New financial ratios based on the compositional data methodology

TL;DR

This paper introduces a compositional data methodology for financial ratio analysis that addresses statistical issues like skewness and outliers, providing more reliable insights into firms' financial health.

Contribution

It proposes a novel compositional data approach for financial ratios, overcoming limitations of traditional ratios related to asymmetry and arbitrary numerator-denominator choices.

Findings

Reduces outliers and skewness in financial data

Results are invariant to numerator and denominator permutation

Improves the reliability of financial health analysis

Abstract

Due to their type of mathematical construction, the use of standard financial ratios in studies analysing the financial health of a group of firms leads to a series of statistical problems that can invalidate the results obtained. These problems are originated by the asymmetry of financial ratios. The present article justifies the use of a new methodology using compositional data (CoDa) to analyse the financial statements of a sector, 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 of the wine sector is provided. The results show that when using CoDa, outliers and skewness are much reduced and results are invariant to numerator and denominator permutation.