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EN
The paper is devoted to the bankruptcy prediction problem. Analyzed concept is the usage of Maximum Margin Fuzzy Classifiers. The article gives a brief overview of approaches used for the purpose of bankruptcy prediction. The most important theoretical aspects of MMFC method are presented. The final part contains results and conclusions of a study on real-world data regarding Warsaw Stock Exchange companies.
EN
Research background: Since the first bankruptcy prediction models were developed in the 60's of the 20th century, numerous different models have been constructed all over the world. These individual models of bankruptcy prediction have been developed in different time and space using different methods and variables. Therefore, there is a need to analyse them in the context of various countries, while the question about their suitability arises. Purpose of the article: The analysis of more than 100 bankruptcy prediction models developed in V4 countries confirms that enterprises in each country prefer different explanatory variables. Thus, we aim to review systematically the bankruptcy prediction models developed in the countries of Visegrad four and analyse them, with the emphasis on explanatory variables used in these models, and evaluate them using appropriate statistical methods. Methods: Cluster analysis and correspondence analysis were used to explore the mutual relationships among the selected categories, e.g. clusters of explanatory variables and countries of the Visegrad group. The use of the cluster analysis focuses on the identification of homogenous subgroups of the explanatory variables to sort the variables into clusters, so that the variables within a common cluster are as much similar as possible. The correspondence analysis is used to examine if there is any statistically significant dependence between the monitored factors ? bankruptcy prediction models of Visegrad countries and explanatory variables. Findings & Value added: Based on the statistical analysis applied, we confirmed that each country prefers different explanatory variables for developing the bankruptcy prediction model. The choice of an appropriate and specific variable in a specific country may be very helpful for enterprises, researchers and investors in the process of construction and development of bankruptcy prediction models in conditions of an individual country.
PL
Artykuł zawiera obszerny przegląd i analizę modeli stosowanych w ocenie kondycji finansowej przedsiębiorstw pod kątem widzenia prawdopodobieństwa ich bankructwa. W celu usystematyzowania wiedzy na temat determinant bankructwa firm dokonano metaanalizy modeli predykcyjnych stosowanych w badaniach empirycznych z tego zakresu. Wyróżniono główne grupy czynników uwzględnianych w badaniach upadłości przedsiębiorstw: płynność finansowa, rentowność, produktywność aktywów, zabezpieczenie spłaty długu, dźwignia finansowa, wiek i wielkość firmy. Z dostępnej literatury wybrano 26 studiów poświęconych tej problematyce i zbudowano bazę danych zawierającą informacje o oszacowanych modelach. Stosując współczynnik rang i współczynnik korelacji, analizę wariancji, nieparametryczny test Kruskala-Wallisa oraz regresję tobitową, dokonano oceny wpływu zmiennych objaśniających w poszczególnych badaniach na trafność predykcji opartych na danym modelu. W ocenie porównawczej uwzględniono liczbę zmiennych zawartych w modelu, rodzaj zmiennych objaśniających, metodę estymacji oraz liczebność próby. Na podstawie analizy statystyczno-ekonometrycznej stwierdzono, że rozważane charakterystyki poszczególnych modeli były nieistotne dla dokładności wyprowadzanych z nich prognoz bankructwa.
EN
The paper includes a comprehensive review of the literature and comparative analysis of models used in assessing financial condition of an enterprise from the point of view of bankruptcy prediction. In order to systematize the knowledge of factors underlying firm’s bankruptcy, the authors have carried out a meta-analysis of bankruptcy prediction models applied in empirical research. The main groups of factors considered in bankruptcy research include the following indicators: cash-flow, profitability, asset productivity, debt repayment ability, financial leverage, firm’s age and size. Based on the available stock of studies, the authors have selected 26 papers and constructed a database including information on the estimated models. Using rank correlation, correlation coefficient, variance analysis, non-parametric Kuskal-Wallis test, and tobit regression, they assessed the impact of the explanatory variables considered in individual models on the accuracy of predictions rendered by a given model. In a comparative assessment consideration was given to the number and type of explanatory variables included in the model, estimation method and the sample size. The results of the statistical and econometric analysis suggest that the investigated characteristics of the individual models are not significant for their prediction precision as regards bankruptcy.
XX
В статье содержится обширный обзор и анализ моделей, применяемых при оценке фи- нансового состояния предприятий с точки зрения вероятности их банкротства. С це- лью систематизации знаний на тему детерминант банкротства авторами был проведен мета-анализ моделей прогнозирования, применяемых в эмпирических исследованиях этой проблемы. Были выделены главные группы факторов, появляющихся в исследо- ваниях банкротств предприятий: финансовая рентабельность, эффективность активов, обеспечение погашения кредитов, финансовый рычаг, возраст и величина фирмы. Из доступной литературы было выбрано 26 разработок, посвященных этой проблематике; была построена база данных, содержащая информацию о примененных в них моделях. Авторы использовали коэффициент рангов и коэффициент корреляции, анализ вариа- ции, непараметрический тест Краскала-Уоллиса и регрессию Тобина для анализа влия- ния объясняющих переменных на точность прогноза, рассчитанного по данной модели. В сравнительной оценке было учтено количество переменных, содержащихся в модели, вид объясняющих переменных, метод эстимации и величина пробы. На основе стати- стико-эконометрического анализа было отмечено, что рассматриваемые характеристики отдельных моделей не являются существенными с точки зрения точности сделанных на их основании прогнозов банкротства.
EN
The purpose of the article is to present Support Vector Machines (SVM) as a potentially useful tool in evaluation of bankruptcy risk and bankruptcy prediction. Invented by Vapnik, SVM method can be seen as a generalization of the classification by discriminant hyperplanes. In recent years, this method has gained high popularity in a number of applications where the problem of data classification is considered, including the task of bankruptcy prediction. Due to its good theoretical properties and high performance, this method has been applied in a number of problems where data classification is considered, including the task of bankruptcy prediction. In particular Platt's method can be used to obtain estimation of probability of bankruptcy. In the article we will present empirical results leading to the analysis of financial indicators of some companies.
EN
The impact the last financial crisis had on the small- and medium-sized enterprises (SMEs) sector varied across countries, affecting them on different levels and to a different extent. The economic situation in Poland during and after the financial crisis was quite stable compared to other EU member states. SMEs represent one of the most important segments of the economy of every country. Therefore, it is crucial to develop a prediction model which easily adapts to the characteristics of SMEs. Since the Altman Z-Score model was devised, numerous studies on bankruptcy prediction have been written. Most of them involve the application of traditional methods, including linear discriminant analysis (LDA), logistic regression and probit analysis. However, most recent studies in the area of bankruptcy prediction focus on more advanced methods, such as case-based reasoning, genetic algorithms and neural networks. In this paper, the effectiveness of LDA and SVM predictions were compared. A sample of SMEs was used in the empirical analysis, financial ratios were utilised and non-financial factors were taken account of. The hypothesis assuming that multidimensional discrimination was more effective was verified on the basis of the obtained results.
EN
The purposes of this article are to present validation techniques according to their discriminatory power, while indicating the reservations about such techniques, and to check the adjustment of the existing Polish bankruptcy prediction models in the context of their discriminatory power. This is the first study that performs a validation of such models. Based on the analysis, it was found that the fifth model developed by Hadasik was characterised by a very high discriminatory power. The decision was made to base the evaluation of the discriminatory power of the modules on the Gini index, the Kolmogorov-Smirnov statistic, the H measure, the information value (IV), and the precision of the estimates of bankruptcy.
EN
The aim of the paper is to compare accuracy of some bankruptcy prediction models based on Bayesian networks. Some network structure learning algorithms were analyzed as a tool for classifiers construction. Empirical analysis was applied to companies listed on Warsaw Stock Exchange. The paper gives short overview of theoretical background behind discussed issues and presents results of empirical analysis.
EN
The paper deals with the topic of modelling the probability of bankruptcy of Polish enterprises using convolutional neural networks. Convolutional networks take images as input, so it was thus necessary to apply the method of converting the observation vector to a matrix. Benchmarks for convolutional networks were logit models, random forests, XGBoost, and dense neural networks. Hyperparameters and model architecture were selected based on a random search and analysis of learning curves and experiments in folded, stratified cross-validation. In addition, the sensitivity of the results to data preprocessing was investigated. It was found that convolutional neural networks can be used to analyze cross-sectional tabular data, especially for the problem of modelling the probability of corporate bankruptcy. In order to achieve good results with models based on parameters updated by a gradient (neural networks and logit), it is necessary to use appropriate preprocessing techniques. Models based on decision trees have been shown to be insensitive to the data transformations used.
EN
Economical activities of enterprises should be based on such managerial decisions that assure quick and effective adjustment of the company to the changes that appear in the market. Enterprises, which are not able to use their opportunities and avoid threats, are bound to face the thread of insolvency. Effects of the insolvency are felt not only by the enterprise, but also by its creditors. Therefore, it is necessary to elaborate a warning system that will beforehand allow diagnosing the condition of the enterprise and setting necessary directions for the company to avoid insolvency. The article presents research results on the use of characterization theory in the creation of insolvency threat evaluation model based on Polish enterprises.
EN
Research background: In a modern economy, full of complexities, ensuring a business' financial stability, and increasing its financial performance and competitiveness, has become especially difficult. Then, monitoring the company's financial situation and predicting its future development becomes important. Assessing the financial health of business entities using various models is an important area in not only scientific research, but also business practice. Purpose of the article: This study aims to predict the bankruptcy of companies in the engineering and automotive industries of the Slovak Republic using a multilayer neural network and logistic regression. Importantly, we develop a novel an early warning model for the Slovak engineering and automotive industries, which can be applied in countries with undeveloped capital markets. Methods: Data on the financial ratios of 2,384 companies were used. We used a logistic regression to analyse the data for the year 2019 and designed a logistic model. Meanwhile, the data for the years 2018 and 2019 were analysed using the neural network. In the prediction model, we analysed the predictive performance of several combinations of factors based on the industry sector, use of the scaling technique, activation function, and ratio of the sample distribution to the test and training parts. Findings & value added: The financial indicators ROS, QR, NWC/A, and PC/S reduce the likelihood of bankruptcy. Regarding the value of this work, we constructed an optimal network for the automotive and engineering industries using nine financial indicators on the input layer in combination with one hidden layer. Moreover, we developed a novel prediction model for bankruptcy using six of these indicators. Almost all sampled industries are privatised, and most companies are foreign owned. Hence, international companies as well as researchers can apply our models to understand their financial health and sustainability. Moreover, they can conduct comparative analyses of their own model with ours to reveal areas of model improvements.
EN
The EU Restructuring Directive (2019/1023) requires Member States to provide a preventive restructuring framework for financially distressed entities that remain viable or are likely to readily restore economic viability. The first step to a successful restructuring is the approval of an arrangement between the debtor and creditors. The main research objective of the article is to identify factors affecting the conclusion of an arrangement in restructuring proceedings. In the process of filtering companies initiating a restructuring procedure, these factors are seen as increasing the probability of concluding an arrangement between debtor and creditors. Moreover, an additional research objective is to construct a turnaround prediction model aimed at assessing the probability of a conclusion of an arrangement in restructuring proceedings. The study covered the companies in Poland for which restructuring proceedings opened between 2016 and 2021 ended with the approval of an arrangement, and a similar number of companies that failed to restructure successfully. Binary logistic regression was applied to achieve the aims of this study. The results show that two financial variables affected companies in terms of their chances to conclude the arrangement: the current ratio and return on assets were among the statistically significant indicators and they are characterized by higher values for debtors reaching the arrangement with their creditors. A direct positive relationship was also identified between the company’s lifespan and the outcome of the proceedings. The probability of the conclusion of the arrangement was also affected by the type of industry. Models assessing the probability of completing restructuring proceedings with an arrangement can be useful for insolvency practitioners and financial analysts during viability assessments.
EN
This article is devoted to considerations on sample biases in bankruptcy modelling. Typically, the models are estimated based on non-random samples with proportion of bankrupt companies differing from that in the population. This causes bias in estimated bankruptcy probabilities for single companies. The paper opens with remarks on samples used in bankruptcy research in Poland which are followed by exposition on sample choice biases, starting with the findings of Zmijewski [1984]. The major issue presented is the development of Skogsvik and Skogsvik [2013] formula of a relationship between biased and unbiased estimated probability of bankruptcy of a given company. It is shown that the formula coincides with Anderson-Maddala correction (Anderson 1973, Maddala 1983) for the logit model. Comments on sample bias in classification modelling conclude the paper.
PL
Przedmiotem artykułu są rozważania na temat błędów doboru próby w modelowaniu ban-kructwa. Modele są zazwyczaj szacowane na podstawie nielosowych prób, w których udział bankrutów odbiega od ich udziału w populacji przedsiębiorstw. Błędy wynikające z takiego podejścia powodują obciążenie ocen prawdopodobieństwa bankructwa pojedynczych firm. Problem badań bankructw w Polsce autor przedstawił w szerszym kontekście, począwszy od wyników Zmijewskiego [1984]. Zaproponował konkretyzację zależności Skogsvików [2013] między obciążonym i nieobciążonym prawdopodobieństwem bankructwa danej firmy. Dla modelu logitowego zależność okazała się zgodna z korektą Andersona-Maddali. Opracowa-nie zostało wzbogacone o uwagi na temat modeli klasyfikacji.
EN
Insolvency prediction is one of the crucial abilities in corporate finance and financial management. It is critical in accounts receivable management, capital budgeting decisions, financial analysis, capital structure management, going concern assessment and co-operation with other companies. The purpose of this paper is to compare the efficiency of selected deep learning and machine learning algorithms trained on a representative sample of Polish companies for the period 2008–2017. In particular, the paper tested the following popular machine learning algorithms: discriminant analysis (DA), logit (L), support vector machines (SVM), random forest (RF), gradient boosting decision trees (GB), neural network with one hidden layer (NN), convolutional neural network (CNN), and naïve Bayes (NB). The research hypotheses evaluated in the paper state that if one has access to a large sample of companies, the most accurate algorithm (first choice) in bankruptcy prediction will be gradient boosting decision trees (H1), random forest (H2) and neural networks (H3) (deep learning) algorithms. The initial hypotheses were formulated based on the practitioners’ opinions regarding the usefulness of various machine learning and artificial intelligence algorithms in bankruptcy prediction. As the results of the research suggest, both deep learning and machine learning algorithms proved to have very comparable efficiency. The new factor introduced in the paper was that the training of the models was carried out on a representative sample of companies (for years 2008–2013) and also the testing phase used a significant number of bankrupt and active companies (validation included a completely different set of companies than those used in the training phase: data were taken from a different time period, 2014–2017, and companies in both sets were also completely different).
PL
Poprawne przewidywanie niewypłacalności przedsiębiorstw jest niezwykle istotne z perspektywy zarządzania finansami przedsiębiorstw, gdyż ma ono kluczowe znaczenie w zarządzaniu należnościami, ocenie projektów inwestycyjnych, zarządzaniu kapitałem obrotowym, oceną zdolności do kontynuowania działania, podejmowaniu współpracy i podpisywaniu umów z innymi przedsiębiorstwami. Celem artykułu jest porównanie skuteczności wybranych algorytmów uczenia maszynowego i deep learningu, które zostały zastosowane na reprezentatywnej próbie polskich przedsiębiorstw z wykorzystaniem danych za lata 2008–2018. W artykule podjęto próbę porównania skuteczności następujących algorytmów machine learning (uczenia maszynowego): analizy dyskryminacyjnej (DA), funkcji logitowej (L), support vector machines (SVM), random forest (RF), gradient boosting decision trees (GB), sieci neuronowych z jedną warstwą ukrytą (NN), konwolucyjnych sieci neuronowych (CNN) oraz metody naïve Bayes (NB). Zgodnie z hipotezami badawczymi jeśli ma się dostęp do dużej próby firm, najskuteczniejszym algorytmem (pierwszym wyborem) w prognozie bankructwa są algorytmy: gradient boosting decision trees (H1), random forest (H2) i nierekurencyjne wielowarstwowe sieci neuronowe (H3). Wstępne hipotezy zostały sformułowane na podstawie opinii praktyków dotyczących przydatności różnych algorytmów uczenia maszynowego i algorytmów sztucznej inteligencji w prognozowaniu upadłości przedsiębiorstw. W artykule wykorzystano do uczenia algorytmów bardzo dużą (reprezentatywną) grupę przedsiębiorstw komercyjnych (dane za lata 2008–2013), a do walidacji skuteczności algorytmów również bardzo dużą populację przedsiębiorstw (dane za okres 2014–2018); obydwie populacje obejmowały zupełnie inne podmioty gospodarcze i inne okresy, co pozwoliło na rzetelne porównanie skuteczności badanych algorytmów.
PL
Zasadniczym celem artykułu jest prezentacja problematyki kryzysu pandemicznego na przykładzie jednego z największych przedsiębiorstw w kraju specjalizujących się w kolejowym transporcie pasażerskim. Przeprowadzono wobec niego dwie metodycznie odmienne analizy kondycji finansowej w okresie pięciu lat, tuż przed jego wystąpieniem. Uzyskane wyniki analiz okazały się odmiennie różne. Metoda porównywania wyników sprzedażowych, choć wskazała wyraźną dekoniunkturę, to nie dawała powodu do zmartwień. Metoda dyskryminacyjna natomiast wskazała, że kondycja przedsiębiorstwa jest na bardzo dobrym poziomie w okresie czterech lat przed pandemią. Kolejne dwa lata były nieco słabsze, choć nie alarmujące. Krytycznym momentem stał się ostatni rok analizy, w którym wybuchła pandemia. Wskaźniki wyraźnie zbliżyły się do wartości granicznych, co wskazywałoby na stan bliski upadłości. Wobec zaistniałej sytuacji autorzy wskazali potrzebę przeprowadzenia działań zmierzających do zniwelowania skutków kryzysu. Do podstawowych zadań zaliczono potrzebę rekonstrukcji modelu biznesowego oraz ponowną identyfikację procesów strategicznych mających na celu weryfikację polityki przedsiębiorstwa wobec zachodzących zmian. Zabieg ten stanowi kluczowe działanie zmierzające do poprawy konkurencyjności przedsiębiorstwa na rynku transportowym. Istotnym staje się również dbałość o gospodarkę taborową oraz poziom świadczonych usług. Wartością dodaną zaś jest sprawnie funkcjonująca komunikacja realizowana na wszystkich poziomach przedsiębiorstwa. Kontrola i zarządzanie nim jest możliwe tylko wtedy, gdy obraz działalności zwizualizowany zostanie w formie mierników, których wyniki uzależnione są od poziomu motywacji pracowników. W celu napisania artykułu wykorzystana została literatura naukowa, zarówno polska, jak i zagraniczna oraz oficjalne wyniki finansowe badanego przedsiębiorstwa.
EN
The main aim of the article is to introduce the problem of pandemic crisis on the case of one of the largest companies in the country which specialise in passenger rail transport. Two different analyses of its financial condition were methodically carried out over a period of five years, just before its occurrence. The results of the analyses turned out to be different. The method of comparing sales results, although it indicated a clear downturn, gave no cause for concern. The discriminant method, on the other hand, indicated that the company’s health was at a very good level in the four years before the pandemic. The next two years were a little less good, although not alarming. The critical moment became the last year of the analysis, when the pandemic began. The indicators clearly approached the limit values, which would indicate a state of near bankruptcy. This procedure is a key action aimed at improving the competitiveness of the company on the transport market. It is also important to take care of the rolling stock management and the level of services provided. In view of the situation, the authors have pointed out the need to carry out actions aimed at levelling the effects of the crisis. The basic tasks included the need to reconstruct the business model and to re-identify strategic processes aimed at verifying the company’s policy towards the changes taking place. This procedure is a key action aimed at improving the competitiveness of the company on the transport market. It is also important to take care of the rolling stock management and the level of services provided. The added value is effective communication at all levels of the company. It can only be audited and managed if the performance is visualised in the form of indicators, the results of which depend on the level of employee motivation. In the writing of the article, scientific literature, both Polish and foreign, as well as official results of the analysed company were used.
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