Outline of CRD Models

Outline of CRD Models
I. Model 3 for Corporations
II. Model 4 for Sole Proprietors
㵩 BS Model 㵩

March 2006

CRD㩷 Association,a Limited Liability Intermediate Corporation

This document outlines CRD's models that credit guarantee
corporations use in determining their guarantee charge rates,with a summary of the features of CRD-developed default
probability estimate models, model structures and theirperformance.

0Outline of CRD Models

Contents

I. Model 3 for Corporations ................... 3

1. Features of Model 3 ................................ 3
2. Structure of Model 3 ............................... 3
2.1. Data used for the construction of Model 3....... 3
2.2. Steps in estimating default probability......... 4
2.3. Primary business classification model........... 5
2.4. Comprehensive integrated default indicators..... 6
2.5. Classification of businesses used for the Model. 7
2.6. Calculation of default probability by a secondary
scoring model................................... 7
2.7. Calculation of multiyear cumulative default
probability..................................... 8
2.8. Score calculation by Model 3.................... 8
3. Verification for Model 3 ........................... 8
3.1. Performance of the model........................ 8
3.2. Fit between an estimated PD and an actual default rate................................................ 81

Outline of CRD Models

II. Model 4 for Sole Proprietors (BS Model) .. 10

1. Features of Model 4 (BS Model) .................... 10
2. Structure of Model 4 (BS Model) ................... 11
2.1. Data used for the construction of Model 4...... 112.2. Steps to calculate default probability......... 11
2.3. Complementation of sole proprietors data....... 122.4. Creation of explanatory variables.............. 122.5. Calculation of scores with Model 4............. 13
3. Verification of Model 4 (BS Model) ................ 13
3.1. Performance of the model....................... 13
3.2. Fit between an estimated PD and an actual default rate............................................... 13

2

Outline of CRD Models

I. Model 3 for Corporations
1. Features of Model 3
Model 3 is a model for estimating default probability, (PD)developed by improving Model 2. The main features of Model
3 are described in Table 1.
Table 1. Main features of Model 3
Main features
Specific contents
1 Able to estimate
In order to meet membership
multiyear (two-year,
requests, this model canthree-year cumulative) estimate two-year, three-year
default probability,
cumulative default probability.
going beyond one year.
2 Able to estimate
To meet requests for estimating
default probability by default probability for smaller
intermediary businessbusinesses, this model isclassification.
designed to enable theestimation of a default
probability (PD) according to anintermediary businessclassification.
3 Detects with a high
The huge database accumulated atdegree of accuracy
CRD over many years enables thecompanies likely toconstruction ofdefault.
high-performance models.
4 Has anThis model is designed to ensureeasy-to-understandeasy understanding of its
model structure.
structure and the rate ofcontribution of financial
indicators.

2. Structure of Model 3
2.1. Data used for the construction of Model 3
To construct Model 3, we used the data accumulated at CRD
as shown in Table 2. With this large data set, we can achievea high degree of discriminating power as a whole.

3Outline of CRD Models

Table 2. Data used for the construction of Model 3
Volume of data in use
Number of cases used to
About 2.93 million
construct Model 3
Number of default cases About 40,000

2.2. Steps in estimating default probability
In calculating default probability, we followed the threesteps as described below (Chart 1).
Step 1:Categorizing businesses according to a primarybusiness classification model.
Target companies are categorized into two groups
based on their creditworthiness 㵩 "good" and"ordinary."

Step 2:Creating a "integrated default indicator"
A variable named "integrated default indicator"
for the explanation of corporate default
probability is created by combining varieties offinancial indicators according to theclassification in each business sector.

Step 3:Calculating default probability using secondary
scoring model䌳.
Using the default indicator, we calculate thedefault probability for a target company in themodel for its business industry.

4Outline of CRD Models

Chart 1.

Flowchart for the calculation of default
probability

Primary business classification

Secondary scoring models

A model that classifies small andmedium-sized enterprises (SMSs) into
"good SMSs" and "ordinary SMSs"

Create a comprehensive default indicator by
the type of business. A model by which toestimate default probability

Corporatefinancial data

Estimation of default
probability

Good
丵
丵
丵
丵
丵
丵
丵

Good
group

Integrated
default
indicator by
the type ofbusiness

丵
丵
丵
丵
丵
丵
丵
丵

Ordinarygroup

Integrated
default
indicator by
the type ofbusinessmodels to
calculate default
probability
according to thetype of business

OrdinaryBadmodels to
calculate default
probability
according to thetype of business2.3. Primary business classification modelWe㩷 distinguish good companies from ordinary companies fromthe viewpoint of foreseeable bankruptcies. We can obtain amore accurate estimate of these two types if we use different
financial indicators for each type.
Therefore, a primary business classification model has
been introduced with the aim of roughly classifying companies
into a "good" or an "ordinary" group, based on their current
financial position. The classification of companies into two
types 㵩 good or ordinary 㵩 enables the estimation of default
probability more accurately in the secondary scoring model.

5Outline of CRD Models

2.4. Integrated default indicators
An integrated default indicator is a variable to indicate
corporate default likelihood by combining a number ofcorporate financial indicators.
For processing missing values, conventional wisdom had to
exclude financial items with many missing values or to
replace them by some values. These processes decrease thenumber of indicators available, thereby often posing
impediments in constructing models.
Model 3 introduces an integrated default indicator to avoid
these problems 㵩 a variable that indicates default
likelihood. The model calculates a comprehensive default
indicator by using 22 to 28 financial indicators for both
good and ordinary companies in each business sector, and thisindicator has specific features as mentioned below.
(1) An integrated default indicator synthesizes various
financial indicators to assess a target company without
dependence on specific financial indicators.
Usually financial items with many missing values were notavailable in model building. Because of these shortcomings,
at most 10 financial indicators were used as appropriate
indicators for credit assessments. However, this single
indicator can accommodate the maximum number of financial
indicators available for each company, without being
affected by missing values.
(2) This indicator is less subject to outlying or missing
values.
Every financial indicator is discretized in advance: therange of values is divided into a few groups, with a newparticular value assigned to each group. This value, relevant
to each group of financial indicators in respective businesssectors, is named default index.
Each financial indicator of a debtor is translated into
the correspondent default index, respectively. And thesedefault indexes are averaged by the number of indicators
available for a debtor. That is why this average is called
an integrated default index.
Therefore, this single indicator makes the resulting
credit score less vulnerable to the changes in financial
indicators due to the descretization, or to extreme values
due to the averaging procedure. And this integrated indicator
can avoid the difference in the number of financial indexes

6Outline of CRD Models

available among debtors because of missing values, due tothe averaging.
2.5. Classification of businesses used for the Model
After classifying all the debtors in the "ordinary" or"good" group, Model 3 applies different sector-specificmodels to a debtor in each of these groups.
Table 3. Classification of businesses for Model 3

1
2
3
4
5
6
7

Type of modelbusiness
Manufacturing
Construction
Real estate
Wholesale
RetailServices
OthersRemarks (large grouping)
Manufacturing
Construction
Real estate
Wholesale
RetailRestaurants and services
Agriculture, forestry, and fisheries;
mining; electricity, gas, heat supply andwater utilities; transportation andtelecommunications; finance andinsurance; civil service; andnonclassifiable business2.6. Calculation of default probability by a secondary
scoring model
The secondary scoring models calculate default probability
for each debtor. The default probability is calculated byusing an integrated default indicator as the single
explanatory variable in one of 12 secondary models
applicable.
With x (comprehensive default indicator) as a single
explanatory variable, default probability (PD) is calculated
by using a logistic function as indicated below (logit model).
Parameters such as㩷 D, E and J vary in every secondary modelso that estimation can reflect actual default rates
accurately in each sector with each business model.
PD1㩷 㩷 㩷 㩷 㩷 㩷 㩷 㩷 㩷 㩷 㩷 㩷 Z ǩǪx J
1  exp( Z )7

Outline of CRD Models

2.7. Calculation of multiyear cumulative default probability
Model 3 calculates the two-year cumulative default
probability (PD) — the probability of default occurring
within two years. It calculates the three-year cumulative
PD,㩷 too.
Multiyear PD can be used to estimate loss amount from thedefault of a specific long-term loan, for example.
2.8. Score calculation by Model 3
Model 3 gives each debtor's PD reflecting its financial
conditions. However, some users want to use 0-to-100 grading,rather than a percentage. Model 3 gives 0-to-100 scores bytranslating PD according to a certain standard. PDs or thegrading scores are comparable across the sectors: users do
not have to adjust the level of two debtors'㩷 PDs or scoresfrom different sectors to make the comparison.
3. Verification for Model 3
3.1. Performance of the model
When all the debtors' PDs are ranked, an excellent model cancatch all the defaulters with higher PDs than all the othernon-defaulters'.
Accuracy is usually evaluated based on an index called
AR (Accuracy Ratio). The larger the value, the higher is theaccuracy of the model to detect would-be defaulters.
The result shows that Model 3 has good AR statistics andoutperforms the other preceding CRD models.
3.2. Fit between an estimated PD and an actual default rate
It is a problem in practice if the actual default rate does
not follow the estimated rate, regardless of AR value.㩷
Calculated AR value might be high, but when a calculated PD
does not fit reality, this poses a problem in businesspractice.
Chart 2 below compares the average estimated PD from Model
3 for each segment with its actual default rate. These samples
are evenly divided into 20 ranked groups in terms of theirPD. The chart shows a good fit between the estimated PD andthe actual default rate.

8Outline of CRD Models

Chart 2.

Fit between estimated PD and actual default rate㪈㪉㪅㪇㪇㩼
ታ❣䊂䊐䉤䊦䊃₸
Actualdefault rate㪈㪇㪅㪇㪇㩼

ផ⸘䊂䊐䉤䊦䊃⏕₸Estimated
PD

㪏㪅㪇㪇㩼

㪍㪅㪇㪇㩼

㪋㪅㪇㪇㩼

㪉㪅㪇㪇㩼

㪇㪅㪇㪇㩼

Good
<Precentile
Good <Percentile䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭⦟䈇䇭㸠䇭䍨䍽䍎䍜䍻䍞䍐䍷䇭㸢䇭ᖡ䈇

9-> BadOutline of CRD Models

II. Model 4 for Sole Proprietors (BS Model)
1. Features of Model 4 (BS Model)
Model 4 was newly designed, built on the preceding CRD model
for sole proprietors.
Model 4 improves upon the weakness of the old model thatconsisted in large part of BS and PL data. The new model adds
qualitative data and the type of business as an explanatory
variable to allow for the correlation between the type ofbusiness and actual defaults.
(1) Use of qualitative data
CRD, in collaboration with its members, has been
accumulating data on sole proprietors in recent years. In
the construction of Model 4, CRD utilized qualitative data
to the maximum.
(2) Use of a detailed business sector classification.
Model 4 uses㩷 the detailed business sector classification
to allow for the correlation between the sector anddefaulters.
The major points of Model 4 (BS Model) are summarized inTable 4.
Table 4. Major points of Model 4 (BS Model)
Major points of Model 4 (BS Relevant descriptions
Model)(1) Use of qualitative
2.4.2. Creation of explanatory
data
attribute variables (qualitative
information)
2.4.3. Reflection of qualitativedata
3.1. Performance of the model(2) Use of a detailed
2.4.2. Creation of explanatoryclassification
attribute variables (qualitative
business sector
information) (described in thefollowing chapter)In the next chapter, we outline the BS Model used todetermine the credit guarantee charge rates by credit
guarantee corporations.

10Outline of CRD Models

2. Structure of Model 4 (BS Model)
2.1. Data used for the construction of Model 4
In the construction of Model 4, we extracted data, as shownin Table 5, from the CRD database. Such an abundance of data
ensures a high degree of overall accuracy.
Table 5. Data used for the construction of Model 4
Volume of data inuse
Number of cases used to construct
About 1.2 million
Model 4
Number of default cases
About 20,000

2.2. Steps to calculate default probability
Model 4 has been designed for estimating the default
probability within one year of a sole proprietor.㩷 Estimation
uses a logistic regression (logit model) 㵩 a common methodin creating credit risk estimation models.
Steps to calculate PD are illustrated in Chart 3 below.
Chart 3.

Flow of calculating default probability

Obtain financial statement data for the target sole proprietor.

Supplement missing data by realigning data as described in 2.3.

Create an explanatory variable based on data described in 2.4.

Calculate PD, using the variable.

11Outline of CRD Models

2.3. Complementation of sole proprietors data
Many sole proprietors do not file balance sheets. Therefore,
unlike the case with corporations, it is difficult toconstruct a highly accurate model without BS information.
One of the critical issues involves the way to fill in thelack of information of sole proprietors.
(1) Because debt on the balance sheet and interest expenses
on the income statement indicate debtors' ability to repay
debt, the two accounts are essential as explanatory variables
in estimating default probability. Therefore, Model 4complements one of the two, if it is missing, with an estimatedvalue from the other.
(2) Likewise, operating profit, if missing, is estimatedfrom information in other lines of the income statement.
Operating profit = gross profit on sales – total expenses.
Data complementation like this applies to 20 items in thebalance sheets and income statements.
2.4. Creation of explanatory variables
2.4.1. Creation of explanatory financial variables

Model 4 selects a set of useful financial indicators, as
explanatory variables, from 272 indicators.
2.4.2. Creation of explanatory attributes qualitative variables

In addition to the financial data, non-financial data makeup the explanatory variables.
Analysis of 27 qualitative indicators identified some ofthose relevant to defaults or those relevant to sales andprofit. These indicators, given a particular score according
to the information, are synthesized into an integrated
qualitative score, an explanatory variable in the model.
2.4.3. Addition of qualitative data

Model 4 produces two different results, depending onwhether to allow qualitative data or not. Model 4 withqualitative information is a "Comprehensive Model" and themodel without it is a "Financial Model."12Outline of CRD Models

2.5. Calculation of scores with Model 4
Model 4 produces an estimated PD for a sole proprietor.
Some users want to use, in addition to PD, 0-to-100 scoresfor easy comparison of creditworthiness across debtors.
Model 4 also gives such scores by converting PD according
to a certain standard.

3. Verification for Model 4 (BS Model)
3.1. Performance of the model
As was the case with Model 3, we checked Model 4's ability
to detect foreseeable defaults, using AR statistics.
Results of AR show that Model 4 outperforms the preceding
models when actual BS data are available. And Model 4 withqualitative data outperforms the financial model.
3.2. Fit between an estimated PD and an actual default rate
Chart 4 compares the averaged estimated PD from Model 4
for each segment with its actual default rate. These samples
were evenly divided into 10 ranked groups. This chartindicates that the estimated default rate closely fit theactual default rate.
Chart 4.

Fit between estimated PD and actual default rate

Actual default rate
Estimated PD

Good <-

Good <-

Precentile

Percentile

13-> Bad