Financial statement data: an empirical analysis
Laura Grassini
Alessandro Viviani
Dipartimento di Statistica”G. Parenti”
Università degli studi di Firenze
Florence, Italy
grassini@ds.unifi.it
viviani@ds.unifi.it
1. Introduction
The statistical analysis of financial ratios is used: (1) by accountants and analysts, for
comparison (and other) purposes. The traditional textbooks on financial analysis emphasise the use
of industry-wide averages as targets (Barnes, 1987); (2) by applied statisticians, in classifying ratios
(Kanto and Martikainen, 1992) and modelling firms’ behaviour (Grassini and Viviani, 1997).
In both field of research, an important topic is the study of the distribution of financial ratios
with the computation of the proper location and variability measures. While simple location
measure, like arithmetic mean, may be unanimous in normal distribution, it will not be in the case
of nonnormality as generally happens for the empirical distribution of financial ratios.
The search for the appropriate location measure for ratio’s distribution, can be approached by
studying the relationship between the numerator Y and the denominator X of the ratio Y/X, within a
linear regression framework (McDonald and Morris, 1984). In this paper we present some results of
an empirical analysis based on a cross-industry sample of 400 firms, operating in the northern
regions of Italy.
2. Problem statement and methodology
In this study, ratios are distinguished by taking into account the nature of the items X and Y.
Denote balance sheet items by b and income statement items by i: b is a stock whereas i is a flow
variable. Here, we consider some of the most used accounting ratios, which are of the form:
• b/b is the typical formula for financial and capital asset ratios. In this work we examined:
current assets/current liabilities (it is the current ratio: CR), fixed assets/operating assets (FOA);
• i/i: it generally characterises profitability ratios. We considered: operating income/sales (ROS);
• i/b: it is the general form of the profitability and turnover measures. We examined operating
income/operating assets (ROI), and sales/operating assets (TUR);
As in McDonald and Morris (1984), the regression models used in the analysis are:
MOD1:
MOD2:
Y/X=α/X+β+u/X
Y=α+βX+u
E(u)=0, V(u)= X2σ2
E(u)=0, V(u)=σ2
where u are uncorrelated disturbances. We can observe that, if α is not significantly different from
zero, the suitable location measure is the ratio of means under MOD2; the mean of ratios under
MOD1. The presence of heteroscedasticity is evaluated through the ratio between the sum of
squared residuals of two separate regressions above and below the median of X. Furthermore, the
estimates of the least squares procedures are compared with those derived by the biweight method
with a tuning constant equal to 6 (Mosteller and Tukey, 1977).
3. Some empirical results
As shown in Table 1, MOD2 specification exhibits significant heteroscedasticity and
substantial nonnormalities of residuals. The presence of heteroscedasticity is proved also by the
biweight method: in MOD2 all the outliers occur for high values of X. MOD1 eliminates
heteroscedasticity and exhibits a small number of outliers, but it does not provide relevant
improvements in the distributional statistics. Under MOD1, α is significantly different from zero
only for CR, but the pattern of residuals does not support these outcomes.
Our results agree with those obtained by various authors. The nonnormality of residuals
suggest that the traditional linear regression approach is untenable because of: (a) some ratios are,
by definition, bounded from below and/or from above; (b) the relationship between Y and X is
influenced also by factors which are under the firm’s control.
7DEOH(PSLULFDOUHVXOWV
Form
Ratios
CR
b/b
FOA
i/i
ROS
ROI
i/b
TUR
Model
MOD1
MOD2
MOD1
MOD2
MOD1
MOD2
MOD1
MOD2
MOD1
MOD2
α
204
221
–43
–807
–6
175
3
206
189
2193
Least squares method
Skewness Kurtosis
β
1.2428
2.457
10.0
1.2036
2.035
27.0
0.2944
3.035
21.9
0.3599
4.654
50.8
0.0680
1.181
7.4
0.0664
0.505
16.2
0.0917
1.302
3.3
0.0849
1.544
13.7
1.3873
3.111
22.4
1.2141
2.179
29.8
Heter.
0.28
37.31
0.67
122.90
0.87
97.90
0.93
103.72
1.02
107.41
Biweight method
Outliers
α
β
74 1.1731
15
784 1.0503
50
–30 0.2676
5
–591 0.3312
49
6 0.0623
11
27 0.0553
64
6 0.0791
14
211 0.0514
65
221 1.3130
5
693 1.2610
63
In this respect, we feel that the approaches based on variance component models (already
used for modelling industry effects: Fieldsend et al., 1987) are more suitable. We also feel that an
hypotheses on the disturbances, as used for the stochastic production frontiers (a normal plus a
nonnormal component), would be a worthwhile approach in order to provide significant target
values of ratios.
REFERENCES
Fieldsend S:, N.Longford, S.McLeay (1987), Industry Effects and the Proportionality Assumption
in Ratio Analysis: a Variance Component Analysis, Journal of Business, Finance and
Accounting, 14, 497-517.
Grassini L., A.Viviani (1997), Una verifica empirica sulle caratteristiche finanziarie delle minori
imprese toscane, in Quintano (ed.), Scritti di Statistica Economica 3, Rocco Curto, Napoli.
Kanto A.J., T. Martikainen (1992). A Test on a priori Financial Characteristics of the Firm,
European Journal of Operational research, 57, 13-23.
McDonald B., M.H.Morris (1984), The Statistical Validity of the Ratio Method in Financial
Analysis: an Empirical Examination, Journal of Business Finance and Accounting, 11, 89-97.
Mosteller F., J.W. Tukey (1977), Data Analysis and Regression, Addison Wesley, Reading.
RESUMÉ
Dan cet article il y a une analyse de régression lineaire par des méthodes traditionnelles et
robustes afin d'esplquer la rélation entre numérateur et dénominateur des rapports des bilans.