Selection of Variables in Data Envelopment Analysis for Evaluation of Stock Performance

Abstract

This study deploys data envelopment analysis (DEA) to identify the appropriate variables for the performance valuation of stocks. For this purpose, sixty-nine non-financial stocks of the Nifty 100 index of The National Stock Exchange of India Ltd (NSE) were selected as a sample for this study. We segregated the selected stocks into three groups of inputs and outputs for DEA based on fundamental indicators (financial ratios); technical indicators (momentum indicators); and both, fundamental and technical indicators. The stock performance indicators are sourced from the ACE database from financial year 2014 to 2019. The results of the study suggest that all three sets of stock performance indicators help in the identification of efficient stocks. However, stocks identified under momentum indicators are seen to have been better performing in stock return compared to the other two groups. The outcome of this study may help academicians and investors construct an effective portfolio and analyse/study its performance evaluation

Keywords

Non-financial stocks fundamental variables momentum variables efficient stocks National Stock Exchange data envelopment analysis

Introduction

Investment in stock market is highly risky, yet a profitable option if the right stocks for investment are chosen. With the increase in the number of stocks listed in the stock exchange, investors and fund managers find it difficult to select stocks from a large number. The data envelopment analysis (DEA) comes to the rescue under such circumstances. This technique has proven to be successful in evaluating a large number of homogeneous groups of samples (decision-making units—DMUs). Also, it is convenient while using multiple attributes for analyses. DEA is a non-parametric linear programming technique used to find the relative efficiency of organizational units termed as DMU. In this study, the DMUs are select stocks listed in the National Stock Exchange (NSE). Over the decades, researchers and academicians have carried out several studies to evaluate the performance of stocks. Fundamental analysis and technical analysis are the common methods for stock evaluation. The literature reveals that fundamental analysis has always been preferred for the evaluation and selection of stocks for long-term investment. It helps investors and analysts to know a firm’s financial health by assessing its performance through published financial statements (Beaver, 1966; Bernard, 1994; Blessing & Onoja, 2015; Chen & Shimerda, 1981; Ou & Penman, 1989). In addition to helping in comparing a firm’s current performance with its past, fundamental analysis also supports inter-firm comparisons too, thus, providing valuable insights for investors to make long-term investment decisions.

Contrary to fundamental analysts, technical analysts believe that past trading activities and price changes of a security are often valuable indicators of the security’s future price movements. They operate based on the assumptions that market discounts everything, price moves in trends and history tends to repeat itself. They use charts and indicators to find patterns in the past price movements to predict future price movement. He posits that Munehisa Homma, a Japanese rice merchant, was the first to use technical analysis in the seventeenth century. His technique is presently known as candlestick patterns and is used by most technical analysts for reading the charts.

Some researchers argue that there is no need of fundamental analysis as all information pertaining to a stock is reflected in its market price (Murphy, 1999). Treynor and Ferguson (1985) demonstrated the usefulness of knowing past price information in making investment decisions by developing a Bayesian probability estimate. They suggest that past price, when combined with valuable information, can achieve unusual profits. Technical analysts suggest using the historical price of a stock and trading volume to predict its future trend rather than analysing a large volume of financial data of a firm (Blume et al., 1994).

Recent studies reveal that fundamental and technical variables can be used together for stock selection (Chen et al., 2016). The integration can be made simple with the advent of trailblazing technology and tools. DEA is one such tool, which has become popular in recent times for its simplicity. The main advantage of the DEA approach is that it takes multiple input and output variables of different measures for evaluating the performance of DMUs. However, it is important to choose the right variables for the DEA analysis to be effective. This article seeks to identify appropriate variables for stock selection by testing three different sets of input and output variables using DEA. The first set consists of fundamental variables, the second set comprises technical variables and the third set includes both fundamental and technical variables. The stocks identified under each case were compared to find the effectiveness of variables in identifying efficient stocks. As far as we know, there is no other study conducted regarding the selection of variables in this manner.

This article attempts to compare the effectiveness of fundamental variables and momentum variables in evaluating stock performance for investment using DEA. The second section of this article reviews the related studies in the literature followed by the methodology used in the third section. The fourth section discusses the results, and the concluding remarks are provided in the fifth and final section.

Literature Review

DEA is used to find the relative efficiency of organizational units termed as DMU. These DMUs can include hospitals (Djema & Djerdjouri, 2012), municipalities (D’Inverno et al, 2018), hedge funds (Eling, 2006) hotels (Min et al., 2008), initial public offerings (Sohail & Anjum, 2016), stocks, etc. The efficiency scores of the respective DMUs help them to identify the areas for improvement. It also helps the concerned stakeholders in their decision-making (Shabbir et al., 2020). In this study, DEA is used to find the relative efficiency of select stocks. Past studies (Ahmadzade et al., 2011; Arif et al., 2020; Arshinova, 2011; Garkaz & Pesarakloo, 2011; Shabbir & Keife, 2020; Yu et al, 2020) prove DEA to be effective in evaluation of stocks’ performances.

Performance evaluation of a firm is imperative in making investment decisions. In order to measure performance, the metrics employed should be carefully chosen so that they reflect the overall financial health of a firm. These metrics can be fundamental, momentum or both. The most common sources of a firm’s financial data are its balance sheet and income statement, taken either in absolute terms or as ratios. Arshinova (2011) used total operational revenue, equity, operating expenses and financial expenses to evaluate stocks for building portfolio. According to the results, the investigated stocks were divided into three groups—stocks with 100% efficiency, above 80% efficiency and below 80% efficiency. He recommends portfolio with 100% efficient stock for conservative investment. Similarly, cost of goods, total revenue, average asset, sales cost, revenues, operating profit and net income were used in the evaluation of stock performance (Chen, 2008; Garkaz & Pesarakloo, 2011; Saleem et al, 2020; Shabbir, 2016). Abad et al. (2004) attempted to link the causal effect of a firm’s current financial data to its future earnings and to its value. For this purpose, a number of variables such as account receivables, inventory, fixed assets, operating expenses, revenue, book value and market capitalization were used. However, they were not able to generate abnormal returns. Bahrani and Khedri (2013) employed average variables of assets, average salaries of stockholders and sale of costs as inputs and variables of income and operating profit as outputs in their study. But the portfolio created was not able to generate a return higher than the average industry return.

Lim et al. (2014), Tehrani et al. (2012), Shabbir and Muhammad (2019) and Siew et al. (2017) used liquidity, activity, leverage and profitability ratios to find the efficiency of firms under investigation. The most common ratios used in these studies were current ratio, quick ratio, debt to equity ratio, debt to assets, account receivable turnover, inventory turnover, asset turnover, return on asset, return on equity, return on capital employed, net income, operating profit to sales, net profit margin, price to earnings and price to book. The resulting portfolio yielded higher risk-adjusted returns when compared to other benchmark portfolios (Lim et al., 2014). Tehrani et al. (2012) and Siew et al. (2017) were able to identify the most efficient companies among a set of companies under investigation. In addition to the above-mentioned ratios Hwang et al. (2007) used owners’ equity to fixed assets, times interest earned and achieved a 100% hit rate in classification of stocks for investors used by employing DEA data analysis (DA) approach. Ling and Kamil (2010) used two sets of variables—one with the absolute values (total assets, current assets, current liabilities and total expenses as inputs and net income after taxes and revenue as outputs) from financial statements and the other set with ratios (current ratio, debt ratio and debt to equity as inputs and return on investment, return on equity and earnings per share as outputs) in evaluating stocks (Nguyen et al., 2020). These factors were screened by using correlation analysis. They found that there is no strong relationship between the inputs and outputs of ratios, and that the first set of variables helped to identify efficient stocks.

As far as technical analysis is concerned, past studies show that return and risk are the two variables used in technical analysis. Sometimes, trading volume is also included. Powers and McMullen (2000) and Muhammad et al. (2020) used returns (i.e., 1-, 3-, 5-, 10-year returns), earnings (EPS and risk-beta, sigma) and performance evolution (PE) ratio to evaluate 185 large-cap stocks and identified 14 efficient stocks. Dia (2009) presented a four-step methodology for portfolio selection and compared it with the model developed, in which beta, rate of return and exchange flow ratio were used as variables to find efficient DMUs. They found the results obtained to be similar but easier to compare.

Gardijan and Kojić (2012) constructed a portfolio of stocks through DEA by using expected monthly return, return variance, value at risk (VaR) and beta coefficient as metrics. They created six portfolios processed with different inputs and found that the results of the portfolios constructed were not superior to the market returns. However, the portfolio, which included VaR as a selection criterion, had better average monthly returns than other portfolios. Lopes et al. (2008) used price-to-earnings ratio, beta, return volatility, earnings per share and 12-,36-, and 60-month returns as the variables to construct portfolios in the Brazilian stock market and found them superior to the market index IBrX100 and Brazilian inter-deposit rate crest depository interest (CDI), especially during market decline Liu et al. (2020).

While most of the studies have provided substantial evidence on the effectiveness of using fundamental and technical variables in stock selection, some studies have examined the complementary nature of both variables in stock selection (Ejaz et al., 2017). Bettman et al. (2009) proposed a model combining both fundamental and technical analyses for equity valuation, and the testing confirmed that both analyses are complementary in nature and are not substitutes. Although both analyses perform well in isolation, their integration have superior explanatory power. Chen et al. (2016) found that accounting information could be a supplement to technical information and found that the combined strategy outperforms the momentum strategy.

This study seeks to identify appropriate variables for stock selection by testing three different sets of input and output variables using DEA. The first set consists of fundamental variables, the second set comprises technical variables and the third set includes both fundamental and technical variables. The stocks identified under each case were compared to find the effectiveness of variables in identifying efficient stocks. As far as we know, there is no other comparative study conducted in this manner.

Data and Methodology

In the present study, stocks that constitute Nifty 100 were taken, and all the financial stocks were removed as certain variables should be treated differently when compared to non-financial stocks. For example, loans are treated as assets in financial stocks and liabilities for non-financial stocks. Out of these, stocks carrying negative values or missing data were eliminated, and the final number of stocks chosen for the study was 69. Three combinations of input and output variables were tested to identify the most suitable attributes in finding efficient stocks for investment. The first combination (case 1) employed financial ratios that showed liquidity, leverage, activity and profitability of companies. The second combination (case 2) included momentum data, that is, the risk and return of stocks. The third combination (case 3) comprised both fundamental and momentum data.

The present study employs the DEA model to identify efficient stocks by using different sets of variables. The DEA is a non-parametric linear programming model. It is used to assess the relative efficiency of DMUs with common inputs and outputs, which needs to be ordinal, but it can be of different units. It helps to attenuate the complexity of the study by simultaneously evaluating the attributes and presenting one composite score referred to as efficiency score. In this study, DMUs that were the stocks of top 69 non-financial firms listed in NSE based on their market capitalization were selected and have been mentioned in Tables 1, 2, and 3, respectively.

Table 1.

Financial Ratios Used for the Study

Financial Parameter	Classification
Current ratio	Input
Quick ratio	Input
Debt to equity ratio	Input
Asset turnover ratio	Input
Price to book ratio	Input
Net profit margin	Output
Return on asset	Output
Return on equity	Output
Return on capital employed	Output
Earnings per share	Output

Source: ACE Equity database.

Table 2.

Momentum Variables Used for the Study

Financial Parameter	Classification
Beta	Input
Sigma	Input
1-year return	Output
3-year return	Output
5-year return	Output

Source: ACE Equity database.

Table 3.

Both Fundamental and Momentum Variables

Financial Parameter	Classification
Debt to equity ratio	Input
Price to book ratio	Input
Sigma	Input
Beta	Input
Net profit margin	Output
Rate of return (5 years)	Output
Earnings per share	Output
Return on asset	Output
Return on equity	Output

Source: ACE Equity database.

The efficiency of the DMUs can be evaluated using the DEA estimator presented by Charnes, Cooper and Rhodes (CCR) in 1978 and the DEA estimator presented which assumes variable returns to scale (VRS). The CCR model assumes constant return to scale (CRS). Assume there are ‘n’ DMUs with ‘m’ number of inputs producing ‘s’ number of outputs. DEA finds the most favourable input weights ‘v_i’ and output weights ‘u_r’ for the DMU under assessment and gives a single composite efficiency score for each DMU.

The CCR model was expressed as follows:

Maximize z = {\sum^{​}}_{r =1}^{s} u_{r} y_{r 0}

subjectto {\sum^{​}}_{r =1}^{s} u_{r} y_{r j} - {\sum^{​}}_{i =1}^{m} v_{i} x_{i j} \leq 0,

j = 1, …, n

{\sum^{​}}_{i =1}^{m} v_{i} x_{i 0 =1,}

v_i ≥ ε, u_r ≥ ε, u₀ free in sign

CCR model was refined where, instead of constant returns to scale, VRS was assumed by introducing a separate variable u₀ to the CCR model. This allowed the BCC model to be flexible in determining the efficiencies of DMUs, when the returns to scale increased, remained constant or decreased. u₀ indicates the returns to scale possibilities.

The model was expressed as follows:

Maximize z = \sum_{r =1}^{s} u_{r} y_{r 0} - u_{0}

subject to \sum_{r =1}^{s} u_{r} y_{r j} - \sum_{i =1}^{m} v_{i} x_{i j} - u_{0} \leq 0,

j = 1, …, n

\sum_{i =1}^{m} v_{i} x_{i 0 =1},

v_i ≥ ε, u_r ≥ ε, u₀ free in sign

Empirical Findings

The input–oriented DEA approach was applied in this study. The efficiency value of stocks was determined by using both CRS approach and VRS approach. Companies with an efficiency score of 1 were considered 100% efficient.

Data Analysis of Case 1

Five inputs (current ratio, quick ratio, debt to equity, asset turnover ratio and price to book ratio) and five outputs (net profit margin, return on asset, return on equity, return on capital employed and earnings per share) were used for the analysis. The results of the companies’ performance are presented in Table 4.

Table 4.

Efficiency Score of Companies (case 1)

Stocks	Efficiency Value
Stocks	Crste	Vrste	Scale
ABB	0.343	0.733	0.469
ACC	0.877	1.000	0.877
ADANIPORTS	0.552	0.632	0.873
AMBUJACEM	1.000	1.000	1.000
ASHOKLEY	0.514	0.548	0.938
ASIANPAINT	0.454	0.466	0.975
AUROPHARMA	0.857	0.885	0.968
BAJAJ-AUTO	1.000	1.000	1.000
BHARTIARTL	0.289	0.380	0.759
BHEL	0.225	1.000	0.225
BIOCON	0.449	0.647	0.694
BOSCHLTD	1.000	1.000	1.000
BPCL	0.868	0.928	0.936
BRITANNIA	0.658	0.796	0.827
CADILAHC	0.677	0.703	0.963
CIPLA	0.335	0.456	0.733
COALINDIA	0.968	1.000	0.968
COLPAL	1.000	1.000	1.000
CONCOR	0.703	0.993	0.709
DABUR	0.586	0.614	0.955
DIVISLAB	1.000	1.000	1.000
DLF	0.503	0.897	0.561
DRREDDY	0.636	0.641	0.992
GAIL	0.668	0.806	0.829
GODREJCP	0.507	0.514	0.987
GRASIM	0.968	1.000	0.968
HAVELLS	0.642	0.782	0.821
HCLTECH	0.782	1.000	0.782
HEROMOTOCO	0.981	1.000	0.981
HINDALCO	0.864	1.000	0.864
HINDPETRO	1.000	1.000	1.000
HINDUNILVR	1.000	1.000	1.000
HINDZINC	1.000	1.000	1.000
INFRATEL	0.340	0.516	0.660
INFY	1.000	1.000	1.000
IOC	0.994	1.000	0.994
ITC	0.881	0.915	0.963
JSWSTEEL	0.638	0.677	0.942
LT	0.560	0.561	0.998
LUPIN	0.540	0.760	0.710
M&M	0.626	0.660	0.948
MARICO	0.810	0.848	0.955
MARUTI	0.971	0.973	0.998
MOTHERSUMI	0.480	0.482	0.996
NHPC	1.000	1.000	1.000
NMDC	1.000	1.000	1.000
NTPC	0.685	0.781	0.876
OFSS	1.000	1.000	1.000
ONGC	1.000	1.000	1.000
PAGEIND	1.000	1.000	1.000
PEL	1.000	1.000	1.000
PETRONET	1.000	1.000	1.000
PGHH	1.000	1.000	1.000
PIDILITIND	0.803	0.874	0.918
POWERGRID	0.673	0.722	0.932
RELIANCE	0.820	0.887	0.925
SHREECEM	0.790	0.820	0.963
SIEMENS	0.829	1.000	0.829
SUNPHARMA	0.373	0.374	0.998
TATAMOTORS	0.322	0.493	0.653
TATASTEEL	0.767	0.847	0.906
TCS	1.000	1.000	1.000
TECHM	0.748	0.857	0.873
TITAN	0.395	0.397	0.994
UBL	0.322	0.536	0.601
ULTRACEMCO	0.453	0.519	0.873
UPL	0.519	0.585	0.888
WIPRO	0.670	0.745	0.900
ZEEL	0.742	0.806	0.920

Source: Computed by authors from the DEA model.

The results show that 18 companies—BAJAJ-AUTO, HINDUNILVR, INFY, ONGC, TCS, AMBUJACEM, BOSCHLTD, COLPAL, DIVISLAB, HINDPETRO, HINDZINC, NHPC, NMDC, OFSS, PAGEIND, PETRONET, PEL and PGHH—were found efficient under the CRS approach, having an efficiency score of 1. High efficiency score of these companies showed their ability of maximizing the volume of output with minimal volume of input.

Under the VRS approach, 26 companies, including ACC, BHEL, COALINDIA, GRASIM, HCLTECH, HEROMOTOCO, HINDALCO and IOC in addition to the above-mentioned 18 companies, were found 100% efficient with an efficiency score of 1. Companies like BHEL and HINDALCO whose profitability positions and GRASIM and IOC whose liquidity positions were not good were also included under the VRS approach. This could be because the VRS model considers either the lowest input value or the highest value of output to identify a stock to be efficient.

Data Analysis of Case 2

Two inputs (sigma and beta) and three outputs (1-year, 3-year and 5-year return) were used to find efficient stocks. The results obtained by using momentum variables for the study are presented in Table 5.

From Table 5, it is evidenced that eight companies, BRITANNIA, HINDUNILVR, INFY, POWERGRID, TITAN, DIVISLAB, HINDPETRO and MARICO were efficient under the CRS approach and 11 companies, including COALINDIA, RELIANCE, TCS and WIPRO in addition to the 8 companies mentioned earlier were found efficient under the VRS approach with an efficiency score of 1. In this case, efficiency refers to generating maximum return (output) for the given level of risk (input). Though stocks like ASHOKLEY, BIOCON and BPCL have generated a 5-year annualized return of more than 30%, their risk level is also high.

Table 5.

Efficiency Score of Companies (case 2)

Stocks	Efficiency Value
Stocks	Crste	Vrste	Scale
ABB	0.262	0.309	0.846
ACC	0.289	0.320	0.902
ADANIPORTS	0.419	0.517	0.811
AMBUJACEM	0.240	0.316	0.760
ASHOKLEY	0.232	0.316	0.735
ASIANPAINT	0.979	0.994	0.985
AUROPHARMA	0.443	0.449	0.987
BAJAJ-AUTO	0.667	0.777	0.858
BHARTIARTL	0.334	0.577	0.579
BHEL	0.118	0.167	0.705
BIOCON	0.489	0.614	0.796
BOSCHLTD	0.208	0.263	0.792
BPCL	0.381	0.522	0.730
BRITANNIA	1.000	1.000	1.000
CADILAHC	0.288	0.435	0.662
CIPLA	0.591	0.773	0.765
COALINDIA	0.714	1.000	0.714
COLPAL	0.730	0.730	1.000
CONCOR	0.329	0.362	0.911
DABUR	0.442	0.449	0.985
DIVISLAB	1.000	1.000	1.000
DLF	0.152	0.162	0.939
DRREDDY	0.684	0.701	0.976
GAIL	0.712	0.741	0.960
GODREJCP	0.377	0.403	0.937
GRASIM	0.326	0.557	0.584
HAVELLS	0.454	0.732	0.621
HCLTECH	0.758	0.772	0.983
HEROMOTOCO	0.270	0.666	0.406
HINDALCO	0.548	0.606	0.903
HINDPETRO	1.000	1.000	1.000
HINDUNILVR	1.000	1.000	1.000
HINDZINC	0.462	0.482	0.960
INFRATEL	0.745	0.858	0.868
INFY	1.000	1.000	1.000
IOC	0.582	0.629	0.926
ITC	0.774	0.816	0.949
JSWSTEEL	0.738	0.791	0.932
LT	0.666	0.774	0.861
LUPIN	1.000	1.000	1.000
M&M	0.428	0.696	0.616
MARICO	1.000	1.000	1.000
MARUTI	0.618	0.774	0.798
MOTHERSUMI	0.658	1.000	0.658
NHPC	0.236	0.276	0.852
NMDC	0.219	0.311	0.705
NTPC	0.726	0.851	0.852
OFSS	0.325	0.509	0.639
ONGC	0.436	0.640	0.681
PAGEIND	0.498	0.507	0.983
PEL	0.418	0.418	0.999
PETRONET	0.723	0.735	0.984
PGHH	0.861	0.870	0.990
PIDILITIND	0.707	0.718	0.985
POWERGRID	1.000	1.000	1.000
RELIANCE	0.977	1.000	0.977
SHREECEM	0.283	0.300	0.943
SIEMENS	0.246	0.279	0.881
SUNPHARMA	0.387	0.510	0.758
TATAMOTORS	0.052	0.468	0.111
TATASTEEL	0.456	0.570	0.800
TCS	0.992	1.000	0.992
TECHM	0.740	0.742	0.998
TITAN	1.000	1.000	1.000
UBL	0.402	0.406	0.991
ULTRACEMCO	0.515	0.690	0.747
UPL	0.698	0.701	0.996
WIPRO	0.938	0.959	0.978
ZEEL	0.270	0.524	0.515

Source: Computed by authors from the DEA model.

Data Analysis of Case 3

In case 3, both fundamental and momentum variables were used to find the efficiency of companies. Four inputs (debt to equity, price to book, sigma and beta) and five outputs (net profit margin, 5-year stock return, earnings per share, return on asset and return on equity) were used. The results of efficient companies under this study are presented in Table 6.

Table 6.

Efficiency Score of Companies (case 3)

Stocks	Efficiency Value
Stocks	Crste	Vrste	Scale
ABB	0.289	0.509	0.568
ACC	1.000	1.000	1.000
ADANIPORTS	0.979	1.000	0.979
AMBUJACEM	0.847	1.000	0.847
ASHOKLEY	0.592	0.595	0.995
ASIANPAINT	0.732	1.000	0.732
AUROPHARMA	0.737	0.749	0.984
BAJAJ-AUTO	1.000	1.000	1.000
BHARTIARTL	0.257	0.681	0.377
BHEL	0.029	0.248	0.117
BIOCON	0.789	0.867	0.911
BOSCHLTD	1.000	1.000	1.000
BPCL	1.000	1.000	1.000
BRITANNIA	1.000	1.000	1.000
CADILAHC	0.617	0.643	0.960
CIPLA	0.523	0.941	0.556
COALINDIA	1.000	1.000	1.000
COLPAL	1.000	1.000	1.000
CONCOR	0.737	1.000	0.737
DABUR	0.501	0.533	0.940
DIVISLAB	1.000	1.000	1.000
DLF	0.514	0.868	0.593
DRREDDY	0.759	0.901	0.842
GAIL	0.940	1.000	0.940
GODREJCP	0.488	0.514	0.950
GRASIM	0.927	1.000	0.927
HAVELLS	0.756	0.783	0.966
HCLTECH	1.000	1.000	1.000
HEROMOTOCO	1.000	1.000	1.000
HINDALCO	0.139	0.561	0.249
HINDPETRO	1.000	1.000	1.000
HINDUNILVR	1.000	1.000	1.000
HINDZINC	1.000	1.000	1.000
INFRATEL	0.932	1.000	0.932
INFY	1.000	1.000	1.000
IOC	1.000	1.000	1.000
ITC	1.000	1.000	1.000
JSWSTEEL	1.000	1.000	1.000
LT	0.667	0.826	0.808
LUPIN	0.179	0.257	0.696
M&M	0.696	0.830	0.839
MARICO	1.000	1.000	1.000
MARUTI	1.000	1.000	1.000
MOTHERSUMI	0.715	1.000	0.715
NHPC	1.000	1.000	1.000
NMDC	0.649	0.655	0.991
NTPC	0.924	1.000	0.924
OFSS	1.000	1.000	1.000
ONGC	0.266	0.733	0.363
PAGEIND	0.987	1.000	0.987
PEL	1.000	1.000	1.000
PETRONET	1.000	1.000	1.000
PGHH	1.000	1.000	1.000
PIDILITIND	0.702	0.718	0.977
POWERGRID	1.000	1.000	1.000
RELIANCE	1.000	1.000	1.000
SHREECEM	0.817	0.817	1.000
SIEMENS	0.764	1.000	0.764
SUNPHARMA	0.549	0.667	0.824
TATAMOTORS	0.194	0.704	0.275
TATASTEEL	0.567	1.000	0.567
TCS	1.000	1.000	1.000
TECHM	0.978	1.000	0.978
TITAN	0.805	0.869	0.927
UBL	0.256	0.399	0.641
ULTRACEMCO	0.549	0.862	0.636
UPL	1.000	1.000	1.000
WIPRO	0.958	1.000	0.958
ZEEL	0.676	0.677	0.999

Source: Computed by authors from the DEA model.

The results show that 28 companies—BAJAJ-AUTO, BPCL, BRITANNIA, COALINDIA, HCLTECH, HEROMOTOCO, HINDUNILVR, ITC, IOC, INFY, JSWSTEEL, MARUTI, POWERGRID, RELIANCE, TCS, UPL, ACC, BOSCHLTD, COLPAL, DIVISLAB, HINDPETRO, HINDZINC, MARICO, NHPC, OFSS, PETRONET, PEL and PGHH—were efficient under the CRS approach, and 42 companies, including ADANIPORTS, ASIANPAINTS, INFRATEL, GAIL, GRASIM, NTPC, TATASTEEL, TECHM, WIPRO, AMBUJACEM, CONCOR, MOTHERSUMI, PAGEIND and SIEMENS, in addition to the above-mentioned 28 companies—were found efficient under the VRS approach. The stocks which were not captured under Case1, such as BPCL, MARUTI and UPL, which has generated around 40% 5-year annualized return and ASIANPAINT and JSWSTEEL with more than 25% were included in this case as it considers both the fundamental data and the momentum data. Table 7 presents the 5-year annualized return of efficient stocks under the CRS approach for the three cases.

Table 7.

Five-year Annualized Returns of Efficient Stocks (CRS)

Case 1		Case 2		Case 3
Stocks	Return (%)	Stocks	Return(%)	Stocks	Return (%)
BAJAJ-AUTO	32.59	BRITANNIA	55.46	BAJAJ-AUTO	32.59
HINDUNILVR	31.27	HINDUNILVR	31.27	BPCL	39.47
INFY	37.77	INFY	37.77	BRITANNIA	55.46
ONGC	5.14	POWERGRID	17.86	COALINDIA	15.90
TCS	36.08	TITAN	36.05	HCLTECH	22.13
AMBUJACEM	7.33	DIVISLAB	27.45	HEROMOTOCO	41.29
BOSCHLTD	43.66	HINDPETRO	55.41	HINDUNILVR	31.27
COLPAL	22.46	MARICO	30.98	ITC	11.79
DIVISLAB	27.45			IOC	37.47
HINDPETRO	55.41			INFY	37.77
HINDZINC	29.32			JSWSTEEL	31.86
NHPC	12.08			MARUTI	42.34
NMDC	5.04			POWERGRID	17.86
OFSS	64.92			RELIANCE	29.28
PAGEIND	62.97			TCS	36.08
PETRONET	32.50			UPL	40.59
PEL	50.94			ACC	19.85
PGHH	54.88			BOSCHLTD	43.66
				COLPAL	22.46
				DIVISLAB	27.45
				HINDPETRO	55.41
				HINDZINC	29.32
				MARICO	30.98
				NHPC	12.08
				OFSS	64.92
				PETRONET	32.50
				PEL	50.94
				PGHH	54.88

Source: Computed by authors from the DEA model.

Table 8 presents the 5-year annualized return of efficient stocks under the VRS approach for the three cases.

Table 8.

Five-year Annualized Returns of Efficient Stocks (VRS)

Case 1		Case 2		Case 3
Stocks	Return(%)	Stocks	Return(%)	Stocks	Return (%)
BAJAJ-AUTO	32.59	BRITANNIA	55.46	ADANIPORTS	16.57
COALINDIA	15.90	COALINDIA	15.90	ASIANPAINT	26.95
GRASIM	21.78	HINDUNILVR	31.27	BAJAJ-AUTO	32.59
HCLTECH	22.13	INFY	37.77	BPCL	39.47
HEROMOTOCO	41.29	POWERGRID	17.86	INFRATEL	18.88
HINDALCO	6.96	RELIANCE	29.28	BRITANNIA	55.46
HINDUNILVR	31.27	TCS	36.08	COALINDIA	15.90
IOC	37.47	TITAN	36.05	GAIL	22.60
INFY	37.77	DIVISLAB	27.45	GRASIM	21.78
ONGC	5.14	HINDPETRO	55.41	HCLTECH	22.13
TCS	36.08	MARICO	30.98	HEROMOTOCO	41.29
ACC	19.85			HINDUNILVR	31.27
AMBUJACEM	7.33			ITC	11.79
BHEL	−5.75			IOC	37.47
BOSCHLTD	43.66			INFY	37.77
COLPAL	22.46			JSWSTEEL	31.86
DIVISLAB	27.45			MARUTI	42.34
HINDPETRO	55.41			NTPC	12.42
HINDZINC	29.32			POWERGRID	17.86
NHPC	12.08			RELIANCE	29.28
NMDC	5.04			TCS	36.08
OFSS	64.92			TATASTEEL	14.47
PAGEIND	62.97			TECHM	20.11
PETRONET	32.50			UPL	40.59
PEL	50.94			WIPRO	10.99
PGHH	54.88			ACC	19.85
				AMBUJACEM	7.33
				BOSCHLTD	43.66
				COLPAL	22.46
				CONCOR	21.71
				DIVISLAB	27.45
				HINDPETRO	55.41
				HINDZINC	29.32
				MARICO	30.98
				MOTHERSUMI	17.76
				NHPC	12.08
				OFSS	64.92
				PAGEIND	62.97
				PETRONET	32.50
				PEL	50.94
				PGHH	54.88
				SIEMENS	18.23

Source: Computed by authors from the DEA model.

Tables 7 and 8 present the list of efficient stocks identified under CCR and BCC models, using the three sets of variables, with their respective 5-year annualized returns. The average returns of the efficient stocks under each case are presented in Table 9.

It can be observed that the average returns of the efficient stocks, under all the three cases, using both the models, are higher than that of the market, proving the effectiveness of DEA. Among the three sets of variables, case 2 variables generate higher return when compared to the other two under both the CCR and BCC models. However, it is not sufficient to say that the momentum variables are most suitable to identify efficient stocks for investment as stocks such as OFSS, PAGEIND, PGHH, SHREECEM, PEL, BOSCH, ACC and HEROMOTOCO have distributed enormous amount of dividends when compared to other stocks but do not have much capital appreciation. Stocks such as ASHOKLEY, BIOCON, BPCL and IOC give more than 30% 5-year annualized return with high risk, which could be preferred by aggressive investors. However, it can be an ideal portfolio for conservative investors. It is also evident that the CCR model gives a better result than the BCC model as the average return is higher with minimal number of stocks to track. Since the resulting stocks using case 2 variables are fewer with higher average return, it can be used to construct a portfolio with manageable stocks to track. Case 3 variables can be used to percolate efficient stocks and can be analysed further to construct an effective portfolio.

Conclusion

This article is devoted to identify the suitable variables for DEA to evaluate stocks and identify the efficient ones. The input–oriented approach of DEA was used for this purpose. The results obtained suggest that the average returns of the efficient stocks, identified using all the three sets of variables, are higher returns than the market return. Among them, portfolios that are constructed, using momentum variables, give higher returns when compared to the other two sets. However, it is not sufficient to declare the momentum variables to be more suitable as it fails to include some stocks with higher annualized returns as the stock prices fail to reflect dividend income. Some stocks that were not found to be 100% efficient such as BPCL, JSWSTEEL, MARUTI and UPL generated more than 30% annualized return. But these stocks were found to be efficient when the fundamental variables and momentum variables were integrated. Though there is only a slight difference in the average return of efficient stocks belonging to case 1 and case 3 variables, fundamental variables when combined with momentum variables help to include stocks with higher returns (Table 9). Further studies can be carried out for a large pool of stocks by testing the same periodically or for different markets. The efficient stocks identified using case 3 variables can further be explored by taking qualitative data into account for effective portfolio construction.

Table 9.

Five-year Annualized Average Return of the Efficient Stocks

	Case 1	Case 2	Case 3
CCR	33.99%	36.53%	34.56%
BCC	29.67%	33.96%	30.01%

Source: Computed by authors from the DEA model.

Footnotes

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The authors received no financial support for the research, authorship and/or publication of this article.

References

Abad

, Thore

S. A.

, & Laffarga

(2004). Fundamental analysis of stocks by two-stage DEA. Managerial and Decision Economics, 25(5), 231–241.

Ahmadzade

, Fazli

, Khosroanjom

, & Mavi

R. K.

(2011). Utilising data envelopment analysis for selecting stock and benchmark firms in Tehran stock exchange. International Journal of Operational Research, 12(4), 446–463.

Arif

, Sadiq

, Shabbir

M. S.

, Yahya

, Zamir

, & Bares

Lopez, L.

(2020). The role of globalization in financial development, trade openness and sustainable environmental-economic growth: Evidence from selected South Asian economies. Journal of Sustainable Finance & Investment, 1–18. https://doi.org/10.1080/20430795.2020.1861865

Arshinova

(2011). Construction of equity portfolio on the basis of data envelopment analysis approach. Scientific Journal of Riga Technical University. Computer Sciences, 45(1), 104–108.

Bahrani

, & Khedri

(2013). Evaluation of relative efficiency and performance of companies using data envelopment analysis (DEA) approach. Elixir Finance Management, 56, 13299–13304.

Beaver

W. H.

(1966). Financial ratios as predictors of failure. Journal of Accounting Research, 4, 71–111.

Bernard

V. L.

(1994). Accounting-based valuation methods, determinants of market-to-book ratios, and implications for financial statement analysis (Working Paper No. 9401). University of Michigan.

Bettman

J. L.

, Sault

S. J.

, & Schultz

E. L.

(2009). Fundamental and technical analysis: Substitutes or complements? Accounting & Finance, 49(1), 21–36.

Blessing

, & Onoja

E. E.

(2015). The role of financial statements on investment decision making: A case of united bank for Africa PLC (2004–2013). European Journal of Business, Economics and Accountancy, 3(2), 12–37.

10.

Blume

, Easley

, & O’hara

(1994). Market statistics and technical analysis: The role of volume. The Journal of Finance, 49(1), 153–181.

11.

Chen

H. H.

(2008). Stock selection using data envelopment analysis. Industrial Management & Data Systems, 108(9), 1255–1268.

12.

Chen

K. H.

, & Shimerda

T. A.

(1981). An empirical analysis of useful financial ratios. Financial Management, 10, 51–60.

13.

Chen

H. Y.

, Lee

C. F.

, & Shih

W. K.

(2016). Technical, fundamental, and combined information for separating winners from losers. Pacific-Basin Finance Journal, 39, 224–242.

14.

Dia

(2009). A portfolio selection methodology based on data envelopment analysis. INFOR: Information Systems and Operational Research, 47(1), 71–79.

15.

Djema

, & Djerdjouri

(2012). A two-stage DEA with partial least squares regression model for performance analysis in healthcare in Algeria. International Journal of Applied Decision Sciences, 5(2), 118–141.

16.

D’Inverno

, Carosi

, & Ravagli

(2018). Global public spending efficiency in Tuscan municipalities. Socio-Economic Planning Sciences, 61, 102–113

17.

Ejaz

, Amir

, & Shabbir

M. S.

(2017). Public expenditure and its impact on economic growth: A case of Pakistan. Kashmir Economic Review, 26(1), 13–21.

18.

Eling

(2006). Performance measurement of hedge funds using data envelopment analysis. Financial Markets and Portfolio Management, 20(4), 442.

19.

Gardijan

, & Kojić

(2012). DEA-based investment strategy and its application in the Croatian stock market. Croatian Operational Research Review, 3(1), 203–212.

20.

Garkaz

, & Pesarakloo

(2011). Determination of portfolio through fuzzy data envelopment analysis in companies accepted in Tehran securities exchange. Middle East Journal of Scientific Research, 8(5), 942–946.

21.

Hwang

S. N.

, Lin

C. T.

, & Chuang

W. C.

(2007). Stock selection using data envelopment analysis-discriminant analysis. Journal of Information and Optimization Sciences, 28(1), 33–50.

22.

Lim

, Oh

K. W.

, & Zhu

(2014). Use of DEA cross-efficiency evaluation in portfolio selection: An application to Korean stock market. European Journal of Operational Research, 236(1), 361–368.

23.

Ling

O. P.

, & Kamil

A. A.

(2010). Data envelopment analysis for stocks selection on Bursa Malaysia. Archives of Applied Science Research, 2(5), 11–35.

24.

Liu

, Saleem

, Shabbir

M. S.

, Irshad

, & Khan

(2020). The relationship between corporate social responsibility and financial performance: A moderate role of fintech technology. Environmental Science and Pollution Research. https://doi.org/10.1007/s11356-020-11822-9

25.

Lopes

, Lanzer

, Lima

, & da

Costa, N.

Jr. (2008). DEA investment strategy in the Brazilian stock market. Economics Bulletin, 13(2), 1–10.

26.

Min

, Min

, Joo

S. J.

, & Kim

(2008). Data envelopment analysis for establishing the financial benchmark of Korean hotels. International Journal of Services and Operations Management, 4(2), 201.

27.

Muhammad

, Shabbir

M. S.

, Saleem

, Bilal

, & Ulucak

(2020). Nexus between willingness to pay for renewable energy sources: Evidence from Turkey. Environmental Science and Pollution Research, 28, 2972–2986.

28.

Murphy

J. J.

(1999). Technical analysis of the financial markets: A comprehensive guide to trading methods and applications. Penguin.

29.

Nguyen

V. K.

, Shabbir

M. S.

, Sail

M. S.

, & Thuy

T. H.

(2020). Does informal economy impede economic growth? Evidence from an emerging economy. Journal of Sustainable Finance & Investment. http://doi.org/10.1080/20430795.2020.1711501

30.

J. A.

, & Penman

S. H.

(1989). Financial statement analysis and the prediction of stock returns. Journal of Accounting and Economics, 11(4), 295–329.

31.

Powers

, & McMullen

(2000). Using data envelopment analysis to select efficient large market cap securities. Journal of Business and Management, 7(2), 31–42.

32.

Saleem

, Shabbir

M. S.

, Khan

, Aziz

, Husin

M. M.

, & Abbasi

B. A.

(2020). Estimating the key determinants of foreign direct investment flows in Pakistan: New insights into the co-integration relationship. South Asian Journal of Business Studies. https://doi.org/10.1108/SAJBS-07-2019-0123

33.

Shabbir

M. S.

(2016). Contributing factors of inland investment. Global Journal of Management and Business Research. https://journalofbusiness.org/index.php/GJMBR/article/view/2031

34.

Shabbir

M. S.

, & Muhammad

(2019). The dynamic impact of foreign portfolio investment on stock prices in Pakistan. Transnational Corporations Review, 11(2), 166–178.

35.

Shabbir

M. S.

, & Keife

(2020). The relationship between corporate social responsibility, environmental investments and financial performance: Evidence from manufacturing companies. Environmental Science and Pollution Research. https://doi.org/10.1007/s11356-020-10217-0

36.

Shabbir

M. S.

, Bashir

, Abbasi

H. M.

, Yahya

, & Abbasi

B. A.

(2020). Effect of domestic and foreign private investment on economic growth of Pakistan. Transnational Corporations Review, 1–13. https://doi.org/10.1080/19186444.2020.1858676

37.

Siew

L. W.

, Fai

L. K.

, & Hoe

L. W.

(2017). An empirical investigation on the efficiency of the financial companies in Malaysia with DEA model. American Journal of Information Science and Computer Engineering, 3(3), 32–38.

38.

Sohail

M. K.

, and Anjum

M. S.

(2016). Efficiency dynamics of initial public offerings using data envelopment analysis and Malmquist Productivity Index approach. Engineering Economics, 27(2), 175–184.

39.

Tehrani

, Mehragan

M. R.

, & Golkani

M. R.

(2012). A model for evaluating financial performance of companies by data envelopment analysis: A case study of 36 corporations affiliated with a private organization. International Business Research, 5(8), 8.

40.

Treynor

J. L.

, & Ferguson

(1985). In defense of technical analysis. The Journal of Finance, 40(3), 757–773.

41.

, Sial

M. S.

, Shabbir

M. S.

, Moiz

, Wan

, & Cherian

(2020). Does higher population matter for labour market? Evidence from rapid migration in Canada. Ekonomska Istraživanja [Economic Research], 1–18.