Some Basic Properties of Financial Ratios: Evidence from an Emerging Capital Market

International Research Journal of Finance and Economics
ISSN 1450-2887 Issue 2 (2006)
© EuroJournals Publishing, Inc. 2006
http://www.eurojournals.com/finance.htm

Some Basic Properties of Financial Ratios: Evidence from an
Emerging Capital Market

Zulkarnain Muhamad Sori, Mohamad Ali Abdul Hamid, Annuar Md Nassir and Shamsher
Mohamad
Department of Accounting and Finance
Faculty of Economics and Management
Universiti Putra Malaysia
43400 Serdang
Selangor, Malaysia


Abstract

This study investigates the distributional characteristics and appropriate remedial
actions of selected financial ratios from failed and non-failed Malaysian listed firms. A
total of 66 listed firms with 330 observations and 65 variables were examined for the
period from 1980 to 1996. The samples were divided into three sectors named mixed
industry, combination of industrial and property and industrial sectors. Normality test was
carried out to the data using Kolgomorov-Smirnov test adjusted to Lilliefors test. The
finding shows that in all instances, only one variable (i.e., current asset percent) conformed
to normal distribution. However, when specific sector was tested, some improvement on
normality was observed after trimming outliers and data transformations. Remedial actions
were carried out using three-transformation techniques namely natural log, square root and
square. The natural log transformation outperforms the other techniques and the square
transformation was the least effective. The findings suggest that outlier trimming improves
the normality of variable after the data transformation, and this technique is more effective
on the specific industry compared to the mixed industry sector.

Key words: normality, distributional properties, transformation techniques, skewness
JEL classification: M40, M49

I. Introduction
Financial ratios have long been used in various study areas in accounting and finance using either
univariate or multivariate methodologies. However, in applying this modus operandi, most of the
researchers assumed the financial ratios are univariate or multivariate normal distribution. The
normality assumption, which was based on the normal distribution1, was considered a pre-requisite in
multivariate analysis and some check of normality is advisable in the early stages of analysis (Afifi and
Clark, 1990). Also, Karels and Prakash (1987) pointed out that the multiple discriminant analysis
procedure will be optimal if the normality conditions are met; otherwise, the conclusions derived are
suspect. Eisenbeis (1977) pointed out that,

1 The normal distribution was originally called the ‘law of errors’; the random effects of different magnitudes and sources
considered “errors”

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International Research Journal of Finance and Economics - Issue 2 (2006)
“In practice, deviations from the normality assumption at least in economic and finance,
appear more likely to be rule rather than exception. Violation of the normality
assumptions may bias the tests of significance and estimated error rates.”

The assumption of normality is important for the interpretation of the tests of significance, and if the
data does not satisfy this assumption, the results obtained may be biased. Even though large sample
sizes tend to diminish the detrimental effects of non-normality, the analyst should assess the normality
for all variables included in the analysis (Hair et al., 1995). In fact, Ariff et al. (1998), Zaidi (1997),
Deakin (1976), Ezzamel et al. (1987) and So (1987) evidenced that most of the financial ratios non-
normally distributed. They found that the financial ratios tend to be skewed and non-normally
distributed.
The importance of normality is that many real world observations can be modelled using the normal
distribution. If the actual situation meets the conditions of this important model, answers of value to the
decision-maker can be found without requiring expensive and time consuming observations. Many
variables in nature, including the field of business, have numerical observations that tend to cluster
around their mean. In other words, it is more likely that an observation will be close to the mean of the
data collected than far away. When this condition holds, the theoretical normal distribution may
provide a good model of the data collection (Hanke and Reitsch, 1991). In addition, the normal
distribution is the key to understand the most important concepts in statistics.
For example, in evaluating credit application or loans, a loan officer and credit manager who uses
financial ratios as a tool to arrived at their decision on the particular firms health with an assumption of
the financial ratios are normally distributed, will derived a decision that departed from the actual one, if
the ratios non-normally distributed. Also, many random variables have been found to be normally
distributed like weight, height, age, time, snowfall, yields, dimension and other measures of interest to
managers in both the public and private sectors (Lee, 1993).
The objectives of the study are to investigate the distributional properties of the failed and non-
failed Malaysian listed firms and the appropriate remedial procedures to overcome the non-normality
problems.
This paper is organised as follows: Section 2 discuss on the previous study on the normality areas,
the statistical framework of the normality are provided in section 3 and followed by the methodology
in section 4. Finally, the research findings and conclusions are discussed in section 5 and section 6
respectively.

II. Literature Review
Ezzamel et al. (1987) studied the distributional properties of financial ratios of firms in textiles, retail
foods and the metal industry for the period of 1980 to 1981. Two statistical tests for normality were
used: the Kolgomorov Smirnov test and the Shapiro-Wilk test. They found that the results were
consistent with previous research, the raw financial ratios exhibiting positive skewness except for the
leverage ratio for the retail food industry. Outliers were detected in the other two industries. They
decided to continue the analysis without trimming the outliers for the reason that detected outliers
arose by chance in small sample and if they were excluded, insight into their possible influence on the
final conclusions would be lost. Finally, they found that the square root transformation technique
outperformed logarithmic transformation in arriving at an approximation of normality.
So (1987) conducted a study similar to Frecka and Hopwood (1983) which investigates the outlier
and the non-normal distribution. He used eleven financial ratios for ten fiscal years from 1970 to 1979.
He found that the outliers are one of the factors that cause the distribution of cross-sectional financial
ratios to be skewed and non-normally distributed. He stressed that the outliers are not the only source
of non-normality, and after removing the outliers, the distribution of many financial ratios are still not
normal, and are asymmetrically distributed. He concluded that the basic assumptions of ratios named
proportionality violated most of the ratios.

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International Research Journal of Finance and Economics - Issue 2 (2006) 73
Karels and Prakash (1987) conducted a study with the objective of investigating whether or not the
financial ratios used in previous firm failure studies satisfy the normality conditions required by the
multiple discriminant analysis technique. Fifty financial ratios were tested. Only nine of the ratios were
found normal, and six ratios found lognormal. They concluded that no matter how complicated the
procedures used, it does not necessarily provide better results if the ratios used depart from the
normality assumptions.
Zaidi (1997) investigates the distribution of financial ratios of Malaysian listed companies in
manufacturing and financial services industries during 1990 to 1995. He found that all ratios in
manufacturing industry are not normally distributed. However, after removing outliers and being
transformed, the distribution close to normal. Also, some other ratios were still not normally
distributed even though remedial procedures have been carried out. Finally, he suggests the used of
industrial average as a benchmark, and non-parametric test as a tool in financial ratio analysis.
Arif et al. (1998) examines the distributional characteristics of the financial ratios of Malaysian
firms after classifying them into relevant industry groups, and inspecting the degree of informational
redundancy among the ratios in a particular sector. Fifty-seven firms for a period of five years, from
1987 to 1991, were investigated using 13 financial ratios. The Kolgomorov Smirnov test was employed
to investigate the approximation of normality. They found that the distribution of ratios did not
conform to normal distribution. Further, transformation and outlier trimming techniques did not
improve the distributional characteristics of the ratios. They claimed that their results were consistent
with the findings of similar studies in the area. Finally, it was found that an informational redundancy
existed between the ratios, and there were differences in the characteristics of the various industries.

III. Statistical Framework
The shape of normal distribution is bell-shaped curve with the shape of the curve to the left of the
mean a mirror image of the shape of the curve to the right of the mean. The tails of the curve extend to
infinity in both directions and not touch the horizontal axis. The model used to obtained the desired
probabilities is
? ( x ?
2
µ x )
1
f (x )
e
2
2 ? x
=
2?? x

Where,
e is the mathematical constant approximated by 2.71828

? is the mathematical constant approximated by 3.14159

µ is the population mean

? is the population standard deviation


x is the value of the continuous variable, where (-?<x<?)
Since e and ? are mathematical constants, the probabilities of the variable x are dependent upon two
characteristics of the normal distribution named the population mean µ and the population standard
deviation ?.
The normality level of the financial ratios may affected by skewed distribution, where the
distribution was not symmetrical. To measure the skewness level, the following formula was used,
Coefficient of skewness = 3 (mean – median)/ Standard deviation

Another factor that contributes to the non-normality is kurtosis. Kurtosis refers to the peakedness of
the distribution. The coefficient of kurtosis is estimated using the following formula,
n
?(x ? x 4
) / (n ? 1)
i
SCK
i
= =1
s4x

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International Research Journal of Finance and Economics - Issue 2 (2006)

Where,

Xi = Variable in sample

__

X = Sample mean

n = Sample size


S = Sample variance

IV. Methodology
The data used in this study is derived from the balance sheets and income statements of sample
companies obtained from the companies’ annual report that available at the Kuala Lumpur Stock
Exchange library. The financial information were converted into selected financial ratios (refer
appendix A).
Matched samples of failed and non-failed firms from the period of 1980 to 1996 were used in this
study where each failed firm has a non-failed “mate” in the sample. The above cut-off period was
selected due to the financial crisis experienced by Asian countries (including Malaysia) between 1997
and 2000 when stock markets in the region were badly affected. This study only focuses on financial
ratios during the period before the Asian Financial Crisis due to the following reasons. First, the
associations of abnormal returns to ‘unexpected’ information components of accounting data are
sensitive to the business cycle (Lev and Thiagarajan, 1993; Johnson, 1993). Second, risk premiums are
not stationary across business cycles (Gooding and O’Malley, 1977; Wiggens, 1992; and Kruegger and
Johnson, 1990) and subsequently; accounting data has been shown to be associated with variations in
risk premiums (Beaver et al., 1969). Finally, the content of accounting data of failed and non-failed
companies differs in periods of recession and non-recession (Richardson et al., 1998). Therefore, firms
from the crisis period were omitted from the sample.

The definitions of ‘failure’ are:
1.
The firms protected under section 176 of the Companies Act 1965 for the period from 1980 to
1996.
2.
The firms approved to undertake a restructuring scheme to revive their financial conditions by
the KLSE, SC or relevant authorities.
3.
The firms that were put under receivership.

The sample companies used in this study came from 6 different industries: 23 companies from the
industrial sector, 6 companies from the property sector, and 1 company each from the consumer,
finance, hotel and mining sectors. Sixty-five financial ratios as listed in appendix A used in this study
were selected from those used by Beaver (1966), Altman (1968) and Ou and Penmen (1989).

V. Research Findings
The simplest diagnostic test for normality is a visual check of the histogram that compares the
observed data values with a distribution approximating the normal distribution. Although appealing
because its simplicity, this method is problematic for smaller samples. A more reliable approach is the
normal probability plot (called Q-Q Plot), that compares the cumulative distribution of actual data
values with the cumulative distribution of normal distribution. The normal distribution makes a straight
diagonal line, and the plotted data values are compared with the diagonal. The summary of
visualisation of the Q-Q plot and the extract of the Q-Q plot for variable number V64 and V65 are
provided in Appendix A.
Although the Q-Q Plot provides a visual basis for checking normality, we must satisfy ourselves to
the degree of departure from normality through statistical tests before the null hypotheses can be
rejected. Two commonly used tests are the Shapiro-Wilks’ test and Lillifors test. The Lillifors test

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International Research Journal of Finance and Economics - Issue 2 (2006) 75
based on modification of the Kolgomorov-Smirnov test is used when means and variances are not
known but must be estimated from the data (Norusis, 1993). Shapiro-Wilks test shows good power in
many statistics situation compared to other tests of normality (Iman and Conover, 1989). However,
Shapiro-Wilks’ test is well suited to small sample size (Afifi and Clark, 1990). In this study, we used
the Kolgomorov Smirnov tests adjusted to Lillifors tests (D Statistics).
The samples were divided into three sectors named mixed industry, combination of industrial and
property, and industrial sector. The null hypothesis will be rejected for large values of D statistic. Also,
we have to look on the shape of the distribution shown by the skewness and kurtosis statistics, which
provided together with D statistics. If the data are normally or symmetrically distributed, then the
computed skewness will be close to zero. Further, from the small-observed significance levels, the
hypothesis of normality can be rejected. According to Norusis (1993), “it is almost impossible to find
data that are exactly normally distributed”. He suggested that for most statistical tests, it is sufficient
that the data are approximately normal distributed.
The D statistics, kurtosis, skewness and the significance level of the raw data for all sectors are
appended in appendix B. In all sectors, only one out of sixty five variables found normal named V15,
and this results proved that the visual checking on normality is not accurate method to asses the
normality as in Appendix A. The minimum accepted significance level was defined at 1% (0.005 at
two tails). In mixed industry sector, D statistics for V15 is 0.046 (near to zero) and the significance
level equal to 0.08. The other variables are significantly departed from normality assumptions with
high skewness statistics and peaked distribution. Therefore, we reject the hypothesis null that all of the
financial ratios tested are normally distributed.

A number of reasons for non-normality situations provided by literature such as:
1. Outliers
2. Flat distribution
3. Skewed distribution
Also, there is an argument that the non-normal arises due to the basic assumption of the ratio named
proportionality (So(1987), Ezammel et al. (1987) and Whittington (1980)).

VI. Test of Outliers and Data Trimming
The first remedy for the non-normality problem is through deletion of outliers. Outlier is defined as the
observations with a unique combination of characteristics identifiable as distinctly different from the
other observations. Cochran (1963) recommended that the removal of outliers from the main body of
population reduces the skewness and improves normal approximation. The criterion to identify the
outliers was set at 95% confidence level (2 standard deviation). Any observation that falls outside this
ellipse is considered as an outlier.
Using computer, outliers were identified from the main body of the data. Further, a frequency
analysis was done to the results to get the percentage of occurrence for each outlier’s cases. Finally, we
decide to eliminate the outliers from the main body of the data for outliers that occur more than 10
times. After trimming outliers, it was found that the skewness of the distribution improved moderately
where some variables improve and the others reduced. A similar situation was observed for the
peakness of the distribution. No new variables were found normally distributed after deletion of
outliers. The results were consistent in the combination of industrial and property, and industrial
sectors. This early finding suggests that outlier trimming does not improve normality when the
procedure was done on the raw data. In order to improve the normality, data transformation procedures
were suggested.

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International Research Journal of Finance and Economics - Issue 2 (2006)
VII. Data Transformation
Data transformation provides a mean to correct violations of normality. There are number of data
transformations techniques adopted in the literature, namely:
1. Natural Log
2. Square Root
3. Square

Both natural logs and square roots suffer from the defect that they cannot be applied if the ratios are
negative (Ezammel et al., 1987). Other alternative that can be used to avoid this difficulty such as
adding or subtracting a constant or taking squares of the ratio or inverse the ratio. However, Ezammel
et al. stressed that such methods tend to accentuate the distortion cause by outliers giving relatively
more weight to large observations. In this study, three most widely accepted transformation methods
named natural log, square root and square transformation were used.
Often, it was not possible to undertake the transformation because a number of observations had
negative value. In this situation, we transform the ratio using its absolute value. The summaries of
normal variables after the three transformation techniques under different industry sector are shown in
tables 1, 2 and 3.

Table 1: Normal Variable Under Normality Tests (Sector: Mixed Industry)
Rdut RDt Logut Logt
Sqrtut
Sqrtt
Sqrut Sqrt
V15 V15 V04 V04
V14
V14
Nil
Nil

V11
V11
V24
V24


V13
V13
V25


V17
V17


V22
V22


V35
V35


V41
V41


V55
V55


V65
V65


Table 2: Normal Variable under Normality Tests (Industrial and Property)
Rdut RDt Logut Logt Sqrtut Sqrtt Sqrut Sqrt
V15 V15 V04 V04
V14
V14
Nil
Nil

V11
V11
V24
V20


V13
V13
V25
V24


V17
V17
V32
V25


V22
V22
V32


V35
V27
V56


V41
V35


V45
V41


V55
V45


V65
V48




V50




V55




V65

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International Research Journal of Finance and Economics - Issue 2 (2006) 77
Table 3: Normal Variable Under Normality Tests (Sector: Industrial)
Rdut RDt Logut Logt Sqrtut
Sqrtt Sqrut Sqrt
V15 V15 V04 V04
V14
V02
Nil
Nil
V09
V09
V24
V14

V11
V11
V29
V24

V13
V13
V32
V29

V17
V17
V52
V32

V22
V22
V52

V27
V27
V56

V35
V30

V41
V34

V45
V38

V48
V41

V50
V45

V52
V48

V55
V50

V65
V52




V55




V57




V65


Annotations:


Rdut
: Raw Data Untrimmed
Sqrtut
: Square Root Untrimmed
RDt
: Raw Data Trimmed
Sqrtt
: Square Root Trimmed
Logut :
Log Untrimmed
Sqrut
: Square Untrimmed
Logt :
Log Trimmed
Sqrut
: Square Trimmed

VIII. Discussion on Normality Tests
Under all sectors (mixed industry, industrial and property, and industrial sector), before data
transformations were done, variable number V15 was consistently normal before and after deletion of
outliers. In all instances, the Kolgomorov-Smirnov statistic (KS) and the significance level improved
after deletion of outliers.

IX. Natural Log Transformation
In mixed industry sector, it is found that nine variables were normal before and after deletion of
outliers (refer table 1). Statistically, the KS statistics do not improve and small reduction in the
significance level recorded in some of the variables after deletion of outliers and transformed into
natural log (table 4). This suggests that deletion of outlier doesn’t improve the normality under natural
log transformation in mixed industry sector.
However, in industrial and property sector, ten variables were found normal before deletion of
outliers and the number increased to 13 when the outliers deleted. The new variables are V27, V48 and
V50 (see table 2). Table 5 shows the statistics of the variables where certain variables record some
improvement and the others reduced. However, all new variables that is normal after deletion of
outliers shows an improvement in KS statistics and significance level.
In industrial sector, the normal variables increased compared to the other sectors. A total of 15
variables found normal before deletion of outliers, and the number increased to 18 after deletion of
outliers, where 4 new variables such as V30, V34, V38 and V57 are added to the lists. However, one
variable (V35) being excluded due to the significance level reduced below minimum accepted level.
Same as the other sectors, under natural log transformation, mixed evidence recorded where some of
the variable statistically improved and the others reduced. All new variables shows an improvement of
KS statistics and significance level (refer table 6).

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International Research Journal of Finance and Economics - Issue 2 (2006)
Square Root Transformation
In mixed industry sector, two variables found normal before deletion of outliers and one new variable
named V25 found normal after deletion of outliers and transformed into square root. Statistically, KS
statistics and the significance level improved after implementation of the procedure. Trimming outliers
give a considerable impact on normality under the square root transformation.
Four variables are found normal before deletion of outliers in industrial and property sector, and the
number increased to 6 when the outliers deleted. Variables number V20 and V56 are the new variables
when data trimming was done. After deletion of outliers, KS statistics and significance level for all
variables improved as shown in table 5.
Finally, in industrial sector, five variables were found normal before deletion outliers and the
number increased to seven after outliers deleted. All variables show some improvement in significance
level.


Square Transformation
There is no variable found normally distributed under this transformation technique in all sectors.

Table 4: Statistics of Normal Variable under Normality Tests (Untrimmed Vs Trimmed Outliers)
Sector: Mixed Industry

Sector:
Rdut RDt
Logut Logt Sqrtut Sqrtt
Mixed
Industry

Stat. Sig. Stat. Sig. Stat. Sig. Stat. Sig. Stat. Sig. Stat. Sig.
V15 0.0461
0.0876
0.0374
0.2000


V04
0.0499 0.0463
0.0561
0.0177

V11
0.0594 0.0217
0.0615
0.0164

V13
0.0347 0.2000
0.0386
0.2000

V17
0.0532 0.0269
0.0457
0.2000

V22
0.0543 0.0243
0.0554
0.0237

V35
0.0559 0.0220
0.0577
0.0181

V41
0.0514 0.0798
0.0499
0.2000

V55
0.0402 0.2000
0.0418
0.2000

V65
0.0552 0.0177
0.0492
0.0633

V14

0.0453
0.0999
0.0343
0.2000
V24

0.0577
0.0101
0.0503
0.0513
V25

0.0678
0.0009
0.0619
0.0052

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International Research Journal of Finance and Economics - Issue 2 (2006) 79
Table 5: Statistics of Normal Variable under Normality Tests (Untrimmed Vs Trimmed Outliers)
Sector: Industrial & Property

Rdut RDt
Logut Logt Sqrtut Sqrtt
Stat. Sig. Stat. Sig. Stat. Sig. Stat. Sig. Stat. Sig. Stat. Sig.
V15 0.056
0.02593
0.043
0.20000








V04




0.048 0.09020
0.056 0.03348




V11




0.054 0.07869
0.057 0.05496




V13




0.034 0.20000
0.039 0.20000




V17




0.061 0.00914
0.054 0.04248




V22




0.059 0.01780
0.062 0.01324




V27




0.068 0.00284
0.065 0.00676




V35




0.058 0.02706
0.062 0.01394




V41




0.043 0.20000
0.044 0.20000




V45




0.057 0.02934
0.060 0.02246




V48




0.072 0.00091
0.061 0.01339




V50




0.075 0.00048
0.062 0.01157




V55




0.032 0.20000
0.030 0.20000




V65




0.062 0.00817
0.057 0.02651




V14

0.038
0.20000
0.029
0.20000
V20

0.076
0.00029
0.064
0.00743
V24

0.056
0.02332
0.047
0.20000
V25

0.061
0.00834
0.058
0.02415
V32

0.055
0.02976
0.046
0.20000
V56

0.185
0.00000
0.065
0.00567

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International Research Journal of Finance and Economics - Issue 2 (2006)
Table 6: Statistics of Normal Variable under Normality Tests (Untrimmed Vs Trimmed Outliers)
Sector: Industrial

Rdut
RDt
Logut
Logt
Sqrtut
Sqrtt

Stat. Sig. Stat. Sig. Stat. Sig. Stat. Sig. Stat. Sig. Stat. Sig.
V15 0.071 0.00515
0.038 0.20000








V04
0.038
0.20000
0.051
0.20000

V09
0.052
0.20000
0.058
0.06516

V11
0.046
0.20000
0.051
0.20000

V13
0.043
0.20000
0.053
0.20000

V17
0.059
0.04281
0.052
0.20000

V22
0.058
0.05633
0.064
0.03208

V27
0.071
0.00741
0.072
0.00923

V30
0.075
0.00314
0.069
0.01549

V34
0.077
0.00204
0.067
0.01809

V38
0.075
0.00224
0.072
0.00695

V41
0.044
0.20000
0.046
0.20000

V45
0.047
0.20000
0.049
0.20000

V48
0.069
0.00896
0.059
0.06328

V50
0.071
0.00633
0.058
0.07943

V52
0.071
0.00968
0.072
0.01130

V55
0.033
0.20000
0.033
0.20000

V57
0.080
0.00075
0.068
0.01304

V65
0.071
0.00534
0.060
0.05081

V02
0.222
0.00000
0.068
0.01358
V14
0.049
0.20000
0.050
0.20000
V24
0.049
0.20000
0.053
0.20000
V29
0.060
0.03470
0.064
0.02599
V32
0.053
0.20000
0.054
0.20000
V52
0.070
0.00607
0.065
0.02405
V56
0.205
0.00000
0.071
0.00838

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