The_bias - SME Bankruptcy Prediction

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The bias of unhealthy SMEs inbankruptcy prediction models

J. Samuel Baixauli and Antonina Modica-MiloDepartment of Management and Finance, University of Murcia,

Espinardo, Spain

Abstract

Purpose This paper aims to construct a financial health indicator to define the degree of financialhealth in order to decontaminate the estimation sample and to make predictions that are not biased byunhealthy firms.

Design/methodology/approach The binomial logit model is used to examine the likelihood thata firm will go bankrupt. In order to evaluate the accuracy of the estimated models, measures proposedby the Basel Committee on Banking Supervision are applied: cumulative accuracy profile (CAP) and

the receiver operating characteristics (ROC).Findings The proposed financial health indicator permits the heterogeneity of the firms to bereduced as well as identifying a strong firm sample to estimate the bankruptcy probability accurately.

Originality/value A drawback of all bankruptcy prediction models comes from the fact thatbankruptcy is an example of a homogeneous observable qualitative response while non-bankruptcywould be expected to be represented by a healthy firm. However, the non-bankruptcy firms areheterogeneous and their actual probabilities of bankruptcy are non-observable. The article adds to theprevious literature on SMEs bankruptcy prediction by using a financial health indicator to constructthe estimation sample and to make accurate bankruptcy predictions.

Keywords Bankruptcy, Business failures, Mathematical modelling

Paper type Research paper

IntroductionThe small and medium-sized enterprise (SME) sector is often viewed as the incubatorof employment, innovation and growth (Craig et al., 2003). The reports by theobservatory of European SMEs use statistics on the number of enterprises, totalemployment and production by firm size to provide an overview of the currentsituation in the SME sector in Europe. Regardless of how they are measured, not onlyare most enterprises in Europe small, but they also account for a significant amount ofEuropean work experience and economic activity. For instance, in 2003 there weremore than 19 million enterprises in Europe, providing jobs for almost 140 millionpeople. In contrast, there were only about 40,000 large enterprises in existence, whichaccounted for only 0.2 per cent of all enterprises. So, the vast majority of enterprises inEurope are SMEs. Zingales (2000) points out that, empirically, the attention paid to

large companies has lead researchers to ignore the rest of the young and small firms,which do not have access to public markets.

SMEs are financially more constrained than large firms and are less likely to haveaccess to the capital market. Nowadays, due to the lack of capital market data, the banksector uses techniques based on models where financial ratios are combined and

The current issue and full text archive of this journal is available at

www.emeraldinsight.com/1462-6004.htm

The authors thank Fundacion Cajamurcia and the Spanish Government (Project ECO2008-02846) for financial support.

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Journal of Small Business and

Enterprise Development

Vol. 17 No. 1, 2010

pp. 60-77

q Emerald Group Publishing Limited

1462-6004

DOI 10.1108/14626001011019134


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weighted to produce a probability of bankruptcy in order to estimate the bankruptcyprobability. Bankruptcy is disruptive and costly to owners, investors andcommunities. Despite the existence of many contributions, the bankruptcyprediction continues to be an important issue. As Altman and Saunders (1998) point

out, an increase in the number of bankruptcies, more competitive margins on loans,and a trend towards disintermediation by the highest quality and largest borrowershave led to the development of new and more sophisticated credit-scoring andearly-warning systems. Altman and Saunders (1998) review new models of credit riskmeasurement, for example the KMV model, models based on the term structure of yieldspreads, mortality-default rate models, and neural network models. These models arebased on capital market data and quoted firms. However, the difficulty of SMEs inaccessing the capital market restricts the use of such models. In Europe only a verysmall percentage of SMEs are quoted firms.

Many bankruptcy prediction models thatcombine financial ratios have beenproposed in the literature. Of these, the models of Beaver (1968), Altman (1968) andAltman et al. (1977) are worthy of note. A drawback of all bankruptcy predictionmodels comes from the fact that bankruptcy is an example of a homogenousobservable qualitative response, while non-bankruptcy would be expected to berepresented by a healthy firm. However, non-bankruptcy firms are heterogeneous andtheir degree of financial health is non-observable.

Our article adds to the previous literature on SMEs bankruptcy prediction byidentifying the characteristics of a healthy firm and by evaluating the effects of usingor not using these characteristics in the sample design on the accuracy of thebankruptcy prediction models. In the evaluation process, statistical methodologiesrecommended by the Basel Committee on Banking Supervision are used. Our proposalis compared with the traditional methodology based on unbalanced samples and onmatching by size and industry.

The structure of the paper is as follows: the next section discusses bankruptcyprediction models and the definition of healthy firms in order to exclude firms withhigh probability of bankruptcy. The subsequent section outlines methods used toanalyse the data. The next section covers the data collection and discusses the findingsof the analysis. The final section concludes with a discussion of the findings.

Bankruptcy prediction and the bias of non-bankruptcy firmsAccording to Berryman (1983) there are different definitions of failure:

. earning a rate of return significantly and continually below prevailing rates onsimilar investments;

. ceased operations; or

. termination for any reason.

When the use of bankruptcy prediction models is the main issue, failure is defined asonly those firms that are declared bankrupt, and non-bankrupt firms are any otherfirms. Such definitions mean that firms with a much more general definition offinancial distress or failure are also included among non-bankrupt firms. They havehigh bankruptcy probability even though they cannot be classified as bankrupt firms.For example, a failure definition could include discontinued ownership (ownership

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changes), business discontinuance (the business ceases to exist) or failing to make ago of it.

Often, firms that satisfy the wide definition of failure are not bad firms to invest in.In this sense, a change in ownership may not imply failure because the business may

continue under a different owner. Watson and Everett (1999) believe thatdiscontinuance may signal actual failure because business resources may have beenreallocated to more profitable areas. Headd (2003) makes a compelling argument thatdiscontinuance may not be associated with failure. Many financially strong firms maycease to continue because of an existing strategy. The meaning of discontinuance is toowide and includes firms that sell because they are successful and are offered a goodprice and firms that are taken over. In this sense, Cochran (1986) points out thatbusinesses may be discontinued because of extraneous factors such as retirement orillness, because alternative opportunities present themselves, or under some definitionsof discontinuance, even because the business is sold at a profit. As Watson and Everett(1996) point out, the broader the definition of failure, the higher the failure rate forsmall firms. In order to show that bankruptcy probabilities are unobservable variables,Carter and Van Auken (2006) define failure as only those firms that declarebankruptcy. All this evidence gives risk managers and researchers a range of firmswith different degrees of failure and different bankruptcy probability. In fact, Watsonand Everett (1999) test the relation of the probability of failure with the years of life of abusiness and with the barriers to entry in an industry sector by considering threedifferent definitions of failure (bankruptcy, discontinuance of ownership and failing tomake a go of it).

The sample design employed by many research studies has been to match a set ofbankrupt firms with the same number of non-bankrupt firms, often controlling for sizeand industry (see Altman, 1968; Theodossiou et al., 1996; Carter and Van Auken, 2006,among others). Matching unhealthy non-bankrupt firms with bankrupt firms in order

to estimate the parameters of a bankruptcy prediction model produces a bias in theestimated parameters and a reduction in the ability to predict bankruptcy accurately.As a consequence, it is necessary to make a previous selection in order to includenon-bankrupt firms with good financial health in a model.

As the degree of financial health is unobservable, in this article an indicator offinancial strength is constructed. If this indicator is positively correlated with thefinancial health, then to match non-bankruptcy firms characterised by having highvalues of the financial health indicator with bankrupt firms should allow us to estimatebankruptcy prediction models with less prediction error than the models that matchnon-bankrupt firms characterised by low values of the financial health indicator withbankrupt firms.

Statistical records are satisfactory for listing bankruptcies or discontinuances, but

they cannot cope with identifying the severity of failures. The definition ofnon-bankruptcy should be devoid of unsuccessful firms with a low degree of financialhealth. The economic definitions of failure take profitability as a common denominator.In this line, Fredland and Morris (1976) state that any firm earning a rate of return oninvestment that is less than the firms opportunity cost is a failure. Following thedefinition of Altman (1968), a non-bankrupt firm is a failure if it is earning a rate ofreturn on invested capital which is significantly and continually below prevailing rateson similar investments. Causes of failure can be classified as endogenous (internal to

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the firm) and exogenous (external to the firm). Exogenous causes, such as exchangerates or high interest rates, ascribe their failure to problems in operational managementand endogenous causes are widely related to poor operational management, high costsof production, poor marketing policy and poor personal management (Hall and Young,

1991).We select four measures of profitability to construct our financial health indicator:. the return on assets;. capital turnover;

. return on equity; and

. net worth variation.

As the profit measures may be managed figures subject to deliberate manipulations,we add the auditing opinion:

. Return on assets (FR1), measured by earnings before interest and taxes over totalassets. This variable measures the economic efficiency of a firm, i.e. its capacityto generate profits independently of its financial structure, debt cost, taxes or theprofitability required by the owners.

. Capital-turnover ratio (FR2), measured by the sales over total assets. This ratio isa standard financial ratio illustrating the ability of the firms assets to generatesales. It is a measure of managements capability in dealing with competitiveconditions.

. Return on equity (FR3), measured by the net income to net worth. This variablemeasures the financial profitability, which depends on the economic profitabilityas well as on the financial structure, debt cost and the profitability required bythe owners. A positive return on equity reflects the opportunity for retainingearnings.

. Change of net worth (FR4), measured by the net worth annual percentage change.This variable represents the solvency increase or decrease.

. Auditing opinion (d5 ): this measures the quality of the financial statements.Edmister (1972) tested the same technique as Altman (1968) for small businesswith some success but warned that three consecutive financial statements ofgood quality must be available for analysis of a small firm.

The expression of the financial health indicator is given by:

FS X4j1

IFRj $ P5 d5; 1

where FRis the financial ratio, P5 is the fifth percentile, d5 is a dummy variable whichtakes the value 1 if the auditing opinion is favourable and 0 otherwise, and I(.) is theindicator function, which takes the value 1 if FR is higher than or equal to P5 and 0otherwise.

If this is a good indicator of the bankruptcy probability of healthy firms, it willallow us to form decontaminated samples and the prediction models will give muchmore accurate bankruptcy predictions. If a firm shows a value of the financial health


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indicator below the fifth percentile, it reveals that it has an abnormal reduced indicatorvalue, which means that it is financially a weak firm. It is expected that, ifFSis a goodproxy of financial health, using firms with an FS value equal to 5 (healthy firms)should allow us to predict bankruptcy more accurately than using firms with FSequal

to 0 (unhealthy firms).The indicator FS is evaluated on several bankruptcy prediction models to avoid

results in which it could be influenced by the selected model. The models we use arethose of Beaver (1966), Altman (1968), and Altman et al. (1977). These models are themost widely cited bankruptcy prediction models in the credit risk literature. Also,Garca et al. (1997) presented a bankruptcy prediction model that represents thereference in the Spanish market. All the models above examine multivariate ratios inlarge and small firms. They are displayed in equations (2)-(5):

Pij fCASHi; NINi; LEVi; WCi; LIQi; NCREi Beaver; 1966; 2

Pij fWCi; CPi; ROAi; CAPi; ACTi Altman; 1968; 3

Pij fROAi; SROAi; DSi; CPi; LIQi; CAPi; SIZEi Altman et al:; 1977; 4

Pij fQLIQi; ATDi; INTi; AMOi; EARi Garcia et al:; 1997: 5

The ratios employed are:

. Beaver (1966) CASH, cash flow to total debt; NIN, net income to total assets;LEV, total debt to total assets; WC, working capital over total assets; LIQ,current assets to current debt; NCRE, no-credit interval measured as quick assetsminus current liabilities to operating expenses minus depreciation, depletion,and amortisation.

. Altman (1968) WC, working capital over total assets; CP, retained earningsover total assets; ROA, earnings before interest and taxes over total assets; CAP,for application purposes a five-year average of the total market value equity overtotal capital has been substituted by book value equity over total capital; ACT,sales over total assets.

. Altman et al. (1977) ROA, earnings before interest and taxes over total assets;SROA, standard error of estimating of ROA; DS, earnings before interest andtaxes over total interest payments; CP, retained earnings over total assets; LIQ,current assets to current debt; CAP, for application purposes a five-year averageof the total market value equity over total capital has been substituted by bookvalue equity over total capital; SIZE, logarithmic transformation of total asset.

. Garca et al. (1997) QLIQ, quick assets over current libialities; ATD, total assetto total debt; INT, total interest payments to sales; AMO, annual amortization toamortizable assets; EAR, earnings before taxes over total debt.

MethodologyWe use the binomial logit model to examine the likelihood that a firm will go bankrupt.Logit analysis uses a set of financial variables to predict bankruptcy probability,assuming that bankruptcy probability is logistically distributed, i.e. the cumulative

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bankruptcy probability takes a logistic functional form and is, by definition,constrained to fall between 0 and 1. In the prediction evaluation process we distinguishbetween the in-sample validation and the out-of-sample validation, in the estimationyear, when applying the model to the non-used sample in the estimation process, as

well as in the next two years to the whole population of firms.Under non-normality, we choose the logistic regression model with maximum

likelihood estimators. The regression model is specified as follows:

Pij 1

1 e2b0X

; 6

where Pij is the probability that firm i is bankrupt, X is a vector of measuredcharacteristics for firm i, and b is the unknown parameter vector.

The estimates of the parameters of this model yield the bankruptcy probabilities fora given firm. The vector of measured characteristics used contains the list of empiricalvariables described in equations (2)-(5). The financial ratios are calculated at the end of

the year prior to the bankrupt year, except the standard error of estimating of ROA ofAltman et al. (1977), which is computed over seven years. If the model, as representedby the likelihood ratio statistic, indicates that the model fits the data significantly, wethen move on to interpret parameter estimates. We also compute the McFadden R2.

In order to classify the firms belonging to the sample under the estimatedbankruptcy probabilities, a cut-off must be fixed which allows the sample to bedichotomise and the prediction errors to be determined. The type I error is defined asthose non-bankrupt firms which have already been classified as bankrupt and the typeII error is defined as those bankrupt firms which have been classified as non-bankrupt.The total error is obtained by weighting type I and type II errors.

Since type I and type II errors are conditioned by the selected cut-off, we apply twoevaluation measures proposed by the Basel Committee on Banking Supervision

(BCBS), which are constructed for all possible cuts-off:(1) the cumulative accuracy profile (CAP); and

(2) the receiver operating characteristics (ROC).

Given a variety of rating methodologies, the question is which of these methodologiesdeliver acceptable discriminatory power between bankrupt and non-bankrupt firms.The Basel Committee on Banking Supervision (2005) has published a working papersummarising statistical methodologies for assessing discriminatory power.

Accuracy ratio of cumulative accuracy profileTo obtain the cumulative accuracy profile (CAP) curve, all firms are first ordered bytheir respective scores, from riskiest to safest, i.e. from the firm with the highest scoreto the firm with the lowest score. For a given fraction x of the total number of firms, theCAP curve is constructed by calculating the percentage d(x ) of the bankruptcy firmswhose rating scores are equal to, or higher than, the maximum score of fraction x. Thisis done for x ranging from 0 per cent to 100 per cent. Figure 1 illustrates the CAPcurves.

A real credit model lies somewhere in between the two extremes of a perfect ratingcredit model and a random model. In a perfect rating model, the CAP increases linearlyto 1 then remains constant, since a perfect rating model will assign the highest scores


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to bankrupt firms. In a random model, the fraction x of all firms with the highest ratingscores will contain x per cent of all bankrupt firms. The accuracy ratio (AR) is definedas the ratio of the area between the real credit model and the random model ar, and thearea between the perfect rating model and the random model, ap. The closer the AR isto 1, the better the rating model:

ARCAP ar

ap: 7

Accuracy ratio of receiver operating characteristicThe decision as to which firms will not go bankrupt during the next period and which

firms will is made by introducing a cut-off value C, as in Figure 2. Thus, a firm with abankruptcy probability lower than C is classified as a non-bankrupt firm and a firmwith a bankruptcy probability higher than C is classified as a bankrupt firm.Consequently, a hit rate HR(C ) is defined as the fraction of bankrupt firms that areclassified correctly for a given cut-off value C:

Figure 1.Cumulative accuracyprofile curves

Figure 2.Distribution ofbankruptcy probability forbankrupt andnon-bankrupt firms

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HRC HC

NB: 8

In equation (8), H(C) is the number of bankruptcies predicted correctly with the cut-off

value C, and NB is the total number of bankruptcies in the sample. The false alarm rateFAR(C) is defined as:

FARC FC

NNB; 9

where F(C ) is the number of non-bankrupt firms that were classified incorrectly asbankrupt by using the cut-offCand NNB is the total number of non-bankruptcy firms.In Figure 2, HR(C ) is the area to the right of the cut-off value C under the probabilitydistribution of the bankrupt firms, while FAR(C) is the area to the right ofCunder theprobability distribution of the non-bankrupt firms.

The receiver operating characteristic (ROC) curve is a plot ofHR(C) versus FAR(C),

illustrated in Figure 3. To construct the ROC curve, HR(C ) and FAR(C) are computedfor different possible cut-off values in the range 0 to 1. Like the CAP curve, the largerthe area under the ROC curve, the better the model. The area is called AUROC.

In a random model with no discriminative power, AUROC is equal to 0.5. In aperfect model AUROCis equal to 1. Engelmann et al. (2003) showed a measure between0 to 1 as an accuracy ratio for ROC, which is computed using the following expression:

ARROC 2 AUROC2 1 2

Z10

HRFARdFAR2 1: 10

Data and empirical results

The period is divided into two subperiods to estimate the bankruptcy predictionmodels:

(1) from January 1994 to December 2000 we compute the financial variables; and

(2) from January 2001 to December 2004 we estimate the models and evaluate theirpredictive capacity.

Figure 3.Receiver operating

characteristic curves


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Firms belonging to a financial sector were excluded from the sample. Our sampleconsists of firms which satisfy the European Commission definition of SMEs andwhich have accounting data from January of 1994 to December 2004. Following theEuropean Commission definition, we consider SMEs as:

. companies with fewer than 250 employees;

. sales below e40 million; and

. total assets under e27 million.

We use a database that includes financial information of more than 190,000 Spanishfirms. This database is called SABI, and is managed by Informa SA.

In the database, 76 bankrupt firms were found during the period January 2001 toDecember 2004. From the 76 bankrupt firms, 27 firms were deleted due to lack ofcontinuous information in at least one of the five years previous to the bankruptcyevent, and one firm was deleted because it was not considered a SME. Therefore, thefinal sample is formed by 48 bankrupt firms. This gives a total sample of 2,211 firms in

2000, where 2,194 are non-bankrupt firms and 17 are bankrupt firms. In 2001, thesample consists of 2,130 firms, where 2,113 are non-bankrupt firms and 17 arebankrupt firms. In 2002 there are 2,299 firms, consisting of 2,292 non-bankrupt firmsand seven bankrupt firms. In 2003 there are a total of 2,310 firms, of which 2,303 arenon-bankrupt firms and seven are bankrupt firms.

We equate the number of non-bankrupt firms selected from each year to the numberof bankrupt firms for such year. We select three samples of non-bankrupt firms:

(1) the high financial health sample (strong firms);

(2) the low financial health sample (weak firms); and

(3) the classical sample (control firms).

We also use the whole sample to estimate the model (total firms). In the high financialhealth sample, the non-bankrupt firms are selected from the firms that obtain anindicator value equal to 5. In the low financial health sample, the non-bankrupt firmsare selected from those firms that obtained an indicator value equal to 0. In the classicalsample, the non-bankrupt firms are selected from the firms that belong to the samesector as the bankrupt firms.

Using each of these four samples, in 2001 we estimate the bankruptcy predictionmodels of Beaver (1966), Altman (1968), Altman et al. (1977) and Garca et al. (1997).Then, given the estimated bankruptcy probabilities, we measure the in-sampleprediction capacity and the out-of-sample predictive ability of such models. Thein-sample prediction capacity is measured using the firms that were not employed inthe estimation process in 2001, and the out-sample prediction capacity is computed

using the whole firm population in the two next years. We repeat the analyses,re-estimating the models in 2002. We do not repeat the estimation in 2003 and 2004because of the small size of the bankrupt sample.

In the estimation process, we estimate several logit models. The estimation results ofthe Beaver (1966, 1968) model are reported in Table I. These results show that thesamples formed by weak firms and total firms have the lowest McFaddens R2 in 2001,while the control firm sample has a quite good value in 2001, taking into account thistype of data, but a very small one in 2002. The significance of22logL the statistics

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2001

Year

Strongfirms

Weakfirms

Controlfirms

Totalfirms

Strongfir

ms

Weakfirms

Controlfirms

Totalfirms

Constant

2

15.32

2

11.34*

2

17.50

2

10.98*

2

6.8

7

2

2.4

2

2

22.13*

2

10.81*

(11.40)

(5.5

6)

(17.1

0)

(2.4

8)

(9.4

9)

(3.3

0)

(12.94)

(3.2

5)

CASH

17.47

19.34

15.65

2

7.47

2

0.4

3

2

5.5

8

2

22.39

2

3.63

(25.06)

(12.1

6)

(41.0

6)

(7.4

9)

(20.0

6)

(9.8

0)

(18.19)

(7.6

4)

NIN

2

71.34

6.38

2

142.0

7*

1.63

2

6.9

6

9.0

1

20.98

2

15.64

(51.75)

(9.7

0)

(80.0

5)

(9.2

3)

(27.9

1)

(13.0

8)

(22.68)

(10.74)

LEV

15.92

11.78*

20.19

6.31*

12.1

8

5.9

9

2

1.55

8.49*

(12.26)

(5.8

5)

(19.0

0)

(2.6

8)

(7.8

7)

(3.7

2)

(5.6

1)

(2.7

1)

WC

2

1.3

2

2

4.49

2

0.61

2

3.62

8.2

9

5.6

1

2

30.72

1.74

(10.78)

(4.6

1)

(12.6

6)

(2.7

2)

(14.7

6)

(4.6

7)

(20.45)

(4.1

8)

LIQ

3.1

4

1.65

4.11

1.68*

2

2.4

4

2

2.2

5

23.56

2

0.30

(4.6

5)

(1.6

4)

(4.3

9)

(0.8

7)

(7.7

5)

(1.9

0)

(13.88)

(2.2

1)

NCRE

2.6

6

0.82

0.82

2

0.38

2

2.0

4

2

1.5

3

2

3.24

2

0.28

(4.1

3)

(1.2

2)

(5.2

3)

(0.9

0)

(5.2

6)

(2.2

7)

(3.7

6)

(1.0

7)

2

2log

L

22.61

16.42

31.82

58.69

24.0

5

9.3

2

14.38

65.75

x2p-value

0.0

00

0.0117

0.0000

0.0000

0.0

005

0.1

565

0.0257

0.0000

McFadden

R2

0.4

797

0.3484

0.6751

0.2943

0.5

103

0.1

977

0.3051

0.3319

Accuracyin-sample

Percentageclassified

85.29

79.4

1

91.18

99.41

88.2

4

64.7

1

76.47

99.30

TypeIerror(percent)

17.65

23.5

3

11.76

0.00

11.7

6

41.1

8

23.53

0.05

TypeIIerror(percent)

11.76

17.65

5.88

76.47

11.7

6

29.4

1

23.53

82.35

ARCAP

0.9

298

0.8728

0.9140

0.7879

0.9

524

0.7

981

0.8506

0.7829

ARROC

0.7

625

0.7586

0.7165

0.3079

0.7

901

0.5

733

0.8461

0.3199

Notes:Thesampleiscomposedof17bankruptfirms.Thed

ependentvariabletakesthevalueon

eforthe17bankruptfirmsandzero

forthenon-

bankruptfirms.Standard

errorsaregiveninparentheses.

*Significantatthe5percentlevel

Table I.Estimates of the logit

target prediction modelbased on the Beaver

(1966) variables


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behaves likewise. The percentage of correctly classified companies during theestimation period is relatively high using the strong firm and the control firm samples.The results for the total firm sample are over-valued due to bankrupt firms having a verysmall weight in the total sample. On fixing a cut-off equal to 0.5, the weak firm sample

has high type I and II errors. In the total sample, the type I error is insignificant while thetype II error is very high. The CAP and ROC measures indicate that a strong firm sampleallows the model to be estimated with the best in-sample predictive capacity.

The results concerning the Altman (1968), Altman et al. (1977) and Garca et al.(1997) models are likewise summarised in Tables II, III, and IV, respectively.

In general, Tables IIIV illustrate that the strong firm and control firm sampleshave the highest McFaddens R2 in 2001 while the strong firm sample does so in 2002.The percentage of correctly classified companies during the estimation period isrelatively high using the strong firms, from 82.35 per cent to 88.24 per cent. The CAPand ROC measures point out that the strong firm sample allows the model to beestimated with the best in-sample predictive capacity with values up to 0.9751. Thetotal firm sample has the highest type II error, up to 99.41 per cent, which means that topredict that no firm is going to be bankrupt minimises the total error, since itrepresents a reduced percentage of the total number of firms used in the estimationprocess. On the other hand, the control firm sample shows different results dependingon both the year and the model. In this sense, the percentage correctly classified goesfrom 64.71 per cent to 91.18 per cent, the type II error goes from 5.88 per cent to 35.29per cent and the type I error goes from 5.88 per cent to 41.18 per cent. The CAP andROC values of the control firm sample are lower than the strong firm sample andhigher than the weak firm sample.

The out-of-sample predictive capacity of the models is reported in Tables V and VI.When the total sample is considered to estimate the model, out-of-sample resultscannot be computed in the estimation year.

Concerning the strong firm sample, Table V reports that, in 2001, the type I errorranges from 24.38 per cent to 29.72 per cent, the type II error is equal to 11.76 per cent inall models and the CAP values go from 0.871 to 0.893 while the ROC values go from0.7423 to 0.8520. These values do not worsen when the model is applied one or twoyears after the estimation. In the worst case, the type I error rises to 33.35 per cent, thetype II error rises to 42.86 per cent, the CAP decreases to 0.801 and the ROC rises to0.662. In general, the weak firm sample gives higher type I and II errors and lower ROCand CAP values than the strong firm and the control firm samples. The control firmsample has higher values of CAP and ROC as well as lower type I and II errors than theweak firm sample. In contrast, the total firm sample has the highest type II error.

Table VI shows that, as in 2001, in 2002 the strong firm sample shows the mostaccuracy. Type I error in 2002 goes from 28.16 per cent to 30.76 per cent, type II error

ranges from 5.88 per cent to 11.76 per cent in all the models and the CAP values go from0.872 to 0.88 while ROC values go from 0.79 to 0.814. The results remain similar in 2003and 2004. Inthe worst case, the type I error is 28.85 per cent, the type IIerror rises to 28.57per cent, the CAP decreases to 0.785 and the ROC rises to 0.712. In general, the weak firmsample gives higher type I and II errors and lower ROC and CAP values than the strongfirm and the control firmsamples. It must be highlighted that the control firm sample hashigher values of CAP and ROC and lower type I and II errors than the weak firm samples.In contrast, the total firm sample has the highest type II error.

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2001

2002

Strongfirms

Weakfirms

Controlfirms

Totalfirms

Strongfir

ms

Weakfirms

Controlfirms

Totalfirms

Constant

2.24*

0.7

5

5.2

2*

2

3.0

6*

1.60

2

1.51

0.19

2

2.76*

(1.2

8)

(0.9

2)

(2.2

1)

(2.2

1)

(1.58)

(1.1

0)

(1.1

6)

(0.6

4)

WC

1.82

2

1.6

2

1.6

2

2

2.1

6

4.20

5.32

3.21

1.00

(3.0

7)

(2.1

4)

(7.0

2)

(1.4

4)

(4.48)

(3.4

7)

(2.6

4)

(1.8

1)

CP

2

0.35

1.7

7

2

2.9

7

2.3

4

2

9.87

9.82*

0.63

1.15

(7.1

5)

(3.6

7)

(8.1

5)

(2.7

2)

(9.13)

(5.9

0)

(6.5

3)

(3.5

6)

ROA

2

11.3

0

4.4

3

2

34.83*

2

8.1

4*

2

10.58

2

0.12

2

7.69

2

12.23*

(9.9

6)

(3.0

8)

(17.6

0)

(3.7

0)

(7.88)

(4.9

4)

(5.9

7)

(4.1

6)

CAP

2

6.02*

2

3.3

5

2

6.0

4

2

3.9

0*

2

5.01

2

10.18*

2

2.59

2

5.97*

(3.3

0)

(2.8

0)

(5.0

6)

(1.2

4)

(3.08)

(4.2

9)

(2.3

9)

(2.2

5)

ACT

0.04

2

0.0

3

2

0.6

2

2

0.1

7

1.09

2.06*

0.31

0.11

(0.4

5)

(0.3

6)

(0.4

7)

(0.3

0)

(0.82)

(0.8

9)

(0.5

1)

(0.2

6)

2

2log

L

20.2

9

7.8

0

27.42

54.8

2

25.37

14.12

7.22

52.51

x2p-value

0.0011

0.1

674

0.0

000

0.0

000

0.000

1

0.0148

0.2046

0.0000

McFadden

R2

0.44305

0.1

655

0.5

817

0.2

749

0.538

3

0.2997

0.1532

0.2650

Accuracyin-sample


82.3

5

70.5

9

88.24

99.3

2

88.24

76.47

64.71

99.30

TypeIerror(percent)

23.5

3

35.2

9

17.65

0.6

4

17.65

23.53

41.18

0.00


11.7

6

23.5

3

5.8

8

83.0

3

5.88

23.53

29.41

88.24

ARCAP

0.9231

0.8

461

0.8

683

0.7

810

0.950

2

0.7303

0.8980

0.7687

ARROC

0.7424

0.6

007

0.7

171

0.2

702

0.802

2

0.4959

0.6722

0.2469

Notes:Thesamplewascomposedof17bankruptfirms.Thed

ependentvariabletakesthevalue1forthe17bankruptfirmsand0forthen

on-bankrupt

firms.Standarderrorsar

eshowninparentheses.

*Significant

atthe5percentlevel

Table II.Estimates of the logit

target prediction modelbased on the Altman

(1968) variables


71


13/18

2001

2002

Strongfirms

Weakfirms

Controlfirms

Totalfirms

Strongfir

ms

Weakfirms

Controlfirms

Totalfirms

Constant

16.77

2

0.65

7.2

9

2

1.54

4.36

13.71

12.96*

0.26

(11.69)

(6.8

3)

(9.4

6)

(3.4

6)

(8.15)

(8.3

5)

(7.0

8)

(3.3

5)

ROA

2

4.9

5

22.83*

2

39.09*

2

5.45

2

2.82

17.12

2

6.87

2

9.03*

(20.03)

(10.3

6)

(19.4

2)

(3.9

8)

(8.90)

(10.6

2)

(7.0

8)

(4.5

1)

SROA

174.31

30.08

2

23.53

7.09

36.28

53.51*

12.04

18.0

4*

(113.6

1)

(21.0

6)

(24.4

6)

(4.8

8)

(29.70)

(22.7

8)

(14.4

5)

(7.4

2)

DS

1.2

3

0.22*

0.1

3

0.03

0.33

0.01

0.40

0.0

2

(1.0

4)

(0.1

2)

(0.3

2)

(0.0

8)

(0.41)

(0.1

3)

(0.3

1)

(0.0

9)

CP

9.7

5

5.40

2

7.3

7

5.42

2

10.27

2.78

2

1.64

0.30

(11.23)

(5.7

7)

(8.9

0)

(3.3

1)

(9.87)

(7.1

8)

(7.7

0)

(3.6

0)

LIQ

24.81

2

0.63

0.0

4

0.14

6.15

2.03

6.32

1.7

9

(16.45)

(2.6

8)

(9.5

1)

(1.8

0)

(5.62)

(4.3

4)

(3.7

4)

(1.8

6)

CAP

2

56.31

2

13.14*

2

8.3

1

2

12.42*

2

12.04*

2

12.14*

2

7.09

2

9.88*

(35.11)

(6.3

4)

(11.6

1)

(3.4

7)

(6.87)

(7.3

3)

(5.1

6)

(3.3

4)

SIZE

2

1.4

7

0.12

2

0.1

7

2

0.15

2

0.19

2

1.45*

2

1.32*

2

0.36

(1.1

7)

(0.7

1)

(1.0

1)

(0.3

6)

(0.91)

(0.8

6)

(0.7

5)

(0.3

7)

2

2log

L

32.21

17.93

27.57

62.22

27.12

22.03

13.66

61.8

6

x2p-value

0.0

000

0.012

0.0

003

0.0000

0.000

3

0.0025

0.0575

0.0

000

McFadden

R2

0.6

834

0.3805

0.5

850

0.3120

0.575

4

0.4673

0.2899

0.3

122

Accuracyin-sample


85.29

76.4

7

85.29

99.41

85.29

82.35

73.53

99.3

4

TypeIerror(percent)

17.65

29.4

1

17.65

0.00

17.65

17.65

29.41

0.0

0


11.76

17.65

11.76

76.47

11.76

17.65

23.53

82.3

5

ARCAP

0.9

751

0.8682

0.9

162

0.7967

0.966

1

0.7936

0.9389

0.7

853

ARROC

0.7

424

0.7154

0.7

166

0.3130

0.815

4

0.5706

0.7555

0.2

976



on-bankrupt



*Significant

atthe5percentlevel

Table III.Estimates of the logittarget prediction modelbased on the Altman et al.(1977) variables

JSBED17,1

72


14/18

2001

2002

Strongfirms

Weakfirms

Controlfirms

Totalfirms

Strongfir

ms

Weakfirms

Controlfirms

Totalfirms

Constant

6.9

7*

5.9

7*

10.05

3.3

8*

6.4

6*

4.72*

2.48

1.56

(4.2

2)

(2.7

6)

(6.7

8)

(1.9

4)

(3.1

8)

(2.3

7)

(2.3

1)

(1.5

5)

QLIQ

1.8

5

2

0.1

3

4.9

8

2

0.6

3

1.7

7

0.45

2

2.16

2

1.14

(2.2

7)

(1.4

3)

(3.9

2)

(0.9

9)

(1.9

8)

(1.5

3)

(1.5

1)

(0.9

8)

ATP

2

8.7

8*

2

3.9

4

2

10.85

2

5.9

6

2

6.7

7*

2

2.15

2

2.76

2

3.93*

(4.3

8)

(2.4

2)

(6.8

0)

(1.7

1)

(2.7

1)

(1.7

6)

(2.0

0)

(1.1

1)

INT

40.14

2

4.8

9

1

13.72*

16.1

2*

93.7

5

2

21.34

6.91

18.0

5*

(35.38)

(8.2

4)

(63.2

5)

(6.2

6)

(58.4

0)

(20.0

9)

(20.7

1)

(10.1

5)

AMO

26.55

2

4.5

0

2.1

8

2

0.0

6

2

0.4

1

2.88

4.29

2

0.88

(17.97)

(5.2

1)

(12.5

6)

(3.1

8)

(6.5

7)

(4.2

7)

(5.2

9)

(2.9

6)

EAR

2

16.15

8.1

1*

2

28.63

2

6.8

2*

2

1.1

9

2.85

2

1.66

2

9.74*

(9.8

6)

(4.1

3)

(16.4

4)

(3.0

7)

(5.6

1)

(3.3

0)

(4.4

9)

(3.1

3)

2

2log

L

26.49

10.5

0

31.85

61.0

4

25.9

4

9.55

5.69

52.7

7

x2p-value

0.0

000

0.0

62

0.0

000

0.0

000

0.0

000

0

0.0891

0.3372

0.0

000

McFaden

R2

0.5

620

0.2

229

0.6

757

0.3

061

0.5

504

0.2025

0.1208

0.2

664

Accuracyin-sample


88.24

61.7

6

91.18

99.2

8

88.2

4

67.65

64.71

99.3

0

TypeIerror(percent)

11.76

35.2

9

5.8

8

0.0

5

17.6

5

35.29

35.29

0.0

0


11.76

41.1

8

11.76

88.2

4

5.8

8

29.41

35.29

88.2

4

ARCAP

0.9

592

0.8

552

0.8

751

0.8

142

0.9

683

0.7190

0.8461

0.7

744

ARROC

0.7

987

0.6

295

0.7

599

0.2

601

0.8

147

0.4764

0.6183

0.2

353



on-bankrupt



*Significant

atthe5percentlevel

Table IV.Estimates of the logit

target prediction modelbased on the Garca et al.

(1997) variables


73


15/18

2001

2002

2003

Strong

firms

Weak

firms

Control

firms

Total

firms

Strong

fi

rms

Weak

firms

Control

firms

Tot

al

firm

s

Strong

firms

Weak

firms

Control

firms

Total

firms

Beaver(1968)

TypeI

error

29.7

2

70.65

32.6

3

2

9.11

67.1

6

33.46

0.0

0

33.35

65.39

37.63

0.48

TypeII

error

11.7

6

17.65

5.88

2

3.53

35.2

9

23.53

94.1

2

14.29

14.29

14.29

85.71

ARCAP

0.8398

0.5316

0.7484

0.801

0.4

73

0.713

0.7

86

0.834

0.512

0.771

0.786

ARROC

0.7625

0.7006

0.7586

0.733

0.5

98

0.679

0.2

12

0.816

0.652

0.776

0.321

Altman(1968)

TypeI

error

24.3

8

26.39

28.0

8

2

2.91

24.1

4

27.45

0.0

0

23.4

8

23.48

28.94

0.48

TypeII

error

11.7

6

23.53

5.88

2

3.53

29.4

1

17.65

94.1

2

14.2

9

28.57

14.29

85.71

ARCAP

0.8937

0.7843

0.8305

0.873

0.7

38

0.813

0.7

47

0.873

0.775

0.838

0.759

ARROC

0.7423

0.6007

0.7171

0.721

0.5

71

0.646

0.2

21

0.737

0.578

0.710

0.300

Altmanetal.

(1977)

TypeI

error

26.1

6

44.35

27.5

3

2

6.31

41.6

5

27.54

0.0

0

22.7

4

36.53

28.33

0.83

TypeII

error

11.7

6

17.65

11.7

6

3

5.29

41.1

8

17.65

88.2

4

28.5

7

28.57

14.29

71.43

ARCAP

0.8818

0.7504

0.7744

0.801

0.6

74

0.740

0.7

49

0.844

0.775

0.786

0.781

ARROC

0.8520

0.7166

0.7154

0.662

0.6

29

0.654

0.2

63

0.725

0.714

0.736

0.361

Garcaetal.(1997)

TypeI

error

24.4

8

47.90

26.7

1

2

4.94

46.1

0

25.93

0.0

05

25.6

7

41.34

25.01

0.48

TypeII

error

11.7

6

47.06

11.7

6

3

5.29

29.4

1

17.65

94.1

2

14.2

9

42.86

14.29

85.71

ARCAP

0.8711

0.7007

0.8058

0.809

0.7

42

0.743

0.7

85

0.846

0.698

0.765

0.783

ARROC

0.7987

0.6295

0.7599

0.681

0.6

44

0.680

0.2

24

0.799

0.577

0.706

0.313

Note:Theout-of-sample

predictiveabilityofthemodelsismeasuredonthewholepopulationoffir

msin2001,

2002and2003

Table V.Out-of-sample accuracyof the models estimatedin 2001

JSBED17,1

74


16/18

2002

2003

2004

Strong

firms

Weak

firms

Control

firms

Total

firms

Strong

fi

rms

Weak

firms

Control

firms

Tot

al

firm

s

Strong

firms

Weak

firms

Control

firms

Total

firms

Beaver(1968)

TypeI

error

28.9

6

24.8

9

61.2

4

2

8.85

23.8

3

63.38

1.1

4

28.18

23.27

63.74

1.31

TypeII

error

11.7

6

29.4

1

23.5

3

1

1.76

23.5

3

11.76

29.4

1

14.29

57.14

28.57

42.86

ARCAP

0.8

80

0.406

0.8

35

0.879

0.4

29

0.733

0.7

96

0.856

0.473

0.622

0.754

ARROC

0.7

90

0.573

0.6

16

0.790

0.5

15

0.630

0.4

08

0.831

0.447

0.681

0.577

Altman(1968)

TypeI

error

28.1

6

31.5

2

20.7

8

2

8.11

30.9

9

23.09

0.7

1

26.5

3

30.26

22.93

0.65

TypeII

error

5.8

8

17.6

5

29.4

1

5.88

5.8

8

11.76

35.2

9

28.5

7

28.57

14.29

42.86

ARCAP

0.8

73

0.740

0.7

76

0.849

0.7

44

0.813

0.7

74

0.785

0.714

0.759

0.763

ARROC

0.8

02

0.495

0.6

72

0.775

0.5

40

0.745

0.3

33

0.712

0.669

0.680

0.528

Altmanetal.

(1977)

TypeI

error

28.5

8

40.5

1

26.9

3

2

3.83

39.0

2

21.30

0.9

5

23.3

2

34.04

20.67

0.87

TypeII

error

11.7

6

17.6

5

23.5

3

5.88

11.7

6

11.76

29.4

1

28.5

7

0.00

14.29

28.57

ARCAP

0.8

77

0.716

0.7

79

0.856

0.7

58

0.787

0.7

73

0.815

0.814

0.812

0.763

ARROC

0.8

15

0.570

0.7

75

0.774

0.6

45

0.721

0.3

67

0.736

0.726

0.756

0.606

Garcaetal.(1997)

TypeI

error

30.7

6

38.8

1

16.3

3

2

7.72

37.8

4

17.50

0.5

2

25.7

1

36.04

17.76

0.48

TypeII

error

5.8

8

29.4

1

35.2

9

1

1.76

5.8

8

11.76

35.2

9

14.2

9

42.86

14.29

57.14

ARCAP

0.8

72

0.743

0.7

46

0.853

0.7

54

0.806

0.7

88

0.850

0.605

0.758

0.745

ARROC

0.8

14

0.476

0.6

18

0.754

0.5

24

0.678

0.3

14

0.827

0.487

0.615

0.398

Note:Theout-of-sample

predictiveabilityofthemodelsismeasuredonthewholepopulationoffir

msin2001,

2002and2003

Table VI.Out-of-sample accuracyof the models estimated

in 2002


75


17/18

ConclusionsMany efforts have been devoted to developing models to predict bankruptcyprobability and banks, investors and firms are interested in using these models.However, since the models have been developed in the aim to estimate the bankruptcy

probability of quoted firms, less attention has been paid to non-quoted SMEs. Usually,the bankruptcy probability of non-quoted SMEs is studied by analysing financialratios using discriminating techniques. These models are based on constructing anestimation sample using bankrupt and non-bankrupt firms, controlling by size andindustry or unbalancing the sample using all firms.

In our article, we propose an alternative to control the heterogeneity of healthyfirms. In doing this, we construct a financial health indicator to define the degree offinancial health. Our results are obtained under four different models of credit scoring.We show in-sample and out-of-sample bankruptcy predictions. We apply measuresproposed by the Basel Committee on Banking Supervision to evaluate the creditscoring of the models depending on the criterion considered to select the firms.

Focusing on the non-bankrupt firms, the financial health indicator allows firms tobe classified before the estimation process. This procedure permits the heterogeneity ofthe firms to be reduced as well as identifying a strong firm sample to estimate thebankruptcy probability accurately. The in-sample and out-of-sample evaluation basedon the CAP and ROC indicators, proposed by the BCBS, leads to the conclusion that themodels estimated under the strong firm sample are much more accurate.

References

Altman, E.I. (1968), Financial ratios, discriminant analysis and the prediction of corporatebankruptcy, Journal of Finance, Vol. 23 No. 4, pp. 589-609.

Altman, E.I. and Saunders, A. (1998), Credit risk measurement: developments over the last

20 years, Journal of Banking and Finance, Vol. 21, pp. 1721-42.Altman, E.I., Haldeman, E. and Narayanan, P. (1977), Z analysis: a new model to identify

bankruptcy risk of corporations, Journal of Banking and Finance, Vol. 10, pp. 29-54.

Basel Committee on Banking Supervision (2005), Studies on the validation of internal ratingsystems, Working Paper No. 14, Basel Committee on Banking Supervision, Basel.

Beaver, W.H. (1966), Financial ratios as predictor of failure, Empirical Research in Accounting:Selected Studies, Supplement to Journal of Accounting Research, Vol. 5, pp. 71-111.

Beaver, W.H. (1968), Alternative accounting measures as predictor of failure, The AccountingReview, Autumn, pp. 112-22.

Berryman, J. (1983), Small business failure and bankruptcy: a survey of the literature,European Small Business Journal, Vol. 1 No. 4, pp. 47-59.

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About the authorsJ. Samuel Baixauli is an Associate Professor at the Department of Management and Finance atthe University of Murcia, Spain. He received his PhD in Business Administration for work onfinancial economics. He has been research visitor at the Department of Economics at theUniversity of York, UK. His main research areas include financial modeling and estimation ofmarket and credit risk. He has published on these topics in international journals such as

European Journal of Operational Research, Journal of Financial Research, Review of Quantitative

Finance and Accountingand

European Journal of Finance. J. Samuel Baixauli is the

corresponding author and can be contacted at: [email protected] Modica-Milo is an Associate Professor at the Department of Management and

Finance at the University of Oriente, Venezuela. She received her PhD in Business Economicsfrom the Department of Management and Finance at the University of Murcia, Spain. Her mainresearch areas include financial modeling and estimation of credit risk. She has experienceworking as a financial advisor for relevant private companies.


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