Relationship between Operational Efficiency and Financial Performance

DECISION SCIENCES INSTITUTE of Indian Banks: An Application of Analytics (Full Paper Submission) Ramachandran Natarajan College of Business, Tennessee Technological University RNAT@tntech.edu Ravi Kumar Jain Symbiosis Institute of Business Management Hyderabad Campus, Symbiosis International University, Hyderabad, India rk.bandamutha@gmail.com Bhimaraya Metri International Management Institute New Delhi, India metriba@gmail.com ABSTRACT This paper investigates the relationship between operational efficiency and financial performance of Indian Banks. Operational performance is measured by variable returns to scale efficiency scores of Data Envelopment Analysis. Financial performance is measured by Capital Adequacy Ratio (), Return on Assets (ROA) and Non-Performing Assets (NPA) percentages. Correlation and multiple regression analytics were performed on the data from public and private sector banks and hypotheses were tested. The results show a statistically significant association between and efficiency scores, a statistically weak association between ROA and efficiency scores, and no statistical association between NPA and efficiency scores. KEYWORDS: Operational efficiency and financial performance; Indian banking sector; Technical efficiency of banks in India; Financial performance of banks in India. INTRODUCTION The review of the literature on performance of the banking sector seems to suggest that generally the studies have focused on financial performance or the productivity performance. A few studies have addressed the relationship between the financial and non-financial aspects of bank performance, but mainly in the context of Balanced Score Card (BSC). They do not investigate the relationship between the operational and financial performance. These studies are discussed in the literature review section. The reasons the methodologies used in those studies are not suited for the study in this paper are also discussed. There are several ways to measure operational efficiency and productivity in banks. In the context of banking, metrics such as revenue or business per employee and cost per employee, cost per $ of revenue have been used. These metrics are measures of partial productivities that take into account only one input (i.e., labor) while a more comprehensive metric that includes more than one input and output is desired. The efficiency scores of decision making units

(DMUs) of Data Envelopment Analysis (DEA) provide one such metric. However, in banking there is no agreement on what constitutes inputs and outputs. It all depends on how a bank is viewed, for example, as an intermediary or as a production unit. Also several models of a bank different types of inputs and outputs are available for DEA. This implies a choice has to be made among these alternatives. These issues and a rigorous approach for selecting the model of inputs and outputs to which DEA is applied, are discussed in the paper. For the selected models, the efficiency scores from the variable returns to scale (VRS) DEA model are calculated. The metrics for financial performance were selected to represent the three key dimensions of a bank s financial performance, i.e., a) capital adequacy b) profitability and c) asset quality. Capital adequacy is measured by Capital Adequacy Ratio (), profitability by Return on Assets (ROA) and asset quality by Gross Non-performing Assets (NPA) as percentage of assets/loans. It may be noted that they are related to CAMEL (Capital Adequacy, Asset Quality, Management Quality, Earning Quality, and Liquidity), a set of measures that has been used by researchers for examining the financial performance of banks. The relationship between the VRS efficiency scores and the three financial performance metrics is studied through correlation and regression analytics. The non-parametric Spearman correlation coefficient between the ranks of the VRS efficiency scores and ranks of the, ROA and NPA data are calculated separately. This is done for the combined data set of 28 public (state-owned) and 20 private banks and for the separate data sets of public banks, private banks, old private banks, and new private banks. The relationship is also investigated via multiple linear regression models where the ranking of VRS efficiency regression scores is the dependent variable and the rankings of the three financial metrics are the independent variables. Multiple regressions are performed on the combined (public and private) and separate ranks. Hypotheses were tested and the results were interpreted. The results show a statistically significant association between and efficiency scores, a statistically weak association between ROA and efficiency scores and the association between NPA and efficiency scores is statistically non-existent. There are many studies that assess either the financial performance or technical efficiency and productivity of banks in India but there is a gap in the studies that investigate the relationship between the financial and operational performances. This study contributes to the literature in the following ways. 1. It fills a gap in the studies that relate efficiency/productivity performance to financial performance, especially in the context of the Indian banks.2.it uses objective data that are consistent over time and the types of banks. It does not rely on survey or questionnaire responses that measure for example, customers perceptions of operational performance. 3. It uses a rigorous (Decision Tree) methodology for selecting the inputs and outputs of banks for computing the DEA operational efficiency scores. LITERATURE REVIEW Literature on Performance of Indian Banks Literature on banking has abundant references of studies devoted to assessing the performance of banks in India. Many studies in banking literature focused on the performance evaluation of Indian banking sector a special emphasis on comparison between banks across different ownership groups and assessing the impact of ownership on a bank s performance. Bhattacharya et al., (1997) conducted a study on 70 banks during the period 1986-91 to assess the impact of the limited liberalization initiated before the complete deregulation of the nineties

on the performance of the scheduled commercial banks operating in India. The study revealed that the public sector banks have shown greater efficiency, foreign and private banks having much lower efficiencies. However, the public sector banks started showing a decline in efficiency after 1987, while the private banks showed no change and the foreign banks showed a sharp rise in efficiency. Similarly, Sarkar, Sarkar and Bhaumik (1998) compared performances of public, private and foreign bank, operating in India, using two measures of profitability - return on assets and operating profit ratio - and four efficiency measures - net interest margin, operating profit to staff expense, operating cost ratio and staff expense ratio- to assess the ownership effect on the performance of a bank. The study found that the effect of ownership is weak when performance was compared between private banks and public sector banks. However, it was found that the ownership effect is strong on the performance in favor of foreign banks vis-à-vis private banks. Ram Mohan (2002) found a trend towards convergence in performance among the public, private and foreign banks respect to financial measures of performance. Petya Koeva (2003) examined the impact of liberalization on the performance of commercial banks in India in terms of the behavior of industry concentration, cost of intermediation, and profitability of the banking sector for a period between 1991-92 and 2000-01. The study revealed that the industry concentration has declined due to the entry of new domestic and foreign private banks during the period of study. The cost of financial intermediation and bank profitability had decreased significantly during the same period. The author also concluded that the nationalized banks had significantly lower profitability compared to that of private sector and foreign banks. Further, it is established that the factors like operational costs, priority sector lending, non-performing loans, investment in government securities and composition of deposits play an important role in explaining the variation in intermediation costs and profitability at bank level. Milind Sathye (2003) measured the productive efficiency of banks (publicly owned, privately owned and foreign owned) to study the impact of various market and regulatory initiatives on efficiency and profitability of banks in India ever since the implementation of financial sector reforms in the year 1992 and 1997. The study reveals that the mean efficiency score of banks in India compares well the world mean efficiency score and the efficiency of private sector commercial banks as a group is, paradoxically, lower than that of public sector banks and foreign banks in India. Deepak Khatri and Nitin Kumar (2004) studied the impact of ownership on the performance (measured in terms of ROA) of banks and found no evidence to believe that the competition or ownership has any impact on the banks performance. The authors observed that though the private and foreign banks appeared to have fared well during the initial period of the study, the public sector banks have caught up them in terms of performance efficiency. Shanmugam and Das (2004) measured the technical efficiency (TE) of banks operating in India across four different ownership groups State bank of India (SBI) group, nationalized banks (NBs), privately owned domestic banks and privately owned foreign banks - during the reform period, 1992 1999. The results indicate that the efficiency of raising interest margin is time invariant while the efficiencies of raising other outputs like non-interest income, investments and credits are time varying. It shows that SBI group and foreign banks are more efficient than the nationalized banks and privately owned banks. Ram Mohan and Subhash Ray (2004) compared efficiency and productivity of public sector banks (PSBs) private sector and foreign banks during the period 1992-2000. The authors used Tornqvist and Malmquist total factor productivity growth, as measures of productivity to draw the comparison between 27 PSBs, 21 old private sector banks and 14 foreign banks. They used interest income, investment income and non-interest income as outputs, and interest cost

and operating cost (which includes labor and non-labor, non-interest costs) as inputs. The study reveals that public sector banks are better in two cases and foreign banks are better in one case out of four sets of comparisons made. Sahoo et al., (2007) studied the productivity performance trends in terms of technical efficiency, cost efficiency and scale elasticity among Indian commercial banks for the period 1997-98 to 2004-05. The study concludes that there is a strong positive effect of the reform process on the performance of the overall banking sector in the country as reflected by an increasing average annual trend in technical efficiency for all groups of banks (public, private and foreign). The authors also concluded that the private banks have higher cost efficiency vis-à-vis the nationalized banks thus indicating the inability of nationalized banks to translate their learning experience into cost minimizing behavior. The findings also highlight that the possible stronger disciplining role played by the capital market indicating a strong link between market for corporate control and efficiency of private enterprise assumed by property right hypothesis. They also concluded that as far as the scale elasticity behavior is concerned the technology and market-based results differ significantly supporting the empirical distinction between returns to scale and economies of scale, often used interchangeably in the literature. In a similar study Mihir Das and Christabel Charles (2009), investigated the technical efficiency of forty nine select banks operating in India and concluded that foreign banks were relatively more efficient than their public and private sector counterparts; and that there was not much of a difference between the efficiency of public and private banks. However, the study finds a clear difference among the sample banks in terms of their utilization/underutilization of inputs and underproduction of outputs. Ahmed (2014) has studied the efficiency of regional rural banks (RRBs) a special reference to Meghalaya Rural Bank (MRB). The author studied the labor productivity (deposits, advances and total business on per employee basis) and branch productivity (deposits, advances and total business on per branch basis) across 58 branches of MRB, spread across 6 districts of Meghalaya, and concludes that MRB has achieved consistent improvement in productivity at par the average productivity of RRBs across India. This is notable given the fact that the state of Meghalaya is located in the remote part of north eastern India limited commercial activities. A similar trend is observed respect to the income, expenditure and profitability per employee and per branch basis and on total return on investment basis. The author concludes that despite MRB s performance being relatively better than that of the RRBs, a wide variation in its productivity across time is an area of concern. Gowda et al., (2013), conducted a comparative study on the performance of 59 banks across different ownership structures (public, private and foreign) over 5 years between 2006-2011 using CAMEL framework. The authors observe that excepting for capital adequacy ratio there is a significant difference in the performance of public, private and foreign banks reference to the other parameters (capital adequacy Management quality, Asset quality, earning ability, liquidity) of the CAMEL framework. Sharad and Sreeramulu (2009) compare the employee productivity and employee cost ratios between the traditional banks (public sector and old private sector banks) and modern banks (new private sector banks and foreign Banks) during the period from 1997 to 2008 and conclude that the performance of the modern banks was superior to that of the traditional banks though the gap has reduced significantly across on all the parameters studied over the period of the study. The study uses the parameters of employees productivity, i.e., business per employee (BPE) and profit per employee (PPE) and the parameters involving employees cost i.e., employee cost to operating expenses, employee cost to total business and employee cost to

total assets. It employs Gap Index analysis to study the difference in the performance of the sample banks. DEA Studies Bhattacharya et al., (1997) examined the efficiency of Indian banks using a two-step procedure, DEA technique to determine the technical efficiency and then applying stochastic frontier approach to explain variation in calculated efficiency. They applied intermediation approach using two inputs (interest expenses and operating expenses) and three outputs (deposits, advances and investments) of 70 banks, for the period 1986-1991. They constructed one grand frontier on the entire data set for DEA analysis and found that the public sector banks were more efficient than the foreign banks, which in turn were marginally more efficient than private sector banks. After performing a regression analysis in the second stage, they concluded that public sector bank efficiency declined over time whereas that of the foreign banks improved over time. The performance of the Indian private sector banks remained almost unchanged. Saha and Ravishanker (2000) studied the 25 Public Sector Banks (PSB) in India for the period 1992 to 1995 and provided a ranking based on DEA efficiency score. They used number of branches, number of employees, establishment expenses and non-establishment expenses as inputs and deposits, advances, investments, spread, total income, interest income and noninterest income as outputs. They found that the efficiency, in general, of PSBs improved over the time period of their study. Mukherjee et al., (2002) explored technical efficiency and benchmarked the performance of 68 commercial banks using DEA for the period 1996-1999. They observed that in India, public sector banks (PSBs) are more efficient than both private and foreign banks. Also, the performance of PSBs improved over the study period. Sathye (2003) measured the productive efficiency of 94 Indian banks (27 public sector commercial banks, 33 private sector commercial banks and 34 foreign banks) by using variable returns to scale input oriented model of the DEA methodology. Two models were constructed to show how efficiency scores vary change in inputs and outputs. The first model used interest expenses, non-interest expenses as inputs and net interest income and non-interest income as outputs. The second model used deposits and staff numbers as inputs and net loans and non-interest income as outputs. The study showed that the mean efficiency scores of Indian PSBs were higher than that of the private sector and foreign commercial banks in India and Indian PSBs compared well the world mean efficiency score. The study recommends that the existing policy of reducing non-performing assets and rationalization of staff and branches may be continued to make the Indian banks internationally competitive. Kumbhakar and Sarkar (2005) used stochastic frontier analysis (SFA) to evaluate the efficiency of public and private sector banks in India over the period 1986 to 2000. In Indian banking this translated into examining the effect of ownership, and especially the effect of the then deregulation measures. They found that the deregulation had led to an increase in the cost inefficiency of the Indian banks. The study also revealed that the private banks, on average, were generally more cost efficient than public banks. Das and Ghosh (2006) examined the performance of Indian commercial banking sector during the post reform period of 1992 2002 using non-parametric Data Envelopment Analysis (DEA). Three different approaches viz., intermediation approach, value-added approach and operating approach were employed to differentiate how efficiency scores vary changes in inputs and

outputs such as bank size, ownership, capital adequacy ratio, non-performing loans and management quality. They found that medium-sized public sector banks performed reasonably well and were more likely to operate at higher levels of technical efficiency. The empirical results also showed that technically more efficient banks were those that had, on an average, less nonperforming loans. Ataullah and Le (2006) examine the impact of various elements of economic reforms (ER) on the efficiency of banks in India during 1992 1998. Bank efficiency is measured using data envelopment analysis (DEA) and the relationship between the measured efficiency and various bank-specific characteristics and environmental factors associated the economic reforms were examined using the OLS (ordinary least square) and the GMM (generalized method of moments) estimations. They found that the efficiency of the banking industry improved during the post-er era due to the improvement in the efficiency of all three ownership groups, namely: public sector banks; domestic private banks; and foreign banks. They also found a positive relationship between the level of competition and the efficiency of banks. Sahoo and Tone (2009) studied the capacity utilization of Indian banking industry during 1997 to 2001 by using DEA. They adopted the intermediary approach to study the industry and used fixed assets, borrowed fund and labor as inputs along investments, performing loan assets and non-interest income as outputs. Their results found that increased competitive pressure after the liberalization of the banking industry helped to reduce excess capacity of the banking industry. Their study also highlighted that the short run cost was higher for the public sector banks than the private sector banks. Kumar & Gulati (2008)evaluated the technical efficiency of 27 PSBs operating in India and provided a ranking of these banks based on those efficiency scores the help of two popular data envelopment analysis (DEA) models, namely, CCR model and Andersen and Petersen s super-efficiency model (Anderson and Peterson, 1993) for the financial year 2004-2005. Their study found that only 7 (seven) of the 27 banks were efficient technical efficiency scores ranging from 0.632 to 1. Andhra Bank was the most efficient bank. The study also found that the banks affiliated State Bank of India (SBI) group were more efficient than the other public sector banks. The regression results indicated that the exposure to off-balance sheet activities, staff productivity, market share and size were the major determinants of the technical efficiency. Gupta et al., (2008) analyzed the performance of the Indian banking sector through DEA and found the determinants of productive efficiency through TOBIT model. Inputs (interest expenses and operating expenses) and outputs (interest income, fee based income and investment income) were measured in monetary value and efficiency scores determined for the period 1999-2003. The study found that SBI and its group had the highest efficiency, followed by private banks and the other nationalized banks. The results were consistent over the period, but efficiency differences diminished over period of time. For measuring productive efficiency through TOBIT, the authors used five independent variables, profitability, productivity, size, regulatory measures and asset quality and found that the capital adequacy ratio had a significantly positive impact on the productive efficiency whereas assets size had no significant influence. Therefore, bank efficiency was independent of the size of the bank. Zhao et al., (2008) examined the impact of regulatory reform on the performance of Indian commercial banks for a period of 1992 to 2004 using a balanced panel data set and employing a DEA-based Malmquist index of total factor productivity (TFP) change. The empirical results indicated that, after an initial adjustment phase, the Indian banking industry experienced sustained productivity growth, driven mainly by technological progress. Banks ownership

structure seems to have an impact on bank efficiency but does not appear to have an effect on total factor productivity change. Study revealed that during the deregulation process foreign banks appeared to be technological innovators, thereby increasing even further the competitive pressure in the Indian banking industry. While the Reserve Bank of India reports provide data on both financial, productivity and efficiency (measured by cost ratios and DEA) performance there is a void in the literature on studies relating the two types of performance for Indian banks,(reserve Bank of India Publications, 2013). There have been studies where the non-financial dimensions of performance such as customer satisfaction, timeliness, service quality were assessed from responses to surveys or interviews. The unit of the study was particular bank and its branches and the study were administered once at a given point of time (Mohamed and Hussain, 2010; Gunu Umar and Olabisi Jimoh Olatunde, 2011). Such data is not useful in studies such as the present one where the performance of many banks over several years are considered. HYPOTHESES AND MODELS The following hypotheses were tested for the public and private banks (old and new) combined and separately for Spearman Correlation Coefficients Ho: The VRS efficiency scores and are statistically independent Ho: The VRS efficiency scores and NPA are statistically independent Ho: The VRS efficiency scores and ROA are statistically independent To examine the combined effect of the three financial metrics on the operational efficiency, the following multiple regression model was specified. Y = a + b1*x1 + b2*x2 +b3*x3 (1) where Y is the dependent variable represented by the ranks of VRS efficiency scores,x1, X2 and X3 are the independent variables representing the ranks of, ROA, and NPA respectively. The following hypotheses were tested for the public and private banks combined and separately Ho: The slope coefficient for is zero Ho: The slope coefficient for ROA is zero Ho: The slope coefficient for NPA is zero Ho: The slope coefficients for, ROA and NPA are simultaneously zero vs. the Alternate Hypothesis that at least one slope coefficient is not zero. This hypothesis is tested by the F statistics obtained by ANOVA. METHODS This section is in two parts. The first subsection discusses the methodology used to derive the operational efficiency scores. The second subsection discusses the methodology for investigating the relationship between the efficiency scores and, NPA, and ROA each considered separately and together.

Method for Operational Efficiency Data Envelopment analysis (DEA), a non-parametric performance assessment methodology, was developed by Charnes, Cooper and Rhodes (Charnes et al., 1978) to measure the relative efficiencies of organizational units or decision making units (DMUs) under evaluation [in the present case thebanks] from the data for the same set of inputs and outputs. This technique aims to measure how efficiently a DMU (bank) uses the resources (inputs) available to generate a set of outputs. The DEA approach applies linear programming techniques to construct an efficient production frontier based on best practices over the data set. Each DMU s efficiency is then measured relative to this frontier. A majority of the studies related to efficiency in banking sector throughout the world have used DEA. The basic model of Charnes, Cooper and Rhodes, usually referred to as the CCR model, assumes constant returns to scale (CRS) and estimates the gross efficiency of a DMU which comprises the technical and scale efficiency. Technical efficiency describes efficiency in converting inputs to outputs, while scale efficiency recognizes that economy of scale cannot be attained at all scales of production and that there is one most productive scale size (MPSS) where the scale efficiency is maximum at 100 per cent (Banker, Charnes and Cooper, 1984). The BCC model takes into account the variation in efficiency respect to the scale of operation and separates scale efficiency from pure technical efficiency. The scale efficiency of a DMU can be computed as the ratio of its CRS efficiency to its VRS efficiency. The CRS efficiency of a DMU is always less than or equal to its pure technical (VRS) efficiency. The body of research assessing the technical efficiency of Decision Making Units (DMUs) a special reference to Indian banking sector suggests that a majority of these studies have employed Data Envelopment Analysis (DEA) for measuring technical efficiency twoinput/two-output or three-input/three-outputs or models several combinations of various input and output factors. In all most all the cases, the choice of input and output factors were based on the judgment of the researchers. They lack the rigorous justification pertaining to the appropriateness of or the efficacy of such input-output factors to measure the true technical efficiency of the DMUs. Typically, two different approaches are used to model a bank. a. Production Approach bank is defined as a typical production unit that use purchased inputs (physical assets like labor, space, material etc.) to provide services to customers. Often deposits and various bank assets are taken as proxies for quantum of services provided (produced) as outputs (Benston, 1965; Das and Ghosh, 2006; Kumar and Gulati, 2008). This approach is employed in studying the branch level efficiency of a bank. b. Intermediary Approach banks, as financial institution are viewed as intermediating funds between savers and borrowers. They produce intermediation services through collection of deposits and other liabilities and their application in interest earning assets, such as loans and advances, securities and other investments (Das and Ghosh, 2006; Kumar and Gulati, 2008).

For this paper, the intermediary approach is appropriate because the performance of a number of banks as opposed to the performance of branches of single bank is being considered. Table 1: DEA Models Used by Various Papers Discussed in Literature Review Section Model No. M 1 Ataullah & Le (2006) (Intermediary approach) Author/s Input Output M 2 Kumar & Gulati (2008) (Intermediary approach) M 3 Sathye (2003) (Intermediary approach) M 4 Kumbhkar and Sarkar (2004) (Value-added approach) M 5 Das & Ghosh (2006) (Production approach) M 6 Bhattacharjee et al. (1997) (Intermediary approach) M 7 Gupta et al. (2008) (Intermediary approach) M 8 Zhao et al. (2008) (Intermediary approach) M 9 Sathye (2003) (Intermediary approach) M 10 M 11 Das & Ghosh (2006)(Intermediary approach) Mukesh & Charles (2008) (Intermediary approach) Interest expenses, Operating expenses. Net fixed assets, Labor, Loanable fund Interest expenses, noninterest expenses. Labor, Capital, Operating cost Interest Expenses, Operating expenses, employee expenses Interest expenses, Operating expenses Interest expenses, Operating expenses Total Operating costs Deposits, Staff numbers Demand Deposits, savings Deposits, Fixed Deposits, Operating expenses, Labor expenses Total Expenses, Deposits Interest income, operating income Interest spread, non-interest income Net interest income, noninterest income Deposits, loans and advances, investment, no. of branches Net interest income, noninterest income Deposits, Advances, investments Interest income, Fee Based income, Investment income Total Loan, Fee based Income, Other earning assets Net loans, non-interest income Advances, Investments Total Loans, Other earning assets.

M 12 Zhao et al (2008) (Intermediary approach) M 13 Sahoo & Tone (2008) (Intermediary approach) Total Operating costs Fixed Assets, Borrowed Fund, Labor, Performing Loan, Fee based Income, Other earning assets Investments, non-interest income, Performing Loan assets The efficiency of the DMUs is measured by using a scientific method of input-output selection. Towards that end, this study evaluates eleven select DEA models representing the intermediary approach various input output factors and investigates the relationship between the computed efficiency scores and a single performance measure of DMUs by using Decision Tree approach, as suggested by (Lim, S, 2008). A set of eleven different input-output combinations representing intermediary approach (Table 1) from the literature that used fourteen different inputs and ten different outputs (Table 2) were selected for the first stage of analysis. Table 2: The List of Inputs and Output Factors Used in DEA Studies of Banks (Intermediary approach only) Interest expenses, Operating expenses. Non-interest expenses Net fixed assets, Loanable fund Labor (staff no.) Deposits, Demand Deposits, savings Deposits, Fixed Deposits, Inputs Factors Labor (employee) expenses Total Expenses Fixed Assets Borrowed Fund Interest Income, Operating Income Interest spread, Deposits, Advances (total loans) Output factors Investments (other earning assets) Fee Based income, Investment income Performing Loan, non-interest income First, the relative efficiency scores of 48 banks representing private and public commercial banks from eleven different variable returns to scale (VRS) DEA models input orientation are computed using standard DEA software. Decision Tree (DT) analysis is performed by T algorithm (Breiman et al, 1984) Gini Index as splitting criterion It is evident from the Tree shown in Figure 1 (see Appendix), that model M1 plays the most decisive role in classifying the banks into two classes; the first corresponding to those banks whose average change in operating income is above the median and the second class below the median. In other words, input-output factors from model M1 are the most appropriate in

measuring the true relative efficiency of a bank vis-a-vis other banks. Table 3 provides a summary of results from DT analysis. It can be observed from table that when the efficiency score from model M1 is higher than 0.904 and that from model M9 is higher than 0.7745, the probability of a bank belonging to the first class reaches 100%. This implies that model M9 plays the next decisive role in classifying the banks into better or otherwise. These results suggest that the management of a bank from our study should focus their efforts and resources on increasing the efficiency scores from model M1 to improve their ability to generate profits. The next best would be to focus on increasing the efficiency scores from model M9. The VRS technical efficiency score from the better of these two models, i.e., M1, is the measure of operational efficiency used in this paper (highlighted in bold and italics in Table 4 in the Appendix). Methods for Analyzing the Relationship between Operational and Financial Performance The relationship between the VRS efficiency score and the financial metrics, NPA and ROA are analyzed as follows. Exploratory data analysis in the form of histograms suggests the need to perform non-parametric analysis (see Table 4 & Figures 2-5 in the Appendix). The skewed nature of the distributions -especially for VRS efficiency scores - invalidates the assumptions of normality. Hence, the Spearman Correlation analysis is performed. The bank scores for VRS efficiency,, NPA and ROA were ranked in the order of performance. For VRS, and ROA, banks higher performance had higher ranks. For NPA, this meant that banks higher NPA were ranked lower. If certain banks had the same rank, the average of the rank for the bank if there were no ties was computed and assigned to each bank in the tie. Spearman correlation coefficient was computed the formula (see Appendix) that took into account the ties (see Tables5, 6, and 7 in the Appendix). RESULTS The results of the Spearman s Correlation analysis are given in Tables 11a and 11b Table 11a: Spearman s Correlation Coefficient (rs)and Tests of Hypotheses Critical Values Public and Private Banks Combined (n= 48) z=1.96 (two tailed.05) 0.2859 z=1.645 (one tailed.05) 0.2399 z=2.57 (two tailed.01) 0.3748 z=2.33 (one tailed.01) 0.3398 0.738 Reject Ho at 5% and 1% levels Public Banks (n= 28) 0.377 (two tailed,.05) 0.317 (one tailed,.05) 0.496 (two tailed, 0.01) 0.448 (one tailed, 0.01) 0.722 Reject Ho at 5% and 1% levels Private Banks (n= 20).45 (two tailed,.05) 0.377 (one tailed,.05).0.591 (two tailed,.01) 0.522 (one tailed,.01) 0.751 Reject Ho at 5% and 1% levels

Public and Private Banks Combined (n= 48) Public Banks (n= 28) Private Banks (n= 20) NPA 0.045 Do not Reject Ho -0.041 Do not Reject Ho 0.272 Do not Reject Ho ROA 0.632 Reject Ho at 5% and 1% levels 0.597 Reject Ho at 5% and 1% levels 0.682 Reject Ho at 5% and 1% levels Table 11b: Spearman s Correlation Coefficient (rs) and Tests of Hypotheses Old Private Banks n=13 New Private Banks n=7 Critical Values 0.560 (two tailed.05) 0.483(one tailed.05) 0.703(two tailed.01) 0.648(one tailed.01) 0.786 (two tailed.05) 0.714(one tailed.05) 0.929(two tailed.01) 0.893 (one tailed.01) 0.597 Reject Ho at 5% level NPA 0.188 Do not Reject Ho ROA 0.807 Reject Ho at 5% and 1% levels 0.678 Do not Reject Ho 0.036 Do not Reject Ho 0.321 Do not Reject Ho For n greater than or equal to 30, the quantity rs*sq.rt (n-1) is approximately standard normal. For n less than 30, the critical values for Spearman s Correlation Coefficient rs is read from the tables. The results form Table 11ashow that for all banks and for public and private banks that operational efficiency is positively correlated and ROA but it is statistically independent of NPA. If we consider old and new private sector banks separately, then for the old private banks similar results as the above are obtained (see Table 11b) but for new private banks, VRS efficiency is not statistically associated any of the financial performance metrics (see Table 11b).However, this result is not robust enough because of the small sample size (n=7). The results of the multiple regression analysis are given in Tables 8, 9, and 10,(see Appendix) and summarized in Table 12.

Table 12: Multiple Regression Results and Tests of Hypotheses Public and Private Banks Combined (n= 48) Public Banks (n= 28) Private Banks (n= 20) R Square 0.614083 0.568882 0.643768 Slope Coefficient b1 Prob Value for Slope Coefficient b1 ROA Slope Coefficient b2 0.55293 0.577659 0.54214 1.53E-05 Reject Ho at 5% and 1% levels 0.002237 Reject Ho at 5% and 1% levels 0.01263 Reject Ho at 5% level 0.312795 0.253099 0.291886 ROA Prob Value for Slope Coefficient b2 NPA Slope Coefficient b3 0.008753 Reject Ho at 5% and 1% levels 0.141817 Do not Reject Ho 0.170623 Do not Reject Ho 0.070474 0.052537 0.105321 NPA Prob Value for Slope Coefficient b3 0.453232 Do not Reject Ho 0.703186 Do not Reject Ho 0.51353 Do not Reject Ho F Significance from ANOVA 3.41786E-09 Reject Ho at 5% and 1% levels 0.000129 Reject Ho at 5% and 1% levels 0.000715 Reject Ho at 5% and 1% levels The results given in Table 12 above lead to two unambiguous conclusions: 1) independent variable has a positive slope coefficient for all banks and also for public and private banks considered separately. Increases in are associated increases in operational efficiency.2) there is no statistically discernible linear relationship between operational efficiency and NPA. This holds for all banks and also for public and private banks considered separately. DISCUSSION AND CONCLUSIONS From the data analysis (see Tables11a, 11b, and 12) the following can be concluded: 1. The positive and strong association of operating efficiency of a bank provides evidence to conclude that a bank s operating efficiency is strongly rooted in its ability to absorb any business risk emerging out of market uncertainty. This association essentially reflects the fact that a bank that maintains better can cope market aberrations resilience and continue its operations. This contributes to profitability in the both long and short run. These results (beta coefficients) also indicate that the relation between and operational efficiency holds good for public and old private banks. This is in agreement the results obtained by Gupta et al., (2008) in their study. The contrary result for the new private banks is to be interpreted caution because of the small sample size.

2. The analysis also supports the conclusion that a better technical/operational efficiency may - but not necessarily always -translate into a better financial performance or better profitability. Thus suggesting a weak positive association between ROA and VRS. This implies that an operationally efficient bank may have below par financial performance and vice versa. In other words a bank may be efficient in utilizing its operating resources optimally while their financial assets may be troubled thus affecting its profitability and ability to do well in business. 3. The results also support that the quality of assets of a bank, as measured by NPA, is not reflected in its operating efficiency. This implies that the quantum of NPA on a bank s books will not have any bearing on its operational efficiency. NPA is a financial entry indicating the quantum of potentially troubled assets which may affect, if they go bad, the profitability and erode the capital in future but may not have any impact on the bank s ability to conduct business (advances, deposits and other revenue generating activities). While one can attribute a business logic that higher the quantum of troubled loans a bank has, greater will be the risk of failure and lesser the propensity to expand loan portfolio, thus affecting profitability. However, the evidence does not show any statistically significant direct association/correlation between NPA and VRS. It is to be noted that this contradicts the results of the study by Das and Ghosh (2006). 4. It is noteworthy that the association between VRS and financial performance as measured by, ROA and NPA holds across the public and private banks in the Indian context both when the financial measures are considered separately and as well as collectively. These results may not be generalizable to the banks in other countries.

APPENDIX The DEA formulation, according to Banker, Charnes, and Cooper (1984) of input minimization an assumption of variable returns to scale (VRS) to calculate the efficiency scores is given below. The relative efficiency of a Decision Making Unit DMUo is obtained from the following linear programming (LP) model: Min θ 0subject to n θ ox ijo j x ij 0, j = 1 i = 1,, m n jy r j y rjo, j = 1 r = 1,, s n j = 1 j= 1,, n (convexity constraint) j = 1 j 0, j= 1,, n where, y rj is the amount of the r th output of DMU j, x ij is the amount of the i th input to DMU j, λ j are the weights of DMU j and θ is the shrinkage factor. The model seeks a set of non-negative λ values which add up to 1 and which minimizes θ 0 to θ 0* and identifies a point in the production possibility set which uses the lowest proportion θ 0* of input levels of DMU j while offering output levels which are at least as high as those of DMU j. This point is a composite DMU corresponding to the linear combination of efficient DMUs: n n * j x ij, * j y rj j = 1 j = 1 It can be said that: n n i = 1,...,m and r = 1,...,s. * j x ij, * j y rj out performs (θ 0x j0, y j0) when θ 0* < 1 j = 1 j = 1 The VRS LP is identical to the CRS LP, except we include the convexity constraint. The convexity constraint ensures that the DMUs that are operating at different scales are recognized as efficient. It also ensures that DMUS are only benchmarked other DMUs of similar size.

Figure 1: Results of Decision Tree Analysis 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 Figure 2: Distribution of VRS Efficiency scores VRS Efficiency 75-80 81-85 86-90 91-95 96-100 14 12 10 8 6 4 2 0 Public Banks Private Banks

1 0.8 0.6 0.4 0.2 0 Figure 3: Distribution of 20 15 10 5 0 Public Banks Private Banks Figure 4: Distribution of NPA NPA% 1 0.8 0.6 0.4 0.2 0 9 8 7 6 5 4 3 2 1 0 Public Banks Private Banks Figure 5: Distribution of ROA ROA% 1.00 0.80 0.60 0.40 0.20 0.00 10 8 6 4 2 0 Public Bank Private Bank

Table 3: Pattern of Efficiency Scores and the Probabilities of the Rate of Increase in Operating Income Being Above the Median Type Pattern of efficiency scores Probability 1 M1<.904; M6<.833 0% 2 M1<.904; M6>=.833 20% 3 M1>=.904; M9<.7745;M2<.113 80% 4 M1>=.904; M9<.7745;M2>=.113 40% 5 M1>=.904; M9>=.7745; 100% Table 4: Technical and Scale Efficiencies of Banks in India using DEA Models M1 and M9 DEA Models -> M1 M9 Name Category VRS Scale VRS Scale INDIA Public 1 0.908 1 0.794 INDORE Public 0.915 0.998 0.549 0.994 BIKANER AND JAIPUR Public 0.919 0.995 0.816 0.99 HYDERABAD Public 0.975 0.968 0.775 0.995 MYSORE Public 0.917 1 0.829 0.991 PATIALA Public 0.992 0.972 0.791 0.997 SAURASHTRA Public 0.897 0.969 0.453 0.99 TRAVANCORE Public 0.928 0.985 0.83 0.992 PUNJAB AND SIND BANK Public 0.876 0.983 0.72 0.994 CENTRAL BANK OF INDIA Public 0.909 0.945 0.677 0.999 BANK OF BARODA Public 0.995 0.953 0.781 0.999 BANK OF INDIA Public 0.991 0.939 0.801 0.999 CANARA BANK Public 1 0.919 0.736 0.999 PUNJAB NATIONAL BANK Public 1 0.969 0.856 0.912 UCO BANK Public 0.927 0.957 0.735 0.993 INDIAN OVERSEAS BANK Public 0.952 0.959 0.777 0.999 SYNDICATE BANK Public 0.937 0.967 0.78 0.993 UNION BANK OF INDIA Public 0.993 0.95 0.801 0.993 ANDHRA BANK Public 0.982 0.97 0.794 0.999 ORIENTAL BANK OF COMMERCE Public 1 0.985 0.739 0.998 UNITED BANK OF INDIA Public 0.892 0.969 0.649 0.991

DEA Models -> M1 M9 Name Category VRS Scale VRS Scale INDIAN BANK Public 0.961 0.971 0.754 0.993 ALLAHABAD BANK Public 0.955 0.964 0.733 0.999 VIJAYA BANK Public 0.907 0.977 0.716 0.996 DENA BANK Public 0.896 0.987 0.747 0.996 CORPORATION BANK Public 1 0.963 0.801 1 BANK OF MAHARASHTRA Public 0.898 0.967 0.699 0.999 IDBI BANK LIMITED Public 1 1 0.867 0.688 HDFC BANK. Private 1 1 0.894 0.986 ICICI BANK LIMITED Private 1 0.959 1 1 AXIS BANK LIMITED Private 0.99 0.981 0.847 1 KOTAK MAHINDRA BANK. Private 1 1 0.841 0.999 JAMMU & KASHMIR BANK Private 1 1 0.657 0.997 FEDERAL BANK Private 1 1 0.755 0.999 DEVELOPMENT CREDIT BANK. Private 0.815 0.977 0.667 1 CITY UNION BANK LIMITED Private 1 1 0.814 0.999 TAMILNAD MERCANTILE BANK Private 0.973 0.997 0.774 0.998 LAKSHMI VILAS BANK Private 0.896 0.995 0.746 0.999 THE DHANALAKSHMI BANK Private 0.799 0.981 0.743 0.992 CATHOLIC SYRIAN BANK Private 0.813 0.997 1 1 YES BANK. Private 0.977 0.97 0.817 0.84 UNITED WESTERN BANK (acquired by IDBI 2006) Private 0.826 0.999 0.279 0.962 KARUR VYSYA BANK Private 0.964 0.999 0.835 0.999 BANK OF RAJASTHAN (merged ICICI in 2010) Private 0.824 0.971 0.472 0.996 SOUTH INDIAN BANK Private 0.928 1 0.778 0.996 INDUSIND BANK Private 0.943 0.996 0.831 1 KARNATAKA BANK Private 0.901 0.998 0.662 0.996 ING VYSYA BANK Private 0.865 0.999 0.811 0.993

Table 5: Scores and s of VRS,, NPA and ROA of Public and Private Sector Banks Bank VRS Scores VRS NPA% NPA ROA % ROA ALLAHABAD BANK 95.5 25 9.87 31 2.52 16 0.815 40.5 ANDHRA BANK 98.2 31 10.05 35 1.45 32.5 0.965 47 AXIS BANK LIMITED 99 32 9.98 34 0.90 43 1.000 48 BANK OF BARODA 99.5 36 10.34 39 2.57 13 0.815 40.5 BANK OF INDIA 99.1 33 6.59 5 2.58 12 0.665 27 BANK OF MAHARASHTRA BANK OF RAJASTHAN 89.8 12 9.27 26 3.03 5 0.536 15 82.4 4 5.36 4 0.98 39 0.041 3 CANARA BANK 100 42.5 10.30 38 1.75 25.5 0.814 39 CATHOLIC SYRIAN BANK CENTRAL BANK OF INDIA CITY UNION BANK LIMITED CORPORATION BANK 81.3 2 6.78 6 1.50 31 0.142 5 90.9 15 8.04 11 3.12 3 0.428 10 100 42.5 8.62 19 0.77 44 0.831 42 100 42.5 11.10 43 1.55 30 0.903 46 DENA BANK 89.6 9 7.92 10 2.43 17 0.634 22 DEVELOPMENT CREDIT BANK. 81.5 3 8.06 12 4.01 1-0.037 2 FEDERAL BANK 100 42.5 11.76 46 3.08 4 0.659 24 HDFC BANK. 100 42.5 11.10 44 0.70 45 0.308 6 ICICI BANK LIMITED 100 42.5 10.95 41 2.04 20 0.662 25 IDBI BANK LIMITED 100 42.5 10.97 42 1.65 27 0.484 11 INDIAN BANK 96.1 26 9.22 25 1.29 36 0.879 44 INDIAN OVERSEAS BANK 95.2 24 9.93 33 2.60 11 0.638 23 INDUSIND BANK 94.3 23 10.06 36 0.92 42 0.702 31 ING VYSYA BANK 86.5 6 9.16 24 1.84 24 0.558 16

Bank JAMMU & KASHMIR BANK KARNATAKA BANK KARUR VYSYA BANK KOTAK MAHINDRA BANK. LAKSHMI VILAS BANK ORIENTAL BANK OF COMMERCE PUNJAB AND SIND BANK PUNJAB NATIONAL BANK SOUTH INDIAN BANK BIKANER AND JAIPUR HYDERABAD INDIA INDORE MYSORE PATIALA SAURASHTRA TRAVANCORE VRS Scores VRS NPA% NPA ROA % ROA 100 42.5 10.63 40 1.40 35 0.748 33 90.1 13 8.56 18 1.94 22 0.515 14 96.4 27 9.74 30 0.96 40 0.765 35 100 42.5 12.67 48 1.41 34 0.754 34 89.6 10 7.31 8 1.75 25.5 0.415 9 100 42.5 9.37 28 2.92 6 0.783 38 87.6 7 8.45 13 2.75 8 0.588 18 100 42.5 10.10 37 2.78 7 0.882 45 92.8 20.5 9.92 32 0.94 41 0.572 17 91.9 18 8.70 20 1.61 29 0.673 28 97.5 29 8.55 17 1.24 37 0.497 13 100 42.5 11.79 47 3.23 2 0.766 36 91.5 16 7.27 7 1.45 32.5 0.663 26 91.7 17 9.12 23 2.56 14.5 0.682 29 99.2 34 8.50 15 1.63 28 0.617 20 89.7 11 2.88 2 0.31 46 0.097 4 92.8 20.5 8.86 21 2.12 19 0.769 37 SYNDICATE BANK 93.7 22 8.89 22 2.56 14.5 0.727 32

Bank TAMILNAD MERCANTILE BANK THE DHANALAKSHMI BANK VRS Scores VRS NPA% NPA ROA % ROA 97.3 28 3.03 3 0.30 47 0.403 8 79.9 1 8.47 14 1.13 38 0.331 7 UCO BANK 92.7 19 8.53 16 2.73 9 0.628 21 UNION BANK OF INDIA UNITED BANK OF INDIA UNITED WESTERN BANK 99.3 35 9.50 29 2.67 10 0.875 43 89.2 8 7.68 9 2.31 18 0.488 12 82.6 5 1.15 1 1.85 23-0.077 1 VIJAYA BANK 90.7 14 9.29 27 1.97 21 0.595 19 YES BANK. 97.7 30 11.69 45 0.13 48 0.696 30 Table 6: Scores and s of VRS,, NPA and ROA of Public Sector Banks Public Bank VRS Scores VRS NPA% NPA ROA % ROA ALLAHABAD BANK 95.5 15 9.87 15 2.52 14 0.815 22.5 ANDHRA BANK 98.2 18 10.05 18 1.45 24.5 0.965 28 BANK OF BARODA 99.5 22 10.34 22 2.57 11 0.815 22.5 BANK OF INDIA 99.1 19 6.59 19 2.58 10 0.665 14 BANK OF MAHARASHTRA 89.8 5 9.27 5 3.03 3 0.536 6 CANARA BANK 100 25.5 10.30 25.5 1.75 19 0.814 21 CENTRAL BANK OF INDIA CORPORATION BANK 90.9 7 8.04 7 3.12 2 0.428 2 100 25.5 11.10 25.5 1.55 23 0.903 27 DENA BANK 89.6 3 7.92 3 2.43 15 0.634 11 IDBI BANK LIMITED 100 25.5 10.97 25.5 1.65 20 0.484 3

Public Bank VRS Scores VRS NPA% NPA ROA % ROA INDIAN BANK 96.1 16 9.22 16 1.29 26 0.879 25 INDIAN OVERSEAS BANK ORIENTAL BANK OF COMMERCE PUNJAB AND SIND BANK PUNJAB NATIONAL BANK BIKANER AND JAIPUR HYDERABAD INDIA INDORE MYSORE PATIALA SAURASHTRA TRAVANCORE 95.2 14 9.93 14 2.60 9 0.638 12 100 25.5 9.37 25.5 2.92 4 0.783 20 87.6 1 8.45 1 2.75 6 0.588 7 100 25.5 10.10 25.5 2.78 5 0.882 26 91.9 10 8.70 10 1.61 22 0.673 15 97.5 17 8.55 17 1.24 27 0.497 5 100 25.5 11.79 25.5 3.23 1 0.766 18 91.5 8 7.27 8 1.45 24.5 0.663 13 91.7 9 9.12 9 2.56 12.5 0.682 16 99.2 20 8.50 20 1.63 21 0.617 9 89.7 4 2.88 4 0.31 28 0.097 1 92.8 12 8.86 12 2.12 17 0.769 19 SYNDICATE BANK 93.7 13 8.89 13 2.56 12.5 0.727 17 UCO BANK 92.7 11 8.53 11 2.73 7 0.628 10 UNION BANK OF INDIA UNITED BANK OF INDIA 99.3 21 9.50 21 2.67 8 0.875 24 89.2 2 7.68 2 2.31 16 0.488 4 VIJAYA BANK 90.7 6 9.29 6 1.97 18 0.595 8

Table 7a: Scores and s of VRS,, NPA and ROA of Private Sector Banks Private Bank THE DHANALAKSHMI BANK CATHOLIC SYRIAN BANK DEVELOPMENT CREDIT BANK. BANK OF RAJASTHAN UNITED WESTERN BANK ING VYSYA BANK LAKSHMI VILAS BANK KARNATAKA BANK SOUTH INDIAN BANK VRS Scores VRS NPA% NPA ROA % ROA 79.9 1 9.98 13 0.90 16 1.000 20 81.3 2 5.36 3 0.98 12 0.041 3 81.5 3 6.78 4 1.50 8 0.142 4 82.4 4 8.62 9 0.77 17 0.831 19 82.6 5 8.06 6 4.01 1-0.037 2 86.5 6 11.76 19 3.08 2 0.659 12 89.6 7 11.10 17 0.70 18 0.308 5 90.1 8 10.95 16 2.04 3 0.662 13 92.8 9 10.06 14 0.92 15 0.702 15 INDUSIND BANK 94.3 10 9.16 10 1.84 6 0.558 10 KARUR VYSYA BANK TAMILNAD MERCANTILE BANK 96.4 11 10.63 15 1.40 10 0.748 16 97.3 12 8.56 8 1.94 4 0.515 9 YES BANK. 97.7 13 9.74 11 0.96 13 0.765 18 AXIS BANK LIMITED 99 14 12.67 20 1.41 9 0.754 17 HDFC BANK. 100 17.5 7.31 5 1.75 7 0.415 8 ICICI BANK LIMITED 100 17.5 9.92 12 0.94 14 0.572 11 KOTAK MAHINDRA BANK. JAMMU & KASHMIR BANK 100 17.5 3.03 2 0.30 19 0.403 7 100 17.5 8.47 7 1.13 11 0.331 6 FEDERAL BANK 100 17.5 1.15 1 1.85 5-0.077 1 CITY UNION BANK 100 17.5 11.69 18 0.13 20 0.696 14