Description
Financial parameters of banks and industries have been used in forecasting failure and bankruptcy over the past four decades. Beaver's study changed the way such analyses are conducted in the field of evaluating and forecasting potential company failures and bankruptcies (Beaver, 1966).
International Journal of Scientific & Engineering Research Volume 4, Issue 2, February-2013 1
ISSN 2229-5518
IJ SER ©2013http://www.ijser.org
Financial Ratios Performance of Major Indian
Industries to Evaluate their Performances using
Multivariate Analyses and Perceptual Mapping
R. Chandrasekaran
1
, G. Manimannan
2
and R. Lakshmi Priya
3
1
Head of the Department (Retd.)
2
Assistant Professor
Department of Statistics, Madras Christina College, Tambaram, Chennai
3
Assistant Professor
Department of Statistics, Dr. Ambedkar Govt. Arts College, Vysarpadi, Chennai.
The present research is aimed at analyzing financial performances of companies to assess their financial strengths and enable the decision
makers to understand the financial scenario of their firms. The dataset relates to 247 companies from five major industries in the Indian
corporate database. The time frame of the data pertaining to the present study is 2001-2010. The salient feature of this study is the
application of Factor, K-means clustering, Discriminant Analyses and Perceptual Mapping as data mining tools to explore the hidden
structures present in the dataset for each of the study periods (Anderson, 1984). Factor analysis is applied first and the factor scores of
extracted factors are used to find initial groups by K-means clustering algorithm. A few outlier industries, which could not be classified to any of
the groups, are discarded as some of the ratios possessed unusual values. Finally, attribute based perceptual mapping is applied and the
groups are identified as companies belonging to H-Class (High performance), M-Class (Moderate performance) and L-Class (Low
performance). The results of the present study indicate that Perceptual maps can be used as a feasible tool for the analysis of large set of
financial data.
Keywords: Financial Ratios, Data mining, Factor Analysis, K-means Clustering, Discriminant Analysis, Perceptual Map (PM)
1.0 INTRODUCTION
Financial parameters of banks and industries have been
used in forecasting failure and bankruptcy over the past
four decades. Beaver’s study changed the way such
analyses are conducted in the field of evaluating and
forecasting potential company failures and bankruptcies
(Beaver, 1966). One approach is to explore for the best
predictors that lead to minimum misclassification errors
while the other is to select the statistical method that
would lead to improved correct classification with
greater accuracy. The company failure does have
unpleasant consequences for its shareholders as well as
its employees. Hence there seem to be continued
interests in bankruptcy and failure models. It is generally
recognized that company financial statements provide
information on a company’s performance, stability and
indication of future commercial and financial prospectus.
Analysis and interpretation of financial statements using
various financial ratios may provide a shareholder,
creditor or banker, useful information about the
company’s financial status, position, and also borrowing
power.
2.0 BRIEF REVIEW OF LITERATURE
Financial ratio analysis involves comparing the
relationship between figures in the financial statements in
relative terms. Financial ratios appear frequently in
company annual reports, auditors’ reports and internal
management reports. Green (1978) stated that financial
ratios have long been regarded as barometers of
corporate health, being used for reporting liquidity,
leverage, productivity and profitability, and that an
investor may use financial ratios to appraise a company’s
performance and its future prospect of success. Chen
and Shimerda (1981) have shown that financial ratios
played an important role in evaluating the financial
conditions of an entity. Further, based on their analytical
studies over the years, they have demonstrated the
usefulness of financial ratios. Chandrasekaran and
Manimannan, et al. (2011) have graded companies that
reflected the performance of companies based on certain
financial ratios.
The earliest study using multivariate data analysis on
failure prediction was conducted by Altman (1968) using
a set of financial and economic ratios as possible
determinants of corporate failures. The study used sixty
six companies from manufacturing industries comprising
of bankrupt and non-bankrupt firms and twenty two
ratios from five categories, namely, liquidity,
profitability, leverage, solvency and activity. Five ratios
were finally selected for their performance in the
prediction of corporate bankruptcy and the derived
International Journal of Scientific & Engineering Research Volume 4, Issue 2, February-2013 2
ISSN 2229-5518
IJ SER ©2013http://www.ijser.org
model correctly classified 95 percent of the total sample
one year prior to bankruptcy. The percentage of accuracy
declined with increasing number of years before
bankruptcy. Altman (1994) reported the use of neural
network in identification of distressed business by the
Italian central bank. Using 1000 sampled firms with ten
financial ratios as independent variables, the found that
the neural network is not a clearly dominant
mathematical model technique compared to traditional
statistical techniques. Other studies relating to company
failure and bankruptcy using financial parameters are
reported in Beaver (1966), Chen and Shimerda (1981), Gepp and
Kumar (2008), Green (1978) and Li and Sun (2010).
The objective of the present study is to uncover the
intrinsic groups or classes and identify the most
influencing ratios that would reflect the performance of
top ranking companies in India, using the concepts of
data mining, factor analysis, multivariate discriminant
analysis and perceptual map.
3.0 METHODOLOGY
This section brings out the discussion of the database, the
ratios selected and the Data Mining Techniques.
3.1. DATABASE AND SELECTION OF VARIABLES
The financial data published by Capital Market (Indian
Corporate Database) was considered as the database.
The data mainly consists of five major types of industries
in India and under each type of industry, there are
several companies. The data consists of financial ratios of
each company for the time period of ten years (from 2001
to 2010), around 120 copanies. Among the listed
companies, number of companies varied over the study
period owing to removal of those companies for which
the required data are not available. In this study, 14
ratios are carefully chosen among the many that had been
used in previous studies (Table 1). These 14 ratios are
chosen to assess profitability, solvency, liquidity, and
cash-equity ratio. The choice of ratios used is based on
two main criteria, namely their popularity as evidenced
by their frequent usage in the finance and accounting
literature and that the ratios have been shown to perform
well in previous studies.
3.2 DATA MINING TECHNIQUES
Although data mining is relatively a new term, the technology is
not. Data Mining or Knowledge Discovery in Databases
(KDD) is the process of discovering previously hitherto
unknown and potentially useful information from the
data in databases. In the present context, data mining
exhibits the patterns by applying few techniques namely,
factor analysis, k-means clustering and discriminant rule.
As such KDD is an iterative process, which mainly
consists of the following steps:
Step 1: Data cleaning; Step 2: Data Integration; Step 3:
Data selection and transformation;
Step 4: Data Mining and Step 5: Knowledge
representation.
Of the above iterative process, Steps 4 and 5 are very
important. If appropriate techniques are applied in Step
5, it provides potentially useful information that explains
the hidden structure. This structure discovers knowledge
that is represented visually to the user, which is the final
phase of data mining.
3.2.1 FACTOR ANALYSIS
Factor analysis provides the tools for analyzing the
structure of the interrelationships (correlations) among
the large number of variables by defining sets of
variables, mostly labeled, that are highly interrelated,
known as factors (Anderson, 1984). In the present study,
factor analysis is initiated to uncover the patterns
underlying financial ratio variables (Table 1). In factor
extraction method the number of factors is decided based
on the proportion of sample variance explained.
Orthogonal rotations such as Varimax and Quartimax
rotations are used to measure the similarity of a variable
with a factor by its factor loading (Everitt and Dunn,
2001; Hair, Black, Babin and Anderson, 2010).
TABLE 1. LIST OF FINANCIAL PARAMETERS USED
IN THE PRESENT STUDY
Ratios Description Ratios Description
DEB_EQU
Debt -
Equity Ratio
PBDITM
Profit Before
Depreciation
Interest Tax
Margin
LONG_TE
Long Term
Debt-Equity
Ratio
PBITM
Profit Before
Interest Tax
Margin
CURREN
Current
Ratio
PBDTM
Profit Before
Depreciation Tax
Margin
FIX_ASS Fixed Assts CPM
Current Profit
Margin
INVENTO Inventory APATM
Adjusted Profit
After Tax Margin
DEBTORS Debtors ROCE
Return on Capital
Employed
INTERES Interest RONW
Return on Net
Worth
International Journal of Scientific & Engineering Research Volume 4, Issue 2, February-2013 3
ISSN 2229-5518
IJ SER ©2013http://www.ijser.org
3.2.2. K-MEANS CLUSTERING METHODS
Nonhierarchical clustering techniques are designed to
group items, rather than variables, into a collection of K
clusters (Everitt and Dunn, 2001; Hair, Black, Babin and
Anderson, 2010). The number of clusters, K, may either
be specified in advance or determined as part of the
clustering procedure. The term K-means method is
coined for describing an algorithm that assigns items to
the k-clusters having the nearest centroid (mean).
Generally this technique uses Euclidean distances
measures computed by variables. Since the group labels
are unknown for the data set, k-means clustering is one
such technique in applied statistics that discovers
acceptable classes, in the present study, groups of
companies.
3.3.3 DISCRIMINANT ANALYSIS
Multivariate Discriminant Analysis is a multivariate
technique using several variables simultaneously to
classify an observation vector into one of several a priori
groups of companies as obtained by the K-means
method. In the present study, discriminant analysis is
used to exhibit groups graphically and judge the nature
of overall performance of the companies (Everitt and
Dunn, 2001; Hair, Black, Babin and Anderson, 2010).
3.3.4 PERCEPTUAL MAP
Perceptual mapping has been used as a strategic
management tool for about thirty years. It offers a
unique ability to communicate the complex relationships
between marketplace competitors and the criteria used
by buyers in making purchase decisions and
recommendations. Its powerful graphic simplicity
appeals to senior management and can stimulate
discussion and strategic thinking at all levels of all
several types of organizations. Perceptual mapping can
be used to plot the interrelationships of consumer
products, industrial goods, institutions, as well as
populations.
Virtually any subjects that can be rated on a range of
attributes can be mapped to show their relative positions
in relation both to other subjects as well as to the
evaluative attributes. Perceptual maps may be used for
company performance, concept development and
evaluation, and tracking changes in companies
perceptions among other uses. In this paper, perceptual
map is used to identify contribution of financial ratios to
different groups of companies.
4.0 ALGORITHMS
A brief step-by-step algorithm to grade the companies
during each of the study period based on their overall
performances is described below:
Step 1: Factor analysis is initiated to find the
structural pattern underlying the data set.
Step 2: K –means analysis is used to partition the
data set into k-clusters using the factor
scores obtained in Step 1 as input.
Step 3: Discriminant analysis is then performed with
the original ratios by considering the
groups formed by the k-means algorithm.
Step 4: Perceptual map is drawn with the
standardized canonical discriminant
function and centroid values of financial
parameters of groups of companies.
5.0 RESULTS AND DISCUSSION
As mentioned in Section 3.2.1, Varimax and Quartimax
criterion for orthogonal rotation have been used for the
pruned data. Even though the results obtained by both
the criterions were very similar, the varimax rotation
provided relatively better clustering of financial ratios.
Consequently, only the results of varimax rotation are
reported here. We have decided to retain 75 percent of
total variation in the data, and thus accounted
consistently four factors for each year with eigen values
little less than or equal to unity. Table 2 shows variance
accounted for each factors.
TABLE 2. PERCENTAGE OF VARIANCE
EXPLAINED BY FACTORS
Factors
Variance explained
2001 2002 2003 2004 2005
1
2
3
4
37.06
17.00
14.39
8.43
37.85
15.33
14.63
8.50
35.58
18.78
13.53
8.30
35.85
16.84
14.07
8.28
40.22
19.21
11.30
7.88
Total 76.88 76.31 76.19 75.04 78.61
2006 2007 2008 2009 2010
1
2
3
4
33.24
16.63
14.47
13.30
38.42
13.82
12.49
11.17
39.06
15.59
11.29
9.68
38.14
18.26
10.17
9.21
37.43
16.88
11.61
9.46
Total 77.64 75.90 75.62 75.78 75.38
International Journal of Scientific & Engineering Research Volume 4, Issue 2, February-2013 4
ISSN 2229-5518
IJ SER ©2013http://www.ijser.org
From the above table we observe that the total variances
explained by the extracted factors are over 75 percent,
which are relatively high. Also, for each factors the
variability is more or less the same for the study period,
though the number of companies in each year, after data
cleaning and selection, kept varying owing to various
reasons.
The financial ratios loaded in the factors are presented in
Table 3. Only those ratios with higher loadings are
indicated by (*) symbol. From the Table 3 it is clear that
the clustering of financial ratios is stable during the study
period. We observe slight changes in factor loadings
during the periods considered. The differences in factor
loadings may be due to statistical variations in the
original data.
TABLE 3. FINANCIAL RATIOS IN ROTATED
FACTORS (YEAR -WISE)
* I ndicates financial ratios highly loaded in respective
factors
After performing factor analysis, the next step is to assign
initial group labels to each company. Step 2 of the
algorithm is applied with factor scores extracted by Step
1, by conventional k-means clustering analysis.
Formations of clusters are explored by considering 2-
clusters, 3-clusters, 4-cluster and so on. Out of all the
possible trials, 3-cluster exhibited meaningful
interpretation than two, four and higher clusters. Having
decided to consider only 3 clusters, it is possible to rate a
company as Grade H, Grade M or Grade L depending on
whether the company belonged to Cluster 1, Cluster 2 or
Cluster 3 respectively.
Cluster 1 (Grade H) is a group of companies that have
high values for the financial ratios, indicating that these
companies are performing well. The companies with
lower values for the financial ratios are grouped into
Cluster 3 (Grade L). This suggested that Cluster 3 is a
group of companies with low-profile. Cluster 2 (Grade
M) are those companies which perform moderately well
as compared to the Cluster 1 and Cluster 3. In spite of
incorporating the results for each year, only the summary
statistics are reported in Table4.
TABLE 4. NUMBER OF COMPANIES IN THE
CLUSTERS
Years
Initial
Cluster
Discriminant
Classification
1 2 3 1 2 3
2001
2002
2003
2004
2005
17
32
30
06
55
55
52
86
32
63
47
35
03
81
01
47
52
04
81
01
55
35
86
06
55
17
32
29
32
63
2006
2007
2008
2009
2010
10
17
23
27
44
44
41
58
57
74
65
61
38
35
01
10
17
58
35
74
65
61
23
57
44
44
41
38
27
01
1 – Grade H 2 – Grade M 3 – Grade L
Table 4 indicates that majority of companies are in the
moderate performance category except for the year 2004
and 2006. The possible reasons that kept most of the
companies in lower profile in the year 2004 and 2006 may
be due to the then government policies. And also MNC’s
have found their way to open business in India, pushing
Indian companies back. Figures 1 through 10 shows the
groupings of companies into 3 clusters for each year of
the study period. It is interesting to note that the mean
vectors of these clusters can be arranged in the increasing
order of magnitude as show in Table 4.
International Journal of Scientific & Engineering Research Volume 4, Issue 2, February-2013 5
ISSN 2229-5518
IJ SER ©2013http://www.ijser.org
FIGURES 1 – 10. CLUSTERED GROUPS
In order to identify the factors that are mainly responsible
for the formation of the groups, perceptual mapping is
drawn using the standardized discriminant coefficients
and the unstandardised discriminant functions evaluated
at the group centroids. From the perceptual maps in
Figure 11, it is evident that the three groups of rated
companies are very well separated and represented in the
perceptual maps for all the ten year periods.
The two-dimensional graph clearly indicates that, in the
year 2001, dimension 1 comprises Liquidity and Equity
ratios factor, the dimension 2, Profitability and Leverage
ratios factor. In the year 2002, dimension 1 seems to
comprise Equity and Profitability ratios factor and
dimension 2, Liquidity, Leverage ratios factor. In the
year 2003, in dimension 1, Liquidity ratio factor and
dimension 1 accommodates only Equity, Leverage and
Profitability ratio factor. In the year 2004, in dimension
1 seems to comprise Profitability ratio factor, and in
dimension 2, Leverage, Equity and Liquidity ratios
factor. In the year 2005, in dimension 2, Equity, and
Profitability ratios factor, in dimension 1 comprises of
Leverage and Liquidity ratios factor.
In the year 2006, dimension 1 consists of Profitability
and Liquidity ratios factor, and the dimension 2, Equity
and Leverage ratios factor. In the year 2007,
Profitability and Liquidity ratios in dimension 1, and
Equity and Leverage ratios factor in dimension 2. In the
year 2008, dimension 1 consists of Liquidity, equity and
Leverage ratios factor, and in dimension 2 Profitability
ratio factor. In the year 2009, dimension 2 consists of
Profitability, Liquidity and leverage ratios factor, and
dimension 1 comprises Equity ratio. In the year 2010,
Liquidity, Leverage ratios in dimension 2 and Equity
ratio factor in dimension 1. It is interesting to note that
in all the ten years, all financial ratios contribute the
company position to some extent.
Figure 11. Perceptual Maps for the years
2001 – 2010.
6.0 CONCLUSION
The purpose of this paper is to identify the meaningful
groups of companies that are rated as best with respect to
their performance in terms of financial ratios using data
mining and perceptual map techniques. An attempt is
made to analysis the financial data relating to major
industries of public and private sector companies over a
period of ten years from 2001 to 2010. The present
analysis has shown that only 3 groups could be
meaningfully formed for each year. This indicates that
only 3 types of companies existed over a period of ten
years. Further, the companies find themselves classified
into High (Grade H), Medium (Grade M) and Low (Grade
L) categories depending on the financial ratios. Financial
Analyst can make use of these techniques of rating, and
the companies can project the performance on the basis of
financial ratios that has been considered in this study.
Perceptual maps may be used for financial ratios
performance and evaluation, and tracking changes in
companies perceptions, among other uses. A
generalization of the results is under investigation to
obtain a set of 3 groups of companies for any given year.
7.0 REFERENCES
[1] Anderson T. W. (1984). An Introduction to Multivariate
Statistical Analyis, 2/e, John Wiley and Sons, Inc., New
York.
[2] Altman, E. I. (1968). Financial ratios, Discriminant analysis and
the prediction of corporate bankruptcy, Journal of Finance,
23(4), pp. 589-609.
[3] Altman, E. I. (1994). An international survey of business failure
classification models, N.Y. University Salomon
Center, Volume 6, Number 2, 1997, p. 23.
[4] Beaver, W. H. (1966). Financial ratios as predictors of failure,
Journal of Accounting Research, Vol 4. pp. 71-111.
[5] Chandrasekaran R, Manimannan G and Lakshmi Priya (2011).
Assessing Indian industries on the basis of financial
International Journal of Scientific & Engineering Research Volume 4, Issue 2, February-2013 6
ISSN 2229-5518
IJ SER ©2013http://www.ijser.org
ratios using certain data mining tools, Paper presented at
the International Conference on Statistics and Information
Analytics (ICSIA 2012), August 23-25 2012, Department of
Statistics, Loyola College, Chennai.
[6] Chen, K. H. and Shimerda T. A. (1981). An empirical analysis of
useful financial ratios, Financial Management, Spring, pp.
51-60.
[7] Everitt, B. and Dunn, G. (2001). Applied Multivariate Data
Analysis, 2
nd
Ed., Hodder Arnold, New York.
[8] Gepp, A. and Kumar, K. (2008). The role of survival analysis in
financial distress predictions, International Research
Journal of Finance and Economics, Issue 16, pp13-34.
[9] Green, D. (1978). To predict failure, Management Accounting, July
pp.39-45.
[10] Hair, J. F., Black, W. C., Babin, B. J., and Anderson, R. E. (2010).
Multivariate Data Analysis, 7th ed.,Prentice Hall, New
York.
[11] Li, H. and Sun, J. (2010). Business failure prediction using
hybrid case-based reasoning HCBR, Computers &
Operations Research January 2010. pp. 137-151.
doc_701400438.pdf
Financial parameters of banks and industries have been used in forecasting failure and bankruptcy over the past four decades. Beaver's study changed the way such analyses are conducted in the field of evaluating and forecasting potential company failures and bankruptcies (Beaver, 1966).
International Journal of Scientific & Engineering Research Volume 4, Issue 2, February-2013 1
ISSN 2229-5518
IJ SER ©2013http://www.ijser.org
Financial Ratios Performance of Major Indian
Industries to Evaluate their Performances using
Multivariate Analyses and Perceptual Mapping
R. Chandrasekaran
1
, G. Manimannan
2
and R. Lakshmi Priya
3
1
Head of the Department (Retd.)
2
Assistant Professor
Department of Statistics, Madras Christina College, Tambaram, Chennai
3
Assistant Professor
Department of Statistics, Dr. Ambedkar Govt. Arts College, Vysarpadi, Chennai.
The present research is aimed at analyzing financial performances of companies to assess their financial strengths and enable the decision
makers to understand the financial scenario of their firms. The dataset relates to 247 companies from five major industries in the Indian
corporate database. The time frame of the data pertaining to the present study is 2001-2010. The salient feature of this study is the
application of Factor, K-means clustering, Discriminant Analyses and Perceptual Mapping as data mining tools to explore the hidden
structures present in the dataset for each of the study periods (Anderson, 1984). Factor analysis is applied first and the factor scores of
extracted factors are used to find initial groups by K-means clustering algorithm. A few outlier industries, which could not be classified to any of
the groups, are discarded as some of the ratios possessed unusual values. Finally, attribute based perceptual mapping is applied and the
groups are identified as companies belonging to H-Class (High performance), M-Class (Moderate performance) and L-Class (Low
performance). The results of the present study indicate that Perceptual maps can be used as a feasible tool for the analysis of large set of
financial data.
Keywords: Financial Ratios, Data mining, Factor Analysis, K-means Clustering, Discriminant Analysis, Perceptual Map (PM)
1.0 INTRODUCTION
Financial parameters of banks and industries have been
used in forecasting failure and bankruptcy over the past
four decades. Beaver’s study changed the way such
analyses are conducted in the field of evaluating and
forecasting potential company failures and bankruptcies
(Beaver, 1966). One approach is to explore for the best
predictors that lead to minimum misclassification errors
while the other is to select the statistical method that
would lead to improved correct classification with
greater accuracy. The company failure does have
unpleasant consequences for its shareholders as well as
its employees. Hence there seem to be continued
interests in bankruptcy and failure models. It is generally
recognized that company financial statements provide
information on a company’s performance, stability and
indication of future commercial and financial prospectus.
Analysis and interpretation of financial statements using
various financial ratios may provide a shareholder,
creditor or banker, useful information about the
company’s financial status, position, and also borrowing
power.
2.0 BRIEF REVIEW OF LITERATURE
Financial ratio analysis involves comparing the
relationship between figures in the financial statements in
relative terms. Financial ratios appear frequently in
company annual reports, auditors’ reports and internal
management reports. Green (1978) stated that financial
ratios have long been regarded as barometers of
corporate health, being used for reporting liquidity,
leverage, productivity and profitability, and that an
investor may use financial ratios to appraise a company’s
performance and its future prospect of success. Chen
and Shimerda (1981) have shown that financial ratios
played an important role in evaluating the financial
conditions of an entity. Further, based on their analytical
studies over the years, they have demonstrated the
usefulness of financial ratios. Chandrasekaran and
Manimannan, et al. (2011) have graded companies that
reflected the performance of companies based on certain
financial ratios.
The earliest study using multivariate data analysis on
failure prediction was conducted by Altman (1968) using
a set of financial and economic ratios as possible
determinants of corporate failures. The study used sixty
six companies from manufacturing industries comprising
of bankrupt and non-bankrupt firms and twenty two
ratios from five categories, namely, liquidity,
profitability, leverage, solvency and activity. Five ratios
were finally selected for their performance in the
prediction of corporate bankruptcy and the derived
International Journal of Scientific & Engineering Research Volume 4, Issue 2, February-2013 2
ISSN 2229-5518
IJ SER ©2013http://www.ijser.org
model correctly classified 95 percent of the total sample
one year prior to bankruptcy. The percentage of accuracy
declined with increasing number of years before
bankruptcy. Altman (1994) reported the use of neural
network in identification of distressed business by the
Italian central bank. Using 1000 sampled firms with ten
financial ratios as independent variables, the found that
the neural network is not a clearly dominant
mathematical model technique compared to traditional
statistical techniques. Other studies relating to company
failure and bankruptcy using financial parameters are
reported in Beaver (1966), Chen and Shimerda (1981), Gepp and
Kumar (2008), Green (1978) and Li and Sun (2010).
The objective of the present study is to uncover the
intrinsic groups or classes and identify the most
influencing ratios that would reflect the performance of
top ranking companies in India, using the concepts of
data mining, factor analysis, multivariate discriminant
analysis and perceptual map.
3.0 METHODOLOGY
This section brings out the discussion of the database, the
ratios selected and the Data Mining Techniques.
3.1. DATABASE AND SELECTION OF VARIABLES
The financial data published by Capital Market (Indian
Corporate Database) was considered as the database.
The data mainly consists of five major types of industries
in India and under each type of industry, there are
several companies. The data consists of financial ratios of
each company for the time period of ten years (from 2001
to 2010), around 120 copanies. Among the listed
companies, number of companies varied over the study
period owing to removal of those companies for which
the required data are not available. In this study, 14
ratios are carefully chosen among the many that had been
used in previous studies (Table 1). These 14 ratios are
chosen to assess profitability, solvency, liquidity, and
cash-equity ratio. The choice of ratios used is based on
two main criteria, namely their popularity as evidenced
by their frequent usage in the finance and accounting
literature and that the ratios have been shown to perform
well in previous studies.
3.2 DATA MINING TECHNIQUES
Although data mining is relatively a new term, the technology is
not. Data Mining or Knowledge Discovery in Databases
(KDD) is the process of discovering previously hitherto
unknown and potentially useful information from the
data in databases. In the present context, data mining
exhibits the patterns by applying few techniques namely,
factor analysis, k-means clustering and discriminant rule.
As such KDD is an iterative process, which mainly
consists of the following steps:
Step 1: Data cleaning; Step 2: Data Integration; Step 3:
Data selection and transformation;
Step 4: Data Mining and Step 5: Knowledge
representation.
Of the above iterative process, Steps 4 and 5 are very
important. If appropriate techniques are applied in Step
5, it provides potentially useful information that explains
the hidden structure. This structure discovers knowledge
that is represented visually to the user, which is the final
phase of data mining.
3.2.1 FACTOR ANALYSIS
Factor analysis provides the tools for analyzing the
structure of the interrelationships (correlations) among
the large number of variables by defining sets of
variables, mostly labeled, that are highly interrelated,
known as factors (Anderson, 1984). In the present study,
factor analysis is initiated to uncover the patterns
underlying financial ratio variables (Table 1). In factor
extraction method the number of factors is decided based
on the proportion of sample variance explained.
Orthogonal rotations such as Varimax and Quartimax
rotations are used to measure the similarity of a variable
with a factor by its factor loading (Everitt and Dunn,
2001; Hair, Black, Babin and Anderson, 2010).
TABLE 1. LIST OF FINANCIAL PARAMETERS USED
IN THE PRESENT STUDY
Ratios Description Ratios Description
DEB_EQU
Debt -
Equity Ratio
PBDITM
Profit Before
Depreciation
Interest Tax
Margin
LONG_TE
Long Term
Debt-Equity
Ratio
PBITM
Profit Before
Interest Tax
Margin
CURREN
Current
Ratio
PBDTM
Profit Before
Depreciation Tax
Margin
FIX_ASS Fixed Assts CPM
Current Profit
Margin
INVENTO Inventory APATM
Adjusted Profit
After Tax Margin
DEBTORS Debtors ROCE
Return on Capital
Employed
INTERES Interest RONW
Return on Net
Worth
International Journal of Scientific & Engineering Research Volume 4, Issue 2, February-2013 3
ISSN 2229-5518
IJ SER ©2013http://www.ijser.org
3.2.2. K-MEANS CLUSTERING METHODS
Nonhierarchical clustering techniques are designed to
group items, rather than variables, into a collection of K
clusters (Everitt and Dunn, 2001; Hair, Black, Babin and
Anderson, 2010). The number of clusters, K, may either
be specified in advance or determined as part of the
clustering procedure. The term K-means method is
coined for describing an algorithm that assigns items to
the k-clusters having the nearest centroid (mean).
Generally this technique uses Euclidean distances
measures computed by variables. Since the group labels
are unknown for the data set, k-means clustering is one
such technique in applied statistics that discovers
acceptable classes, in the present study, groups of
companies.
3.3.3 DISCRIMINANT ANALYSIS
Multivariate Discriminant Analysis is a multivariate
technique using several variables simultaneously to
classify an observation vector into one of several a priori
groups of companies as obtained by the K-means
method. In the present study, discriminant analysis is
used to exhibit groups graphically and judge the nature
of overall performance of the companies (Everitt and
Dunn, 2001; Hair, Black, Babin and Anderson, 2010).
3.3.4 PERCEPTUAL MAP
Perceptual mapping has been used as a strategic
management tool for about thirty years. It offers a
unique ability to communicate the complex relationships
between marketplace competitors and the criteria used
by buyers in making purchase decisions and
recommendations. Its powerful graphic simplicity
appeals to senior management and can stimulate
discussion and strategic thinking at all levels of all
several types of organizations. Perceptual mapping can
be used to plot the interrelationships of consumer
products, industrial goods, institutions, as well as
populations.
Virtually any subjects that can be rated on a range of
attributes can be mapped to show their relative positions
in relation both to other subjects as well as to the
evaluative attributes. Perceptual maps may be used for
company performance, concept development and
evaluation, and tracking changes in companies
perceptions among other uses. In this paper, perceptual
map is used to identify contribution of financial ratios to
different groups of companies.
4.0 ALGORITHMS
A brief step-by-step algorithm to grade the companies
during each of the study period based on their overall
performances is described below:
Step 1: Factor analysis is initiated to find the
structural pattern underlying the data set.
Step 2: K –means analysis is used to partition the
data set into k-clusters using the factor
scores obtained in Step 1 as input.
Step 3: Discriminant analysis is then performed with
the original ratios by considering the
groups formed by the k-means algorithm.
Step 4: Perceptual map is drawn with the
standardized canonical discriminant
function and centroid values of financial
parameters of groups of companies.
5.0 RESULTS AND DISCUSSION
As mentioned in Section 3.2.1, Varimax and Quartimax
criterion for orthogonal rotation have been used for the
pruned data. Even though the results obtained by both
the criterions were very similar, the varimax rotation
provided relatively better clustering of financial ratios.
Consequently, only the results of varimax rotation are
reported here. We have decided to retain 75 percent of
total variation in the data, and thus accounted
consistently four factors for each year with eigen values
little less than or equal to unity. Table 2 shows variance
accounted for each factors.
TABLE 2. PERCENTAGE OF VARIANCE
EXPLAINED BY FACTORS
Factors
Variance explained
2001 2002 2003 2004 2005
1
2
3
4
37.06
17.00
14.39
8.43
37.85
15.33
14.63
8.50
35.58
18.78
13.53
8.30
35.85
16.84
14.07
8.28
40.22
19.21
11.30
7.88
Total 76.88 76.31 76.19 75.04 78.61
2006 2007 2008 2009 2010
1
2
3
4
33.24
16.63
14.47
13.30
38.42
13.82
12.49
11.17
39.06
15.59
11.29
9.68
38.14
18.26
10.17
9.21
37.43
16.88
11.61
9.46
Total 77.64 75.90 75.62 75.78 75.38
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From the above table we observe that the total variances
explained by the extracted factors are over 75 percent,
which are relatively high. Also, for each factors the
variability is more or less the same for the study period,
though the number of companies in each year, after data
cleaning and selection, kept varying owing to various
reasons.
The financial ratios loaded in the factors are presented in
Table 3. Only those ratios with higher loadings are
indicated by (*) symbol. From the Table 3 it is clear that
the clustering of financial ratios is stable during the study
period. We observe slight changes in factor loadings
during the periods considered. The differences in factor
loadings may be due to statistical variations in the
original data.
TABLE 3. FINANCIAL RATIOS IN ROTATED
FACTORS (YEAR -WISE)
* I ndicates financial ratios highly loaded in respective
factors
After performing factor analysis, the next step is to assign
initial group labels to each company. Step 2 of the
algorithm is applied with factor scores extracted by Step
1, by conventional k-means clustering analysis.
Formations of clusters are explored by considering 2-
clusters, 3-clusters, 4-cluster and so on. Out of all the
possible trials, 3-cluster exhibited meaningful
interpretation than two, four and higher clusters. Having
decided to consider only 3 clusters, it is possible to rate a
company as Grade H, Grade M or Grade L depending on
whether the company belonged to Cluster 1, Cluster 2 or
Cluster 3 respectively.
Cluster 1 (Grade H) is a group of companies that have
high values for the financial ratios, indicating that these
companies are performing well. The companies with
lower values for the financial ratios are grouped into
Cluster 3 (Grade L). This suggested that Cluster 3 is a
group of companies with low-profile. Cluster 2 (Grade
M) are those companies which perform moderately well
as compared to the Cluster 1 and Cluster 3. In spite of
incorporating the results for each year, only the summary
statistics are reported in Table4.
TABLE 4. NUMBER OF COMPANIES IN THE
CLUSTERS
Years
Initial
Cluster
Discriminant
Classification
1 2 3 1 2 3
2001
2002
2003
2004
2005
17
32
30
06
55
55
52
86
32
63
47
35
03
81
01
47
52
04
81
01
55
35
86
06
55
17
32
29
32
63
2006
2007
2008
2009
2010
10
17
23
27
44
44
41
58
57
74
65
61
38
35
01
10
17
58
35
74
65
61
23
57
44
44
41
38
27
01
1 – Grade H 2 – Grade M 3 – Grade L
Table 4 indicates that majority of companies are in the
moderate performance category except for the year 2004
and 2006. The possible reasons that kept most of the
companies in lower profile in the year 2004 and 2006 may
be due to the then government policies. And also MNC’s
have found their way to open business in India, pushing
Indian companies back. Figures 1 through 10 shows the
groupings of companies into 3 clusters for each year of
the study period. It is interesting to note that the mean
vectors of these clusters can be arranged in the increasing
order of magnitude as show in Table 4.
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FIGURES 1 – 10. CLUSTERED GROUPS
In order to identify the factors that are mainly responsible
for the formation of the groups, perceptual mapping is
drawn using the standardized discriminant coefficients
and the unstandardised discriminant functions evaluated
at the group centroids. From the perceptual maps in
Figure 11, it is evident that the three groups of rated
companies are very well separated and represented in the
perceptual maps for all the ten year periods.
The two-dimensional graph clearly indicates that, in the
year 2001, dimension 1 comprises Liquidity and Equity
ratios factor, the dimension 2, Profitability and Leverage
ratios factor. In the year 2002, dimension 1 seems to
comprise Equity and Profitability ratios factor and
dimension 2, Liquidity, Leverage ratios factor. In the
year 2003, in dimension 1, Liquidity ratio factor and
dimension 1 accommodates only Equity, Leverage and
Profitability ratio factor. In the year 2004, in dimension
1 seems to comprise Profitability ratio factor, and in
dimension 2, Leverage, Equity and Liquidity ratios
factor. In the year 2005, in dimension 2, Equity, and
Profitability ratios factor, in dimension 1 comprises of
Leverage and Liquidity ratios factor.
In the year 2006, dimension 1 consists of Profitability
and Liquidity ratios factor, and the dimension 2, Equity
and Leverage ratios factor. In the year 2007,
Profitability and Liquidity ratios in dimension 1, and
Equity and Leverage ratios factor in dimension 2. In the
year 2008, dimension 1 consists of Liquidity, equity and
Leverage ratios factor, and in dimension 2 Profitability
ratio factor. In the year 2009, dimension 2 consists of
Profitability, Liquidity and leverage ratios factor, and
dimension 1 comprises Equity ratio. In the year 2010,
Liquidity, Leverage ratios in dimension 2 and Equity
ratio factor in dimension 1. It is interesting to note that
in all the ten years, all financial ratios contribute the
company position to some extent.
Figure 11. Perceptual Maps for the years
2001 – 2010.
6.0 CONCLUSION
The purpose of this paper is to identify the meaningful
groups of companies that are rated as best with respect to
their performance in terms of financial ratios using data
mining and perceptual map techniques. An attempt is
made to analysis the financial data relating to major
industries of public and private sector companies over a
period of ten years from 2001 to 2010. The present
analysis has shown that only 3 groups could be
meaningfully formed for each year. This indicates that
only 3 types of companies existed over a period of ten
years. Further, the companies find themselves classified
into High (Grade H), Medium (Grade M) and Low (Grade
L) categories depending on the financial ratios. Financial
Analyst can make use of these techniques of rating, and
the companies can project the performance on the basis of
financial ratios that has been considered in this study.
Perceptual maps may be used for financial ratios
performance and evaluation, and tracking changes in
companies perceptions, among other uses. A
generalization of the results is under investigation to
obtain a set of 3 groups of companies for any given year.
7.0 REFERENCES
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[3] Altman, E. I. (1994). An international survey of business failure
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