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Compositional data are contemporarily defined as positive vectors, the ratiosamong whose elements are of interest to the researcher. Financial statementanalysis by means of accounting ratios fulfils this definition to the letter.Compositional data analysis solves the major problems in statistical analysisof standard financial ratios at industry level, such as skewness,non-normality, non-linearity and dependence of the results on the choice ofwhich accounting figure goes to the numerator and to the denominator of theratio. In spite of this, compositional applications to financial statementanalysis are still rare. In this article, we present some transformationswithin compositional data analysis that are particularly useful for financialstatement analysis. We show how to compute industry or sub-industry means ofstandard financial ratios from a compositional perspective. We show how tovisualise firms in an industry with a compositional biplot, to classify themwith compositional cluster analysis and to relate financial and non-financialindicators with compositional regression models. We show an application to theaccounting statements of Spanish wineries using DuPont analysis, and astep-by-step tutorial to the compositional freeware CoDaPack.

Accounting statement analysis at industry level. A gentle introduction to the compositional approach