The Distributional Properties of Financial Ratios: The Case of Czech Bankruptcy Data


  • Mária Režňáková
  • Michal Karas


bankruptcy, financial ratios, outlier detection, normality, data transformation


Purpose of the article: The purpose of this paper is to analyse the distributional properties of financial data, suitable for building a bankruptcy forecast model, in the sense of normality deviation and the existence of outliers. Methodology/methods: In praxis, financial data in the form of financial ratios is very often not normály distributed. A Shapiro-Wilk’s procedure was used to test normality (Shapiro, Wilk, 1965) and a Box-Cox transformation (Box, Cox, 1964) for normalizing financial ratios. Scientific aim: We would like to contributed to the previous pieces of research in following ways. Firstly, by analysing a greater range of accounting ratios or indicators (i.e. 44), secondly, by focusing on data of a different character (data suitable for building a bankruptcy forecast model), thirdly, by explaining cases in which the parameter l is not possible to estimate, and finally fourthly, identifying a possible cause of transformation failure in achieving normality of financial ratios. Findings: Before the transformation none of the analysed financial ratios met the condition of one-dimensional normality, not even on the 1-% level. After transformation, the condition of one-dimensional normality was met, at the 1-% level, by 34% of the analysed financial ratios. The same condition, but at the 5 or 10-% level, was met by 27% of the analysed financial ratios. The parameter l was not possible to estimate in the case of 18% of financial ratios. Conclusions: The condition of normality for untransformed Czech bankruptcy data seems almost as impossible to fulfil. This conclusion implies the use of non-parametric methods, such as artificial neural networks. However, the comparison of the parametric method’s performance using untransformed or transformed data is the subject of further research.