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

翻译：组成数据在现代被定义为正向量，其元素间的比率是研究者所关注的对象。通过会计比率进行财务报表分析完全符合这一定义。组成数据分析解决了产业层面标准财务比率统计分析中的主要问题，如偏态、非正态性、非线性以及结果对比率中分子与分母会计项目选择依赖性的问题。尽管如此，组成分析方法在财务报表分析中的应用仍然罕见。本文介绍了组成数据分析中特别适用于财务报表分析的若干变换方法，展示了如何从组成视角计算产业或子产业的标准财务比率均值，说明了如何利用组成双标图可视化产业内的企业、通过组成聚类分析对其进行分类，以及如何借助组成回归模型关联财务与非财务指标。我们以西班牙酒庄的会计财务报表为例，运用杜邦分析法进行了实际应用，并提供了组成分析免费软件CoDaPack的分步操作教程。