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Predicting SME default risk.
Does regional model make sense?
Oliviero Roggi – Associate Professor of Corporate Finance
University of Florece
Email: Oliviero.roggi@unifi.it
Phone:+39-0554374720
Alessandro Giannozzi – Ph.D Candidate - School of Finance in Trieste
Via delle Pandette 9
50127 Florence (Italy)
Phone:+39-0554374916
Email : alessandro.giannozzi@unifi.it
Acknowledgements
This paper results from several contribution as well as from a fruitful support. First of all, we would like to
thank Mr Fabrizio Cipollini and Mr Carlo Porceddu for their useful ideas and advice in the statistical process.
We also would like to thank Prof. Francesco Giunta and his group who gave their contribution for the variable
selection process. A special thank to Mr Marco Ginanneschi from Confindustria Toscana since he played a key
role in developing this project and in obtaining the sponsorship from Tuscany Region. Thanks to Mrs Simonetta
Baldi and Mr Alessandro Compagnino this work and the whole Pro.co.f.i.t. project have been financed by
Tuscany Region. We are grateful to Banca Cr Firenze, Banca Etruria, Banca Nazionale del Lavoro and Monte
dei Paschi di Siena for the data provided. We remain fully responsible for all mistakes and inaccuracies
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Predicting SME default risk. Does regional model make sense?
ABSTRACT
The paper aims to gain a better understanding of regional SME default risk modelling. The
research question addressed is: “Are regional models for SME able to better estimate default
risk than national based models? Does regional model estimation make sense?” The analysis
is based on regional (Tuscany) companies according to the Basel II definition of default and
it presents as well five industry-specific models. The dataset is made of 515 regional
companies and 482 national ones organized in two different “out of the sample” groups. The
geographic sampling approach superiority is demonstrated by comparing “% of misclassified
companies” on both regional and national samples. Results show that the regional research
approach can improve the model accuracy and it better predicts default events due to the
local specificity variables contribution. The paper addresses a second research question. “Is
the regional models highest accuracy due to industry-specific variables?”. Some of these
aspects are not new in the academic literature, however the regional approach presented in
this paper will contribute to widen the research field in default risk estimation.
JEL Classification: G33, G24
Keywords: default risk estimation, regional model, Basel II, model accuracy, discriminant
analysis – logistic regression
INTRODUCTION
As far as risk management study is concerned, default riski makes reference to
insolvency, i.e. the possibility for an enterprise to be able to fulfil its own financial
obligations (interest payments and refund for borrowed capital) towards the holders of its
debts (bonds holders, banks and suppliers). A direct relationship between default risk and
debt cost have been noticed in several studies; therefore several authors, from Altman (1968)
to present ones, have asked the question how to assess company default risk and, thus
indirectly, how to establish the interest rates to be appliedii.
Recently, the official documents issued by the Basel Committee on Banking
Supervision have provided a series of innovations that have a significant impact on credit risk
management carried out by banks; that also implies some consequences in terms of strategies
for capital lending to enterprisesiii. New Basel II Capital Accordiv, better known as “Basel II”,
particularly changed the method to calculate the capital requirements that banks should
observe to support the credit risk that lending portfolio implies. Basel II provides the
implementation of rating systems to assess the credit standing of corporate clients.
Before NAC, a corporate-borrower always took up the same capital for bank, regardless
his credit standing; according to Basel II, on the contrary, the capital to be holden depends on
the borrower’s (the enterprise’s) rating. Basel II, if it is compared with previous practices,
establishes a tight connection among rating, the required bank capital and the debt cost for a
specific enterprise. That may entail an increase of interest rates for borrowing, as for
companies with a low credit standing.
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In addition to that, researchers – and actually all those (banks and enterprises) - who are
“obliged” to take internal rating models into account - are interested in the accuracy of
models aiming at forecasting insolvency. For enterprises in particular, self-evaluation of
credit standing enables the entrepreneur to understand what variables will be the most
important one to determine his banking rating; therefore the optimisation of financial
structures becomes possible as well as desirable.
This research suggests to single out the best geographical sampling approach in order to
estimate the rating model. Standard & Poor’s, Moody’s take into account enterprises location
by introducing a geographical variable in the Italian rating models, aiming at understanding
the different real default rates found in different areas in Italy.
For this paper the main research question is the following one: “Is it possible for regional
models to better assess the default risk if compared with national company based model?” “Is
it significant to estimate regional models?”. The regional (Tuscany) companies, compliant
with the Basel II definition of default, are the basis for this analysis. In this research, five
industry-specific models, which are based on regional companies, are assessed. By
comparing % of misclassified companies out of sample (Tuscany companies vs. national
ones) it is possible to show the best geographical sampling approach to estimate the company
default risk and to confirm or reject the main proposition of this study: regional models better
estimate company default risk than national ones.
This study takes into account the default risk of small and medium enterprises operating
in Tuscany, one of the Italian regions. Geographical limits reduce the statistical population
for the analysis; however its allows to identify possible sources of risk resulting from the
localization. In particular as far as the economic, political and local spheres are concerned.
.
1. Theoretical framework of default risk estimation.
Since “Altman’s 1968 paper”, several studies dealt with the problem of predictive
models for default risk, applying different statistical methods that have evolved since then. A
long pathway has been covered trying to understand the insolvency phenomenon: we began
with studies on techniques of scoring Beaver (1967), Altman (1968), Altman, Narayanan,
Haldeman (1977), Alberici (1975), Forestieri (1986), Luerti (1992), Springate & Gordon
(1978), Fulmer (1984), then we moved to those taking into account the determination of the
probability of default Sironi (2003), Standard & Poor’s (2002), Moody’s (1991), Laitinen &
Laitinen (2000), Martin (1977), Ohlson (1980) Saunders (1997), Zmiewski, Foster (2002),
Friedman, Huang, De Servegny (2003), Altman, Marco, Varetto (1993) till the rating ranking.
From a methodological point of view, taking into consideration researches carried out
till now, most of studies make use of equal samples of observations where the number of in
bonis and in default companies correponds. Other authors Alberici (1975), Luerti (1992) on
the contrary, set up their models by sampling the proportion of unsuccessful business that are
found in a specific country or within a loan portfolio that is considered as the study
population. The relationship between generalisation and specificity in these models has also
been widely debated. Several authors are still discussing about the need to develop industryspecific models rather general ones. In most cases, industry-specific model oriented
researches (Sironi 2003; Standard & Poor 2002; Moody’s 1991; Hammer & Packer 2000;
Friendman, Huang, De Servegny 2003; Alman, Marco & Varetto 1994) are more accurate
than general models. This is probably due to greater homogeneity of financial indicators
within specific industries. It goes without saying, however, that in these cases researchers
have decreased, on their free will, the operational applicability of their own models.
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As far as statistical methodologies are concerned, evolution has been constant. First
researchers [Beaver (1967), Altman (1968), Springate, Gordon (1978), Fulmer (1984),
Altman, Narayanan, Haldeman (1977), Alberici (1975), Forestieri (1986), Luerti (1992)]
made use of multivariate discriminant analysis, and only later they shifted to Logit or Probit
models to assess the probability of default [Martin (1977), Ohlson (1980), Wiginton (1980),
Grablowsky, Talley (1981), Altman, Marco, Varetto (1994), Laitinen & Laitinen (2000),
Friedman (2002), Standard & Poor’s (2002)]. During the latest 15 years, researchers
including Altman, Varetto, Marco (1993), Yang, James, Packer (1997), Coats, Fant (1993),
Wilson, Sarda (1993), Varetto, Marco (1994), Alici (1996) have applied innovative
methodologies taken from other disciplines, such as neural networks and genetic algorithms;
in doing this, they obtained results close to those provided by traditional methodologies. At
present, best practices for rating agencies are based mainly on logit methodologies [Standard
& Poor’s (2002), Moody’s(1991)].
Additional approaches to determine default risk emerged from Merton (1974) option
theory and pricing breakthrough work. Since then other approaches have been developed: the
KMW Corporation model (KMW Credit Monitor) and the JP Morgan CreditMetrics in 1997.
Data provided by capital markets are needed for these models and therefore they can be
applied to enterprises that are listed on regulated markets, only. This restricts the usefulness
of the option theory approach, above all for the Italian context.
As far as geographical sampling is concerned, all the studies above mentioned assess
only the national models. Even if geographical variables are employed by rating agencies in
their rating model.
2. Measuring default risk
Concept of default
Before seeking a model for insolvency prediction it is necessary to clarify the concept
of default.
From a mere economic viewpoint, the concept of default should make reference to the
irreversible financial distress of a customer determining a non observance of contractual
obligations; this may imply, for the bank, the loss of a some quota of the loaned capital.
Therefore several factors, which foresee a failure, can be identified. International banks
often apply the following criteria:





a bankruptcy (failure) or other legal procedures;
debt “restructuring”;
a non-payment after n days (unpaid);
depreciation or specific account allowance;
problematic debt exposure.
The Committee suggests a definition that implies an exposure leading to default
whenever the following credit eventsv occur independently or concomitantly:


signals indicating a debtors’ incapacity to repay a debt (unlikeliness to pay);
borrowing for which the bank has made special allowance, depreciation or restructuring
plans;
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the other party has submitted a bankruptcy suit or other legal procedure;
payments are overdue for more than 90 days on any bank financial obligationvi.
The Basel Committee proposed a clear definition of insolvency for internal rating
methods. At least two reasons justify one single definition: first of all without a clear
definition it would not be possible to apply the “level playing field” principle to banks and
countries, thus creating significant differences in classifying different types of defaults;
secondly, it is necessary to prevent eventual problems in setting up banks’ databases since
that could make the validation process be problematic for the authorities responsible for the
banking supervision.
The Committee provided a definition of default that allows to identify the financial
distress of a customer earlier than previous definitions; at the same time it avoids an
excessive subjectivity in classifying corporate exposure. A “delayed” definition of default,
however, offers the advantage of restraining the analyst’s subjectivity; on the other hand, it
increases the severity of the loss, although with very low probability of default values; this
policy would not be suitable for banks.
Finding a sample of enterprises that apply Basel II concept of default has been not easy.
The required information is not public since it is available to banks only. It is easy to gather
data on failed enterprises while it is much more difficult to know what kind of enterprises has
outstanding debts, like the ones the supervision committee takes into consideration. The
cooperation with several local banks, which provided the data being necessary to develop the
models, allowed to solve the data related problem, as far as this study is concerned.
3. Construction of the interpretative model. Discriminant variables
Financial variables, being mainly selected on a theoretical basis, are applied by almost
all studies concerning the default prediction; attention is paid to those aspects of the
enterprise’s balance-sheet that are the main indicators of future financial distress. In addition
to that, statistical techniques are applied in order to choose the selected variables; in this way
it is also possible to decrease redundant information and to allow the selection of those
indicators that will be effectively distinguished in bonis enterprises compared with those in
default; therefore it is also a way to accept or not the theoretical proposition.
The likelihood that an enterprise will be unable to fulfil its financial obligations can be
determined by two factors:
1. A weaker competitiveness, i.e. the contraction of the an enterprise’s market share that is
relevant to competitors determined, for instance, by a poor technical development or by an
ineffective management of production processes;
2. Unsustainable debts determined by an overuse of the leverage or by a lack of liquidity “to
serve the debt”.
Two aspects enable to measure the competitiveness of an enterprise. The former one is
connected with business development; this managerial aspect is evaluated through the
variation rates that intervene among the elements of the balance sheet and the income
statement such as turnover, fixed assets and net worth. The latter important aspect is the
profitability of invested capital and in particular the profits resulting from the core business:
the enterprise’s survival and the value creation are clearly linked to the achievement of a
performance, which is greater than the cost of the invested capital, as well as to the economic
balance in the long run.
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Indicators of a weakening business development and of the capital performance suggest
that the enterprise’s core business will not become more profitable or that the enterprise has
not succeed in adapting itself to the market changes. Whenever these aspects are found in the
investment policies and the effective management of the production processes, they may
point out the enterprise’s financial distress.
The unsustainable debt, which is the second factor that determines insolvency, is
connected with the enterprise’s financing policies; it also linked to the enterprise since it has
a financial structure that is consistent with the made investmentsvii. Three categories of
indicators allow to examine the above mentioned factors; these indicators express what
follows: the enterprise leverage, its capability to fulfil financial obligations – at any time –
and its exposure to variations in perspectives, in terms of interest rates. The indicators
showing the company leverage allow to analyse the intensity of the use of the enterprise
leverage both for the employed capital and for the turnover; they also allow us to evaluate the
consistency between the financial structure and the investments. Of course, the higher the
enterprise’s indebtedness the higher the likelihood for it not to fulfil its financial obligations
since a negative economic cycle or management mistakes may cause difficulties in refunding
the loans. Moreover, the enterprise is also exposed to a higher interest rate risk because of the
increased incidence of debt in the enterprise’s financial structure since an unexpected
variations in the interest rate will have a significant impact on the operating costs. The
analysis of liquidity indicators leads to the investigation of the enterprise’s capability to
tackle with short term debt. This is why it is important to check whether liquid assets are
enough to refund short term debts as well as whether the core business is able to generate
cash flow able to pay interests. In addition to that, in order to assess the liquidity, it is also
useful to analyse the perspective variations in the enterprise’s trade policies as for the
inventories and the deferments that are provided to customers and suppliers.
Thirty-six variables were selected making reference to the core academic literatureviii. Five
categories gathered the extensive balance-sheet indicators.
Table 1: Type of variables
Category
Business development
Profitability
Interest rate risk
Liquidity
Leverage
TOTAL
Number of
indicators
4
10
2
13
7
36
Sample selection
The sample for the analysis consisted of 3137+515+482 enterprises that were selected
according to the following criteria, taking into consideration the period 2004-2007:
-
Limited companies (S.r.l. and S.p.A) localised in Tuscany;
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Companies not listed on regulated capital markets;
Profits over 5 million and below 50 million euro according to SME definition of Basel
II Agreement;
Business sectors – AtecoFin Codeix (see tab. n. 2 in appendix)
o
o
o
o
o
textiles and fashion;
building industry;
mechanical industries;
tourism industry;
other activities.
These selection criteria were identified to correctly represent the population of enterprises in
the Tuscan economy, avoiding possible distortions due to the introduction of micro-enterprises and
market listed enterprisesx; for these company the risk factors may be different from the SMEs
ones. This sample is also compliant with the Small and Medium Enterprises definition
provided by Basel II.
The percentage of default companies in the sample does not represent the real default
rate in Tuscany. Therefore, it will be necessary to measure the models in order to assess the
rating scale.
The tables below summarise the dimensions of the in-sample, national out of sample and
Tuscany out of sample.
Table 2: Dimension and structure of the sample
default
bonis
Textile
180
213
Building
270
378
Mechanist Tourism Others
224
117
484
351
291
629
Total
1275
1862
Table 3: Dimension and structure of Tuscany out of sample
default
bonis
Textile
50
64
114
Building
41
46
87
Mechanist Tourism Others
38
36
65
47
51
77
85
87
142
Total
515
Table 4: Dimension and structure of National out of sample
default
bonis
Textile Building Mechanist Tourism Others
42
39
40
31
58
71
50
41
45
65
113
89
81
76
123
Total
482
For each enterprise, data were collected with regards to the balance sheets of a three year
period; the following sampling scheme was applied.
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Table 5: Design for sample of businesses in default and in bonis. Traditional statistical techniques
2003 2004 2005 2006 2007
N1
N2
N3
D
D
D
NB
If we go into details as far as the sampling process is concerned, we made use of the
above mentioned traditional scheme where the balance sheets of ND enterprises in default
were chosen taking into consideration the same year for all of them, for example 2004.
Among the ND, of the sample, N1, failed in 2005, others, N2 after two years in 2006 and
finally the last ones, N3, after three years, in 2007. Clearly, N1 + N2 + N3 = ND. Similarly, the
balance sheets for NB in bonis enterprises make all reference to the same year, that is to say
2004. According to this approach, only one balance sheet represents each enterprise, as it
follows.
From an operational point of view, it has not been possible to include in the sample the
balance-sheets of enterprises in default making all reference to a specific fixed year. As a
matter of fact, that would have remarkably reduced the numerousness of samples. According
to the main literature stream, the sampling process has been realized as the following: some
balance sheets make reference to the 2004 financial year while the default occurred in 2006,
others make reference to the 2005 financial year and the default occurred in 2007.
Like all the rating models for the Italian system, there is in particular a time lag of two years
between the reference year of the balance sheet and the taking place of the default. This is
due to the fact that enterprises put at one’s disposal their balance sheets one half year after the
balance sheet closing. This is the reason why models make use of 2004 balance sheets to
estimate the insolvency probabilities concerning 2006. However, a “one-year probability”
will be evaluated (and not a probability for two years) concerning the 12-24 month period
following the reference date of the balance sheet.
Industry-specific models
In developing models, we implemented an industry-specific approach since we think
that this is an effective way to assess insolvency probabilitiesxi. We found, in fact, that SMEs,
which were included in the survey, have a structure of the balance, depending on the carried
out activity, that is rather heterogeneous among all of them.
This is why it is not possible to assess general models. In addition to that, in view of a selfassessment of the creditworthiness, it is important to know the relevant indicators in different
industrial sectors and, consequently, the managerial “levers” to act on. xii. The decision to
estimate industry-specific models is also supported by the significant unsteadiness of real
insolvency rates among different sectors, as the table below underlines.
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Fig. 1: Default rate by industry in Italy – source: Standard & Poors (2004), Credit risk tracker
In fact, one single general model could under-evaluate the PD for some industrial sectors
while it could be conservative for others.
Nevertheless, given the limited available data, we made use of a sleight of hand in order to
gather the sample enterprises in “macro sectors”. This industry articulation is achieved by
gathering enterprises following the first two digits of AtecoFin Code. It make possible to
establish five groups (textiles, mechanics, building, tourism and other activities) that will
represent five different learning samples to estimate specific models, as the table below
highlights. The aggregation process was carried out on a qualitative basis, onlyxiii, taking into
account the similarities in terms of risk profile and trade off existing between the sample size
and the homogeneity of the enterprises the sample includes. More restricted samples and
therefore a higher homogeneity should guarantee better models performances. However, their
operational applicability is lower.
Table 6: Model industry – AtecoFin codes
AtecoFin
codes
Business Sector
17
Textile industry
18
Clothes
19
Tan industries
45
Buildings
27
Metallurgy
28
Metal products
29
Mechanical devices
30
Office equipments
Model Sector
Textile
Building
Mechanics
Electrical machines, motor
31; 32; 33; vehicles, means of transport,
34; 35
radio and television sets,
medical instruments
55
Tourism Service
Tourism
Other codes
Others
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Enterprises location
Most of the enterprises that the database includes have their headquarter in Tuscany.
Essentially, the assessed models are conceived for Tuscany economic structure. This
decision, although it limits the applicability of our work, allows to include all the risk
elements connected with the reference economic sphere. This choice is supported by the high
variability of default rates in Italy. For instance, in the South of Italy there are much higher
insolvency rates.
Fig. 2: default rate by region in Italy – source: Standard & Poors (2004), Credit risk tracker
In order to take into the account the high variability of default rates in Italy, Standard
& Poors and Moody’s introduces a “localization” variable in their national models.
In this work, this research design is not necessary since the sample is homogeneous in
terms of geographical localization. In our opinion, this choice should allow to improve the
anticipatory capability of the models. However, their application will be restricted to Tuscany
enterprises.
Exploratory analysis and treatment of outliers
This study made use of and tested a very wide group of indicators. For this reason, an
exploratory analysisxiv of the variables is needed. It aims at:
-
identifying the outlier values;
identifying the individual predictive power of variables (univariate logit);
analyzing the correlation matrices and selecting the independent variables by means of
an iterative processxv.
During the analysis, we found and treated all outlier values that could determine
significant distortions in the development of the models. In most cases we found outlier data
were not relevant in describing the current financial situation of the enterprise.
In developing the model, we defined outliers as those (superior or inferior) values for
each variable that are 2,5 standard deviations away from the mean of the values in the
population and we replaced them according to winsorization methods [Barnett & Lewis
(1994)]. The “boundary values”, are calculated as it follows:
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Population mean  ( 2,5 * Standard Deviation)
(1)
This allowed us to improve the performance of the models while maintaining the original
characteristics of the data.
During the analysis, we employed an additional transformation of variables: the natural
logarithm. We essentially tested the anticipatory capability of each variable both in its
original and logarithmic form that is expressed in the following way:
ln
a
 ln a  ln b
b
(2)
In many cases the indicators showed negative values, yet (consider Ebit/turnover where Ebit
may have of course negative values); in this case it was not possible to apply the natural
logarithm.
In order to get round of this, we applied the following logarithmic difference where the
possible negative value is “drawn out” from the application of the logarithm to the absolute
value of the numerator and the denominator:
Sign of a * ln(| a  1 |)  sign of b * ln(| b  1 |)
(3)
This transformation provides a double advantage: on one hand it allows to obtain in any way
the “beneficial effects” of the logarithm in terms of statistic distribution of data; on the other
hand it allows to keep the sign of the ratio.
During the analysis, we noticed a remarkable improvement in the adaptation of data to the
model resulting from these logarithmic transformations.
Method of analysis
For this work, the employed statistical methods result from the carried out sampling
selection. Given the sampling scheme we applied, we above-discussed about, there is no
autocorrelation among the explanatory variables since each enterprise is represented in the
dataset with one balance-sheet only. In this way it is possible to make use of the traditional
survey methods in order to assess the models. In particular, we applied the method of the
logistic regression. This technique allows to estimate a default probability instead of a credit
score; therefore it allows an easier articulation of the merits classes.
***
As far as the details of the applied analysis process are concerned, for each sector, we
carried out an analysis of the individual discriminant power of each variable. This analysis
was possible through a logistic regression to an explanatory variable. This process allowed to
identify, for each sector, the index with the highest discriminant power on an individual basis.
The model has been developed by means of an iterative process, similar to a logit stepwise.
First of all, we identified, for each business sector, the variable with the highest
performances. This variables has been tested in relation with each others to identify the best
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couple of indicators. This process finished when, adding a new variable, it was not possible to
improve the aggregate model performance.
The carried out process was repeated for each of the five singled out industrial sectors. In this
way, it was possible to assess the models with the highest discriminant power.
The model indicators undergoes an additional revision process in order to check whether the
assessed models were significant, for the user, from an economic and financial point of view.
In particular, together with the correlations among them, we checked:
-
the sign of the coefficient that had to be consistent with the theoretical ratio between the
insolvency risk and the variable itself;
the mono-tonicity of the variable: the analysis doesn’t take in consideration the variable
showing a non monotonic trend that could not be explained from an economic and
financial point of view.
Nevertheless, not to be forgotten that other variables could also be included among
models. Often, we had to choose between two correlated indicators (for example
worth/gross investments vs financial debts/gross investments) that could not coexist at
same time. In these cases, following the above-explained iterative process, we chose
indicator that mostly contributed to the aggregated performances of the model.
the
net
the
the
4. Analysis of results
4.1. Discriminant variables
From the empirical analysis emerges that some indicators were significant in most of
the assessed models. The enterprise’s capitalization level (net worth/investments) is
significant in four, over five, estimated models. The incidence of the financial charges
(interests) on the turnover is significant for each sector of the survey. In addition to this, the
operating profitability on sales characterizes four out of the five models. That leads us to
conclude that these variables are significant regardless the enterprise’s business industry.
Yet, we noticed a substantial difference as for the importance of the three above-mentioned
variables in the different industries of the survey. This leads us to conclude that the industryspecific models assessment allows to best single-out the relevant variables for each business
sector and therefore to forecast more correctly the default event with regards to general
models.
The table below summarizes the most important variables in the models.
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Table 7: Discriminant variables in our industry-specific model
Variables
Net worth / gross
investments
Financial charges /
turnover
Ebit /Turnover
Financial
charges/financial debts
Net commercial working
capital/turnover
Net worth/Financial debts
External costs/Turnover
Total assets
Quick ratio
Category
Textile Building Mechanics Tourism Others
Leverage
X
X
X
Leverage
X
X
X
Profitability
Risk of rate
change
X
X
X
X
X
X
X
Liquidity
X
X
X
Leverage
Profitability
Dimension
Liquidity
X
X
X
X
As regard to our theoretical model, we noticed that the indicators of the activity development
are not significant. In fact, their discriminant capability appears limited: the variation of the
turnover seems to be slightly correlated with the insolvency risk, only. This evidence could
be determined by numerical problems caused by indicators that are made of “variations”.
Often ratios consisting of variations have several negative and positive values in each of the
two groups of enterprises (bonis and default) that invalidate the discriminant capability of the
group as for the model assessment. Nevertheless, the ratio is still relevant regarding when an
individual financial analysis of an enterprise is done.
As far as the liquidity indicators are concerned, we notice their poor anticipatory capability.
In fact, in the “Others” model, as well as in the “Mechanics” one only, the two indicators
(quick ratio and CCN commercial / turnover), are significant.
That leads us to think that generally the insolvency risk depends on the indicators of property
soundness as well as of operating return on sales, in compliance with the main literature in
the field.
4.2. In sample results
Running discriminant models, we obtain the results presented in the following table.
Considering the Textile sector as an example, 159 enterprises are correctly classified in bonis,
corresponding to 75.35% of the total in bonis sample; 111 enterprises are classified in default
equal to 80.43% of the total default sample. This implies that the remaining enterprises are
incorrectly classified with a percentage of error of Type 1 (enterprises in default classified by
the model in bonis), equal to 19.56% and of error of Type 2 equal to 24.64. Making a
comparison among the results, we notice that the residual model provides performances, both
in terms of classification errors and of Rocxvi curve, whose quality is lower than the others.
This evidence strengthens our conviction that the industry-specific approach allows to obtain
lower percentages of prediction error. In fact, the “Residual” sample includes enterprises
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belonging to several economic industry and so it is rather heterogeneous in terms of structure
of economic and financial indicators. Therefore, we can state what follows:
1) samples, where enterprises’ balance sheets were more homogeneous, provided better
model performances;
2) the more homogeneous the activity carried out by industry sample enterprises the
more considerable this improvement.
Table 8: Textile model
Table 9: Building model
y classified
0
159
Y 0
75,35%
true
1
27
19,56%
ROC = 82,20%
1
52
24,64%
111
80,43%
Total
samplexvii
y classified
0
267
Y 0
78,53%
true
1
42
27,45%
ROC = 80,54%
211
138
349
Table 10: Mechanics model
340
153
493
Table 11: Tourism model
y classified
0
237
Y 0
74,76%
true
1
37
22,84%
ROC = 81,5%
1
73
21,47%
111
72,55%
Total
sample
1
80
25,24%
125
77,16%
Total
sample
y classified
0
163
Y 0
72,77%
true
1
14
17,72%
ROC = 80,1%.
317
162
479
1
61
27,23%
65
82,28%
Total
sample
224
79
303
Table 12: Residual model
y classified
0
478
Y 0
76,11%
true
1
110
28,94%
ROC = 73,2%
1
150
23,89%
270
71,06%
Total
sample
628
380
1008
4.2. Comparison of out of sample accuracy
In order to answer to the main research question, we applied the models assessed on
out of the sample data. It is therefore possible, on one hand, to assess the anticipatory
capability of the models and, on the other, to compare the accuracy results between Tuscany
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enterprise samples and national (not Tuscany) enterprise samples. The results show that the
correct classification percentages are still high where new data about enterprises, not included
in the assessment sample, are processed. We notice, in fact, a decline of the classification
error from 1.11%, for the residual sector, to 1.87% for the building sector.
Table 13: Tuscany in sample vs. Tuscany out of sample results
Model
In – sample
Textile
Building
Mechanics
Tourism
Residuals
22,64%
23,33%
24,43%
24,75%
25,79%
Tuscany out of
sample
24,30%
25,20%
26,20%
25,90%
26,90%
Decline
1,66%
1,87%
1,77%
1,15%
1,11%
On the contrary, as far as the comparison of the anticipatory capabilities of models on
Tuscany enterprises and on national enterprises is concerned, the results show higher error
percentages for the national out of sample data.
The error slightly increases of 0.30% in the Mechanics model while it increases significantly,
3.30%, in the Textile one.
Table 14: Tuscany out of sample vs. National out of sample results
Textile
Building
Mechanics
Tourism
Residual
%
% error
correct
%
correct
% error
%
correc % error
t
%
correct
%
error
National out
72,4% 27,6% 73,6% 26,4%
of sample
73,5%
26,5%
72,1%
27,9%
71,8%
28,2%
Tuscany out
75,1% 24,3% 74,7% 25,2%
of sample
73,8%
26,2%
74,1%
25,9%
73,1%
26,9%
Methodology
%
correct
Error
Variation
%
error
3,30%
1,20%
0,30%
2,00%
1,30
Table 15: Tuscany out of sample vs. national out of sample Mean Error
Mean Error
National out
of sample
Mean Error
Tuscany out
of sample
27,32%
25,70%
In the carried out analysis we noticed, as an average, a prediction error equal to 25.70% for
the Tuscany out of the sample and an error equal to 27.32% in the national out of sample.
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Conclusions
In this studies we gained a better understanding of regional SME default risk
modelling answering to the main research question “Are regional models for SME able to
better estimate default risk than national based models? Does regional model estimation make
sense?”.
The empirical analysis is based on regional (Tuscany) companies according to the
Basel II definition of default. On regional data, we estimated five industry-specific models
that are consistent with the main proposition: regional models better estimate company
default risk than national ones.
The geographic sampling approach superiority is demonstrated by comparing “% of
misclassified companies” on both regional and national samples, where the mean errors in the
out of sample regional data is lower than where national data is applied. This results is
confirmed in all industry-specific models.
The models we assessed do not require the introduction of geographical variables and
may be immediately adjusted on the real default rates found in Tuscany; that makes
considerable simplifications be possible during the implementation phase of the rating
system.
Others research design could address the research question taking into the account in
the national rating model one or more localization dummy variables. Nevertheless, the high
level of accuracy in our research suggest that this is a viable option to address the geographic
sampling. Future studies may profit on this preliminary research to gain a better
understanding of the phenomena and to reject or confirm the results we found.
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Appendix
Employed Variables
Variables
Turnover variation
Fixed assets variation
(Depreciation fund/fixed assets) variation
Number of employees variation
Equity variation
Ebit variation
(EBIT + financial profit) / (Total assets – non
financial debt)
Ebit / turnover
(Ebit / turnover) variation
Personnel costs / added variation
Inventories change / turnover variation
Cost of goods sold / turnover
Added value / fixed assets
Added value/ number of employees
Depreciation rate variation
Interest costs / financial debt
(EBIT + Financial profit) / (Total assets – not
financial debt) – (interest costs / financial
debt)
Current ratio
Liquid assets / current assets
Quick ratio
Ebitda / turnover
(working capital / turnover)
Days of clients variation
Days of inventories variation
Days of debtors variation
(Ebitda – tax) / short term financial debt
(Ebitda – tax) / financial debt
Ebitda / interest costs
Net profit + amortization / short term financial
debt
(Financial debit – cash) / turnover
(Financial debt – cash) / equity
(Financial debt – cash) / (equity – intangibile
assets)
Short term financial debt / financial debt
Equity / fixed assets
Intangibile costs / total assets
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Category
Business
development
Profitability
Rate risk
Liquidity
Leverage
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For a definition of default risk see Baron, D. P. (1974). “Default risk, homemade leverage and the Modigliani-Miller
theorem”. American Economic Review, 66, 176-182; Lotz, C., Schlogl, L. (2000). “Default risk in a market model”. Journal
of Banking & Finance, 24, 301-327. For a detailed analysis on such risk referes to the pioneer work of Altman E.I. (1968),
“Financial ratios, discriminant analysis and the prediction of corporate bankruptcy”, Journal of Finance, 23(4), 589-609.
ii As it was mentioned above, pricing relates to the default risk of the borrower and to other important variables such as “loss
given default”, and “exposure at default”.
iii The bank loans are, for SMEs, the most important source of fund to finance business development and investments.
iv Basel Committee On Banking Supervision (2004), International convergence of capital measurement and capital
standards: a revised framework, Basel, Bank for International Settlements.
v Basel Committee On Banking Supervision (2004), International convergence of capital measurement and capital
standards: a revised framework, Basel, Bank for International Settlements.
vi For Italian credit portfolio the unpaid limit is increased to 180 days for a transaction period of 5 years.
vii Investments linked to fixed assets must be financed by means of long-term funding. The optimal situation, often not
achievable, would be to cover fixed assets by means of one’s own capital. But more usually than not, fixed investments are
financed by making use of the debt that needs to be long-term one in order to guarantee consistency between financial
structure and fixed investments.
viii See Giunta, F. (2003). Analisi di bilancio. Florence, IT: Copisteria il Prato.
ix
This is the classification of business activities made by Istat.
x Data published by rating agencies shows that the size of an enterprise is also a variable that impacts on default risk, insofar
as default rates are much higher for micro-enterprises, and decrease with increases in scales of business.
xi Some methodological tests, which were performed on a more restricted sample, showed a significant improvement of the
industry-specific models performance compared with the general ones. With this regard, see O. Roggi (2006), “Basel II and
default risk estimation”, conference paper, Small business and banking financing International Conference, Cagliari 2007.
This evidence is also confirmed by the main literature in this field. See Standard & Poor’s, Credit Risk Tracker.
i
xii
This reasoning will be confirmed afterwards, depending on the results the models will obtain.
xiii
The best solution in order to unite enterprises in homogeneous groups would be the cluster analysis. For this work we
decided not to apply this method because the number of observations was too low and it did not allow a right
individualization of groups.
xiv For the empirical analysis we used R software.
xv We used a stepwise regression to identify the multivariate predictive power of variables.
xvi The area under the Roc (receiver operating characteristic) curve indicates the accuracy of the model. Roc values goes
from 0 to 1, according to the increased accuracy.
xvii The difference between collected data and employed ones results from the fact that some remarks have been deleted from
the analysis because one of the following characteristics have happened:
A high presence of missing values;
Turnover equal to zero and consequently idle enterprises;
Default state and financial indebtedness equal to zero.
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