong
debt structure is usually more complex than assumed in Merton model
debt structure not constant over time
Numerical valuation of risky credits using binomial
trees
• Standard in complex option pricing
• In every time step, asset value goes up by factor u or down
by factor d
S
uS
with prob = q
dS
with prob = 1-q
∆t
• The no arbitrage value is the present value of the
expected terminal value under the risk neutral probability
„Cook book receipt“ for binomial valuation of risky credit
1. Step: Set up a tree for the evolution of customer asset value
a)
b)
c)
d)
Chose ∆t (for example omne month: ∆t = 1/12)
Estimate asset volatility σ and safe interest rate r (r = 10%, σ = 40%)
Evaluate current asset value, e.g. S = 100
Derive up- and down factors and pseudoprobability (u, d, q):
u = eσ
∆t
d = e −σ
q =
e
r ∆t
∆t
= 1,1224
= 0,8909
−d
= 0,5076
u −d
q = „risikoneutrale
Wahrscheinlichkeit“
eines „up“
Resulting binomial tree for evolution of asset value
Assume: credit has 5 month maturity Æ 5 step tree required
Asset Value Evolution
178,13
158,71
141,40
125,98
112,24
100,00
141,40
125,98
112,24
100,00
89,09
112,24
100,00
89,09
79,38
89,09
79,38
70,72
70,72
63,01
56,14
2. Step: Determine Pay Off at T and set default condition
• Example:
The customer has one credit with notional amount = 80
• You believe that:
– default bevor T occurs, when asset value drops below 70
– default in T occurs, when asset value is below 80
– recovery rate is 50%
Derivation of terminal pay offs
Asset Value Evolution
178,13
158,71
141,40
141,40
125,98
125,98
112,24
112,24
100,00
112,24
100,00
100,00
89,09
89,09
89,09
79,38
79,38
70,72
70,72
63,01
56,14
Terminal Payoff
80,00
x
x
80,00
x
x
x
x
x
80,00
x
x
x
x
80,00
x
x
x
40,00
40,00
40,00
Step 3: Derive present value of credit by backward
induction
[
]
= q * S u + (1 − q) * S d e−r∆t
Value of Credit
69,91
80,00
79,34
78,68
78,02
75,10
69,91
80,00
79,34
78,68
73,36
65,75
80,00
79,34
69,13
59,03
80,00
59,79
49,63
40,00
40,00
40,00
Step 4: Derive the fair credit premium
• 69,91 is the present value of a risky zerobond with face
value of 80
• We find: 69,91* (1 + 175%) *
5
= 80
12
Æ 175% is the fair anual interest rate!
Æ 175% - r = 165% is the fair credit risk premium!
Vergleich KMV vs. Logit-, Diskriminanzanalyse
• Lineares vs. nichtlineares Modell
(Erhöhung des Verschuldungsgrades um x%
⇒ Erhöhung des Z-Wertes um ß*x, unabhängig von Startwert
⇒ Erhöhung der Distance to Default abhängig von Startwert wegen
Konvexität der Black-Scholes Formel
• Andere Inputdaten
• Aktualität, Reagibilität: KMV‘s EDF ändert sich für börsennotierte
Unternehmen täglich in Abhängigkeit von Aktienmarktentwicklung
⇒ ständiges „Marking to Market“ von Krediten
Rating agencies and banks typically combine both
quantitative and qualitative criteria into their ratings
Financial risk (financial ratio analysis...)
Business risk (product range, competitive position, industry and country risk...)
Management quality
....
⇒ Judgmentally combined into a rating
Banks typically use different rating approaches for
different clients
Retail clients
Small and mediumsized businesses
Large Caps
Quantitative
information
Qualitative
assessment
External
ratings
scoring model
-
-
scoring model
complementary
if available
as complement to external ratings
primary source
Validation techniques for internal ratings become
important
Selected overview of validation techniques
comparison of default rates across rating classes
- is it lower for better rated companies?
comparison of expected and realized default rates
Brier Score: sum of squared errors:
If default occured:
error = (1 – pd)
If no default occured: error = (pd – 0),
Power Curve analysis (next slide)
Analyse der classification errors: Typ 1 und Typ 2 Fehler
• Evaluiere für verschiedene z* die Güte der Trennschäfe
Wahrscheinlichkeit
Sample: Kein Konkurs
Sample: Konkurs
Z
Z*
Schlechte Kredite akzeptiert (Typ 1 Fehler)
Gute Kredite abgelehnt (Typ 2 Fehler)
The power curve analysis investigates the discrimatory
power of rating systems
power curve of perfect model
100%
Defaults (in%)
realized
power
curve
cumulative
power curve of
worst model
Size of area is a
measure of quality
100%
companies, ordered from bad to good, in %
Leistungsfähigkeit der Ratingmodelle steigt
(4000 observations, 50 defaults)
„Power Curve“ verschiedener Modelle
1.00
% of Defaults Excluded
0.75
C-score Rated
C-score Pub
Shumway Public
0.50
C-score Private
Z-score (4)
0.25
Compustat Daten 1990 - 97
4000 Beobachtungen
50 Ausfälle
0.00
0.00
0.25
0.50
Quelle: Falkenstein Commercial Credit Risk Modelling (1999)% of Sample Excluded
0.75
1.00

Commercial Banking - Goethe

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