09.2 credit scoring

Copyright © 2018 CapitaLogic Limited
Chapter 9
Credit Scoring
This presentation file is prepared in accordance with
Chapter 9 of the text book
“Managing Credit Risk Under The Basel III Framework, 3rd ed”
Website : https://sites.google.com/site/crmbasel
E-mail : crmbasel@gmail.com

Copyright © 2018 CapitaLogic Limited 2
Declaration
 Copyright © 2018 CapitaLogic Limited.
 All rights reserved. No part of this presentation file may be
reproduced, in any form or by any means, without written
permission from CapitaLogic Limited.
 Authored by Dr. LAM Yat-fai (林日辉),
Director, CapitaLogic Limited,
Adjunct Professor of Finance, City University of Hong Kong,
Doctor of Business Administration,
CFA, CAIA, CAMS, FRM, PRM.

Outline
 Quantitative credit assessment
 Explanatory variables
 Cluster analysis
 Linear discriminant analysis
 PD modelling
 Appendices

Quantitative credit assessment
 Explanation
 Use a set of historical lending records to identify
a few variables that can explain effectively the
credit quality of a borrower
 Discover a quantitative relationship between the
credit quality of a borrower and the few
explanatory variables in numerical format
 Assessment
 Use this quantitative relationship to assess the
credit quality of a potential borrower outside the
set of historical lending records

Classification of borrowers
 Good borrower
 A survival borrower remains as a survival
borrower after one year
 Bad borrower
 A survival borrower defaults in one year
Example 9.1

Credit scoring process
Credit
scoring
Historical
lending
records
Explanatory
variables
Scoring
formula

Outline
 PD modelling
 Appendices

Quantitative explanatory variables
 Numeric
 Economically intuitive to explain credit quality
 Monotonic relationship with credit quality
 Statistically significant to explain credit quality
 Low inter-dependency among explanatory variables
 No. of explanatory variables ranges from 4 to 8

Explanatory variables identification
 Regression

 With significant explanatory power
 Large F-statistic / Small sufficiency of F
 Large R2
 Coefficients
 Significantly different from 0
 Large t-statistic / Small p-value
0 1 1 2 2 3 3 N NDefault status = β + β x + β x + β x + ... + β x
Example 9.3
Example 9.2

Categorical variables
 Binary variable
 0 – male
 1 – female
 Rank order
 1 – no education
 2 – primary school
 3 – secondary school
 4 – undergraduate
 5 – postgraduate

Corporate credit scoring
 Profitability (23%)
 ROA
 Growth of ROA
 Interest coverage
 Capital structure (19%)
 War chest
 Leverage
 Liquidity (19%)
 Cash position
 Quick ratio
 Others (38%)
 Total assists to CPI
 Growth of sales
 Stock return

Retail credit scoring
 Application form
 Employment
 Residence
 Financial
 Personal
 Credit bureau
 Payment history
 Credit utilization
 Credit history
 Credit experience
 Recent credit enquiry
 FICO score

Behavoural explanatory variables
 Utilization of credit limit
 Overdue amount
 Overdue period
 Age of overdue record

Outline
 Quantitative credit assessments
 PD modelling
 Appendices

Survival and default groups
 Assume that personal credit quality is characterized by
 x1 : monthly income
 x2 : outstanding loan amount
 Historical lending record
 Based on a bank’s internal records, plot the default and survival
borrowers into two groups
 At least 30 and preferably 60 in each group
 Determine the centre of two groups
 Potential borrower
 Classified as a good borrower if near the centre of survival group
 Classified as a bad borrower if near the centre of default group

Historical distribution

Euclidean distance
 Euclidean distance
 Potential issues
 Dependency between x1 and x2
 Scale mis-match between x1 and x2
 
 
   
1 1
2 2
2 2
Po Po
1 1 2 2
x = Average x
x = Average x
Euclidean distance = x - x + x - x

Statistical distance
 
 
 
   
   
 
1 1
2 2
1 1 2
1 2 2
T
Po Po
-11 1 1 1
Po Po
2 2 2 2
x = Average x
x = Average x
Var x Cov x ,x
CovMat =
Cov x ,x Var x
x - x x - x
Statistical distance = CovMat
x - x x - x
 
 
 
   
   
      
X
X

Statistical distance
 
 
 
 
     
     
     
 
1 1
2 2
3 3
1 2 1 3 1
1 2 2 3 2
1 3 2 3 3
T
Po Po
1 1 1 1
-1Po
2 2 2
Po
3 3
x = Average x
x = Average x
x = Average x
Var x Cov x ,x Cov x ,x
CovMat = Cov x ,x Var x Cov x ,x
Cov x ,x Cov x ,x Var x
x -x x -x
Statistical distance = x -x CovMat x
x -x
 
 
 
 
 
 
 
 
 
  
X
X Po
2
Po
3 3
-x
x -x
 
 
 
 
  
Example 9.4

Three-group classification
Example 9.5

Borrower distribution in a real bank

Outline
 Quantitative credit assessments
 PD modelling
 Appendices

Linear discriminant analysis
 Linear discriminant formula
 Cutoff score
 When the N independent explanatory variables of a
borrower are substituted into the linear discriminant
formula
 Z > Cutoff score => good borrower
 Z < Cutoff score => bad borrower
1 1 2 2 3 3 N NZ = α x + α x + α x + ... + α x

Linear discriminant formula
   
   
 
1 1 2 2 3 3 N N
2
Good Bad
2 2
Good Bad
Z = α x + α x + α x + ... + α x
Average All Z s - Average All Z s
To maximize
S.D. All Z s + S.D. All Z s
Unbiased cutoff score = Average All Zs
 
 
   
   
Example 9.6

Credit scoring function
 A linear function
 Maximize inter class variability
 Minimize intra class variability

Prudent cutoff score with
mis-classification cost
 Mis-classification
 Lend to a bad borrower
 Default loss
 Turn down a good borrower
 Interest loss
 Prudent cutoff score
Example 9.7
   Good Bad
Loss of classifying a good borrower as bad borrower a
=
Loss of classifying a bad borrower as good borrower b
b × Average All Z s + a × Average All Z s
Prudent cutoff score =
a + b

Outline
 PD modelling
 Appendices

Linear unbound PD regression
 Maximum = 1
 Minimum = 0
0 1 1 2 2 3 3 N NUnbounded PD = β + β x + β x + β x + ... + β x

Probit transformation

Probit transformation
   
-1 No. of total records
Probit coefficient = Φ
No. of total records + 1
No. of total records
= Normsinv
No. of total records + 1
Probit = Probit coefficient × 2 × Unbounded PD - 1 - ,+
Bounded P
 
 
 
 
 
 
 
     D = Φ Probit = Normsdist Probit 0,1
Example 9.8

Credit assessment with credit scoring
Step Input Objective/output
Explanative variables
identification
A total of at least 30 good and
30 bad records of borrowers
To identify a set of effective
explanatory variables
Discriminant analysis At least 30 good and 30 bad
records of borrowers with
effective explanatory
variables
To calibrate a linear
discriminant formula and an
unbiased cutoff score
Mis-classification cost To calibrate a prudent cutoff
score
Linear PD regression Effective explanatory
variables
To derive an unbound PD
formula
Probit transformation Unbound PD formula To derive the bound PD

Outline
 PD modelling
 Appendices

Probit regression
       
 
0 1 1 2 2 3 3 N N
2
Probit
-
Bad Bad Bad Bad
1 2 3 U
Good Good Good Good
1 2 3 V
Bad
1 2
Probit = β + β x + β x + β x + ... + β x
1 τ
PD = exp - dτ
22π
L = PD × PD × PD × × PD
× 1 - PD × 1 - PD × 1 - PD × × 1 - PD
ln(L) = ln PD + ln PD

 
 
 

     
       
Bad Bad Bad
3 U
Bad Bad Bad Bad
1 2 3 V
+ ln PD + + ln PD
+ ln 1 - PD + ln 1 - PD + ln 1 - PD + + ln 1 - PD
Example 9.9

09.2 credit scoring

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