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.
discriminant analysis, support vector machines, bankruptcy prediction, SMEs
ABDOU, H., POINTON, J., MASRY, A. E., (2008). Neural Nets Versus Conventional Techniques in Credit Scoring in Egyptian Banking. Expert Systems with Applications, 35(2), pp. 1275–1292.
ALTMAN, E. I., (1968). Financial ratios, Discriminant analysis and the prediction of corporate bankruptcy. Journal of Finance, 23(4), pp. 589–609.
ANDREEVA, G., CALABRESE, R., OSMETTI, S. A., (2014). A comparative analysis of the UK and Italian small businesses using Generalised Extreme Value models. https://arxiv.org/pdf/1412.5351.pdf.
APPENZELLER, D., SZARZEC, K., (2004). Forecasting the bankruptcy risk of Polish public companies. Rynek Terminowy, 1, pp. 120–128.
BACK, B., LAITINEN, T., SERE, K., VAN WEZEL, M., (1996). Choosing bankruptcy predictors using discriminant analysis, logit analysis, and genetic algorithms, Technical Report, Turku Centre for Computer Science.
BALINA, R., BĄK, M. J., (2016). Discriminant Analysis as a Prediction Method for Corporate Bankruptcy with the Industrial Aspects. Waleńczów: Wydawnictwo Naukowe Intellect.
BERG, D., (2007). Bankruptcy prediction by generalized additive models. Applied Stochastic Models in Business and Industry, 23(2), pp. 129–143.
BLANCO, A., PINO-MEJÍAS, R., LARA, J., (2013). Credit scoring models for the microfinance industry using neural networks: Evidence from Peru, Expert Systems with Applications, 40(1), pp. 356–364.
BROŻYNA, J., MENTEL, G., PISULA, T., (2016). Statistical methods of the bankruptcy prediction in the logistics sector in Poland and Slovakia. Transformations in Business & Economics, 15, pp. 80–96.
BRYANT, S. M., (1997). A case-based reasoning approach to bankruptcy prediction modelling. Intelligent Systems in Accounting, Finance and Management, 6(3), pp. 195-214.
CALABRESE, R., MARRA, G., OSMETTI, S. A., (2015). Bankruptcy prediction of small and medium enterprises using a flexible binary generalized extreme value model. Journal of the Operational Research Society, 67(4).
CHAUDHURI, A., DE, K., (2011). Fuzzy support vector machine for bankruptcy prediction. Applied Soft Computing, 11(2), pp. 2472–2486.
DERELIOGLU, G., GÜRGEN F., (2011). Knowledge discovery using neural approach for SME’s credit risk analysis problem in Turkey. Expert Systems with Applications, 38(8), pp. 9313–9318.
DESAI, V. S., CROOK, J. N., OVERSTREET, G. A., (1996). A Comparison of Neural Networks and Linear Scoring Models in the Credit Union Environment. European Journal of Operational Research, 95(1), pp. 24–47.
DU JARDIN, P., (2009). Bankruptcy prediction models: How to choose the most relevant variables?. Bankers, Markets & Investors, 98, pp. 39-46.
GAJDKA, J., STOS, D., (1996). Wykorzystanie analizy dyskryminacyjnej do badania podatności przedsiębiorstwa na bankructwo. In: J. Duraj ed. Przedsiębiorstwo na rynku kapitałowym, Wydawnictwo Uniwersytetu Łódzkiego, Łódź.
GĄSKA, D., (2016). Predicting Bankruptcy of Enterprises with the use of Learning Methods. Ph.D. dissertation, Wrocław University of Economics.
GORDINI, N., (2014). A genetic algorithm approach for SMEs bankruptcy prediction: Empirical evidence from Italy, Expert Systems with Applications, 41(14), pp. 6067–6536.
GRUSZCZYŃSKI, M., (2003). Models of microeconometrics in the analysis and forecasting of the financial risk of enterprises. Zeszyty Polskiej Akademii Nauk, 23.
GUPTA, J., GREGORIOU, A., HEALY, J., (2015). Forecasting bankruptcy for SMEs using hazard function. A review of quantitative finance and accounting, 45 (4), pp. 845–869.
HADASIK, D., (1998). The Bankruptcy of Enterprises in Poland and Methods of its Forecasting. Wydawnictwo Akademii Ekonomicznej w Poznaniu, 153.
HAMROL, M., CZAJKA, B., PIECHOCKI, M., (2004). Enterprise bankruptcy– discriminant analysis model. Przegląd Organizacji, 6, pp. 35–39.
HOŁDA, A., (2001). Forecasting the bankruptcy of an enterprise in the conditions of the Polish economy using the discriminatory function ZH. Rachunkowość, 5, pp. 306–10.
HUANG, Z., CHEN, H., HSU, C. J., CHEN, W. H., WU, S., (2004). Credit Rating Analysis with Support Vector Machines and Neural Networks: A Market Comparative Study. Decision Support System, 37(4), pp. 543–558.
HUANG, J. J., TZENG, J. H., ONG, C. S., (2006). Two-stage genetic programming (2sgp) for the credit scoring model. Applied Mathematics and Computation, 174, pp. 1039–1053.
JAGIEŁŁO, R., (2013). Discriminant and Logistic Analysis in the Process of Assessing the Creditworthiness of Enterprises. Materiały i Studia, 286. Warszawa: NBP.
KALAK I. E., HUDSON, R., (2016). The effect of size on the failure probabilities of SMEs: An empirical study on the US market using discrete hazard model. International Review of Financial Analysis, 43, pp. 135–145.
KARBOWNIK, L., (2017). Methods for Assessing the Financial Risk of Enterprises in the TSI Sector in Poland. Łódź: Wydawnictwo Uniwersytetu Łódzkiego.
KIM, H. S., SOHN, S. Y., (2010). Support Vector Machines for Default Prediction of SMEs Based on Technology Credit. European Journal of Operational Research, 201(3), pp. 838–846.
KOROL, T., PRUSAK, B., (2009). Upadłość przedsiębiorstwa a wykorzystanie sztucznej inteligencji, Warszawa: CeDeWu.
KOROL, T., (2004). Assessment of the Accuracy of the Application of Discriminatory Methods and Artificial Neural Networks for the Identification of Enterprises Threatened with Bankruptcy. Gdańsk: Doctoral dissertation.
KOROL, T., (2010a). Early Warning Systems of Enterprises to the Risk of Bankruptcy. Warszawa: Wolters Kluwer.
KOROL, T., (2010b). Forecasting bankruptcies of companies using soft computing techniques. Finansowy Kwartalnik Internetowy “e-Finanse”, 6, pp. 1–14.
MĄCZYŃSKA, E., (1994). Assessment of the condition of the enterprise. Simplified methods. Życie Gospodarcze, 38, pp. 42–45.
MĄCZYŃSKA, E., (2004). Early warning systems. Nowe Życie Gospodarcze, 12, pp. 4–9.
MICHALUK, K., (2003). Effectiveness of corporate bankruptcy models in Polish economic conditions. In: L. Pawłowicz, R.Wierzba ed. Corporate Finance in the Face of Globalization Processes. Warszawa: Wydawnictwo Gdańskiej Akademii Bankowej.
MODINA, M., PIETROVITO, F., (2014). A default prediction model for Italian SMEs: the relevance of the capital structure. Applied Financial Economics, 24(23), pp. 1537–1554.
ORŁOWSKI, W., PASTERNAK, R., FLAHT, K., SZUBERT, D., (2010). Procesy inwestycyjne i strategie przedsiębiorstw w czasach kryzysu, Raport PARP Warszawa.
POCIECHA, J., PAWEŁEK, B., (2011). Bankruptcy Prediction and Business Cycle, Contemporary Problems of Transformation Process in the Central and East European Countries. Paper presented at 17th Ukrainian-Polish-Slovak Scientific Seminar, Lviv, Ukraine, September 22–24; Lviv: The Lviv Academy of Commerce, pp. 9–24.
POCIECHA, J., PAWEŁEK, B., BARYŁA, M., AUGUSTYN, S., (2014). Statistical Methods of Forecasting Bankruptcy in the Changing Economic Situation. Kraków: Fundacja Uniwersytetu Ekonomicznego w Krakowie.
POGODZIŃSKA, M., SOJAK, S., (1995). The Use of Discriminant Analysis in Predicting Bankruptcy of Enterprises. Ekonomia XXV, 299.
PRUSAK, B., (2018). Review of Research into Enterprise Bankruptcy Prediction in Selected Central and Eastern European Countries. International Journal of Financial Studies, 6, 60.
PRUSAK, B., WIĘCKOWSKA, A., (2007). Multidimensional models of discriminant analysis in the study of the bankruptcy risk of Polish companies listed on the WSE. In: B. Prusak ed. Economic and Legal Aspects of Corporate Bankruptcy. Warszawa: Difin.
PRUSAK, B., (2005). Modern Methods of Forecasting Financial Risk of Enterprises. Warszawa: Difin.
PSILLAKI, M., TSOLAS, I. E., MARGARITIS, D., (2010). Evaluation of credit risk based on firm performance. European Journal of Operational Research, 201 (3), pp. 873–881.
PTAK-CHMIELEWSKA, A., MATUSZYK, A., (2017). The importance of financial and non-financial ratios in SMEs bankruptcy prediction. Bank i Kredyt, 49(1), pp. 45–62.
PTAK-CHMIELEWSKA, A., (2016). Statistical Models for Corporate Credit Risk Assessment–Rating Models. Acta Universitatis Lodziensis Folia Oeconomica, 3, pp. 98–111.
PTAK-CHMIELEWSKA, A., (2012). Wykorzystanie modeli przeżycia i analizy dyskryminacyjnej do oceny ryzyka upadłości przedsiębiorstw. Ekonometria, 4 (38), pp. 157–172.
POLSKA AGENCJA ROZWOJU PRZEDSIĘBIORCZOŚCI, (2012). Raport o stanie sektora małych i średnich przedsiębiorstw w Polsce w latach 2010–2011, Warsaw.
SARTORI, F., MAZZUCCHELLI, A., DI GREGORIO, A., (2016). Bankruptcy forecasting using case-based reasoning: the CRePERIE approach. Expert Systems with Applications, 64, pp. 400–411.
SOHN, S. Y., KIM, D. H., YOON, J. H., (2016). Technology credit scoring model with fuzzy logistic regression. Applied Soft Computing, 43, pp. 150-158.
SOJAK, S., STAWICKI, J., (2001). Wykorzystanie metod taksonomicznych do oceny kondycji ekonomicznej przedsiębiorstw. Zeszyty Teoretyczne Rachunkowości, 3(59), pp.45-52.
STĘPIEŃ, P., STRĄK, T., (2004). Multidimensional logit models for assessing the risk of bankruptcy of Polish enterprises. In: D.Zarzecki ed. Time for Money, t. I., Szczecin: Wydawnictwo Uniwersytetu Szczecińskiego.
WĘDZKI, D., (2000). The problem of using the ratio analysis to predict the bankruptcy of Polish enterprises-Case study. Bank i Kredyt, 5, pp. 54–61.
WĘDZKI, D., (2004). Logit model of bankruptcy for the Polish economy-Conclusions from the study. In: D.Zarzecki ed. Time for Money. Corporate finance. Financing enterprises in the EU. Szczecin: Wydawnictwo Uniwersytetu Szczecińskiego.
WIERZBA, D., (2000). Early Detection of Enterprises Threatened with Bankruptcy Based on the Analysis of Financial Ratios-Theory and Empirical Research. Zeszyty Naukowe nr 9. Warszawa: Wydawnictwo Wyższej Szkoły Ekonomiczno- Informatycznej w Warszawie.
YIP, A. Y. N., (2006). Business failure prediction: a case-based reasoning approach. Review of Pacific Basin Financial Markets and Policies, 09, pp. 491-508.
ZIĘBA, M., TOMCZAK, S. K., TOMCZAK, J. M., (2016). Ensemble boosted trees with synthetic features generation in application to bankruptcy prediction. Expert Systems With Applications, 58, pp. 93-101.
ZMIJEWSKI, M. E., (1984). Methodological issues related to the estimation of financial distress prediction models. Journal of Accounting Research, 22, pp. 59-82.