Principal component analysis of financial statements. A compositional approach

Abstract

Financial ratios are often used in principal component analysis and related techniques for the purposes of data reduction and visualization. Besides the dependence of results on ratio choice, ratios themselves pose a number of problems when subjected to a principal component analysis, such as skewed distributions. In this work, we put forward an alternative method drawn from compositional data analysis (CoDa), a standard statistical toolbox for use when data convey information about relative magnitudes, as financial ratios do. The method, referred to as the CoDa biplot, does not rely on any particular choice of financial ratio but allows researchers to visually order firms along the pairwise financial ratios for any two accounts. Non-financial magnitudes and time evolution can be added to the visualization as desired. We show an example of its application to the top chains in the Spanish grocery retail sector and show how the technique can be used to depict strategic management differences in financial structure or performance, and their evolution over time.