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 a.k.a. financial 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, outliers, and dependence of the results on the choice of which accounting figure goes to the numerator and to the denominator of the ratio. Despite 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 by means of geometric means. We show how to visualise firms in an industry with a compositional principal-component-analysis biplot; how to classify them into homogeneous financial performance profiles with compositional cluster analysis; and how to introduce financial ratios as variables in a statistical model, for instance to relate financial performance and firm characteristics with compositional regression models. We show an application to the accounting statements of Spanish wineries using the decomposition of return on equity by means of DuPont analysis, and a step-by-step tutorial to the compositional freeware CoDaPack.

翻译：组合数据通常定义为元素比值受到研究者关注的正向量。通过会计比率（亦称财务比率）进行的财务报表分析完全符合这一定义。组合数据分析解决了行业层面标准财务比率统计分析中的主要问题，例如偏态性、非正态性、非线性、异常值以及结果依赖于分子与分母会计科目选择的问题。尽管如此，组合方法在财务报表分析中的应用仍然罕见。本文介绍了一些对财务报表分析特别有用的组合数据分析变换方法。我们展示了如何通过几何均值从组合视角计算行业或子行业的标准财务比率均值；如何利用组合主成分分析双标图可视化行业内的企业；如何通过组合聚类分析将企业归类为同质财务绩效画像；以及如何将财务比率作为变量引入统计模型，例如通过组合回归模型关联财务绩效与企业特征。我们以西班牙酿酒企业的财务报表为例，利用杜邦分析分解净资产收益率，并提供了组合免费软件CoDaPack的分步教程。