New Financial Ratios Based on the Compositional Data Methodology

Abstract

Due to the type of mathematical construction, the use of standard financial ratios in studies analyzing the financial health of a group of firms leads to a series of statistical problems that can invalidate the results obtained. These problems originate from the asymmetry of financial ratios. The present article justifies the use of a new methodology using Compositional Data (CoDa) to analyze the financial statements of an industry, improving analyses using conventional ratios, since the new methodology enables statistical techniques to be applied without encountering any serious drawbacks, such as skewness and outliers, and without the results depending on the arbitrary choice as to which of the accounting figures is the numerator of the ratio and which is the denominator. An example with data on the wine industry is provided. The results show that when using CoDa, outliers and skewness are much reduced, and results are invariant to numerator and denominator permutation.