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：组分数据目前定义为正向量，其元素间的比率是研究者关注的焦点。通过会计比率进行的财务报表分析完全符合这一定义。组分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，如偏态性、非正态性、非线性以及结果对会计数值选择作为比率分子或分母的依赖性。尽管如此，组分分析在财务报表分析中的应用仍然很少。本文介绍了组分数据分析中一些对财务报表分析尤为有用的变换方法。我们从组分视角展示了如何计算行业或子行业标准财务比率的均值，并说明了如何通过组分双标图可视化行业内的企业，利用组分聚类分析对其进行分类，以及通过组分回归模型将财务与非财务指标相关联。我们以西班牙酒庄的财务报表为例，运用杜邦分析展示了实际应用，并提供了组分分析免费软件CoDaPack的分步教程。