1 New financial ratios based on the compositional data methodology Salvador Linares -Mustarós a Maria Àngels Farreras -Noguer a

2025-04-30 0 0 581.24KB 19 页 10玖币

侵权投诉

New financial ratios based on the compositional data methodology

Salvador Linares-Mustarós a, ∗, Maria Àngels Farreras-Noguer a,

Núria Arimany-Serrat b, Germà Coenders c

a Department of Business Administration, University of Girona, Carrer Universitat de Girona, 10,

17071, Girona, Spain

b Department of Economics and Business, University of Vic-Central University of Catalonia, Carrer

de la Sagrada Família, 7, 08500 Vic, Barcelona

c Department of Economics, University of Girona, Carrer Universitat de Girona, 10, 17071, Girona,

Spain

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.

Keywords: financial ratios; management ratios; compositional data (CoDa); financial performance;

sectoral analysis.

1. Introduction

While standard financial ratios help to accurately evaluate the financial statements of firms and

corporations at an individual level (Whittington, 1980; Barnes, 1987, Bernstein, 1993; Gallizo,

2005), unfortunately when they are used as variables in statistical analyses of the financial health of a

sector, the reliability of the results of these diagnoses cannot be accepted as valid given that, as this

study will show, the loss of symmetry produced when defining standard financial ratios causes

potentially significant distortions when analysing financial health. Although this asymmetry in

financial ratios has been known for some time (Lev and Sunder, 1979; Cowen and Hoffer 1982;

Mcleay and Omar, 2000), it has not received due attention from the area of accounting, despite the

serious problem of it casting doubt on the results of multiple current studies that use standard ratios

as variables (Fernández-Olmosá et al., 2009; Hammervoll et al., 2014; Newton et al., 2015; Delord et

al., 2015; Lorenzo et al., 2018). The statistical problems of ratios have also been reported in other

∗ Corresponding author.

E-mail addresses: salvador.linares@udg.edu (S. Linares-Mustarós), angels.farreras@udg.edu (M.A. Farreras-Noguer), nuria.arimany@uvic.cat (N.

Arimany-Serrat), germa.coenders@udg.edu (G. Coenders)

scientific fields (Isles, 2020). The present article aims to correct this fact by providing a detailed

explanation of the reason for this problem, which is also the root cause of other identified and related

problems such as the emergence of spurious outliers (So, 1987; Watson, 1990; Creixans–Tenas et al.,

2019), and by showing how the results obtained are incoherent if ratios where the numerator and the

denominator are permuted are used (Frecka and Hopwood, 1983; Linares–Mustarós et al., 2018;

Creixans-Tenas et al., 2019).

In the first part of this article, a mathematic counterexample will be used to evidence the serious

drawbacks of using standard financial ratios in statistical studies of economic sectors. Once the

danger of incurring serious methodological problems when using standard financial ratios in this

type of study has been explained, a new type of financial ratios based on the methodology of

compositional data analysis, or simply compositional data (CoDa), will be suggested, the validity of

the results of which has already been extensively tested in other fields (Aitchison, 1986; Pawlowsky-

Glahn and Buccianti, 2011; Van den Boogaart and Tolosana-Delgado, 2013; Pawlowsky-Glahn et

al., 2015; Filzmoser et al., 2018; Greenacre, 2018). While the CoDa methodology emerged from the

fields of geometry and chemistry at the end of the last century (Aitchison, 1982; 1986), it has since

been extended to all the other scientific fields of study, including economics and other social

sciences (Coenders and Ferrer-Rosell, 2020), and has started to be regularly used in studies in the

area of finance (Voltes-Dorta et al., 2014; Ortells et al., 2016; Belles-Sampera et al., 2016; Davis et

al., 2017; Verbelen et al., 2018; Boonen et al., 2019; Kokoszka et al., 2019; Wang et al., 2019;

Gámez-Velázquez and Coenders, 2020; Maldonado et al., 2021a; 2021b; Porro, 2022; Vega-Baquero

and Santolino, 2022), and, more recently, in the area of accounting (Linares-Mustarós et al., 2018;

Creixans-Tenas et al., 2019; Carreras-Simó and Coenders, 2020; 2021; Saus-Sala et al., 2021;

Arimany-Serrat et al., 2022). The present article aims to show that the CoDa approach can be used in

the accounting field ensuring the validity of results, and to provide the research community in

finance and accounting with a reasoned case for using a new methodology to analyse the financial

statements in a sector. To achieve this end, the study concludes with a simple example of an analysis

of the financial statements of the wine sector 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.

Based on the line of argument presented, this study is organised in three main sections. Section 2

focuses on showing the serious problems arising from the use of standard ratios in sectoral studies,

which result from the lack of symmetry of ratios and can lead to the invalidity of the results of the

analysis. Financial ratios based on the CoDa methodology are presented in section 3 as possible

candidates to replace standard or conventional financial ratios. Section 4 presents a research example

in the wine sector comparing the use of conventional and compositional ratios, which aims to show

the need to change from the usual working methodology in sectoral studies based on standard

financial ratios by exposing the significant discrepancies in the two sets of results. Sections 5 and 6

present the discussion and conclusions, respectively.

2. Theory. The problem of the asymmetry of standard ratios. The appearance of spurious

outliers

This section explains in detail why methodological works that use standard financial ratios as

variables in sectoral statistical analyses cannot be considered as valid. To this end, the starting point

is the fictitious data of a group of ten firms, the values of two accounting magnitudes of which are

given in the first two columns of Table 1.

Table 1.

Artificial data of a ten-firm sector.

Magnitude 1

Magnitude 2

Mg 2

Mg 1

Mg 2

Firm 1

0.5

~82.875 (=45+37.875)

0.125

Firm 2

1.5

~63.435 (=45+18.435)

0.5

Firm 3

1.5

2.5

~59.035 (=45+14.035)

1. 6

�

0.6

Firm 4

1.8

~59.035 (=45+14.035)

1. 6

�

0.6

Firm 5

1.5

~45 (=45+0)

Firm 6

~45 (=45-0)

Firm 7

1.8

~30.965 (=45-14.035)

0.6

1. 6

�

Firm 8

2.5

1.5

~30.965 (=45-14.035)

0.6

1. 6

�

Firm 9

1.5

~26.565 (=45-18.435)

0.5

Firm 10

0.5

~7.125 (=45-37.875)

0.125

Given that this section focuses on the problems related to asymmetry, the data Magnitude 1 and

Magnitude 2 in Table 1 are represented graphically in Cartesian coordinates. A look at Figure 1

shows that the magnitudes recorded in Table 1 are chosen because they are symmetrical with respect

to the 45º angle in the computation of the angles α of the rays that start at the origin and pass through

the points, as shown in Figure 2. This symmetry is reflected in the column headed α in Table 1.

Fig. 1. Graphical representation of the ten firms in Table 1 (E1 to E10).

Fig. 2. Angles (α) of the ten firms (E1 to E10).

The column in Table 1 headed “Mg2/Mg1” contains the values of the ratio Magnitude

2/Magnitude 1. The same ratio values in this column for firms 3 and 4 and firms 7 and 8 are justified

by firms with proportional magnitudes having the same ratio.

Geometrically, the ratio Magnitude 2 / Magnitude 1 can be interpreted as the tangent of the angle

α formed between the abscissa axis and the ray that starts at the origin of coordinates and joins all the

points with the same ratio value, as can be observed in Figure 3.

Fig. 3. Graphical relationship between the tangent of an angle and the different points on the ray that starts from the

origin of coordinates (tan(α) can be written as 

 or 

 ).

Consequently, given that two points (a,b) and (A,B) that share the same ray starting from the

origin of coordinates always fulfil the expression b/a = B/A, in the case that a = 1, b = B/A. This fact

shows that the ratio Magnitude 2 / Magnitude 1 can be interpreted geometrically as the height of the

cut-off point of the ray with the line of equation x=1, as shown in Figure 4.

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

1NewfinancialratiosbasedonthecompositionaldatamethodologySalvadorLinares-Mustarósa,∗,MariaÀngelsFarreras-Noguera,NúriaArimany-Serratb,GermàCoenderscaDepartmentofBusinessAdministration,UniversityofGirona,CarrerUniversitatdeGirona,10,17071,Girona,SpainbDepartmentofEconomicsandBusiness,UniversityofVic-...

展开>> 收起<<

1 New financial ratios based on the compositional data methodology Salvador Linares -Mustarós a Maria Àngels Farreras -Noguer a.pdf

共19页,预览4页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

1 New financial ratios based on the compositional data methodology Salvador Linares -Mustarós a Maria Àngels Farreras -Noguer a

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: