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A New Methodological Proposal for Classifying Firms According to the Similarity of Their Financial Structures Based on Combining Compositional Data with Fuzzy Clustering
Xavier Molas-Colomer, Salvador Linares-Mustarós, Maria Àngels Farreras-Noguer and Joan Carles Ferrer-Comalat
The main aim of this paper is to show that the methodology of classifying firms of the same sector according to the similarity of their classical financial ratios results in serious problems of incoherence and, consequently, it is necessary to find a viable alternative. With this objective in mind, simple examples are used to show that the appearance of multiple unsolvable problems make it impossible to accept the validity of grouping firms according to homogeneous groups based on these ratios using the usual clustering techniques. Once this fundamental fact has been verified, the proposal of classifying firms based on the ratios created in compositional data methodology and fuzzy clustering is shown to offer a viable alternative for this purpose. The paper ends with a complete analysis using real data.
Keywords: Compositional data analysis, CoDa, financial ratio, cluster analysis, fuzzy cluster; classifying firms