Mathematical Models in Banking Sector in the Context of the new Economy

Transcription

1 Mathematcal Models n Bankng Sector n the Contet of the new Economy Mara V. Mavr Athens Unversty of Economcs & Busness Abstract Recent advances n communcaton technology are changng the way that tradtonal bankng s done. Technology has added a new dmenson to the compettve pressures that are already reshapng the bankng ndustry. The resultng changes wll have a great mpact frstly on the reconfguraton of a bank branches network accordng to the dctates of the market, secondly on the desgn of new products and on the development and the use of alternatve dstrbuton channels and fnally on the customers swtchng behavor.. In ths study that presents an overvew of my PhD thess, dfferent ssues relatng to the reorganzaton of bankng ndustry are eamned. Specfcally the performance of a bank branch network, the onlne bankng as an alternatve dstrbuton channel and the duraton of the relatonshp among customers (ndvduals or enterprses) are the three nterrelated partes of ths thess. Optmzaton technques, generalzed lnear models and proportonal hazard models are used n order to determne products and servces whch are offered to bank clents through tradtonal and Internet channels, forecastng customers atttudes (adopton or reecton) to the new products and the tme horzon of ther cooperaton wth ther bank. All three sectons are eplorng ssues that put n the fundamentals of Customer Relatonshp Management (CRM) ntatves. Bank s management team could use the fndngs of ths study, n order to determne specfc attrbutes n desgnng fnancal servces and products, whch would add n customers satsfacton. The proposed approach could have sgnfcant mplcatons for enlargng the duraton of the relatonshp among customer and bank and for mamzng bank s performance. 1. Introducton In today s retal bankng envronment, where a more sophstcated consumer wth less bank loyalty s becomng the norm, customer servce qualty s an ndspensable compettve strategy. Furthermore, the stff competton and the compresson of the nterest rates, forces banks to set up and put nto effect all necessary decson support systems that wll enable them to dynamcally plan new locatons, evaluate ther performance, forecast customers atttude to new offered products and servces, estmate clents swtchng behavour, and fnally provde marketng support to ther geographcally separate unts. Bank branch constructon has slowed senstve not only to changng technology and changng customer needs, but also to a more volatle economy. As a consequence of deregulaton and nformaton technology banks offer new servces and products (Burton, 1990) A branch of the future must be framed wthn a fleble organzaton and can be changed wthn mnmal human and resource costs n order to keep pace wth ever-changng customer needs (Mountnho et al, 1997). Snce branches occupy the key poston n the bank s organzaton, ts performance s n the core of strategc drectons of each bank. The relaton between branch and communty s performance must also be eplored n order to dentfy the optmal scale sze for a network of estng and new branches The eploson of Internet usage and the huge fundng ntatves n electronc bankng have drawn the attenton of researchers towards Internet bankng. The new bankng busness reles on electronc delvery of ts products and servces, supported by nformaton systems and telecommuncatons (Hempel, G., & Smonson, D., 1998). Although mllons of dollars have been spent on buldng Internet bankng systems, reports have shown that potental users may not use the systems n spte of ther avalablty. Ths ponts out the need for research to dentfy the factors that determne acceptance of Internet bankng by the users. (Luaurn, P.,& Ln, H., 2005)) Moreover, customer satsfacton s recognzed as beng hghly assocated wth customer value and wth product prce; whereas servce qualty s not generally consdered to be dependent upon prce. The more satsfed the customers, the more tolerant to prce ncreases they are lkely to be, thus resultng n greater profts (Anderson, E., Fornell, C., & Lehmann, D., 1994; Garvn, 1988). 1

2 Accordng to Berry (1995) the transton from transacton to relatonshp-based marketng s netrcably lnked wth the ncreased role of qualty and satsfacton gven n servces. The remander of the paper s organzed as follows: Secton 2 provdes a bref overvew of the estng lterature on performance measurement; the mathematcal formulaton of the branch network and modular servce optmzaton model and outlnes a new teratve procedure for solvng the model. Secton 3 summarzes estng research on e-bankng, descrbes the used generalzed lnear model, provdes the hypotheses under eamnaton and presents the results of the analyss. Secton 4 descrbes the problem and the hypothess that would be consdered under eamnaton by usng survval functons, lfe tables and the proportonal hazard model. Last secton summarzes the conclusons of ths work and suggests further research. 2. Performance Measurement and technques of optmzaton 2.1 A bref lterature revew The lterature addressng branch performance measurng s large, but manly focuses on management accountng approaches (e.g. Hansen, 1990; Smth & Schwekart, 1992; Thygerson, 1991), utlzng econometrc models (Clawson, 1974; Doyle et al., 1979), multple regresson analyss (Heald, 1972; Boufounou, 1995), Data Envelopment Analyss (Camanho et al., 1999; Vassloglou & Gokas, 1990; Avkran, 1999) and artfcal neural network-based approaches (Athanassopoulos & Curram, 1996). On the subect of branch proftablty, lttle research has been conducted to-date (Avkran, 1997). Below, we provde a bref overvew of the estng approaches. Tradtonal measures of bank proftablty, ROA and ROE, are beset wth problems of allocatng assets, equty and net ncome when appled at branch level (Smth & Schwekart, 1992). Durng the 1990s Data Envelopment Analyss (DEA) has been used etensvely to evaluate bankng nsttutons. The relaton between effcency and profts was frst addressed by Oral (1990, 1992) through two DEA models for analyzng both effcency and proftablty. The proftablty model conssted of a desegregaton of epenses and ncome, whch were consdered as nputs and outputs, respectvely. However, the mplcaton of usng such models nstead of a usual proftablty measure was not dscussed. Drake and Howcroft (1994) correlated the DEA techncal effcency score wth cost-ncome ratos. Ther results ndcated that more effcent branches had lower cost-ncome ratos. Another study by Schaffnt et al. (1997) concluded that branch effcency has a very clear postve effect on proft. Recent publcatons determne the performance goals usng data analyss n order to defne the factors or varables that nfluence performance measures of a bank branch (e.g., Avkran, 1999; Hartman, 1999). Fre & Harker (1999) present a methodology that determnes the role of desgn n calculatng the effcency of servce delvery processes. The effcency of these processes s determned by usng a varaton of fronter estmaton (data envelopment analyss [DEA]-lke) technques. The proposed methodology reples to the queston of how much neffcency s due to process-desgn choce The evaluaton of the performance of a bank branch has been wdely addressed, consderng fed branch networks and offerng models for evaluatng ther performance. Most of the approaches set performance goals wthout consderng overall performance measures, and eamne a very large number of varables, some of whch are not statstcally sgnfcant; ths lmts the applcablty of the models to small-scale eamples and prohbts the applcaton to practcal cases where the number of branches can be n the order of hundreds. All the models developed to-date address the tradtonal bankng sector where most servces and products are offered at all locatons, and as a result they do not take nto account the varous modular servces that one branch could offer, or the overall branch network. 2.2 Problem Descrpton To concentrate on the problem we address n ths study, consder a geographcal area where bank branches are dspersed. The wde dversty of the types of customers served and the unequal competton condtons that the branches face n the dfferent sub-areas enforce top eecutves to set standards or norms n order to measure the performance of each branch and satsfy n a more effcent way customer needs. The demographcal, soco-economcal and market data of the area under consderaton are known, whle management goals and strategc plans are also set, as s the number of employees necessary to accomplsh customers requrements. In order to meet management goals, evaluaton and ratonalzaton of the current branch network must be conducted, especally f the bank s strategy has focused on busness growth through the acquston of other fnancal nsttutons and the reengneerng of busness processes. 2

3 The goal s to reach the optmum number of branches, gven a certan level of operatonal and fed costs, and the optmum m of servces that each should provde. Ths combned obectve can be lnked to the weghted sum of the performance of each ndvdual branch wthn the area under eamnaton. Metrcs may nclude: depost balances per branch, number of new accounts per month, average of retal lendng balances, number of new lendng accounts, balances of fnancal nvestments, etc. The value of the metrcs s a functon of varous nternal and eternal (to the bank) factors, whch are the problem varables. Internal factors may nclude: a) number of employees, e.g. tellers, corporate representatves, receptonsts, admnstrators, etc.; b) number and level of the management staff; and c) operatonal varables, e.g. number of ATM s or transactons. Eternal factors may nclude: area populaton and growth rate, average famly ncome, number of small/corporate busness establshments etc Mathematcal Model for Branch Optmzaton Performance Varables: Let n be the number of branches and ther nde. The effcency of a branch nvolves the dentfcaton of performance varables, whch reflect the corporate obectves and strateges. For branch, we model these varables by vector y =[y 1, y 2,, y m ] T of order m (number of varables per branch), where (T) denotes the transpose operand. Each element of vector y represents one performance varable for branch. The overall performance of branch (denoted by P ) s defned as follows: y 1 y2 (1 T P = = w y [ w1, w2,..., wm 1, wm]. ). ym In (1) w s a vector of dmenson m representng the weghts w k of the k-th performance varable, y k, of branch ; k s the nde of performance varables (k=1,, m). Internal and Eternal Factors As dscussed above, branch effcency s related to eternal (non-controllable) factors and nternal (controllable) factors. We model these factors, for each branch, usng the followng l-dmenson T =,,..., ] of [ 1 2 vector l. Each element represents one eternal or nternal factor for branch. Note that s the nde of factors. Relatonshps Each performance varable (.e., element y k of vector y ) s related to some nternal and eternal factors, relevant to branch ; gven the data concernng the ntal (current) branch confguraton, we can determne these relatonshps through regresson analyss, and obtan the a k regresson coeffcents. Equaton (2) epresses the relatonshps: y 1 a y a 2 = ym a m1 a a a m 2... a l c a c 2l y = A + C aml l cm In (2), A s an m l matr ncorporatng all regresson coeffcents that relate performance varables and nternal/eternal factors, whle C s the vector of constant terms resultng from the regresson analyss. The dfferent nternal and eternal factors have mplct relatonshps that can also be determned va regresson analyss on the ntal data. Eq. (3) provdes ths relatonshp: 1 0 b12... b = l bl1 bl2... b1 l 1 d1 b d 2l ( I l B) = D l dm (3) In (3), Il s the unt l l square matr, and B s an l l square matr wth zero dagonal terms (no regresson coeffcents between and tself). Each b-coeffcent s determned by regressng the factor on the remanng ones. Some of the b s may be zero, denotng a non-estng relatonshp between two factors. Fnally, D s a vector of constants resultng from the regresson analyss. A necessary condton for better performance measurement s the determnaton of the relatonshps between the values of the same group of factors, among dfferent branches. Inequalty (4) depcts such a relatonshp for factor : [,,..., ] n T z z z 0 z ( ) 0... (4) n In (4), z s an n-dmensonal vector, each element 1 2 n = [,,..., ]. Inequaltes (4) come by nferrng relatonshps through the eamnaton of approprate data sets, and the eplanaton s as follows: We observe data concernng a specfc set of factors for dfferent branches. The data mply some relatonshps between these factors. The relatonshps are ( ) T of whch s 1, 1, or 0, and (2) 3

4 captured n the form of constrants to the model. If such constrants are not establshed, the results of a soluton approach may be questonable. Inequalty (4) can be epressed for each factor ; e.g., f 5 s the number of tellers for branch, and we know that branch 2, by desgn, must have a smaller number of tellers than branch 3, we can wrte , mplyng that z 25 =1 and z 3 5 =-1. Bounds The elements,, of vector may be bounded by known parameters L and U, whch are mposed by management or eternal condtons. Such relatonshps can be epressed as follows: L U In (5), L =(L ) and U =(U ) are l-dmenson vectors ncorporatng boundng parameters. Inequalty (5) can be epressed for all the factors, snce both controllable and non-controllable factors may be bounded for branch operaton Lnear Programmng Formulaton Gven all the above defntons and relatonshps, we can proceed to the formulaton of a lnear program to mamze the overall performance for the geographcal area under eamnaton. The model s as follows: Mamze (6) Subect to: y = A + C = B + D z T ( ) 0 L m y R+ l R+ (10) U n = 1 w T y (5) =1, 2,, n (7) =1, 2,, n (8) =1, 2,, l (9) =1, 2,, n, =1, 2,, n (11), =1, 2,, n (12) The model of (6)-(12) s a typcal lnear program, whch s approprate for measurng both the performance of a bank s network and of each ndvdual branch separately. To recap, the obectve functon (6) sums up all the ndvdual branch performances. Equaton (7) relates performance varables and factors va regresson analyss coeffcents. Equaton (8) correlates branch factors through regresson analyss coeffcents. Inequalty (9) correlates dfferent branches for the same factor. Inequalty (10) bounds controllable or non-controllable factors. Fnally, constrants (11) and (12) force the problem varables to assume nonnegatve real values Soluton algorthm Up to ths pont, we have provded a model for bank s branch performance by ntegratng nternal and eternal factors wth performance varables. Bank s management team determnes whch performance varables and factors wll be under eamnaton accordng to the strategy that had already been decded to be appled. Although strategc plans cannot be quantfed, what we really can measure, s some parameters crucal for the development and the applcaton of the plan. Usng mathematcal technques we can model and formulated factors (fnd optmum value, or a set of possble values for each factor) and to make a predcton estmaton for the applcablty and usefulness of the proposed plan. In ths study we developed an algorthm called PERFORMANCE to solve the optmzaton problem of (6)-(12). To elmnate a branch we measure the performance of all branches and we select the one wth the lowest performance score. By resolvng the problem, we calculate the new performance of the reconfgured network. If the dfference O t between the overall performance and the operatng costs (.e. staff s salares, rent for buldngs etc.) for all branches ncreases, the procedure s repeated untl O t+1 <O t. In ths case the network has reached the pont of operatonal effcency. Note that t s an nde of teratons, whch s dentcal to the number of branches elmnated through the teratve procedure, and O t = S =1,,n [P -(Operatng Cost) ]. The Steps of the algorthm are provded below: Algorthm PERFORMANCE Step 0: Input: number (n) of branches, number and values of performance varables y (branch data), and current values of the eternal and nternal varables. Step 1: Regress performance varables on eternal (non-controllable) and nternal (controllable) varables, to determne matr A and vector C n Equaton (2). Step 2: Regress eternal and nternal varables on themselves to determne matr B and vector D n Equaton (3). Step 3: Observe the value of the same nternal or eternal varable among dfferent 4

5 branches and form nequalty (4) wth approprate z. Step 4: Impose the bounds L and U of nequalty (5) for each varable. Step 5: Calculate the performance of each branch separately P and of the whole bank branch network from (1), before optmzaton. Step 6: Solve the lnear programmng problem of (6)-(12) to determne the overall optmum performance for the bank branch network and of each branch. Step 7: Branch Elmnaton Procedure Step 7.1: Set t=1. Step 7.2: Calculate the dfference Ot Step 7.3: Fnd branch * wth lowest Step 7.4: performance P. Elmnate branch * and reformulate problem (6)- (12). Step 7.5: Resolve the problem wthout the branch *. Step 7.6: Calculate the dfference O t+1 for the n-t branches. Step 7.7: IF O t+1 >O t THEN a new elmnaton s suggested; set t=t+1 and RETURN to Step 7.3; OTHERWISE, keep all branches n the bank branch network snce t operates effectvely, and GOTO Step 7.8. Step 7.8: Termnate Effcent branch network reached. The algorthm termnates by provdng the target number of branches n the catchment area, the m of servces that defne the optmum performance for the bank branch network, and the operatonal parameters of each branch (through the values of the controllable factors). Note that we nclude operatonal costs of branches n the teratve procedure n order to ensure that branch elmnatons are preferred, whch s the case n the maorty of branch network reconfguratons. The proposed algorthm could be re-appled n any network, whch s under evaluaton and reconfguraton. Its man advantage s that the performance and factoral varables, whch are under eamnaton, are defned each tme by the management team. All necessary coeffcents that the algorthm uses are calculated through the update values of the above varables. So the algorthm becomes a tool that s always up-date accordng to the dctates of the market. 3. Electronc delvery channels 3.1 A bref lterature revew Recent advances n communcaton technology, ncludng the development of more powerful computers, are pavng the way for new bankng products and servces, changng the way that tradtonal bankng s done. The resultng changes wll have a great mpact on the development and use of alternatve dstrbuton channels. The most recent delvery channel s onlne bankng. Electronc or onlne bankng s the newest delvery channel to be offered by retal banks n many developed countres and there s a wde agreement that ths channel wll have a sgnfcant mpact on the market. Banks know that the Internet opens up new horzons for them and moves them from local to global fronters. Customer adopton s a recognsed dlemma for the strategc plans of fnancal nsttutons. Several studes have nvestgated why ndvduals choose a specfc bank. Important consumer selecton factors nclude: convenence, servce facltes, reputaton, and nterest rates (Kennngton et al., 1996; Zneldn, 1996). Accordng to Delvn (1995) customers have less tme to spend on actvtes such as vstng a bank and therefore want a hgher degree of convenence and accessblty. Lao and Cheung, (2002), employed survey data and regresson analyss to measure consumer atttudes toward Internet based e-retal bankng as a fnancal nnovaton. They found that ndvdual epectatons regardng accuracy, securty, network speed, user- frendlness, and user nvolvement and convenence, were the most mportant qualty attrbutes n the perceved usefulness of Internetbased e-retal bankng. Many studes n the lterature etended the Technology Acceptance Model whch s a theoretcal framework, whch dentfes the perceved ease of use and perceved usefulness as the key reasons for usng Internet Bankng. Luaurn, P.,& Ln, H.,(2005) etended TAM and they added perceved credblty, perceved self- effcacy and perceved fnancal cost to the model. Boml Suh & Ingoo Han, (2002) n ther study ntroduced trust as another belef n TAM that has an mpact on the acceptance of Internet bankng. Wang et al, (2003) also used the TAM and they ntroduce "perceved credblty" as a new factor that reflects the user's securty and prvacy concerns n the acceptance of Internet bankng. The study also eamnes the effect of computer self-effcacy on the ntenton to use Internet bankng. It also 5

6 demonstrates the sgnfcant effect of computer selfeffcacy on behavoural ntenton through perceved ease of use, perceved usefulness, and perceved credblty. Koufars, et al (2002) eamned the mpact of consumer eperence and atttudes on ntenton to return and unplanned purchases on lne. Kambl et al, (2000), show that senor management s support and techncal ssues such as nformaton securty are of the most sgnfcant mpacts to frms that take ther busness onlne. Mols, (1999), determnes that bank customers are dvded nto Internet bankng segment and a branch bankng segment. The Internet nfluences the future dstrbuton channel structure n two ways: (a) t s n tself a new dstrbuton channel for fnancal servces and (b) t nfluences consumers n a way that they nvest tme and resources n becomng PClterate and n famlarzng themselves wth the Internet. Users of PC bankng are more satsfed, are less prce senstve, have hgher ntentons to repurchase and provde more postve word-ofmouth than non-users. Htt and Fre, (2002), eamne whether and how characterstcs or behavors mght dffer between customers who use electronc delvery systems and those who use tradtonal channels. By usng logstc regresson they conclude that demographc characterstcs and changes n customer behavor followng adopton of PC bankng account only a small fracton of overall dfferences. Karaluoto, et al. (2002) eplored the effect of dfferent factors affectng atttude formaton towards Internet Bankng n Fnland. By usng factor analyss they determned that pror eperence of computers and technology as well as demographc factors mpact heavly consumers onlne behavour. Jun and Ca, (2001) used the Crtcal Incdent Technque (CIT) to uncover the key dmensons of Internet bankng customers and to dentfy crtcal satsfyng and dssatsfyng factors whch were relablty, responsveness, access and accuracy. 3.2 Problem Descrpton The purpose of s to present a methodology for dentfyng factors that affect someone s decson usng or not usng onlne servces. In order to meet ths goal we use a generalsed lnear model, specfcally a logstc regresson model, and we are tryng to estmate the factors that mprove someone s fnal decson and the contrbuton of each one. The scope of ths study s to descrbe bank-customers behavour n Greek onlne market, whch s fragmented and Internet adopton wthn the populaton s qute low, up to 22,4% due to a survey that s completed by Natonal Statstcal Organzaton n 2005, a fact that offers a bass for ntal estmatons. The study therefore, focused on dentfyng the sgnfcance of the followng factors: H 1 : Speed of transacton of electronc delvery channels provdes a compettve advantage for them. H 2 : Dffcultes n the use of the new technology prevent some customers from usng t. H 3 : Many people beleve that today s tradtonal bankng system operates well and thus, the onlne presence of the banks s characterzed as not necessary. H 4 : Internet bankng costs nclude those assocated wth Internet actvtes as well as bank costs and charges. Cost nfluences consumers atttudes toward electronc servces. H 5 (a) : Accordng to lterature, young people, from 20 up to 40 years old, are famlar to Internet use H 5 (b) : People who use electronc bankng servces have a hgher educaton level than others. Maybe educaton s another factor that s characterzed as mportant for usng or not usng onlne servces. H 6 : Many people complan about lack of nformaton concernng the new electronc channels that fnancal nsttutons use today. The above hypotheses are tested due a feld survey questonnare that took place n Athens and Thessalonca durng March of Fndngs of the questonnares show that: The compettve advantage of e-banks or electronc bankng servces s the speed of the transactons. More than 90% of the respondents consder t, to be a valuable attrbute n the electronc fnancal ndustry. Avodng queues or delays are the prmary reason for choosng onlne transactons. It s useful for the banks to advertse ther onlne presence, the servces and the facltes that they offer to the clents; 89% of the respondents ascrbe defcency of nformaton concernng the electronc bankng servces as the man reason for ther reecton n onlne bankng. It was found that costs from the use of the Internet and from bank charges are of slght mportance. Ths may be due to the fact that nether the charges nor the net-epenses are overprced. Sty - eght percent of the partcpants estmate t as a non mportant factor. On the other hand, the dffcultes of the user s nvolvement n the electronc system are found to be of mportance, as ths restrcts the control 6

7 that an ndvdual eercses over the process (.e. access to onlne servces depends on access to the Internet). Only 27% consder the Internet s use as somethng etremely dffcult whle less than 20% beleve that usng electronc bankng servces s a wearsome task Wllngness of use onlne bankng servces A logstc regresson model, was employed n order to dentfy the sgnfcance of the factors, whch play a crucal role n an ndvdual s decson whether or not to use onlne bankng servces and to estmate the probablty of each ndvdual usng e- servces. Logstc regresson model estmates for each customer the logarthm of the probablty of usng on lne servces to the probablty of not usng onlne bankng servces. Eght factoral varables are under eamnaton for ther contrbuton n the logt (p ) of the -th customer, whch were 1 = age, 2 = educaton, 3 = monthly ncome, 4 = transactons speed, 5 = fear of change, 6 = lack of Informaton, 7 = dffcultes of usng Internet, 8 = cost of usng Internet own property. The proposed logstc regresson model s: logt (p )= log (p /(1-p ))= 1.60* 1, -1.26* 5, -1.84* 6, -2.69* 7, (13) or ep(1.60* 1, -1.26* 5, -1.84* 6, -2.69* 7, ) p = 1+ep(1.60* -1.26* -1.84* -2.69* ) 1, 5, 6, 7, The p represents the probablty of the ndvdual to use on-lne bankng servces, whle the eplanatory varables 1, 5, 6, and 7 represent overall measures of factors regardng age, fear of change, lack of Informaton and dffcultes of usng Internet, respectvely. Snce our survey dd not eplctly ntroduce cost and transactons speed, the effects of these factors are parameterzed n terms of the logstc constant. The followngs are depcted when we use the proposed generalzed model 1. Indvdual s age s a sgnfcant determnant of someone s decson to use or not electronc servces. Ths fndng regards respect to all prevous studes that defned the profle of onlne bankng customer as a young man or woman who s famlar to technology advancements, and to PC and Internet navgaton. Ths result s consstent wth hypothess 5 (a). 2. The fear of change sgnfcantly affects the decson of use. An ncrease n ths factoral coeffcent would ncrease the wllngness of use. Ths fndng s consstent to hypothess The factor nformaton n someone s decson s of maor mportance. Hypothess 6 s affrmed by ths proposton. 4. User- frendlness s a sgnfcant determnant of an ndvdual s acceptance or reecton of electronc servces. Ths s consstent wth hypothess Varables educaton and monthly ncome are are denoted as non-sgnfcant varables Accordng to these results hypothess 5(b) does not contrbute to the wllngness of usng onlne bankng servces. 6. The results of varables transactons speed, and Cost of usng the Internet sgnfe that these varables could be sgnfcant f some of the parameters were to change (.e. take nto account and other varables). Hypotheses 1 and 4 seem to be less mportant n the wllngness of use. 7. The constant coeffcent ß? s consstent wth our constructon, under whch the transacton s speed and the cost of e-servces are parameterzed n the logstc constant. However as, the constant term s statstcally sgnfcant, t s ndcated that a rse n cost varable or n transacton s speed varable s relatvely mportant wth regard to decson of use. 4. Customer swtchng behavour n greek bankng servces usng survval analyss 4.1. A bref lterature revew In nowadays, understandng and reactng to changes of customer behavor s an nevtable aspect of survvng n a compettve and mature market (Larvere & Poel,. 2004). Banks are facng the ncreased competton due to two dfferent reasons: (a) the entrance of fnancal and nsurance frms n the tradtonal bankng market, and (b) the wde range of offered products and servces to publc. As a consequence the bankng ndustry strves to succeed by puttng the topc of rapd and changng customers needs to ther agenda (Krshnan, Ramaswamy, Meyer & Damen, 1999). The economc value of customer retenton s wdely recognzed n the lterature: (1) Successful customer retenton lowers the need for seekng new and potentally rs ky customers and allows organzatons to focus more accurately on the needs of ther estng customers by buldng relatonshps 7

8 (Dawes & Swales, 1999). (2) Long-term customers buy more and, f satsfed may provde new referrals through postve word-of-mouth for the company. (3) Long-term customers become less costly to serve due to the bank s greater knowledge of the estng customer and to decrease servng costs. (4) They tend to be less senstve to comparatve marketng actvtes (Ganesh et al., 2000; Colgate et al., 1996). (5) Loosng customers not only leads to opportunty costs because the reduced sales, but also to an ncreased need for attractng new customers whch s fve to s tmes more epensve than customer retenton (Athanassopoulos, 2000). Many researchers n the lterature have nvestgated the churn behavor of the bankng customers. Proportonal hazard models are used by Bolton (1998) and Van den Poel & Larvere (2004) n order to eamne the lnk between customer satsfacton and retenton. they found that (a) demographc characterstcs, envronmental changes and stmulatng nteractve and contnuous relatonshps wth customers, are of maor concern when consderng retenton and that (b) customer behavor predctors only have a lmted mpact on attrton n terms of total products owned as well as nter-purchase tme. Regresson models are used by Bloemer, Ruyter and Peeters, (1998) and Athanassopoulos (2000). They reveal that mage s ndrectly related to bank loyalty va perceved qualty. proposed an nstrument of customer satsfacton n retal bankng servces The emprcal results have confrmed that customer satsfacton s a functon of servce qualty (staff servce and corporate mage), prce, convenence and nnovaton. Levesque & McDougall, (1996), pont out that that servce problems and the bank s servce recovery ablty have a maor mpact on customer satsfacton and ntentons to swtch. They dentfed the determnants, whch ncluded servce qualty dmenson, servce features, servce problems, servce recovery and products used. They concluded The relatonshp between commercal banks and clent companes was studed usng t-test by Pauln et.al, (1998).Swtchng costs are ncreasngly fndng ther way nto models of customer loyalty. Accordng to Jones et.al., (2002), swtchng costs can be thought of as barrers that hold customers n servce relatonshps. Krshnan et.al., (1999), va a Bayesan analyss, found that satsfacton wth product offerngs s a prmary drver of overall customer satsfacton.?n summary, many studes nvestgated the problem of customers swtchng behavour. In ths study we contrbute n the estng lterature at three dfferent levels: (a) We eamne the mpact of qualtatve groups of factors n retenton behavour (b) we eamne customers attrton consderng the tme aspect and (c) we use lfe tables n order to estmate the churn behavour of clents n dfferent perods of tme Problem Descrpton Deregulaton and ncreased competton from new products and delvery channels prompt bankng ndustry to reconsder the economc value of customer retenton. Customers lfe cycles are becomng ncreasngly transtory due to severe mpact of compettors actons on estng relatonshps (Renartz and Kumar, 2000). Typcally, customers splt ther purchases among several compettve banks (Dwyer, 1997). In ths study we eamne the problem of customers attrton, whch s a classc problem of bnary classfcaton: churn behavor or not. More specfcally we want to eplan customers swtchng behavor by eamnng a seres of factors and by dentfyng the contrbuton of each one. The study therefore, focused on determnng the sgnfcance of the followng factors: H 1 : There s no evdence that customers gender affects ther decson of breakng down ther relatonshp wth the bank. H 2 : Bank s credblty contrbutes postvely n the duraton of the relatonshp between customer and bank. H 3 : Customers satsfacton s the most mportant factor for enlargng the duraton of ther cooperaton wth the bank H 4 : The qualty of offered servces and products determne the lfe cycle of the eamned relatonshp. H 5 : Interest Rate s not recognzed as a sgnfcant factor n customers swtchng behavor H 6 : Indvduals educatonal level s consdered as a valuable factor n the length of the eamned relatonshp. We use Lfe Tables to estmate the tme of the churn event. A proportonal hazard model s performed to fnd the factors whch would pay n the reducton of customers secesson. Survval analyss s a collecton of statstcal methods for data analyss for whch the outcome varable of nterest s tme untl an event occurs (n our case: customer churn behavor) wth the am to develop 8

9 predctve models n whch the rsk of an event depends on covarates We usually refer to the outcome varable as survval tme, as t gves the tme that an ndvdual has survved over some follow-up perod and we refer to the event as a falure. For some customers the tme to falure (end the cooperaton wth the bank) may be observed completely, whereas for others we only have partal observaton untl some specfc censorng tme c. We denote by T, the random varable for a customer s survval tme. The dstrbuton of survval tmes s characterzed by three functons: [1] The probablty that a customer contnues to cooperate wth the bank longer than t, s defned by survval functon S(t) S(t)=P(a customer contnues to cooperate wth the bank longer than t)=p(t>t) (14) The cumulatve dstrbuton functon of T s denoted by F(t), and hence S(t)=1-P(a customer ends ts relatonshp wth the bank before tme t)=1-f(t) (15) [2] The probablty densty functon of the survval tme, T, s denoted by f(t) and s defned as the lmt of the probablty that a customer breaks down ts relatonshp wth the bank n the short nterval (t to t+?t) per unt wdth?t. It s epressed as (16) P{ a customer ends ts relatonshp wth th e bank n the nterval ( t, t+? t) } f( t) =lm?t 0 The densty functon s known as the uncondtonal falure rate. [3] The hazard functon h(t) of survval tme T gves the condtonal falure rate or the nstantaneous falure rate (churn behavor). It s defned as the probablty of falure durng a very small tme nterval, assumng that the customer has decded to contnue hs/her cooperaton wth the bank to the begnnng of the nterval. It s epressed as (17) P{ a customer of age tends ts relatonshp wth the bank n the nterval ( tt, +? t) } h( t) =lm?t 0 The hazard functon s defned n terms of cumulatve dstrbuton functon F(t) and the probablty densty functon f(t) as ( ) = f ( t) { 1- F( t) } = f ( t) S ( t) h t (18) From equatons (2) and (3) we conclude for the cumulatve dstrbuton functons? t? t d d f ( t) = F( t) = 1 S( t) dt dt Lfe Table Analyss (19) The lfe table s a method for measurng churn behavor and descrbng survval eperence of bank s customers. These tables summarze the swtchng behavor of the customers for a specfc perod of tme. Consderng that the perod under eamnaton s dvded to d ntervals of wdth r d, where r d =t d+1 -t d, provde nformaton about the number of customers that enter n each nterval, the number of customers eposed to rsk of secesson, the probablty of churn behavor n the d-th nterval per unt wdth and an estmaton of the survval rate n ths nterval. Fgure 1 depcts the lfe cycle nformaton n a perod of tme T. In the begnnng of the study we observe the behavor of n customers, whle at the end of the eamned perod the number has changed to n as some clents broke down ther cooperaton wth the bank (churn behavor) whle for some others we don t have any nformaton (censored behavor) The Proportonal Hazard Model Let n be the number of customers and ther nde. The Proportonal Hazard Model gves an epresson for the hazard at tme t for the -th customer wth a gven specfcaton of a set of eplanatory varables. We model these factoral varables, for each customer, usng the followng p-dmenson vector: T =[,,...,] 1 2 p. Each element of represents products attrbutes or demographcal data for customer. Note that s the nde of eplanatory varables. The Proportonal Hazard Model proposed by Co can be wrtten as follows: ( ) ( ) ( ) b h t, = h t e o = ho ( t) ep( b+b bpp) h ( t, ) In (20) p =1 represents the hazard for the -th h ( ) customer at tme t, 0 t : represents the baselne hazard functon and b : represents the coeffcent of the covarate, represents the value of the -th customer for the varyng covarate. (20) 9

10 4.3. Results from Survval Analyss We have consdered 6 ndependent (=1,,n) and (=1, 6) factoral varables whch are 1 = gender, 2 = bank s accuracy, 3 = customers satsfacton, 4 = servce qualty, 5 = nterest rates, 6 = educatonal level. A European fnancal servces company that offers bankng and nsurance servces provded the data for ths study. Investgatng the survval probabltes, due to lfe tables we conclude that churn behavor dffers among the range of the factors. Some results from our analyss are presented below: The medan tme, s estmated equal to 45,6 years old for men and to 45,08 for women. In order to eamne the power of the Hypothess H1 we used Wlcoon test, accordng to whch we found that there s no dfference between men and women n the duraton of ther relatonshp wth the bank. A bnary varable also represents the factor bank s credblty. The medan tme of survval for the customers who consder bank s credblty as a strong factor for contnung ther cooperaton wth bank s estmated up to years old and up to for the customers belongng to second category. Ths fndng s consstent wth Hypothess H2. Customer Satsfacton s modelled by an ordnal varable wth 7scales. (1= totally satsfed, 7= no-satsfed). The medan tme for the fully satsfed customers s calculated equal to years old, whle the respectvely value for the dssatsfed customers s 38 years. Hypothess H3 s affrmed by ths proposton. Servce qualty s also model by an ordnal varable wth 7 scales from 1 (=non mportant) to 7 (=etremely mportant). The maorty of the customers of our samples rates ths factor wth values between 4 to 7. The medan lfe for these categores s estmated years old. These results are consstent wth Hypothess 4. The deregulaton and the reformaton of economc markets turned nterest rates to a very mportant ssue for the customers. Varable nterest rates s modelled by a seven-tem scale. The lkelhood of swtchng behavour for the customers that characterzed the nterest rates as low or hgh s hgher than the customers who rank nterest rates wth values 1-2, 4 and 6-7. These proportons suggest that the hypothess H5 does not totally approved. The varable Educatonal level has four categores (1=prmary school or less, 2= hgh school, 3= unversty studes and 4=postgraduate studes). Accordng to the results, apart form the customers wth low educatonal level whch seem to break down the relatonshp wth the bank n the age of years old, the mpact of ths varable s ncreasng the duraton of the eamned relatonshp for the other three categores s lmted. Thus, the power of Hypothess 6 sn t strong enough. Churn Behavor and Churn Predctors usng Co Regresson Fgure 2 presents the survval functon at mean of covarates for all customers ncluded n ths study. The plot shows that the epected decreasng shape suggestng the fact that the longer an ndvdual has been a bank customer the smaller the probablty of survval. From the graph we note that customers eperence a hgh swtchng probablty (>0.6) (swtchng probablty =1-survval probablty accordng to equaton (15)) n the age of After the age of 50 years old the probablty of survve decreases. Cum Survval 1,0 0,8 0,6 0,4 0,2 0,0 Survval Functon at mean of covarates 0,00 20,00 40,00 60,00 80,00 Fgure 2: Survval Behavor for all customers The mpact of the observed covarates on the retenton s nvestgated by the use of the Co Proportonal Model, as we descrbed t n equaton (16)-(20). A number of nterestng fndngs emerge from proportonal hazard model: In terms of demographc characterstcs, the lower educatonal level has a postve mpact n the lmtaton of the rsk of churn behavor Both the qualty of the offered servces and the bank s brand name has a negatve effect n the decrease of the attrton. We conclude to the same argument for customers satsfacton The values of beta coeffcents (b ) for nterest rates sgnfy that hgh and low nterest rates ncrease the rsk of retenton. 5. Conclusons age 10

11 In ths study an ntegrated approach for reconfgurng a communty branch network accordng to the dctates of the market s developed, the nternal bank resources and the strategc polcy constrants. a lnear programmng model whch was solved va an teratve algorthm that targets the optmum number of branches and the optmum m of servces that each branch should offer, s proposed. The results ndcate that through the ths approach, the branch network at the communty level can be streamlned and transformed nto en effectve, revenue-generatng group of bank nodes. Secondly a framework n predctng consumer s behavor n new products and servces s proposed. An estmated probablty of an ndvdual to use or not to use onlne bankng servces s provded by a generalzed lnear model. Indvdual s age, the dffcultes of usng the Internet, the fear of the changes provoked to the bankng sector due to technologcal development and the lack of nformaton concernng products and servces provded to customers through electronc delvery channels, are dentfed as crucal factors that affect someone s decson to use or not to use onlne servces. Fnally the churn behavor of bank customers s nvestgated n greek market. Wth the help of Lfe Tables and the proportonal hazard model we fnd out that the qualty of the offered bankng products and servces n combnaton wth the bank s brand name have a postvely effect n the decrease of swtchng behavor whle demographcal characterstcs such as gender and educatonal level have a lmted mpact. Consderng ths fndngs n the contet of customer behavor we conclude that a bank needs to develop a CRM systems, n order to estmate the adopton of new products and servces, decrease the rate of retenton and brngs on ts performance. Opportuntes for further research resde n determnng segments of customers wth common characterstcs that wll contrbute n the above three obectves. References Anderson, E., Fornell, C., & Lehmann, D. (1994). Customer Satsfacton, Market Share, and Proftablty: Fndngs from Sweden. Journal of Marketng, 58, Athanassopoulos, A.D, & Curram, S. (1996). A comparson of Data Envelopment Analyss and Artfcal Neural Networks as Tools for Assessng the Effcency of Decson Makng Unts. Journal of the Operatonal Research Socety 47, Athanassopoulos, D.A. (2000). Customer Satsfacton Cues to Support market segmentaton and Eplan Swtchng Behavor. Journal of Busness research, 47, Avkran, N.K. (1997). Models of retal performance for bank branches: predctng the level of key busness drvers. Internatonal Journal of Bank Marketng,15(6), Avkran, N.K. (1999). An applcaton reference for data envelopment analyss n branch bankng: helpng the novce researcher. Internatonal Journal of Bank Marketng 17(5), Berry, L. (1995). Relatonshp Marketng of Servces-Growng Interest, Emergng Perspectves. Journal of the Academy of Marketng Scence, 23(4), Bloemer, J., Ko de Ruyter, & Peeters, P. (1998). Investgatng drvers of bank loyalty: the comple relatonshp between mage, servce qualty and satsfacton. Internatonal Journal of bank Marketng, 16(7), Bolton, N, R. (1998). A dynamc model of the duraton of the customer s relatonshp wth a contnuous servce provder: the role of satsfacton. Marketng Scence, 17 (1), Boufounou, P.V.(1995). Evaluatng bank Branch Locaton and Performance: A case study. European Journal of Operatonal Research 87, Boml, S., Ingoo, H. (2002) Effect of trust on customer acceptance of Internet bankng. Electronc Commerce Research and Applcatons, Burton, D. (1990). Competton n the UK retal fnancal servce sector: some mplcatons for the spatal dstrbuton and functon of bank branches. Servce Industres Journal, 10(3), Camanho A.S., & Dyson, R.G. (1999). Effcency, Sze, Benchmarks and Targets for Bank branches: an applcaton of data envelopment analyss. Journal of the Operatonal Research Socety 50, Clawson, J. (1974). Fttng Branch locatons, performance standards, and marketng strateges to local condtons. Journal of Marketng 38(1), Colgate, M., Stewart, K., & Knsella, R. (1996).Customer defecton: A study of student 11

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