On default definition in
rating based models for
small business
S.-M. Lin, J. Ansell, G.Andreeva
Credit Research Centre,
The University of Edinburgh
Small business banking and financing: a global perspective
Cagliairi, 25th May 2007
Outline
 Approaches to small business (SME) risk




modelling
Data description and approach taken
Predictor variables and their
transformation
Different definitions of default
Conclusions
Small business risk
Small business risk shares the features of
corporate and retail sectors
Banks that manage small-business-related
exposures in a manner similar to retail
exposures may apply the less capital requiring
retail IRB treatment to such exposures, provided
that the total exposure of a bank to an individual
SME is less than € 1 Million.
Possible modelling approaches
Corporate models
– Merton-type structural models
– Reduced-form models
– Accounting – based approach
Retail (credit scoring) models
Previous research
There is evidence that small companies
experience problems in obtaining credit
Research shows that adoption of credit scoring
techniques increases lending to small
businesses
Credit scoring has relatively recently been
applied to small business lending
Data description
A sample of 445 UK SME from ‘Datastream’
Oil & Gas, Basic Materials, Industrials,
Consumer Goods, Healthcare, Consumer
Services, Utilities, Telecommunications and
Technology sectors
Annual turnover less than € 50 Million (Basel II
definition)
Financial statements available for at least 3
years
Different levels of financial
health
‘Dead’ insolvent companies
Stock-based distress
– Insolvency Ratio =
Shareholders
Funds/ Total Assets = (Total Assets – Total
Liabilities)/ Total Assets = 1 – Total Liabilities/
Total Assets
Cash flow-based distress
– Interest Coverage =
Payable
EBITAD/Interest
Levels of Financial Health
Group of SMEs
Group 1
Insolvent
Group 2
Flow-Based
and StockBased
Distress
Flow-Based
Distress
Healthy
Group 3
Group 4
Number of
SMEs
Delisted 28
Dead and
delisted
SMEs
Insolvency
Active
Ratio < 0 and
Interest
Coverage <1
Interest
Active
Coverage < 1
Listed healthy Active
Total
32
160
225
445
Modelling details
Logistic regression
SMEs performance determined at the end
of 2004
Financial ratios from 2001 used as
predictors
Financial ratios
1.
2.
3.
4.
5.
6.
7.
8.
9.
Profitability Ratios
Liquidity Ratios
Assets Utilization Ratios
Structure Ratios (Leverage)
Growth Rate Ratios
Cash Flow Related Ratios
Activity (Efficiency)
Employees Efficiency Ratios
Financial Scale
Example of coarse-classification
(Cash Ratio)
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Missing
0
Group 1
20
40
Group 2
60
Group 3
80
Group 4
100
Different definitions of default
Indeterminate groups are deleted from modelling,
Group 1 is modelled as ‘Bad ‘ against Group 4 –
‘Good’;
Leaving all 4 groups in the analysis, with Group 4
defined as ‘Good’, and all other categories considered
as ‘Bad’;
Taking Groups 1 and 2 as ‘Bad’ and modelling it
against Group 4 as ‘Good’;
Opposing Group 3 (Bad) to Group 4 (Good) with the
first two groups removed from the analysis.
Composition of models with different
definitions of default
Model
(A) Original
untransformed
ratios
Default Definition
Group 1 vs
Group 4
Groups 1,2,3 vs Group 4
Groups 1,2 vs Group 4
Group 3 vs Group 4
Assets
Turnover
Operating
Cash Flow
Cash Ratio
Liquidity Ratio
Debtors/Cash Flow
Profit per Employee
Liquidity Ratio
Operating Cash
Flow/ Sales
Cost of Employees/
Operating Revenue
Operating Cash Flow
Cash Ratio
Total Liabilities/
Shareholders Funds
Debtors/Cash Flow
Profit per Employee
Cash Ratio
Liquidity Ratio
Debtors/Cash Flow
Operating Cash Flow/
Shareholders Funds
Profit per Employee
Operating Cash
Flow/ Sales
Cost of Employees/
Operating Revenue
Operating Cash Flow
Cash Ratio
Debtors/Cash Flow
Operating Cash
Flow/ Shareholders
Funds
Credit Period (days)
(B)
Operating
Untransformed Cash Flow
ratios, those
with missing
values removed
Composition of models with different
definitions of default
Model
(C) Full list of
coarseclassified
ratios
Default Definition
Group 1 vs Group 4
Groups 1,2,3 vs
Group 4
Groups 1,2 vs
Group 4
Group 3 vs Group 4



EBIT Growth
Net Profit Growth
Cash Flow/ Current
Liabilities
Working Capital/
Sales
Credit Period (days)
Operating Revenue
per Employee
Operating Revenue

EBITDA
Margin
Change in Net
Income
Operating Cash
Flow

Profit
Margin
Cash
Ratio
EBIT
Growth
Net Profit
Growth



Total Assets per
Employee
Cash Flow/ Current
Liabilities
Total Assets

EBITDA
Margin
Debt/ EBITDA
Change in Net
Income
Creditors/
Debtors

Profit per
Employee








(D) Coarseclassified
ratios, those
with missing
values
removed














EBITDA Margin
ROCE
Change in Net
Income
Operating Cash
Flow
Profit per
Employee
EBITDA Margin
Cash Ratio
Debt / EBITDA
Change in Net
Income
Creditors/
Debtors
Model
(A)
(B)
(C)
(D)
Observed
Number
Default Definition / Number Accepted
G 1 vs G 4
G1,2,3 vs G 4
G 1,2 vs G 4
G 3 vs G 4
1 (16)
6
10
3
9
2 (19)
6
5
7
7
3 (80)
32
24
40
24
4 (116)
72
77
66
76
1 (16)
6
11
3
10
2 (19)
6
6
6
7
3 (80)
25
22
33
25
4 (116)
79
77
74
74
1 (16)
1
5
5
7
2 (19)
8
7
4
6
3 (80)
38
21
27
20
4 (116)
69
83
80
83
1 (16)
4
7
7
7
2 (19)
8
6
5
7
3 (80)
29
27
22
21
4 (116)
75
76
82
81
Conclusions
Default definition has a notable effect on the
composition of the models
Most frequent variables are Cash Flow Related,
Growth and Employees Efficiency ratios
All default definitions produced prediction better
than a random selection
The choice of a particular definition would
depend on the prioritisation of objectives