Principal component analysis of financial statements. A compositional approach

Abstract

Financial ratios are often used in principal component analysis and related techniques for the purposes of data reduction and visualization. Besides the dependence of results on ratio choice, ratios themselves pose a number of problems when subjected to a principal component analysis, such as skewed distributions. In this work, we put forward an alternative method drawn from compositional data analysis (CoDa), a standard statistical toolbox for use when data convey information about relative magnitudes, as financial ratios do. The method, referred to as the CoDa biplot, does not rely on any particular choice of financial ratio but allows researchers to visually order firms along the pairwise financial ratios for any two accounts. Non-financial magnitudes and time evolution can be added to the visualization as desired. We show an example of its application to the top chains in the Spanish grocery retail sector and show how the technique can be used to depict strategic management differences in financial structure or performance, and their evolution over time.

New Financial Ratios Based on the Compositional Data Methodology

“…The main objective of this article is to show that the use of standard financial ratios in studies at the industry level is not recommended because the results produced can be invalid, even when applying the most elementary statistical techniques. The present article complements the already existing research that exposes the serious consequences of using financial ratios in multivariate statistical analyses [5,16,22,[45][46][47][48], while revealing the causes of the problems and showing them with two simple examples, of which one consists of real data. In line with what was shown in this article, it must be remembered that because asymmetrical distributions can lead to the relations between the standard financial ratios being non-linear [5], using the latter can impede, for example, the application of factor analysis, regression analysis, and other linear models [46].…”

“…Once the danger of incurring serious methodological problems when using standard financial ratios in this type of study is explained, a new type of financial ratio based on the methodology of compositional data analysis, or simply Compositional Data (CoDa), is suggested, the validity of the results of which has already been extensively tested in other fields [23][24][25][26][27][28]. While the CoDa methodology emerged from the fields of geometry and chemistry at the end of the last century [23,29], it has since been extended to all the other scientific fields of study, including economics and other social sciences [30], and has started to be regularly used in studies in the area of finance [31][32][33][34][35][36][37][38][39][40][41][42][43] and, more recently, in the area of accounting [16,22,[44][45][46][47][48]. The article uses a second example with real data of a particular industry in a European country, which shows the invalidity of the results obtained using the traditional methodology and how the proposed methodology avoids the abovementioned problems.…”

Multivariate cumulative sum control chart for compositional data with known and estimated process parameters

“…Table 1 shows the values of the OOC ARL 1 's for the MCUSUM-CoDa chart for selected values of the number of variables 𝑝 having values (3,5,10,20), the values of IC ARL 0 selected to be (200, 500) and the values of shift 𝛿 that are (0.25, 0.5, 0.75, … , 3). Table 1 also presents the different chosen values of ℎ according to the IC ARL 0 and the number of variables 𝑝.…”

“…Table 2 shows the values of the UCL's for the MCUSUM-CoDa chart with estimated parameters for selected values of the number of variables 𝑝 having values (3,5,10,20), the subgroup size 𝑚 having values (3,5,10,15), the values of IC ARL 0 selected to be (200, 500). The values of shift 𝛿 that are (0.25, 0.5, 0.75, … , 3) and the number of samples 𝑛 that are (30,40,50,100,500,1000,2000).…”

“…Blasco-Duatis et al 9 worked on the agenda-setting theory, priming, and the spiral of silence in political party Twitter accounts are explored. Carreras-Simo and Coenders 10 studied Principal Component Analysis of Financial Statements using compositional data. Recently, Coenders and Ferrer-Rosell 11 analyzed compositional data for tourism.…”