A data envelopment analysis approach for ranking Iranian banks based on financial indices

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1 A data evelopmet aalysis approach for rakig Iraia baks based o fiacial idices Pariaz Zarehparvari, Zahra Alipour Darvish Departmet of Iformatio Techology, North brach of Islamic Azad Uiversity, Tehra, Ira Abstract There are may performace aalysis techiques cocetrates o evaluatig efficiecy of orgaizatios. As a part of them, data evelopmet aalysis is a popular maagemet tool, aims at evaluatig the efficiecy of decisio makig uits based o a o-parametric approach. This paper will focus o the metioed techique ad perform a case study o some Iraia baks to ivestigate their efficiecy ad rakig those usig data evelopmet aalysis method. This study compares the metioed baks i two mai areas, called operatioal efficiecy ad beeficial efficiecy. Aalyzig the obtaied results will determie the superiority of outstadig bak. Keywords- Data evelopmet aalysis; Decisio makig uit; Bak efficiecy; Noparametric compariso. 1- Itroductio Performace aalysis is a importat issue i orgaizatios leads maagers to make suitable decisios ad hereby improve the efficiecy. Oe the most powerful methods for such aalysis is data evelopmets aalysis. Data evelopmet aalysis (DEA) refers to a well-kow o parametric techique aims at evaluatig the efficiecy of uits based o iput-output aalysis. The iceptio of DEA is preseted i Farrell (1957) where ecoomic research motivatios raise the eed of developig better methods for evaluatig productivity fuctios. However, Farrell did ot carry his developmets to a poit which distiguishes betwee both Farrell efficiet ad Pareto-Koopmas efficiet categories (Pareto, 1927; Koopmas, 1951), referred to as weak efficiecy ad strog efficiecy, respectively (Cooper et al., 2007). The moder versio of DEA origiates from the ideas of Chares, Cooper, ad Rhodes (CCR) through mathematical formulatios. The fudametal idea behid DEA is to provide a methodology whereby a set of bechmark DMUs forms a efficiet frotier ad furthermore this methodology is able to measure the level of efficiecy of iefficiet uits. The idicator set of the DMUs is divided ito two iput ad output categories ad DEA approach attempts to maximize the ratio of weighed outputs to weighted iputs, as a covetioal efficiecy criterio. Sice the very begiig of DEA studies, several extesios of the CCR model have bee developed, such as what Baker, Chares, ad Cooper (BCC) propose to produce frotiers spaed by the covex hull of the existig DMUs (Baker et al., 1984). There have bee several recet reviews that cover both practical ad theoretical developmets of DEA (Cooper et al., 2007; Emrouzejad et al., 2008; Cook ad Seiford, 2009). Other related works ca be foud i Kao ad Lio (2014), Kaur ad Gupta (2015), LaPlate ad Paradi (2015), Razavi Hajiaghaie et al. (2015), Tajbakhs ad Hassii (2015). Despite of the previous models which were based o the simple fiacial ratio, DEA focuses o the ratio of output/iput ad hece aalyzes the effectiveess accordigly. DEA is a icreasigly popular maagemet tool is commoly used to evaluate the efficiecy of a umber of producers. A typical statistical approach is characterized as a cetral tedecy approach ad it evaluates producers relative to a average producer I cotrast, DEA compares each producer with oly the "best" producers. By the way, i the DEA literature, a producer is usually referred to as a decisio makig uit or DMU. DEA is ot always the right tool for a problem but is appropriate i certai cases discussed as stregths ad limitatios of DEA. I DEA, there are a umber of producers. The productio process for each producer is to take a set of iputs ad produce a set of outputs. Each producer has a varyig level of iputs ad gives a varyig level of outputs. For istace, cosider a set of baks. Each bak has a certai umber of tellers, a certai square footage of space, ad a certai umber of maagers (the iputs). There are a umber of measures of the output of a bak, icludig umber of 114

2 checks cashed, umber of loa applicatios processed, ad so o (the outputs). DEA attempts to determie which of the baks are most efficiet, ad to poit out specific iefficiecies of the other baks. A fudametal assumptio behid this method is that if a give producer, A, is capable of producig Y A uits of output with X A iputs, the other producers should also be able to do the same if they were to operate efficietly. Similarly, if producer B is capable of producig Y B uits of output with X B iputs, the other producers should also be capable of the same productio schedule. Producers A, B ad others ca the be combied to form a composite producer with composite iputs ad composite outputs. Sice this composite producer does ot ecessarily exist, it is typically called a virtual producer. The heart of the aalysis lies i fidig the "best" virtual producer for each real producer. If the virtual producer is better tha the origial producer by either makig more output with the same iput or makig the same output with less iput the the origial producer is iefficiet. The subtleties of DEA are itroduced i the various ways that producers A ad B ca be scaled up or dow ad combied. Because of the advatages of this method, it has bee received much attetio ad therefore there ca be foud a rich literature i DEA area. 2- Data evelopmet aalysis I decisio makig area, the term DEA refers to a o-parametric techique aims at determiig the efficiecy of DMUs based o the iput/output aalysis. DEA suggests a more efficiet combiatio of iputs ad/or outputs to improve the efficiecy of a DMU. There are two geeral approaches i DEA models. The first is to reduce iputs i a costat level of outputs ad hece called iput based model. While the secod approach suggests icreasig the outputs i a costat level of iputs. I the other had, DEA is a liear programmig procedure for a frotier aalysis of iputs ad outputs. DEA assigs a score of 1 to a uit oly whe comparisos with other relevat uits do ot provide evidece of efficiecy i the use of ay iput or output. DEA assigs a efficiecy score less tha oe to (relatively) iefficiet uits. A score less tha oe meas that a liear combiatio of other uits from the sample could produce the same vector of outputs usig a smaller vector of iputs. The score reflects the radial distace from the estimated productio frotier to the DMU uder cosideratio. For a detailed descriptio, lets X i ad Y i be the iput ad output vector of i th DMU, respectively. Also X 0 ad Y 0 be the similar otatios for the DMU that we wat to determie its efficiecy. The, the iput based approach ca be modeled as follows: Mi θ i=1 λ i X i θx 0 (1) i=1 λ i Y i Y 0 λ i 0 Where, θ is the efficiecy of the DMU0 ad also λ i is iputs ad outputs weights. So, θ ad λ i are decisio variables. Aother type of DEA based o outputs is also available. Model 2 describes the mathematical programmig model of output based DEA. Max θ i=1 λ i Y i θy 0 (2) i=1 λ i X i X 0 λ i 0 The efficiecy of DMU with θ = 1 meaig that the uit is efficiet. Otherwise, if the value of θ is less tha 1, the correspodig DMU is cosidered as a iefficiet oe that is a liear combiatio with curret iputs ca be foud with more level of output. 3- Methodology of Baks rakig usig DEA 115

3 As metioed i sectio 1, the mai purpose of this research is to performace aalysis of some Iraia baks ad rakig them ad hereby facilitatig maager decisios to achieve a suitable level of efficiecy. For this aim, the items at below are cosidered to be obtaied after the research carried out: Determiig the efficiecy of each bak from operatioal ad beeficial aspects. Idicatig the iefficiet baks accordig to the experimets. Providig a bechmark guidelie for iefficiet baks accordig to the efficiet oes. Rakig the efficiet baks. This research cosiders two mai areas for determiig the efficiecies called operatioal ad beeficial aspects. Operatioal area, usually, focuses o bak visios ad costumers satisfactio of the bak ad the ext aspect, beeficial, teds to ivestigate those regardig ivestmets, beefits ad other fiacial viewpoits. This study cocetrates o five Iraia baks itroduced i Table 1. Table 1- List of baks Number Bak Name 1 Eqtesad Novi 2 Saderat 3 Pasargad 4 Parsia 5 Mellat Iput ad output variables are selected usig expert statemets. I some cases, two or more idices are combied to form a ew variable. The variables are demostrated i Figure 1 for both operatioal ad beeficial areas. Operatioal: Beeficial: Iputs 1- Staffs of electroic services 2- Iterest free costs 3- Iterest Costs Iputs 1- Deposits 2- Loas 3- Trasactios 4- Profits of complemetary services Outputs 1- Deposits 2- Loas 3- Trasactios Outputs 1- Iterest icomes 2- Iterest free icomes 4- Profits of complemetary services Figure 1- Iput ad output variables for operatioal ad beeficial areas Beside of the variables, the weights should also be iitialized. We applied a multi-attribute decisio makig scheme for this aim. I this regard, couple compariso matrix i aalytic hierarchical process (AHP) is used for comparig differet variables. Each matrix is filled by a expert ad the all weights are determied accordigly. Table 2 ad 3 show the obtaied weights for beeficial ad operatioal areas, respectively. Table 2- Iput ad output weights i beeficial area 116

4 Variable Deposits Loa Trasactios Profits of complemetary services Iterest icomes Iterest free icomes Weights Variable Staffs of electroic services Table 3- Iput ad output weights i operatioal area Iterest cost Iterest free cost Deposits Loa Trasactios services Weights After determiig the weights of iput ad output variables, the ext step iclude solvig DEA models with obtaied data ad aalyzig the results. The ext sectio cotais all umerical experimets ad such aalysis. 4- Numerical experimet ad model aalysis Durig the aforemetioed sectios, the methodology of the curret research was described. The curret sectio of this research is assiged to solve the DEA models for 5 itroduced baks ad rak them usig the efficiecy measure. All of the computatios i this sectio are doe usig LINGO 11.0 software o a system with 2.7GH CPU ad 4 GB of RAM. Because all models were solve withi a acceptable time, the CPU time is ot reported i umerical studies. Ivestigatig the DMUs should be partitioed ito the two mai subsectios oe of them discusses operatioal area, while the ext oe aalyzes the beeficial part of the work. The subsectios at below preset the obtaied DEA aalysis Operatioal ivestigatio This subsectio is ot aythig more tha a DEA aalysis usig the operatioal iputs/outputs ad rakig the uder study baks, accordigly. Rememberig that there were 7 factors icludig 3 iputs ad 4 outputs ad also recallig the weights oe ca easily use a dual model of BCC for ruig the experimetal study. The outcomig results for DMUs are appeared as Figure

5 Figure 2- The results for efficacy of DMU 1 i operatioal area If the value of objective fuctio is equal to 1, the the DMU is a techical efficiet uit. However, the less value implies that the DMU is o-techical oe. Accordig to the results, the objective fuctio is equal to which is a o-techical uit ad the value of iefficiecy is equal to This ivestigated DMU is Eqtesad Novi bak. Similar to this, other DMUs should be ivestigated by DEA model ad compared i terms of the efficiecy measure to provide a rakig scheme. Without less of geerality, we focus o efficiet/iefficiet measures ad igore the value of efficiecy. Table 4, outlies the baks i terms of the metioed measures Beeficial ivestigatio Table 4- Operatioal efficiecy of Baks Bak Name Status Eqtesad Novi Iefficiet Saderat Iefficiet Pasargad Iefficiet Parsia Efficiet Mellat Efficiet Similarly, for beeficial area such aalyzig procedure ca be doe to idicate the efficiecy of each bak. As a istace, Figure 3 illustrates the obtaied results of software for DMU

6 Figure 2- The results for efficacy of DMU 1 i beeficial area It is obvious that DMU 1 is ot efficiet i terms of the beeficial measures, meaig that the objective fuctio is ot equal to 1. The efficiecy of this uit ca be computed by iverse value of objective fuctio ad hece is equal to The value of iefficiecy is , accordigly. Table 5 demostrates a outlied report of the results. Table 5- beeficial efficiecy of Baks Bak Name Status Eqtesad Novi Iefficiet Saderat Iefficiet Pasargad Iefficiet Parsia Iefficiet Mellat Iefficiet I operatioal area, Parsia bak is efficiet. This efficiecy comes from this fact that there is a suitable level of icomes from automatic teller systems (ATM), iterest loas ad ivestmets i this bak. Also, all costs due to the admiistrative expeses are miimized. That is why Mellat bak is also a efficiet oe. However, i beeficial area, oe of the baks are efficiet. 5- Coclusio This paper, studied efficiecies of some fiacial istitutio usig a well-kow oparametric techique called DEA. For this aim, 5 baks were selected to ivestigate i terms of the operatioal ad beeficial aspects. The obtaied results showed that i operatioal area, two baks are efficiet while oe of them are efficiet i beeficial area. It was stated that miimizig the costs ad improvig the icomes ca establish a efficiet coditio. All of the baks has have bee raked based o their scores regardig the objective fuctio values. Refereces Baker, R.D., Chares, A., Cooper, W.W., Some models for estimatig techical ad scale iefficiecies i data evelopmet aalysis. Maag. Sci. 30 (9),

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