Alternative bankruptcy models – first results
František Kalouda^1, Roman Vaníček^2
^1 Masaryk University
Faculty of Economics and Administration, Department of Finance
Lipová 41a, 602 00 Brno, Czech Republic
E-mail: kalouda@econ.muni.cz
^2 Ivasoft, l.t.d.
R&D Department
Kupkova 72, 638 00 Brno, Czech Republic
E-mail: roman.vanicek@ivasoft.cz
Abstract: The article is focused on showing first results of two newly created (alternative)
bankruptcy models. The used database contains available data of Czech companies (CreditInfo
database). Based on result comparison with standardized bankruptcy models (IN 05, Z-fce) the two
new models are equivalent in one case and significantly better in the second case.
Keywords: discriminant function, alternative bankruptcy models, standard models
JEL codes: G17, G32, G33
1 Introduction
The exclusive position of bankruptcy models in financial analysis methods is out of question.
However their accuracy is regularly being discussed.
The usual praxis of expressing successful predictions in percentages is more and more often
supplemented or substituted with ROC curves (see later).
Two newly created alternative discrimination functions (CZ2 and FK) are presented in this article.
Their accuracies are evaluated using ROC curves. Relative success of these functions is based on
the comparison of their results with standard bankruptcy model benchmarks – Z function and IN05.
2 Aim and Methodology
The objective of this article is to provide the first objective view of the applicability of the
new created alternative bankruptcy models (CZ2 and FK) in Czech Republic (hereinafter as CR).
The following shall be used to fullfil the above mentioned aim of this article:
a) proposal of new discriminant function (model) and empirical verification of theirs
predicative ability in a full set of available data on businesses based in the CR
b) comparison of the predictive ability this new discriminant functions (models) with
other bankruptcy models.
The used set of methodical instruments consist mainly of:
■ literature review,
■ comparison,
■ analysis,
■ historical analogy and
■ synthesis.
The methodology of the construction of the new created models is out of the scope of this article.
It does not allow us to neither present the process of financial ratios selection nor the process
of calculating the weights of the models.
3 Data
3.1 Database of Businesses
All data used in this work come from the database Firemní monitor (Creditinfo Czech Republic 2010),
formerly known as Albertina. It is a comprehensive database of all registered firms and
organizations in the Czech Republic. It captures the basic data on more than 2,400,000 business and
non-profit economic entities. It has the largest set of financial statements processed into a
structured form. Only financial statements and industry classification CZ-NACE (Český statistický
úřad 2011) was used.
The above suggests that as far as the data base, with which the proposed discriminant function
operates, is concerned; it is basically about working with the base selection. All adjustments to
this set described above follow only one viewpoint - to eliminate irrelevant data.
3.2 Data Export and Import
Even though the source database contains basic information on more than two million entities, at
least one financial statement is available for only 149,423 entities. On average, there are three
financial statements - not necessarily consecutive - available for each entity. The total amount of
financial statements, which meet the verification conditions stated below, is 538,162.
During the import of the database, the data redundancy in the financial statement was used to
detect and sometimes also to repair the incorrect values. The set of these functions were named
verification conditions. Part of the verification conditions requires that the difference between
the summands and their declared sum is insignificant. One condition is also formed by the balance
equation. The value of CZK 10,000 was determined as insignificant. 2.4% of financial statements did
not meet the verification conditions. This article uses data from the database Firemní monitor as
of March 2010. All monetary values are in thousands of CZK, unless otherwise indicated.
3.3 Selection of the Bankrupt and the Surviving
Every financial statement, which precedes the date of bankruptcy, variably depending on the
selected time horizon - in this paper 720 days (min. 2 years) - was considered a bankrupt business
over time. The issue of insolvency is governed by the Insolvency Act No. 182/2006 Coll. with effect
from 1st January 2008. Before this date, insolvency was governed by the Act No. 328/1991 Coll., on
Bankruptcy and Settlement.
3.4 Selection of Sample and Retained Data
Each financial statement prepared for the period of 12 months is considered an individual case
entering the mathematical model. A randomly selected half of all cases is always used as the sample
used for the calculation of the model. The other half of the retained (validation) data serves to
verify the model.
3.5 Data Profile
In terms of frequency of bankrupt firms over time, the database is of the following nature. Among
all financial statements, there are 1,619 firms two years before bankruptcy, i.e. 0.3%. If we limit
the information ability of the group to 3, there are 1,017 bankrupt firms, i.e. again 0.3%. If we
focus on the frequency of bankruptcies declared in individual years, which is the number of
businesses, the database covers 32% of all bankruptcies declared in legal entities in 2009 with a
gradual decrease to 12% in 2005. The database contains a total 1,863 businesses in bankruptcy, for
which at least one financial statement before the date of bankruptcy exists. In addition, the
database contained a sign of bankruptcy in 1,259 businesses without a date of bankruptcy - these
are ceased businesses (or in liquidation for a long time) which cannot be found in the Commercial
Register or ongoing insolvency proceedings. All statements of these businesses were excluded.
An unpleasant aspect of the Czech business environment is occasional huge delays between a debt
that is unpaid for 30 or 90 days and the beginning of the insolvency proceedings. Delays of four
years are not an exception (Klima 2009, p. 2). The result of this situation is the fact that any
bankruptcy model will see the financial data with the goal to classify it as a healthy business for
a time period shorter than the mentioned delay. If it classifies it positively (as bankrupt), it
will be penalized in the form of an error of second kind.
4 Results and Discussion
4.1 Resulting Models CZ2 a FK
The model CZ2 was obtained from the MDA analysis using the Fisher discriminant includes eight ratio
indicators: CapitalReinvested, DaysPayableOutstanding, DaysSalesOutstanding, InventorySales,
CashLiquidity, LiabilitiesHealthPension, ROA, InterestCoverageRatio.
The model FK was obtained by analysis of causalities between financial ratios. It includes only
three ratios, which are listed in Table 2.
The coefficients of the CZ2 model for the horizon of two years are stated in Table 1. The
coefficients of the FK model for the horizon of two years are stated in Table 2.
The definition of financial coefficients is based on standard approach. Exact definitions are not
the goal of the article. Also beware of the coefficients mentioned in Table 1. They are to be used
solely for economic interpretation not for direct evaluation from financial ratios.
Table 1 Linear discriminant model CZ2 with failure time horizon two years
Ratio
Coefficient
CapitalReinvested
0,416
DaysPayableOutstanding
-0,160
DaysSalesOutstanding
-0,103
InventorySales
-0,047
CashLiquidity
0,321
LiabilitiesHealthPension
-0,685
ROA
0,317
InterestCoverageRatio
0,340
Source: Author’s construction based on data base Firemni monitor
Table 2 Linear discriminant model FK
Ratio
Coefficient
CurrentAssets/ShortLiab
2,0
CurrentLiquidAssets/ShortLiab
1,0
Inventory/ShortLiab
-1,0
Source: Author’s construction based on data base Firemni monitor
4.2 Models Comparison
The output of some discriminant models such as MDA or logistic regression is x, to which it applies
that the more the value approaches infinity, the higher is the probability that the correct
classification of the given case. In the field of financial risk, this value is called the score. A
user of these models must determine a threshold value of the score, according to which they will
classify businesses as healthy or acutely at risk of bankruptcy. Each such choice implies the size
of the error of the first kind (FP or false positive) (classification of a healthy business as a
business at risk of bankruptcy) and the error of the second kind (FN or false negative)
(classification of a business at risk of bankruptcy as a healthy business). The function, which
puts both these characteristics indirectly into a relationship, is called ROC curve and is
frequently used in the newer studies on bankruptcy models (Altman, Sabato, and Wilson 2010),
(Escott, Kocagil, Rapallo, and Yague 2001) and (Castro 2008).
The relation between specificity and sensitivity follows the definition in equation 1.
The accuracy of the model is defined as the area under the curve (AUC) which is related to the Gini
coefficient G given by the equation 2 where the meaning of the symbols A and B is shown in Figure
1. Some works (Escott, Kocagil, Rapallo, and Yague 2001), (Castro 2008) use the Gini coefficient
instead of the AUC.
The actual accuracy of the model is not directly compared to another model, but indirectly through
so-called benchmark which is one version of the Z-function by Edward I. Altman.
(1)
(2)
Figure 1 ROC curve
Source: Author’s construction
4.3 Comparison of the Resulting Models
When calculating the model CZ2, the accuracy of the model on the input sample was Gini = 0.701 and
on the holdout (validation) sample it was Gini = 0.703. The difference is less than half a
percentage point. When calculating the model FK, the accuracy of the model was Gini = 0.43. There
is no need to use a validation sample for model FK as the weights were not directly based on the
input data.
We perform the comparison of the accuracy of the model not only against the benchmark Z-function
models (as mentioned in 4.2) but also against other works (Neumaier and Neumaier 2005). For the
comparison only values calculated on the validation (holdout) data were used. The comparison is
divided according to data source in Figure 2.
Figure 2 ROC curve model comparison on two year time horizon
Source: Author’s construction based on data base Firemni monitor
Table 3 Model comparison using Gini and AUC values on two year time horizon
Ratio
Gini
AUC
CZ2
0.703
0.852
IN05
0.500
0.750
Z-fce 1968
0.495
0.748
FK
0.434
0.717
Source: Author’s construction based on data base Firemni monitor
Conclusions
First tests of the newly created bankruptcy models provided encouraging results. Prediction horizon
in this case was chosen to be two years.
The accuracy of all the tested models using the ROC curve with AUC criterion and sorted descending
by accuracy is shown in table 3.
It is clear from the results that the prediction accuracy of the newly created model is fully
comparable with standard models (model FK), and also clearly better (model CZ2).
The results obtained are considered as a work in progress. The final assessment will be done after
a second round of tests; this time with five year accuracy.
It is appropriate to remark that the information capability of the new models is thanks to the
input data base practically absolute.
References
Act No. 328/1991 Coll., on Bankruptcy and Settlement.
Altman, E. I., G. Sabato, and N. Wilson (2010). The value of non-financial information in
small and medium-sized enterprise risk management, The Journal of credit Risk 6, 1–33.
Castro, C.E. (2008). Estimating a financial distress rating system for Spanish firms with a
simple hazard model.
Creditinfo Czech Republic, s.r.o., 2010, Databáze Creditinfo - Firemní Monitor[online]
http://www.creditinfo.cz/?PageID=1314 [cit. 2010-05-13].
Český statistický úřad (2011). Klasifikace ekonomických činností (CZ-NACE)[online]
http://www.czso.cz/csu/klasifik.nsf/i/klasifikace_ekonomickych_cinnosti_(cz_[cit. 2011-04-18].
Escott, P., A.E. Kocagil, P. Rapallo, and M. Yague, 2001, Mody’s RiskCalcTM For Private
Companies: Spain Rating Methodology, Discussion paper Moody’s Investor Service.
Insolvency Act No. 182/2006 Coll. (2006). With effect from 1st January 2008.
Klima, J. (2009). Zpráva o činnosti insolvenčního správce a hospodářské situaci podniku
dlužníka,[online]
https://isir.justice.cz/isir/doc/dokument.PDF?vedlejsi=ne&rowid=AAAE1GAAYAAL%[cit. 2011-04-18].
Insolvenční rejstřík PRINT MEDIA a.s., dříve Mladý svět, akciová společnost, IČ 00553441.
Neumaier, I. and I. Neumaier (2005). Index IN05, Evropské finanční systémy. Sborník příspěvků z
mezinárodní vědecké konference ISBN 80-210-3753-9.