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Ranking Spanish savings banks: A multicriteria approach
Mathematical and Computer Modelling 52 (2010) 1058–1065
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Ranking Spanish savings banks: A multicriteria approach Fernando García 1 , Francisco Guijarro ∗,1 , Ismael Moya 1 Facultad de Administración y Dirección de Empresas, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain
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Article history: Received 21 September 2009 Accepted 5 February 2010 Keywords: Savings banks Multicriteria ranking Goal programming Business performance
abstract Business rankings in general, and those referring to savings banks in particular, are usually based on a single criterion, so that rankings vary according to the criterion used. This paper proposes a multicriteria methodology based on goal programming that considers simultaneously the different dimensions involved in savings bank performance. An analysis of the Spanish savings banks reveals that credit risk is the most important performance dimension of these financial institutions, followed by profitability and productivity. © 2010 Elsevier Ltd. All rights reserved.
1. Introduction Business performance analysis is of great importance for a considerable number of groups and organisations, such as banks, creditors, shareholders, employees, managers, financial analysts, etc. These groups have available a large amount of information about the companies, what in principle could be considered a benefit — the more information available, the easier it is to come to a decision. However, it can also make the decisionmaking process somewhat complicated – it may be necessary to distinguish between the relevant and irrelevant information and eliminate the latter – and involve extra costs due to the large amount of information to be managed. The ranking of firms has always been of interest in business analysis. From a practical point of view, rankings provide information on a great number of institutions showing the relative position of a company within its sector with regard to a certain economic indicator. There are many examples of business rankings that classify firms from a region or commercial sector by earnings, total assets, number of employees, etc. So the ranking of companies is usually carried out on the basis of a single variable and gives no information on the overall situation of an individual company within the sector. The aim of a multicriteria ranking is to synthesize the information contained in a series of single-criterion rankings. The main problem consists of defining the weights of the variables used in the multicriteria ranking, minimising as far as possible the subjectivity of the person who decides the weights. One of the methods proposed to this goal in the literature is CRITIC (Criteria Importance Through Intercriteria Correlation) [1]. In this case, the importance of the criteria is considered to be in proportion to the uniqueness of the information they provide, so the weighting of a criterion will be greater the less it overlaps the other criteria. Another option to address the problem is by means of a modified version of TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) [2], using weighted Euclidean distances together with a measure of entropy to determine the weights. The proposal made in this paper differs from its predecessors in the method by which it obtains the multicriteria performance. Using the multicriteria goal programming technique, weights are calculated in such a way that the similarity is maximum between the values of the different criteria and the multicriteria performance, which is the value which will later
∗
Corresponding author. E-mail addresses: [email protected] (F. García), [email protected] (F. Guijarro), [email protected] (I. Moya).
1 Fax: +34 963877479. 0895-7177/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.mcm.2010.02.015
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be used to rank the companies. Applying different versions of the goal programming model, a collective approach is used (giving greater weighting to those criteria with similar ranking and less to the conflictive criteria), as well as an individual approach (greater weight to the most conflictive). As a compromise between both, a parametric version is considered to amplify the range of decision possibilities, so the two previous approaches become particular cases of the last approach. The aim of the present work is to propose a goal programming-based multicriteria methodology to provide a measure of company performance and then apply it to the ranking of Spanish savings banks. This sector was chosen for its importance in the Spanish financial system [3] at a time when radical changes are expected to take place in its structure. It is therefore of interest to determine how potential mergers would affect the relative positions of the savings banks from a global standpoint rather than from a single-criterion, bearing in mind that the savings banks have no share quotations on the stock market. The remainder of the paper is structured as follows: Section 2 describes in detail the new methodology to create multicriteria rankings. Sections 3 and 4 are devoted to the application of the new methodology on a ranking of Spanish savings banks. Finally, Section 5 concludes. 2. Proposal of a multicriteria methodology for estimating performance As mentioned above, the ranking of companies is usually carried out on the basis of a single variable. These rankings refer only to the situation with reference to the criterion used and gives no information on the overall situation of an individual company within the sector. In order to carry out a multicriteria ranking, various explanatory variables or single-criterion rankings must be available. In fact, the aim of a multicriteria ranking is to synthesize the information contained in a series of single-criterion rankings. The first problem to overcome is how to organise the available information, minimising the impact of the least important factors and emphasising the most important or most representative of the general tendency. This problem can be solved by using statistical techniques such as factor analysis, which reduces the size of the original problem but needs a large number of items. So other approaches must be considered. The second problem is how to weight the variables used in the multicriteria ranking, minimising as far as possible the subjectivity of the decision-maker who decides the weightings. This question can be approached from the multicriteria decision-making theory, considering the different explanatory variables as criteria and the companies that are to be ranked as alternatives. This work proposes the use of a multicriteria technique, goal programming, to obtain the global business performance. Weights are calculated in such a way that the similarity is maximum between uni-criteria variables and the multicriteria performance, which is the variable which will later be used to rank the companies. Applying different versions of the goal programming model, a collective approach is used (giving greater weighting to those criteria with similar ranking and less to the conflictive criteria), as well as an individual approach (greater weight to the most conflictive). As a compromise between both, a parametric version is considered to widen the range of decision possibilities, so that the two previous approaches become particular cases of the last approach. Goal programming [4] is a well-known multicriteria technique consisting of linear or non-linear functions and continuous or discrete variables in which all the functions have been transformed into objectives or goals [5]. Unlike the inflexibility of the optimization concept imposed on mathematical models with a single objective function, goal programming can be interpreted under a satisfying philosophy. From this standpoint, the decision maker is interested in minimising the nonachievement of their objectives [6] since the simultaneous achievement of all goals is not feasible in practical problems. Linares and Romero [7] used goal programming to combine individual preferences in different social groups in a study on the planning of electricity consumption. Starting out from this idea, the present study proposes to combine the different ranking criteria using different goal programming models. According to what norm is used, the solution obtained can be interpreted as a solution in which consensus is maximum between the measurements (penalizing the most conflictive measures as compared to those which follow the general trend) or as a solution in which the most conflictive measures are given preference (penalizing those which share most information with the rest). In the first case, the absolute difference between the multicriteria value and the standardized single-criterion value (norm L1 ) is minimum. In the second, the greatest difference recorded between the multicriteria value and the standardized single-criterion values (norm L∞ ) is minimum. The goal programming model in norm L1 appears in (1): Min
n X c X
nij + pij
i=1 j=1
s.a. c X
wj vij + nij − pij = vij i = 1 . . . n j = 1 . . . c
j=1 c X j=1
wj = 1
(1)
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wj vij = Vi i = 1 . . . n
j =1 n X
nij + pij = Dj
j = 1...c
i=1 c X
Dj = Z
j =1
where: wj = weight to be estimated for the jth criterion. nij pij = negative (positive) deviation variable. Quantifies the difference by excess (defect) between the value of the ith company in the jth criterion and the multicriteria value obtained by applying the weights wj . This is, nij − pij = P vij − cj=1 wj vij , with nij , pij ≥ 0. The objective function of (1) ensures that only one of the deviation variables can have a value greater than zero: nij × pij = 0 Dj = degree of disagreement between the jth criterion and the multicriteria value. Z = magnitude of global disagreement. The model (1) [1] has a total of n × c goal constraints. This means that for each criterion j (j = 1 . . . c) the model implements n constraints, one for each alternative i (i = 1 . . . n) and must determine the weight associated with the criterion j, wj . This is carried out by minimising the difference in absolute terms between the P single-criterion performance c of each alternative in the criterion j, vij , and the multicriteria performance Vi , with Vi = j=1 wj vij . This value is the ultimate objective of the methodology, since on assigning a single value to each alternative as the total of all single-criterion performances, the ranking of the alternatives is immediately obtained. The value of the target function provides the degree of non-achievement of the set of goals. Weightings are restricted to sum 1. The last constraints are used to compute the companies’ multicriteria performance (Vi ), the degree of disagreement of each single-criterion measurement in relation to the multicriteria value (Dj ) and the degree of global disagreement (Z ). In the literature, the model that minimises the sum of absolute deviations is known as the weighted goal programming model (WGP). The L∞ norm is implemented by the MINMAX goal programming model (2), in which D represents the maximum deviation between the multicriteria value and the single-criterion values. The rest of the variables keep the same meaning as in (1). Min D s.a. c X
wj vij + nij − pij = vij i = 1 . . . n j = 1 . . . c
j =1 n
X
nij + pij ≤ D
j = 1...c
i=1 c
X
wj = 1
(2)
j =1 c
X
wj vij = Vi i = 1 . . . n
j =1 n
X
nij + pij = Dj
j = 1...c
i=1 c
X
Dj = Z .
j =1
Criteria weights (vij ) were normalized from the original variables (uij ), so that vij =
u∗ −uij j u∗ −u∗j j
, with u∗j = maxi (uij ) and
u∗j = mini (uij ). Normalization is needed when the original variables are given in different measures (monetary units, percentage, etc.). The solutions provided by models (1) and (2) represent extreme cases in which conflicting strategies are opposed to each other: favouring global consensus (WGP) or favouring the criteria that generate rankings with a higher degree of idiosyncrasy (MINMAX GP). An interesting option for a compromise between (1) and (2) is to employ an extended goal programming model (3) in which the λ parameter provides more balanced solutions. This widens the range of possibilities when deciding which multicriteria value is the most suitable and representative of the individual criteria. Note that if λ = 1 the same solution is
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obtained as in model (1), while if λ = 0 the solution coincides with model (2). Min
λ
n X c X
nij + pij + (1 − λ) D
i =1 j =1
s.a. c X
wj vij + nij − pij = vij i = 1 . . . n j = 1 . . . c
j=1 n X
nij + pij ≤ D
j = 1...c
i =1 c X
wj = 1
j=1 c X
wj vij = Vi i = 1 . . . n
j=1 n X
nij + pij = Dj
j = 1...c
i =1 c X
Dj = Z .
(3)
j=1
3. Selection of representative performance variables The Spanish banking system is composed of banks, savings banks, and cooperative banks. In 2007, there were 45 savings banks. The benefit obtained by the savings banks represents 42% of the total profits of the Spanish banking system, what is in line with their size in terms of assets or liabilities. This fact reveals the importance of the saving banks within the financial system. It is therefore logical that rankings have been made of the savings banks that show their relative positions within the sector based on a series of factors. However, the rankings that are published periodically in the financial press are always based on a single variable, so that a savings bank’s position in the list only depends on the reference criterion used, this usually being selected from: number of employees, number of branches, total assets, loans, deposits, profits, etc. As the use of a single variable does not necessarily give the correct view of the global situation, it seems reasonable to expect that people in need of financial information require something more than variables related to bank size, which are those traditionally used, and are also interested in aspects more closely related to business performance. Banking performance has been the subject of numerous studies, especially in comparative studies [8], in the developed and underdeveloped countries [9], public and private banking [10,11], before and after privatisation in relation to takeovers and mergers [12], or in relation to changes in the financial sector regulations [13,14]. In the studies on financial performance, there are notable differences in the methodologies and criteria used. However, it is possible to identify certain recurring general criteria that determine strategic bank policy. If we concentrate on studies on the Spanish financial system and savings banks, we can group these criteria into: productivity [15], costs [16,17], profitability [13], management of different types of risk [18], and size [19]. Most of the studies employ several of these categories to measure performance. Each of the categories can be defined by many different variables; for example, company size can be defined by number of branches, number of employees, total assets, deposits, etc. To select the variables used in the present study, those used in the above-cited works were considered, as were all the different business aspects (productivity, profits, risk management and size). As is usual in studies on performance, certain areas were assigned several variables that measure different aspects. Table 1 shows these variables together with the dimensions they represent. Productivity of the savings banks was measured from two standpoints: staff productivity (RLS) (considered as the ratio between lending and number of employees) and productivity of the office network (RDB), measured by the ratio between deposits and the number of branches. The first ratio is an indicator of the commercial management and its capacity to generate income from loans, while the second indicates the capacity of the office network to obtain deposits. Savings bank profitability was also defined from two perspectives: return on assets (ROA) and return on equity (ROE). Risk management is a fundamental aspect in the strategy of all financial institutions, as is especially evident in periods of crisis. To represent this aspect, three criteria were chosen related to credit risk. The first was the inverse default rate (IDR). The inverse was used to combine all the criteria directly in the ranking, so the higher the value of any of the criteria, the higher the perception of performance (the greater the productivity the better the performance; the higher the profits, the better the performance, etc.). The second was the coefficient of solvency (SOLV), which refers to the capital adequacy of the credit institution. The third is the provision for bad debts (PBD), in the form of the percentage set aside for this purpose.
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Table 1 Variables used for the multicriteria ranking. Variable
Dimension
RLS: Lending/Staff RDB: Deposits/Number of branches ROA: Results before taxes/Total assets ROE: Results before taxes/Equity IDR: Inverse default rate SOLV: Coefficient of solvency PBD: Provision for bad debts TA: Total assets
Productivity Productivity Profitability Profitability Credit risk Credit risk Credit risk Size
Finally, size was the third dimension considered, not only because it is one of the most commonly used in the literature but also because it is in fact usually used to classify business companies and especially financial institutions. In our case we selected total assets (TA) as the representative variable. The database for the present study was compiled from the annual accounts published by the Spanish savings banks for the financial year 2007. 4. Ranking of Spanish savings banks This section describes the use of the methodology presented in Section 2 to obtain a multicriteria performance ranking of the Spanish savings banks for 2007. The 8 criteria shown in Table 1 are used as a starting point, with the original variables being normalized as stated in the previous section. On solving (3) for different values of λ ∈ [0, 1] we obtain (1) the weighting or relative importance of each individual criterion in the overall ranking and (2) the multicriteria value which ranks the banks according to performance. Table 2 shows the results obtained in accordance with the values assigned to the λ parameter. For each λ value, we present the weight of each criterion, the deviations between the multicriteria performance and each of the criteria (Dj , j = 1 . . . 8), the maximum deviation D between them, and the global deviation Z as the sum of all Dj . The model for λ = 1 obtains non-null coefficients for all variables, which implies that all contribute in the calculation of the multicriteria performance, being ROA noteworthy for its greater weight. We can thus conclude that the profit criterion is representative of the general performance tendency. Indeed, if we add together the weights obtained by the variables which represent this dimension, a value of 43.5% is obtained. The second most important dimension is credit risk (23.9%), followed closely by productivity (22.6%). The least important, at 10% for its only variable, is total assets. As the value of the λ parameter diminishes, the number of variables that intervene in the calculation of multicriteria performance also diminishes. At the extreme λ = 0 only three variables appear with a non-null coefficient: RDB (Productivity), IDR (Credit Risk) and TA (Size). This means that these are the three variables that differ most from the rest as to the amount of information they contribute to the performance. In fact, none of the Profitability variables appear in the solution, although they were decisive in the model with λ = 1. If we evaluate the Dj values for each of the variables we see that the biggest of these corresponds to IDR (D5 ) for any value of parameter λ. In all cases it coincides with the greatest deviation D. This means IDR is the variable most in disagreement with the rest of the single-criterion performance measurements. In other words, the default rate of the savings banks is a variable which cannot be related to any of the other variables employed in the measurement of the performance. The economic interpretation of this fact is the following: While the rest of the criteria employed to measure the performance can be controlled by the management in a more or less direct way, the default rate is beyond this control so it shows no correlation with the other criteria. The last rows of Table 2 are reserved for the weight of each of the dimensions contained in the analysis, obtained as the sum of the individual weights of each criterion. It can be clearly seen that as the value of λ diminishes, Profitability gives part of its weight to Productivity and Credit Risk, while Size remains around 10% or even less for the entire range of λ values analysed. Although the weight of each criterion, or the set calculated for the dimension, offers an idea of the relative importance of each measurement in calculating multicriteria performance, a Spearman correlation analysis must be carried out to analyse the correlation between each of the single-criterion measurements and final performance (Table 3). The variables with the highest correlation coefficient are IDR, with values between 0.678 (λ = 1) and 0.970 (λ = 0), and PBD, with values between 0.605 (λ = 0.6) and 0.879 (λ = 0).The rest of the variables have less significant coefficients for all λ values, with ROA standing out with correlation coefficients in some cases close to 0.5. From these results it can be concluded that Credit Risk clearly has the highest correlation with multicriteria performance and will no doubt be considered a key factor in any decisions that have to be taken in the near future by the Spanish savings bank sector. Bearing in mind the need not only for a business ranking but also the decisive role of this type of result on decisionmaking processes, the different savings banks rankings obtained according to the models used should also be analysed (see Appendix).
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Table 2 Results of applying the extended goal programming model.
λ
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Weights
RLS RDB ROA ROE IDR SOLV PBD TA
0.000 0.488 0.000 0.000 0.497 0.000 0.000 0.014
0.064 0.353 0.131 0.000 0.410 0.000 0.000 0.042
0.107 0.185 0.267 0.000 0.327 0.000 0.000 0.113
0.159 0.103 0.277 0.095 0.287 0.000 0.000 0.078
0.153 0.068 0.280 0.130 0.222 0.030 0.002 0.114
0.156 0.056 0.289 0.166 0.168 0.080 0.000 0.085
0.137 0.056 0.320 0.160 0.145 0.094 0.000 0.089
0.155 0.052 0.297 0.160 0.129 0.108 0.000 0.099
0.177 0.042 0.296 0.146 0.108 0.121 0.011 0.099
0.181 0.045 0.288 0.147 0.107 0.119 0.013 0.100
0.181 0.045 0.289 0.146 0.106 0.119 0.014 0.100
Distances
D D1 D2 D3 D4 D5 D6 D7 D8 Z
11.062 11.062 11.062 11.062 11.062 11.062 11.062 11.062 11.062 99.561
11.135 5.707 11.135 5.336 10.226 11.135 6.034 4.855 9.986 72.973
11.405 5.342 11.405 4.518 10.225 11.405 6.026 4.919 9.314 71.492
11.729 4.800 11.337 4.258 9.830 11.729 5.910 5.270 9.116 70.595
12.821 4.324 10.406 3.659 8.794 12.821 5.134 6.029 8.095 68.454
13.631 4.007 9.709 3.324 8.096 13.631 4.656 6.661 7.561 67.487
13.958 4.040 9.430 3.139 7.870 13.958 4.503 6.857 7.315 67.233
14.224 3.856 9.182 3.256 7.620 14.224 4.415 7.106 7.060 67.088
14.334 3.780 9.130 3.246 7.599 14.334 4.373 7.209 6.962 67.054
14.364 3.756 9.089 3.293 7.553 14.364 4.374 7.232 6.927 67.050
14.365 3.757 9.088 3.291 7.554 14.365 4.375 7.232 6.925 67.050
Dimensions
Productivity Profitability Credit risk Size
0.488 0.000 0.497 0.014
0.417 0.131 0.410 0.042
0.292 0.267 0.327 0.113
0.262 0.372 0.287 0.078
0.221 0.410 0.254 0.114
0.212 0.455 0.248 0.085
0.193 0.480 0.239 0.089
0.207 0.457 0.237 0.099
0.219 0.442 0.240 0.099
0.226 0.435 0.239 0.100
0.226 0.435 0.239 0.100
Table 3 Spearman correlation between each single-criterion measurement and multicriteria performance, according to the value of the parameter λ.
λ
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
RLS RDB ROA ROE IDR SOLV PBD TA
0.324 0.287 0.437 0.040 0.970 0.293 0.879 0.083
0.270 0.276 0.387 0.026 0.923 0.244 0.845 0.064
0.430 0.154 0.282 −0.143 0.834 0.094 0.692 −0.010
0.397 0.178 0.293 −0.070 0.797 0.208 0.700 −0.019
0.342 0.234 0.362 −0.153 0.771 0.145 0.689 0.011
0.171 0.163 0.350 −0.090 0.726 0.209 0.732 −0.073
0.318 0.188 0.296 −0.022 0.696 0.255 0.605 −0.020
0.207 0.195 0.449 −0.136 0.683 0.213 0.736 0.108
0.202 0.280 0.367 −0.026 0.693 0.212 0.737 0.214
0.102 0.245 0.439 −0.046 0.678 0.221 0.650 0.088
0.102 0.245 0.439 −0.046 0.678 0.221 0.650 0.088
The highest ranked saving banks are: BBK, Cajastur, La Caixa and Caja Murcia, which are always placed in the first quartile; the ones with the lowest position in the ranking are: Caixa d’Estalvis de Sabadell, Caixa de Girona, Caixa Penedés, Caixa Manlleu, Caixa Tarragona, Caja España, Cajasol, Caja Canarias and Cajasur, which always appear in the last quartile. With regard to dispersion, 20 banks, or half of the sample, always appear in the same quartile: BBK, Cajastur, La Caixa, and Caja Murcia (first quartile); and Caixa d’Estalvis de Sabadell, Caixa de Girona, Caixa Penedés, Caixa Manlleu, Caixa Tarragona, Caja España, Cajasol, Caja Canarias and Cajasur, (fourth quartile), Caixanova and IberCaja (second quartile); and Caja Duero, Caja Segovia, Caja Cantabria, Caixa Ontiyent, Caja Granada (third quartile). It is also notable that no bank is present in all quartiles and that only six appear in three: Bancaja, Círculo de Burgos, Sa Nostra, Caja Inmaculada, La Caja de Canarias and Caja de Jaén. 5. Conclusions Performance analysis can provide a great deal of important information on business companies. Interest groups have large amounts of public information at their disposal, which can sometimes be a disadvantage when it comes to decision making. Performance can also be used to rank business companies and show their relative positions within the sector. The objective of the present study was to propose a goal programming based multicriteria methodology. Compared with the normally used single-criterion rankings, this methodology provides a global estimation of the performance of a business company, combining the individual criteria in such a way as to include all the dimensions that affect its performance. The proposed methodology was then used to obtain a multicriteria ranking of the Spanish savings banks for the year 2007. The methodology proposed in this paper differs from others by the way in which global performance is estimated. By means of the goal programming multicriteria technique weightings are calculated considering the similarities between values of the different criteria and multicriteria performance, which is the value which will subsequently be used to rank the companies according to performance. Applying different versions of the goal programming model, a collective approach is considered (giving greater weight to criteria that show similar performance over the more conflictive criteria) and an individualistic approach (giving greater weight to the more conflictive criteria). As a compromise solution between the two
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Table A.1 Ranking of the Spanish savings banks based on the interquartile frequency.
BBK CAJASTUR LA CAIXA CAJA MURCIA CAJA MADRID BANCAJA VITAL KUTXA CAM CAJA DE BURGOS CAJA DE EXTREMADURA KUTXA CIRCULO DE BURGOS CCM—CAJA CASTILLA LA MANCHA CAIXA TERRASSA CAJA NAVARRA SA NOSTRA CAJA RIOJA CAIXANOVA IBERCAJA CAJA GALICIA CAIXA CATALUNYA CAIXA MANRESA CAJA INMACULADA LA CAJA DE CANARIAS CAJA DE JAEN CAJA DUERO CAJA SEGOVIA CAJA CANTABRIA CAIXA ONTINYENT CAJA GRANADA CAJA DE GUADALAJARA CAIXA D’ESTALVIS DE SABADELL CAIXA DE GIRONA CAIXA PENEDÉS CAIXA DE MANLLEU CAIXA TARRAGONA CAJA ESPAÑA CAJASOL CAJA CANARIAS CAJASUR
1st quartile
2nd quartile
3rd quartile
4th quartile
11 11 11 11 10 8 7 7 7 6 6 6 5 4 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 2 4 4 4 5 5 4 6 7 9 5 3 11 11 10 7 5 4 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 4 7 0 0 1 4 6 3 5 8 11 11 11 11 11 10 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 2 0 0 0 0 0 1 11 11 11 11 11 11 11 11 11
approaches, a parametric version is developed to widen the range of possibilities open to the decision maker in such a way that the two previous approaches become particular cases of the last approach. In addition to the importance that the methodology concedes to each of the performance dimensions, it also makes it possible to carry out different multicriteria rankings according to the model used. This provides additional information on the relative position of a company according to the weight the model gives to each criterion. Regardless the value of λ chosen, there are savings banks which are always ranked among the first positions, whereas the bad banks always get a low ranking. Appendix See Table A.1. References [1] D. Diakoulaki, G. Mavrotas, L. Papayannakis, Determining objective weights in multiple criteria problems: The CRITIC method, Comput. Oper. Res. 22 (7) (1995) 763–770. [2] H. Deng, C.-H. Yeng, R.J. Willis, Inter-company comparison using modified TOPSIS with objective weights, Comput. Oper. Res. 27 (10) (2000) 963–973. [3] M.A. Garcia-Cestona, J. Surroca, Evaluación de la eficiencia con múltiples fines. Una aplicación a las cajas de ahorro, Rev. Econ. Aplicada 40 (14) (2006) 67–89. [4] A. Charnes, W.W. Cooper, R.O. Ferguson, Optimal estimation of executive compensation by linear programming, Manage. Sci. 1 (1955) 138–150. [5] J.M. Ignizio, C. Romero, Goal Programming, in: H. Bigdoli (Ed.), Encyclopedia of Information Systems, vol. 2, Academic Press, London, 2003, pp. 489–500. [6] C. Romero, Extended lexicographic goal programming: A unifying approach, Omega 29 (1) (2001) 63–71. [7] P. Linares, C. Romero, Aggregation of preferences in an environmental economics context: A goal-programming approach, Omega 30 (2) (2002) 89–95. [8] A. Berger, R. DeYoung, H. Genay, G. Udell, Globalization of financial institutions: Evidence from cross-border banking performance, Brookings Papers on Economic Activity 2 (2000) 23–158. [9] J. Bonin, I. Hasan, P. Wachtel, Bank performance, efficiency and ownership in transition countries, J. Banking Finan. 29 (1) (2005) 31–53.
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[10] G. Iannotta, G. Nocera, A. Sironi, Ownership structure, risk and performance in the European banking industry, J. Banking Finan. 31 (2007) 2127–2149. [11] V. Shih, Q. Zhang, M. Liu, Comparing the performance of Chinese banks: A principal component approach, China Econ. Rev. 18 (2007) 15–34. [12] B. Díaz, M. García Olalla, S. Sanfilippo Azofra, Bank acquisitions and performance: Evidence from a panel of European credit entities, J. Econ. Bus. 56 (2004) 377–404. [13] S.C. Kumbhakar, A. Lozano-Vivas, C.A.K. Lovell, I. Hasan, The effects of deregulation on the performance of financial institutions: The case of Spanish savings banks, J. Money Credit Banking 33 (2001) 101–120. [14] S.N. Brissimis, M.D. Delis, N.I. Papanikolaou, Exploring the nexus between banking sector reform and performance: Evidence from newly acceded EU countries, J. Banking Finan. 32 (2008) 2674–2683. [15] E. Grifell-Tatjé, C.A.K. Lovell, The sources of productivity change in Spanish banking, Eur. J. Oper. Res. 98 (1997) 365–381. [16] J.M. Pastor, Credit risk and efficiency in the European banking system: A three-stage analysis, Appl. Finan. Econ. 12 (2002) 895–911. [17] D. Prior, Long and short-run nonparametric cost frontier efficiency: An application to Spanish savings banks, J. Banking Finan. 27 (2003) 107–123. [18] J. Maudos, J.M. Pastor, La eficiencia del sistema bancario español en el contexto de la Unión Europea, Pap. Econ. Esp. 84–85 (2000) 155–168. [19] M.A. Marco, I. Moya, Factores que inciden en la eficiencia de las entidades de crédito cooperativo, Rev. Esp. Financ. Contab. 105 (2000) 781–808.
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Ranking Spanish savings banks: A multicriteria approach Fernando García 1 , Francisco Guijarro ∗,1 , Ismael Moya 1 Facultad de Administración y Dirección de Empresas, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain
article
info
Article history: Received 21 September 2009 Accepted 5 February 2010 Keywords: Savings banks Multicriteria ranking Goal programming Business performance
abstract Business rankings in general, and those referring to savings banks in particular, are usually based on a single criterion, so that rankings vary according to the criterion used. This paper proposes a multicriteria methodology based on goal programming that considers simultaneously the different dimensions involved in savings bank performance. An analysis of the Spanish savings banks reveals that credit risk is the most important performance dimension of these financial institutions, followed by profitability and productivity. © 2010 Elsevier Ltd. All rights reserved.
1. Introduction Business performance analysis is of great importance for a considerable number of groups and organisations, such as banks, creditors, shareholders, employees, managers, financial analysts, etc. These groups have available a large amount of information about the companies, what in principle could be considered a benefit — the more information available, the easier it is to come to a decision. However, it can also make the decisionmaking process somewhat complicated – it may be necessary to distinguish between the relevant and irrelevant information and eliminate the latter – and involve extra costs due to the large amount of information to be managed. The ranking of firms has always been of interest in business analysis. From a practical point of view, rankings provide information on a great number of institutions showing the relative position of a company within its sector with regard to a certain economic indicator. There are many examples of business rankings that classify firms from a region or commercial sector by earnings, total assets, number of employees, etc. So the ranking of companies is usually carried out on the basis of a single variable and gives no information on the overall situation of an individual company within the sector. The aim of a multicriteria ranking is to synthesize the information contained in a series of single-criterion rankings. The main problem consists of defining the weights of the variables used in the multicriteria ranking, minimising as far as possible the subjectivity of the person who decides the weights. One of the methods proposed to this goal in the literature is CRITIC (Criteria Importance Through Intercriteria Correlation) [1]. In this case, the importance of the criteria is considered to be in proportion to the uniqueness of the information they provide, so the weighting of a criterion will be greater the less it overlaps the other criteria. Another option to address the problem is by means of a modified version of TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) [2], using weighted Euclidean distances together with a measure of entropy to determine the weights. The proposal made in this paper differs from its predecessors in the method by which it obtains the multicriteria performance. Using the multicriteria goal programming technique, weights are calculated in such a way that the similarity is maximum between the values of the different criteria and the multicriteria performance, which is the value which will later
∗
Corresponding author. E-mail addresses: [email protected] (F. García), [email protected] (F. Guijarro), [email protected] (I. Moya).
1 Fax: +34 963877479. 0895-7177/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.mcm.2010.02.015
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be used to rank the companies. Applying different versions of the goal programming model, a collective approach is used (giving greater weighting to those criteria with similar ranking and less to the conflictive criteria), as well as an individual approach (greater weight to the most conflictive). As a compromise between both, a parametric version is considered to amplify the range of decision possibilities, so the two previous approaches become particular cases of the last approach. The aim of the present work is to propose a goal programming-based multicriteria methodology to provide a measure of company performance and then apply it to the ranking of Spanish savings banks. This sector was chosen for its importance in the Spanish financial system [3] at a time when radical changes are expected to take place in its structure. It is therefore of interest to determine how potential mergers would affect the relative positions of the savings banks from a global standpoint rather than from a single-criterion, bearing in mind that the savings banks have no share quotations on the stock market. The remainder of the paper is structured as follows: Section 2 describes in detail the new methodology to create multicriteria rankings. Sections 3 and 4 are devoted to the application of the new methodology on a ranking of Spanish savings banks. Finally, Section 5 concludes. 2. Proposal of a multicriteria methodology for estimating performance As mentioned above, the ranking of companies is usually carried out on the basis of a single variable. These rankings refer only to the situation with reference to the criterion used and gives no information on the overall situation of an individual company within the sector. In order to carry out a multicriteria ranking, various explanatory variables or single-criterion rankings must be available. In fact, the aim of a multicriteria ranking is to synthesize the information contained in a series of single-criterion rankings. The first problem to overcome is how to organise the available information, minimising the impact of the least important factors and emphasising the most important or most representative of the general tendency. This problem can be solved by using statistical techniques such as factor analysis, which reduces the size of the original problem but needs a large number of items. So other approaches must be considered. The second problem is how to weight the variables used in the multicriteria ranking, minimising as far as possible the subjectivity of the decision-maker who decides the weightings. This question can be approached from the multicriteria decision-making theory, considering the different explanatory variables as criteria and the companies that are to be ranked as alternatives. This work proposes the use of a multicriteria technique, goal programming, to obtain the global business performance. Weights are calculated in such a way that the similarity is maximum between uni-criteria variables and the multicriteria performance, which is the variable which will later be used to rank the companies. Applying different versions of the goal programming model, a collective approach is used (giving greater weighting to those criteria with similar ranking and less to the conflictive criteria), as well as an individual approach (greater weight to the most conflictive). As a compromise between both, a parametric version is considered to widen the range of decision possibilities, so that the two previous approaches become particular cases of the last approach. Goal programming [4] is a well-known multicriteria technique consisting of linear or non-linear functions and continuous or discrete variables in which all the functions have been transformed into objectives or goals [5]. Unlike the inflexibility of the optimization concept imposed on mathematical models with a single objective function, goal programming can be interpreted under a satisfying philosophy. From this standpoint, the decision maker is interested in minimising the nonachievement of their objectives [6] since the simultaneous achievement of all goals is not feasible in practical problems. Linares and Romero [7] used goal programming to combine individual preferences in different social groups in a study on the planning of electricity consumption. Starting out from this idea, the present study proposes to combine the different ranking criteria using different goal programming models. According to what norm is used, the solution obtained can be interpreted as a solution in which consensus is maximum between the measurements (penalizing the most conflictive measures as compared to those which follow the general trend) or as a solution in which the most conflictive measures are given preference (penalizing those which share most information with the rest). In the first case, the absolute difference between the multicriteria value and the standardized single-criterion value (norm L1 ) is minimum. In the second, the greatest difference recorded between the multicriteria value and the standardized single-criterion values (norm L∞ ) is minimum. The goal programming model in norm L1 appears in (1): Min
n X c X
nij + pij
i=1 j=1
s.a. c X
wj vij + nij − pij = vij i = 1 . . . n j = 1 . . . c
j=1 c X j=1
wj = 1
(1)
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wj vij = Vi i = 1 . . . n
j =1 n X
nij + pij = Dj
j = 1...c
i=1 c X
Dj = Z
j =1
where: wj = weight to be estimated for the jth criterion. nij pij = negative (positive) deviation variable. Quantifies the difference by excess (defect) between the value of the ith company in the jth criterion and the multicriteria value obtained by applying the weights wj . This is, nij − pij = P vij − cj=1 wj vij , with nij , pij ≥ 0. The objective function of (1) ensures that only one of the deviation variables can have a value greater than zero: nij × pij = 0 Dj = degree of disagreement between the jth criterion and the multicriteria value. Z = magnitude of global disagreement. The model (1) [1] has a total of n × c goal constraints. This means that for each criterion j (j = 1 . . . c) the model implements n constraints, one for each alternative i (i = 1 . . . n) and must determine the weight associated with the criterion j, wj . This is carried out by minimising the difference in absolute terms between the P single-criterion performance c of each alternative in the criterion j, vij , and the multicriteria performance Vi , with Vi = j=1 wj vij . This value is the ultimate objective of the methodology, since on assigning a single value to each alternative as the total of all single-criterion performances, the ranking of the alternatives is immediately obtained. The value of the target function provides the degree of non-achievement of the set of goals. Weightings are restricted to sum 1. The last constraints are used to compute the companies’ multicriteria performance (Vi ), the degree of disagreement of each single-criterion measurement in relation to the multicriteria value (Dj ) and the degree of global disagreement (Z ). In the literature, the model that minimises the sum of absolute deviations is known as the weighted goal programming model (WGP). The L∞ norm is implemented by the MINMAX goal programming model (2), in which D represents the maximum deviation between the multicriteria value and the single-criterion values. The rest of the variables keep the same meaning as in (1). Min D s.a. c X
wj vij + nij − pij = vij i = 1 . . . n j = 1 . . . c
j =1 n
X
nij + pij ≤ D
j = 1...c
i=1 c
X
wj = 1
(2)
j =1 c
X
wj vij = Vi i = 1 . . . n
j =1 n
X
nij + pij = Dj
j = 1...c
i=1 c
X
Dj = Z .
j =1
Criteria weights (vij ) were normalized from the original variables (uij ), so that vij =
u∗ −uij j u∗ −u∗j j
, with u∗j = maxi (uij ) and
u∗j = mini (uij ). Normalization is needed when the original variables are given in different measures (monetary units, percentage, etc.). The solutions provided by models (1) and (2) represent extreme cases in which conflicting strategies are opposed to each other: favouring global consensus (WGP) or favouring the criteria that generate rankings with a higher degree of idiosyncrasy (MINMAX GP). An interesting option for a compromise between (1) and (2) is to employ an extended goal programming model (3) in which the λ parameter provides more balanced solutions. This widens the range of possibilities when deciding which multicriteria value is the most suitable and representative of the individual criteria. Note that if λ = 1 the same solution is
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obtained as in model (1), while if λ = 0 the solution coincides with model (2). Min
λ
n X c X
nij + pij + (1 − λ) D
i =1 j =1
s.a. c X
wj vij + nij − pij = vij i = 1 . . . n j = 1 . . . c
j=1 n X
nij + pij ≤ D
j = 1...c
i =1 c X
wj = 1
j=1 c X
wj vij = Vi i = 1 . . . n
j=1 n X
nij + pij = Dj
j = 1...c
i =1 c X
Dj = Z .
(3)
j=1
3. Selection of representative performance variables The Spanish banking system is composed of banks, savings banks, and cooperative banks. In 2007, there were 45 savings banks. The benefit obtained by the savings banks represents 42% of the total profits of the Spanish banking system, what is in line with their size in terms of assets or liabilities. This fact reveals the importance of the saving banks within the financial system. It is therefore logical that rankings have been made of the savings banks that show their relative positions within the sector based on a series of factors. However, the rankings that are published periodically in the financial press are always based on a single variable, so that a savings bank’s position in the list only depends on the reference criterion used, this usually being selected from: number of employees, number of branches, total assets, loans, deposits, profits, etc. As the use of a single variable does not necessarily give the correct view of the global situation, it seems reasonable to expect that people in need of financial information require something more than variables related to bank size, which are those traditionally used, and are also interested in aspects more closely related to business performance. Banking performance has been the subject of numerous studies, especially in comparative studies [8], in the developed and underdeveloped countries [9], public and private banking [10,11], before and after privatisation in relation to takeovers and mergers [12], or in relation to changes in the financial sector regulations [13,14]. In the studies on financial performance, there are notable differences in the methodologies and criteria used. However, it is possible to identify certain recurring general criteria that determine strategic bank policy. If we concentrate on studies on the Spanish financial system and savings banks, we can group these criteria into: productivity [15], costs [16,17], profitability [13], management of different types of risk [18], and size [19]. Most of the studies employ several of these categories to measure performance. Each of the categories can be defined by many different variables; for example, company size can be defined by number of branches, number of employees, total assets, deposits, etc. To select the variables used in the present study, those used in the above-cited works were considered, as were all the different business aspects (productivity, profits, risk management and size). As is usual in studies on performance, certain areas were assigned several variables that measure different aspects. Table 1 shows these variables together with the dimensions they represent. Productivity of the savings banks was measured from two standpoints: staff productivity (RLS) (considered as the ratio between lending and number of employees) and productivity of the office network (RDB), measured by the ratio between deposits and the number of branches. The first ratio is an indicator of the commercial management and its capacity to generate income from loans, while the second indicates the capacity of the office network to obtain deposits. Savings bank profitability was also defined from two perspectives: return on assets (ROA) and return on equity (ROE). Risk management is a fundamental aspect in the strategy of all financial institutions, as is especially evident in periods of crisis. To represent this aspect, three criteria were chosen related to credit risk. The first was the inverse default rate (IDR). The inverse was used to combine all the criteria directly in the ranking, so the higher the value of any of the criteria, the higher the perception of performance (the greater the productivity the better the performance; the higher the profits, the better the performance, etc.). The second was the coefficient of solvency (SOLV), which refers to the capital adequacy of the credit institution. The third is the provision for bad debts (PBD), in the form of the percentage set aside for this purpose.
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Table 1 Variables used for the multicriteria ranking. Variable
Dimension
RLS: Lending/Staff RDB: Deposits/Number of branches ROA: Results before taxes/Total assets ROE: Results before taxes/Equity IDR: Inverse default rate SOLV: Coefficient of solvency PBD: Provision for bad debts TA: Total assets
Productivity Productivity Profitability Profitability Credit risk Credit risk Credit risk Size
Finally, size was the third dimension considered, not only because it is one of the most commonly used in the literature but also because it is in fact usually used to classify business companies and especially financial institutions. In our case we selected total assets (TA) as the representative variable. The database for the present study was compiled from the annual accounts published by the Spanish savings banks for the financial year 2007. 4. Ranking of Spanish savings banks This section describes the use of the methodology presented in Section 2 to obtain a multicriteria performance ranking of the Spanish savings banks for 2007. The 8 criteria shown in Table 1 are used as a starting point, with the original variables being normalized as stated in the previous section. On solving (3) for different values of λ ∈ [0, 1] we obtain (1) the weighting or relative importance of each individual criterion in the overall ranking and (2) the multicriteria value which ranks the banks according to performance. Table 2 shows the results obtained in accordance with the values assigned to the λ parameter. For each λ value, we present the weight of each criterion, the deviations between the multicriteria performance and each of the criteria (Dj , j = 1 . . . 8), the maximum deviation D between them, and the global deviation Z as the sum of all Dj . The model for λ = 1 obtains non-null coefficients for all variables, which implies that all contribute in the calculation of the multicriteria performance, being ROA noteworthy for its greater weight. We can thus conclude that the profit criterion is representative of the general performance tendency. Indeed, if we add together the weights obtained by the variables which represent this dimension, a value of 43.5% is obtained. The second most important dimension is credit risk (23.9%), followed closely by productivity (22.6%). The least important, at 10% for its only variable, is total assets. As the value of the λ parameter diminishes, the number of variables that intervene in the calculation of multicriteria performance also diminishes. At the extreme λ = 0 only three variables appear with a non-null coefficient: RDB (Productivity), IDR (Credit Risk) and TA (Size). This means that these are the three variables that differ most from the rest as to the amount of information they contribute to the performance. In fact, none of the Profitability variables appear in the solution, although they were decisive in the model with λ = 1. If we evaluate the Dj values for each of the variables we see that the biggest of these corresponds to IDR (D5 ) for any value of parameter λ. In all cases it coincides with the greatest deviation D. This means IDR is the variable most in disagreement with the rest of the single-criterion performance measurements. In other words, the default rate of the savings banks is a variable which cannot be related to any of the other variables employed in the measurement of the performance. The economic interpretation of this fact is the following: While the rest of the criteria employed to measure the performance can be controlled by the management in a more or less direct way, the default rate is beyond this control so it shows no correlation with the other criteria. The last rows of Table 2 are reserved for the weight of each of the dimensions contained in the analysis, obtained as the sum of the individual weights of each criterion. It can be clearly seen that as the value of λ diminishes, Profitability gives part of its weight to Productivity and Credit Risk, while Size remains around 10% or even less for the entire range of λ values analysed. Although the weight of each criterion, or the set calculated for the dimension, offers an idea of the relative importance of each measurement in calculating multicriteria performance, a Spearman correlation analysis must be carried out to analyse the correlation between each of the single-criterion measurements and final performance (Table 3). The variables with the highest correlation coefficient are IDR, with values between 0.678 (λ = 1) and 0.970 (λ = 0), and PBD, with values between 0.605 (λ = 0.6) and 0.879 (λ = 0).The rest of the variables have less significant coefficients for all λ values, with ROA standing out with correlation coefficients in some cases close to 0.5. From these results it can be concluded that Credit Risk clearly has the highest correlation with multicriteria performance and will no doubt be considered a key factor in any decisions that have to be taken in the near future by the Spanish savings bank sector. Bearing in mind the need not only for a business ranking but also the decisive role of this type of result on decisionmaking processes, the different savings banks rankings obtained according to the models used should also be analysed (see Appendix).
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Table 2 Results of applying the extended goal programming model.
λ
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Weights
RLS RDB ROA ROE IDR SOLV PBD TA
0.000 0.488 0.000 0.000 0.497 0.000 0.000 0.014
0.064 0.353 0.131 0.000 0.410 0.000 0.000 0.042
0.107 0.185 0.267 0.000 0.327 0.000 0.000 0.113
0.159 0.103 0.277 0.095 0.287 0.000 0.000 0.078
0.153 0.068 0.280 0.130 0.222 0.030 0.002 0.114
0.156 0.056 0.289 0.166 0.168 0.080 0.000 0.085
0.137 0.056 0.320 0.160 0.145 0.094 0.000 0.089
0.155 0.052 0.297 0.160 0.129 0.108 0.000 0.099
0.177 0.042 0.296 0.146 0.108 0.121 0.011 0.099
0.181 0.045 0.288 0.147 0.107 0.119 0.013 0.100
0.181 0.045 0.289 0.146 0.106 0.119 0.014 0.100
Distances
D D1 D2 D3 D4 D5 D6 D7 D8 Z
11.062 11.062 11.062 11.062 11.062 11.062 11.062 11.062 11.062 99.561
11.135 5.707 11.135 5.336 10.226 11.135 6.034 4.855 9.986 72.973
11.405 5.342 11.405 4.518 10.225 11.405 6.026 4.919 9.314 71.492
11.729 4.800 11.337 4.258 9.830 11.729 5.910 5.270 9.116 70.595
12.821 4.324 10.406 3.659 8.794 12.821 5.134 6.029 8.095 68.454
13.631 4.007 9.709 3.324 8.096 13.631 4.656 6.661 7.561 67.487
13.958 4.040 9.430 3.139 7.870 13.958 4.503 6.857 7.315 67.233
14.224 3.856 9.182 3.256 7.620 14.224 4.415 7.106 7.060 67.088
14.334 3.780 9.130 3.246 7.599 14.334 4.373 7.209 6.962 67.054
14.364 3.756 9.089 3.293 7.553 14.364 4.374 7.232 6.927 67.050
14.365 3.757 9.088 3.291 7.554 14.365 4.375 7.232 6.925 67.050
Dimensions
Productivity Profitability Credit risk Size
0.488 0.000 0.497 0.014
0.417 0.131 0.410 0.042
0.292 0.267 0.327 0.113
0.262 0.372 0.287 0.078
0.221 0.410 0.254 0.114
0.212 0.455 0.248 0.085
0.193 0.480 0.239 0.089
0.207 0.457 0.237 0.099
0.219 0.442 0.240 0.099
0.226 0.435 0.239 0.100
0.226 0.435 0.239 0.100
Table 3 Spearman correlation between each single-criterion measurement and multicriteria performance, according to the value of the parameter λ.
λ
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
RLS RDB ROA ROE IDR SOLV PBD TA
0.324 0.287 0.437 0.040 0.970 0.293 0.879 0.083
0.270 0.276 0.387 0.026 0.923 0.244 0.845 0.064
0.430 0.154 0.282 −0.143 0.834 0.094 0.692 −0.010
0.397 0.178 0.293 −0.070 0.797 0.208 0.700 −0.019
0.342 0.234 0.362 −0.153 0.771 0.145 0.689 0.011
0.171 0.163 0.350 −0.090 0.726 0.209 0.732 −0.073
0.318 0.188 0.296 −0.022 0.696 0.255 0.605 −0.020
0.207 0.195 0.449 −0.136 0.683 0.213 0.736 0.108
0.202 0.280 0.367 −0.026 0.693 0.212 0.737 0.214
0.102 0.245 0.439 −0.046 0.678 0.221 0.650 0.088
0.102 0.245 0.439 −0.046 0.678 0.221 0.650 0.088
The highest ranked saving banks are: BBK, Cajastur, La Caixa and Caja Murcia, which are always placed in the first quartile; the ones with the lowest position in the ranking are: Caixa d’Estalvis de Sabadell, Caixa de Girona, Caixa Penedés, Caixa Manlleu, Caixa Tarragona, Caja España, Cajasol, Caja Canarias and Cajasur, which always appear in the last quartile. With regard to dispersion, 20 banks, or half of the sample, always appear in the same quartile: BBK, Cajastur, La Caixa, and Caja Murcia (first quartile); and Caixa d’Estalvis de Sabadell, Caixa de Girona, Caixa Penedés, Caixa Manlleu, Caixa Tarragona, Caja España, Cajasol, Caja Canarias and Cajasur, (fourth quartile), Caixanova and IberCaja (second quartile); and Caja Duero, Caja Segovia, Caja Cantabria, Caixa Ontiyent, Caja Granada (third quartile). It is also notable that no bank is present in all quartiles and that only six appear in three: Bancaja, Círculo de Burgos, Sa Nostra, Caja Inmaculada, La Caja de Canarias and Caja de Jaén. 5. Conclusions Performance analysis can provide a great deal of important information on business companies. Interest groups have large amounts of public information at their disposal, which can sometimes be a disadvantage when it comes to decision making. Performance can also be used to rank business companies and show their relative positions within the sector. The objective of the present study was to propose a goal programming based multicriteria methodology. Compared with the normally used single-criterion rankings, this methodology provides a global estimation of the performance of a business company, combining the individual criteria in such a way as to include all the dimensions that affect its performance. The proposed methodology was then used to obtain a multicriteria ranking of the Spanish savings banks for the year 2007. The methodology proposed in this paper differs from others by the way in which global performance is estimated. By means of the goal programming multicriteria technique weightings are calculated considering the similarities between values of the different criteria and multicriteria performance, which is the value which will subsequently be used to rank the companies according to performance. Applying different versions of the goal programming model, a collective approach is considered (giving greater weight to criteria that show similar performance over the more conflictive criteria) and an individualistic approach (giving greater weight to the more conflictive criteria). As a compromise solution between the two
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Table A.1 Ranking of the Spanish savings banks based on the interquartile frequency.
BBK CAJASTUR LA CAIXA CAJA MURCIA CAJA MADRID BANCAJA VITAL KUTXA CAM CAJA DE BURGOS CAJA DE EXTREMADURA KUTXA CIRCULO DE BURGOS CCM—CAJA CASTILLA LA MANCHA CAIXA TERRASSA CAJA NAVARRA SA NOSTRA CAJA RIOJA CAIXANOVA IBERCAJA CAJA GALICIA CAIXA CATALUNYA CAIXA MANRESA CAJA INMACULADA LA CAJA DE CANARIAS CAJA DE JAEN CAJA DUERO CAJA SEGOVIA CAJA CANTABRIA CAIXA ONTINYENT CAJA GRANADA CAJA DE GUADALAJARA CAIXA D’ESTALVIS DE SABADELL CAIXA DE GIRONA CAIXA PENEDÉS CAIXA DE MANLLEU CAIXA TARRAGONA CAJA ESPAÑA CAJASOL CAJA CANARIAS CAJASUR
1st quartile
2nd quartile
3rd quartile
4th quartile
11 11 11 11 10 8 7 7 7 6 6 6 5 4 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 2 4 4 4 5 5 4 6 7 9 5 3 11 11 10 7 5 4 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 4 7 0 0 1 4 6 3 5 8 11 11 11 11 11 10 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 2 0 0 0 0 0 1 11 11 11 11 11 11 11 11 11
approaches, a parametric version is developed to widen the range of possibilities open to the decision maker in such a way that the two previous approaches become particular cases of the last approach. In addition to the importance that the methodology concedes to each of the performance dimensions, it also makes it possible to carry out different multicriteria rankings according to the model used. This provides additional information on the relative position of a company according to the weight the model gives to each criterion. Regardless the value of λ chosen, there are savings banks which are always ranked among the first positions, whereas the bad banks always get a low ranking. Appendix See Table A.1. References [1] D. Diakoulaki, G. Mavrotas, L. Papayannakis, Determining objective weights in multiple criteria problems: The CRITIC method, Comput. Oper. Res. 22 (7) (1995) 763–770. [2] H. Deng, C.-H. Yeng, R.J. Willis, Inter-company comparison using modified TOPSIS with objective weights, Comput. Oper. Res. 27 (10) (2000) 963–973. [3] M.A. Garcia-Cestona, J. Surroca, Evaluación de la eficiencia con múltiples fines. Una aplicación a las cajas de ahorro, Rev. Econ. Aplicada 40 (14) (2006) 67–89. [4] A. Charnes, W.W. Cooper, R.O. Ferguson, Optimal estimation of executive compensation by linear programming, Manage. Sci. 1 (1955) 138–150. [5] J.M. Ignizio, C. Romero, Goal Programming, in: H. Bigdoli (Ed.), Encyclopedia of Information Systems, vol. 2, Academic Press, London, 2003, pp. 489–500. [6] C. Romero, Extended lexicographic goal programming: A unifying approach, Omega 29 (1) (2001) 63–71. [7] P. Linares, C. Romero, Aggregation of preferences in an environmental economics context: A goal-programming approach, Omega 30 (2) (2002) 89–95. [8] A. Berger, R. DeYoung, H. Genay, G. Udell, Globalization of financial institutions: Evidence from cross-border banking performance, Brookings Papers on Economic Activity 2 (2000) 23–158. [9] J. Bonin, I. Hasan, P. Wachtel, Bank performance, efficiency and ownership in transition countries, J. Banking Finan. 29 (1) (2005) 31–53.
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