Utilizing recent developments in data envelopment analysis (DEA), this paper examines

Transcription

1 Profitability ad Marketability of the Top 55 U.S. Commercial Baks Lawrece M. Seiford Joe Zhu Departmet of Mechaical & Idustrial Egieerig, Uiversity of Massachusetts at Amherst, Amherst, Massachusetts Departmet of Maagemet, Worcester Polytechic Istitute, Worcester, Massachusetts Utilizig recet developmets i data evelopmet aalysis (DEA), this paper examies the performace of the top 55 U.S. commercial baks via a two-stage productio process that separates profitability ad marketability. Substatial performace iefficiecy is ucovered i both dimesios. Relatively large baks exhibit better performace o profitability, whereas smaller baks ted to perform better with respect to marketability. New cotextdepedet performace measures are defied for profitability ad marketability which employ a DEA stratificatio model ad a DEA attractiveess measure. Whe combied with the origial DEA measure, the cotext-depedet performace measure better characterizes the profitability ad marketability of 55 U.S. commercial baks. The ew approach idetifies areas for improved bak performace over the two-stage productio process. The effect of acquisitio o efficiecy ad attractiveess is also examied. (Data Evelopmet Aalysis (DEA); Profitability; Marketability; Efficiecy; Baks) Maagemet Sciece/Vol. 45, No. 9, September 1999 pp Itroductio Performace aalysis of fiacial istitutios, particularly commercial baks, has received icreased attetio over the past several years. As a result, the focus has moved from attempts to characterize performace i terms of simple ratios (ROA or ROI) to a multidimesioal systems perspective. Although accoutig ad fiacial ratios provide importat ad useful iformatio for bechmarkig a bak s fiacial performace, there are, i fact, may factors relative to bak performace, e.g., assets, reveue, profit, market value, umber of employees, ivestmets, ad customer satisfactio, etc., ad, obviously, a better uderstadig of the relatioship amog these various factors would provide the key for improvig bak productivity. Data evelopmet aalysis (DEA), a mathematical programmig approach for characterizig the relatioships amog multiple iputs ad multiple outputs, has prove itself as a metric for measurig bak performace. Numerous applicatios of DEA have appeared i the bak performace literature. For example, Sherma ad Gold (1985) use DEA to evaluate the performace of braches of a U.S. savigs bak. Other studies o bak brach efficiecy iclude Vassiloglou ad Giokas (1990), Oral ad Yolala (1990), ad Sherma ad Ladio (1995), who evaluate bak brach efficiecy i Greece, Turkey, ad the Uited States, respectively. Other DEA studies have compared performace amog differet baks. For example, Chares et al. (1990) provide a illustrative applicatio of DEA to U.S. commercial baks i the time period , ad Barr et al. (1993, 1994) examie U.S. bak failures over the period Also, the quality, profitability, ad productivity of bakig services have bee studied (Grifell-Tatje ad Lovell 1999, Soteriou ad Zeios 1999) ad models proposed for assessig the market ad cost efficiecy /99/4509/1270$05.00 Copyright 1999, Istitute for Operatios Research ad the Maagemet Scieces

2 Profitability ad Marketability of the Top 55 U.S. Commercial Baks of large-scale bak brach etworks (Athaassopoulos 1998). Berger ad Humphrey (1997) provide a review o 130 studies of fiacial istitutio icludig baks, bak braches, savigs ad loas, credit uios, ad isurace compaies. Fially, see Harker ad Zeios (1999) for recet studies o efficiecy of fiacial istitutios. Most bak performace studies employ labor, iterest (o-iterest) expeses, office space, ad umber of accouts as iputs, ad umber of trasactios, iterest (o-iterest) icome, total loas, ad deposits as outputs. While these iputs ad outputs ca characterize a bak s operatioal performace, they do ot reflect the market valuatio or performace of a bak s stock. To evaluate stock marketability, oe may iclude such additioal factors as market value, earigs per share, ad retur to ivestors i a DEA aalysis. By icorporatig some ew factors i a two-stage approach, the curret paper explores profitability ad (stock) marketability of 55 U.S. commercial baks i A two-stage productio process is defied that geerates profit i the first stage, ad market value i the secod stage. The effect of bak size o profitability ad marketability is revealed by evaluatig both techical ad scale efficiecies. Icreasig returs to scale (IRS) are foud amog relatively small baks baks with less tha $2,000 millio i assets i our data set ad decreasig returs to scale (DRS) amog the larger baks. However, some of the larger baks exhibit IRS i profitability. A examiatio of iput cogestio idicates that a reductio i curret iput levels may actually icrease reveue ad profit levels. Several bak acquisitios occurred i early This allows a performace study o the effect of bak acquisitio o profitability ad marketability. It is show that marketability is, at most, slightly affected by bak acquisitio. The preset study also idicates serious iefficiecies i both profitability ad marketability ad offers a procedure to improve the bak productio process by focusig o profitability ad scale efficiecy. I additio to a stadard DEA aalysis, the paper also measures cotext-depedet bak performace for differet efficiecy levels. This cotext-depedet DEA model allows (i) a bak to bechmark itself agaist its competitors; (ii) the measuremet of the relative attractiveess i profitability ad marketability of each bak agaist the backgroud of a group of baks operatig at a differet efficiecy level; ad (iii) the further study of the effect of bak acquisitios o the performace of other baks. The remaider of the paper is orgaized as follows. Sectio 2 defies the bak productio process ad its correspodig productio factors (iputs ad outputs). Sectio 3 describes the DEA tools employed ad the resultig empirical fidigs for the 55 baks. Our coclusios appear i 4 alog with suggestios for future ivestigatio. 2. Bak Productio Process Fifty-five U.S. commercial baks appear i the Fortue 1000 (Fortue April 29, 1996). 1 Obviously, rakig by reveue while ecessary for iclusio i the Fortue 1000 does ot adequately characterize the performace of these baks. Fortue also provides other factors: e.g., umber of employees (employees), assets, stockholders equity (equity), market value (MV), total retur to ivestors (TRI), ad earig per share (EPS) to further characterize the performace of the top compaies. 2 As poited out by Zhu (1999), ay sigle performace measure based o these eight factors will be usatisfactory i its performace characterizatio; with several measures oe gets coflictig reports ad it is difficult to determie which compay exhibits a better overall. While Fortue s aalysis is based o each sigle 1 The baks are available from the authors or from Fortue April 29, Reveues are iterest ad o-iterest reveues ad are for the fiscal year eded o or before Jauary 31, Profits are after taxes, after extraordiary credits or charges, ad after cumulative effects of accoutig charges. Assets are the compay s year-ed total. Equity is the sum of all capital stock, paid-i capital, ad retaied earigs at the compay s year-ed. MV is obtaied by multiplyig the umber of commo shares outstadig by the price per commo share as of March 15, EPS for each compay is the primary earigs per share that appear o the icome statemet. TRI icludes both price appreciatio ad divided yield to a ivestor i the compay s stock. For more detailed explaatios, see Fortue April 29, Maagemet Sciece/Vol. 45, No. 9, September

3 Profitability ad Marketability of the Top 55 U.S. Commercial Baks Figure 1 Bak Productio Process measure, the curret study illustrates the value of a performace measure that operates simultaeously with multiple dimesios. To fully recocile these eight factors ad have a more complete portrayal of the performace of these 55 baks utilizig these differet factors, Figure 1 describes a bak productio process based o these eight factors. The process is divided ito two stages ad the eight factors are expressed as iputs ad outputs i each stage. The first stage (Stage 1) measures profitability, i.e., a bak s ability to geerate the reveue ad profit i terms of its curret labor, assets, ad capital stock. The secod stage (Stage 2) measures (stock) marketability, i.e., a bak s performace i the stock market by the reveue ad profit it geerates. It ca be see that reveue ad profit serve as itermediate factors i the sese that they are outputs from the first stage ad iputs to the secod stage. The DEA iputs ad outputs selected are based o Fortue s origial choice of factors for performace characterizatio. However, we will ote that other factors, e.g., market value to book value, price to earigs ratio, turover ratio (ratio of traded value to year-ed market value), etc., may also be used to capture marketability. Ufortuately, Fortue does ot provide data o these factors. Therefore, we restrict our aalysis to the eight Fortue factors as described i Figure 1. These are sufficiet to illustrate our approach to explaiig bak performace while attemptig to disetagle marketability from profitability. Valuable isights result from such a chage i perspective. 3. Measurig Profitability ad Marketability of Commercial Baks I this sectio, we aalyze the profitability ad marketability of 55 U.S. commercial baks. To actually characterize the performace of these 55 baks, it is ecessary to exted the basic DEA methodology. For a itroductio to the basic DEA models ad theoretical extesios, readers are referred to Ali ad Seiford (1993b) or Chares et al. (1994). 3.1 Characterizatio of Bak Performace The output-orieted (CCR) DEA model is employed to measure efficiecy i profitability ad marketability (Chares et al. 1978). m max t o i 1 s s i s r t 1, 2 r Maagemet Sciece/Vol. 45, No. 9, September 1999

4 Profitability ad Marketability of the Top 55 U.S. Commercial Baks s.t. j x ij s i x io i 1, 2,..., m; j y rj s r t o y ro r 1, 2,..., s; j, s i, s r 0, (1) where x ij ad y rj are the amout of the ith iput cosumed ad the amout of the rth output produced by the jth DMU (or bak), respectively. I Stage 1 (t 1), we have 55 DMUs (baks), i 3 iputs employees, assets ad equity, ad r 2 outputs reveue ad profit. I Stage 2 (t 2), we have 54 DMUs (baks), i 2, iputs reveue ad profit, ad r 3 outputs MV, TRI, ad EPS. 3 Let 1* o ad 2* o be the optimal values for Stage 1 ad 1* Stage 2 models respectively. If o 1 ad all iput/output slacks are zero, the a bak is said to be CCR-efficiet i profitability. If 2* o 1 ad all iput/ output slacks are zero, the a bak is said to be CCR-efficiet i marketability. Table 1 reports the CCR efficiecy scores. Oly six baks, amely, DMU1 (Citicorp), DMU5 (J. P. Morga & Co.), DMU10 (Bakers Trust New York Corp.), DMU16 (Wells Fargo & Co.), DMU17 (Bak of New York Co.), ad DMU30 (MBNA), are CCR-efficiet i profitability. Six baks, amely, DMU10, DMU13 (PNC Bak Corp.), DMU40 (Fifth Third Bacorp), DMU48 (First Security Corp.), DMU52 (First Empire State Corp.), ad DMU54 (BayBaks), are CCRefficiet i marketability. A sigle bak, DMU10 exhibits best practice i both dimesios. Sice the DMUs are sorted by reveue, the first 31 baks are amog the Fortue 500 with assets greater tha $2,000 millio (with oe exceptio DMU30 MBNA). It ca be see that all CCR-efficiet DMUs for the Stage 1 profitability model are amog the first 30 baks, 3 EPS data for oe bak (Bak 34, Souther Natioal Corp.) was egative. Therefore this bak was excluded from the DEA aalysis of Stage 2 resultig i 55 DMUs i Stage 1 ad 54 DMUs i Stage 2. Although oe could ivoke the traslatio ivariace property of DEA (Ali ad Seiford 1990) to allow egative values, such use is restricted to the covex case, ad some properties, e.g., returs to scale (RTS), are ot traslatio ivariat. whereas most of the CCR-efficiet DMUs for the Stage 2 marketability model are amog the last 16 baks. The average CCR scores for the first 30 baks ad the remaiig 25 baks are respectively 1.28 ad 1.46 i profitability versus 1.69 ad 1.34 i marketability. This may idicate that larger baks are better at geeratig profits, while the smaller baks are more accurately valued. Overall, oly 11% of the baks were efficietly operatig uder profitability ad marketability. Figure 2a b give the distributios of CCR efficiecy scores for Stage 1 ad Stage 2, respectively. Potetial improvemets of 20% to 60% i reveue ad profit are idicated for early 71% of the baks, ad a rage of 20% to 60% improvemet i MV, TRI, ad EPS is expected for approximately 45% of the baks. O average, baks had a relatively better performace with respect to profitability. Scale efficiecy has log bee recogized i the bakig literature as a importat issue. However, the CCR Model (1) assumes costat returs to scale (CRS). I order to determie the scale efficiecy of these 55 baks, we employ the output-orieted BCC DEA model which allows variable returs to scale (VRS) (Baker et al. 1984). max t o m s s i s r t 1, 2 i 1 r 1 s.t. j x ij s i x io i 1, 2,..., m; j y rj s r t o y ro r 1, 2,..., s; j 1 j, s i, s r 0. (2) Let o 1* ad o 2* be the optimal values for (2) i Stage 1 ad Stage 2, respectively. Defie a scale efficiecy measure by Maagemet Sciece/Vol. 45, No. 9, September

5 Profitability ad Marketability of the Top 55 U.S. Commercial Baks Table 1 Efficiecy Results Profitability Marketability Adjusted DMU No. Bak Name CCR BCC RTS CCR BCC RTS CCR 1 Citicorp CRS DRS BakAmerica Corp DRS DRS NatiosBak Corp DRS DRS Chemical Bakig Corp DRS DRS J. P. Morga & Co CRS DRS Chase Mahatta Corp IRS DRS First Chicago NBD Corp IRS DRS First Uio Corp DRS DRS Bac Oe Corp DRS DRS Bakers Trust New York Corp CRS CRS Fleet Fiacial Group IRS DRS Norwest Corp DRS DRS PNC Bak Corp IRS CRS KeyCorp DRS DRS Bak of Bosto Corp IRS DRS Wells Fargo & Co CRS DRS Bak of New York Co CRS DRS First Iterstate Bacorp DRS DRS Mello Bak Corp DRS DRS Wachovia Corp IRS DRS SuTrust Baks DRS DRS Barett Baks DRS DRS Natioal City Corp DRS DRS First Bak System IRS DRS Comerica DRS DRS Boatme s Bacshares IRS DRS U.S. Bacorp IRS DRS CoreStates Fiacial Corp IRS DRS Republic New York Corp IRS DRS MBNA CRS DRS State Street Bosto Corp IRS DRS First of America Bak Corp DRS DRS Norther Trust Corp IRS DRS Souther Natioal Corp IRS 35 Firstar Corp IRS IRS Hutigto Bacshares IRS DRS SouthTrust Corp IRS DRS Crestar Fiacial Corp IRS DRS Amsouth Bacorp IRS DRS Fifth Third Bacorp IRS CRS Mercatile Bacorp IRS DRS Meridia Bacorp IRS DRS Marshall & Ilsley Corp IRS IRS First Teessee Natioal Corp IRS IRS Bapoce Corp IRS IRS UJB Fiacial IRS IRS Itegra Fiacial IRS IRS First Security Corp IRS CRS Regios Fiacial IRS IRS Siget Bakig Corp IRS IRS Old Ket Fiacial Corp IRS IRS First Empire State Corp IRS CRS Bacorp Hawaii IRS IRS BayBaks IRS CRS Uio Platers Corp IRS IRS Maagemet Sciece/Vol. 45, No. 9, September 1999

6 Profitability ad Marketability of the Top 55 U.S. Commercial Baks Figure 2a CCR Efficiecy Distributio i Stage 1 Figure 2b CCR Efficiecy Distributio i Stage 2 Figure 2c BCC Efficiecy Distributio i Stage 1 Figure 2d BCC Efficiecy Distributio i Stage 2 t o t* o t*, for t 1, 2 o t t Obviously, o 1. If o 1, a bak is called t scale-efficiet; otherwise, if o 1, a bak is called scale-iefficiet. Table 1 gives t* o for each bak whe we employ (2) to measure profitability ad marketability. Twelve ad thirtee DMUs were BCC-efficiet i Stage 1 ad Stage 2, respectively. Figures 2c d give the distributio of the BCC scores ( t* o ) for each stage. Note that t o 1 if ad oly if t* o t* o. I our case, withi the 55 baks, oly those baks that were CCR efficiet are scale-efficiet. A paired-differece t-test was applied to CCR ad BCC scores i each stage. The results of the t-test were sigificat, idicatig that a serious scale iefficiecy was preset for the 55 commercial baks i both profitability ad marketability. (For profitability ad marketability, t values are equal to 7.6 ad 6.8, respectively.) We ext determie whether icreasig or decreasig returs to scale (IRS or DRS) is the primary cause of scale iefficiecy. As show i Baker (1984), the optimal solutio for * j ( j 1,..., ) i (1), i.e., the magitude of * j, cotais the iformatio for RTS classificatio. However, because of the possibility of multiple optimal lambda solutios for (1), DMUs may be misclassified with respect to RTS by * j (see Baker ad Thrall 1992). To avoid the misclassificatio, we use the recet result of Zhu ad She (1995) to determie the RTS classificatio. 4 That is, let DMU o be a bak uder evaluatio ad * j be a optimal solutio to (1) associated with t* o, the CRS prevail t* for DMU o if ad oly if o t* t o, i.e., o 1; otherwise, if t* o t* o, i.e., t o 1, the IRS prevail for 4 A alterative approach is to use Baker ad Thrall s (1992) RTS iterval obtaied by calculatig two auxiliary BCC-dual-like liear programmig problems. However, the two methods are equivalet ad our approach is easier. See Seiford ad Zhu (1999a) for the discussio o alterative RTS approaches. Maagemet Sciece/Vol. 45, No. 9, September

7 Profitability ad Marketability of the Top 55 U.S. Commercial Baks DMU o if ad oly if * j 1, ad DRS prevail for DMU o if ad oly if * j 1. Usig this method, oe does ot have to worry about possible misclassificatio errors from multiple optimal solutios for * j, ad the RTS classificatios are readily obtaied from the optimal solutios to (1) ad (2). Table 1 idicates that, for profitability, the BCCefficiet but ot scale-efficiet baks were operatig o a IRS frotier. For marketability, four BCC-efficiet baks were operatig o each of the IRS ad DRS frotiers, respectively. Of the BCC-iefficiet baks, 64% ad 20% were i the IRS regio i Stage 1 ad Stage 2, respectively. As ecoomists have log recogized, a IRS frotier firm would geerally be i a more favorable positio for expasio, compared to a firm operatig i a CRS or DRS regio. Furthermore, o the basis of Stigler (1966), U.S. commercial baks were more ecoomically viable i profitability tha marketability. Note that the cocept of RTS may be ambiguous uless a bak is o the BCC-efficiet frotier, sice we classified RTS for iefficiet baks by their outputorieted BCC projectios. Thus, a differet RTS classificatio may be obtaied for a differet orietatio, sice the iput-orieted ad the output-orieted BCC models ca yield differet projectio poits o the VRS frotier. Thus, it is ecessary to explore the robustess of the RTS classificatio uder the iputorieted DEA method. Note that a IRS DMU (uder the output-orieted DEA method) must be termed as IRS by the iputorieted DEA method (see Appedix A for the proof). Therefore, oe oly eeds to check the CRS ad DRS baks i the curret study. Usig Zhu ad She s (1995) iput-orieted approach, we discover that oly three DRS baks i profitability (DMUs 21, 25 ad 32) ad twelve DRS baks i marketability (DMUs 23, 26, 28, 29, 31, 32, 33, 36, 37, 38, 39 ad 41) are termed as IRS DMUs for the iput-orieted RTS method. These results idicate that (i) i geeral, the RTS classificatio uder profitability is idepedet of the orietatio of DEA model; ad (ii) there are serious output deficiecies i marketability at the curret reveue ad profit levels. The fidigs from most previous empirical research o scale efficiecy i bakig idicate that IRS occurs oly amog relatively small baks, ad DRS amog larger baks. However, the recet study of MacAllister ad MacMaus (1993) demostrates that these previous results were biased by problems i the statistical techiques employed ad by the fact that the models igored a importat iput fiacial capital. Our curret study shows that for profitability, some relatively large baks with assets greater tha $2,000 millio exhibited IRS, whereas for marketability, all of these large baks were i the DRS regio. 3.2 Iput Cogestio i Profitability ad Marketability Iput cogestio, a ecoomic cocept that origiated i the areas of trasportatio ad agriculture, refers to the situatio where reductios i the usage of a proper subset of iputs, holdig the usage of other iputs costat, geerate a icrease i oe or more outputs. For example, too much fertilizer applied to a give plot could easily reduce overall output (Byres et al. 1984). After a iefficiet bak is projected oto the frotier by a proportioal (radial) icrease of outputs or a proportioal decrease i iputs, the iput cogestio measure provides iformatio about the effect o output improvemet of further idividual iput reductio. I DEA, iput cogestio is usually ivestigated uder assumptios of strog ad weak iput disposabilities. However, as show i Ray et al. (1998), iput cogestio ca be measured by ozero iput slacks whe all frotier DMUs are extreme-efficiet. 5 Sice the CCR Model (1) ad BCC Model (2) respectively yield uique optimal solutios for efficiet DMUs, all of the CCR ad BCC frotier baks are extremeefficiet. Thus, iput cogestio ca be determied by the followig liear programmig problem. 6 m c max s i i 1 s.t. j x ij s c i t* x io j E i 1,...,m; 5 A complete classificatio of efficiet ad iefficiet DMUs is defied i Chares et al. (1991). 6 See Cooper et al. (1999) for the situatio whe some frotier DMUs are weakly efficiet Maagemet Sciece/Vol. 45, No. 9, September 1999

8 Profitability ad Marketability of the Top 55 U.S. Commercial Baks j y rj y ro j E r 1,...,s; j 0, j E, (3) where E is the set of all CCR-extreme-efficiet baks ad t* represets the optimal value for the iputorieted CCR model (or, equivaletly, the reciprocal of the optimal value t* o i (1)). If the optimal value to (3) is equal to zero, iput is ot cogested; otherwise, if the optimal value to (3) is ot equal to zero, iput c* cogestio is preset. Furthermore, if a specific s io 0, the the i o th iput is a cause of iput cogestio ad s c* io gives the amout of cogestio. Model (3) measures iput cogestio for a CRS techology. If oe appeds the additioal costrait, j E j 1, to (3), a iput cogestio measure for a VRS techology is obtaied. I this case, t* should be replaced by the optimal value to the iput-orieted BCC model ad E should represet the set of all BCC-extreme-efficiet baks. Table 2 reports the ozero iput slacks, s c* i.itis obvious from Table 2 that a serious iput cogestio exists i profitability. Betwee a third to a half of the baks exhibited iput cogestio uder CRS ad VRS techologies. The iput employee was ot a factor i causig iput cogestio for the CRS techology. Thus, labor does ot appear to be overutilized uder a CRS assumptio. However, for a VRS techology, the amout of employee cogestio is 18.36% of the correspodig employee iput level. I marketability, a very differet picture is portrayed. With the exceptio of reveue cogestio for four large baks, iput cogestio is essetially abset. 3.3 Process Improvemet The aalyses of the previous sectio idicated which baks were efficiet ad which were iefficiet. For each stage, iefficiet baks are able to improve their performace ad the DEA projectios provide a prescriptio for improvemet. For example, DMU1 (Citicorp) was CCR-iefficiet i Stage 2; however, it ca move its performace to best-practice by either (a) icreasig its MV, TRI, ad EPS (proportioally by 123%), or (b) decreasig its reveue ad profit (proportioally by 55% ad some additioal ozero profit slack). If Citicorp chooses to improve its performace with Pla (b), the it may o loger be efficiet i Stage 1 profitability. I additio, a bak may ot have direct cotrol over all Stage 2 outputs, i.e., its performace i the stock market. Thus, to improve performace over Stage 1 ad Stage 2, we focus o maximizig reveue ad profit. However, icreases i reveue ad profit may affect the scale efficiecy i Stage 2. Figures 3a b illustrate this with employees (iput) ad profit (output) i Stage 1, ad profit (iput) ad market value (output) i Stage 2. If maximizig profit is a major goal, the a bak will icrease its curret profit level to poit S (Figure 3a). As metioed earlier, beig positioed i a IRS regio is ideal for ecoomic viability. Therefore, oe should avoid the situatio (illustrated i Figure 3) that a profit icrease (AS) i Stage 1 would move the bak ito a DRS regio i Stage 2, i.e., AS should ot be greater tha UV. If AS UV, the oe may wish to ivestigate alterative approaches to performace improvemet i Stage 1. For example, oe may move the bak oto the best practice poit G by icreasig the profit to P ad the by reducig the umber of employees to G. We formalize this preferece for maitaiig viability while improvig a bak s profitability as: Process Improvemet Rule: The icrease i reveue ad profit for Stage 1 improvemet should ot move a IRS bak i Stage 2 ito a DRS regio. It ca be see that to implemet the process improvemet rule, we must determie a IRS stability regio which preserves the IRS positioig of a bak. As i Seiford ad Zhu (1999b), we formulate the followig liear programmig problem for a IRS bak, DMU o, i Stage 2 * o 1 max j s.t. jx ij x io i 1, 2,..., m; jy rj 2* o y ro r 1, 2,..., s; j 0. (4) 2* where o is the optimal value to (1) for DMU o i Stage 2. Maagemet Sciece/Vol. 45, No. 9, September

9 Profitability ad Marketability of the Top 55 U.S. Commercial Baks Table 2 Iput Cogestio i Profitability ad Marketability Profitability (Stage 1) Marketability (Stage 2) DMU No. Bak Name Employees Assets Equity Reveue Profit BCC CCR BCC CCR BCC BCC CCR BCC 2 BakAmerica Corp NatiosBak Corp Chemical Bakig Corp J. P. Morga & Co Chase Mahatta Corp First Chicago NBD Corp First Uio Corp Bac Oe Corp Norwest Corp PNC Bak Corp KeyCorp Bak of Bosto Corp Wells Fargo & Co First Iterstate Bacorp Mello Bak Corp Barett Baks Natioal City Corp Comerica U.S. Bacorp CoreStates Fiacial Corp Republic New York Corp State Street Bosto Corp First of America Bak Corp Norther Trust Corp Souther Natioal Corp Firstar Corp SouthTrust Corp Fifth Third Bacorp Meridia Bacorp Marshall & Ilsley Corp First Teessee Natioal Corp Bapoce Corp UJB Fiacial Itegra Fiacial First Security Corp Regios Fiacial Siget Bakig Corp Old Ket Fiacial Corp First Empire State Corp Bacorp Hawaii Uio Platers Corp Because DMU o exhibits IRS i Stage 2, the optimal value to (4) must be less tha oe, i.e., * o 1. As show i Seiford ad Zhu (1999b), the IRS classificatio cotiues to hold for { :1 * o }, where represets the proportioal icrease of all iputs, xˆ io x io (i 1,..., m) ad * o is defied by (4). (See 1278 Maagemet Sciece/Vol. 45, No. 9, September 1999

10 Profitability ad Marketability of the Top 55 U.S. Commercial Baks Figure 3 Process Improvemet Appedix A for the proof.) Table 3 reports the value of * o for the 11 IRS baks i Stage 2. By this sesitivity aalysis of RTS classificatio, we ca implemet the process improvemet rule as follows. Step 1. For a IRS bak, DMU o, i Stage 2 which is CCR-iefficiet i Stage 1, calculate (4). (i) If o 1* * o, improve profitability performace by settig Employees Stage1 * employees s employees Assets Stage1 * assets s assets Stage 1 Equity Stage1 * equity s equity Reveue Stage1 1* * o reveue s reveue Profit Stage1 1* * o profit s profit where (*) represets the optimal value i (1); 1* (ii) If o * o, the improve the profitability performace by computig the followig iputorieted CCR model * o mi o 55 s.t. j Employees j s employees o Employees o Table 3 RTS Sesitivity Results for IRS Baks i Stage 2 DMU No. Bak Name Chage Rate 35 Firstar Corp Marshall & Ilsley Corp First Teessee Natioal Corp Bapoce Corp UJB Fiacial Itegra Fiacial Regios Fiacial Siget Bakig Corp Old Ket Fiacial Corp Bacorp Hawaii Uio Platers Corp j Assets j s assets o Assets o 55 j Equity j s equity o Equity o Maagemet Sciece/Vol. 45, No. 9, September

11 Profitability ad Marketability of the Top 55 U.S. Commercial Baks 55 j Reveue j s reveue * o Reveue o 55 j Profit j s profit * o Profit o j 0, j 1,..., 55. I effect, we first icrease DMU o s curret output levels by * o (movig the bak oto poit P as i Figure 3a), the decrease the three iput levels by a iputorieted CCR model (movig the bak oto poit G i Figure 3a). Fially, we obtai a efficiet iput-output level i Stage 1 by settig Employees Stage1 * *o employees s employees Assets Stage1 * * o assets s assets Stage 1 Equity Stage1 * * o equity s equity Reveue Stage1 * * o reveue s reveue Profit Stage1 * * o profit s profit Step 2. Apply case (i) to other baks ad obtai the correspodig efficiet iput-output levels. Step 3. Calculate (1) agai with the ew Reveue Stage1 ad Profit Stage1 levels obtaied from Steps 1 ad 2 as ew iput levels i Stage 2. We the obtai the followig efficiet iput-output levels for DMU o i Stage 2: MV Stage2 2* * o MV s MV TRI Stage2 2* * o TRI s TRI Stage 2 EPS Stage2 2* * o EPS s EPS Reveue Stage2 Reveue Stage1 * s reveue Profit Stage2 Profit Stage1 * s profit The above steps improve the profitability ad marketability ad satisfy the process improvemet rule. Note that the oly differece betwee the Reveue Stage1 (Profit Stage1 ) ad Reveue Stage2 (Profit Stage2 ) is possible ozero iput slacks i Stage 2. However, o the basis of complemetary slackess, oly oe of reveue ad profit has a possible ozero slack for each bak i Stage 2. From our empirical applicatio, oly a ozero reveue slack of $53 millio was foud for DMU13 (PNC Bak Corp.). From Table 3, we observe that the coditio of o 1* * o ( ) is oly satisfied by DMU50 i 11 IRS baks. Therefore, we apply (ii) i Step 1 to the remaiig 10 IRS baks ad apply (i) to DMU50 ad all other baks. The last colum of Table 1 reports the adjusted CCR scores i Stage 2 after all baks become CCR-efficiet i Stage 1. Table 4 reports the adjusted efficiet iput-output levels for three selected baks. DMU2 is a DRS bak i Stage 2, therefore we use the origial CCR results to project the curret levels of employees, assets, equity, reveue, ad profit i Stage 1. The, i Stage 2, we use the ew CCR results to adjust the levels of MV, TRI, ad EPS. Because o iput slack is detected durig CCR aalysis i Stage 2, the adjusted reveue ad profit levels i Stage 2 are the same as those i Stage 1. DMU35 is a IRS bak i Stage 2, ad the sesitivity aalysis of RTS classificatio idicates that the origial CCR score is greater tha * o ( ). Therefore the levels of reveue ad profit are icreased proportioally by , ad we use the iput-orieted CCR model to move DMU35 oto the best-practice frotier i Stage 1. Fially, we move this Stage 1 frotier bak oto the best-practice frotier i Stage 2. 1* DMU50 is a IRS bak i Stage 2 with o * o. Therefore we apply the same procedure as for DMU The Effect of Acquisitio o Profitability ad Marketability Chase Mahatta Corp. (DMU6) ad First Iterstate Bacorp (DMU18) were acquired by Chemical Bakig Corp. (DMU4) (March 31, 1996) ad Wells Fargo & Co. (DMU16) (April 1, 1996), respectively. 7 Employig various expese ratios, Rhoades (1993) shows that durig , horizotal bak mergers did ot yield efficiecy gais. For our curret empirical study, we examie the potetial effect of acquisitios o these baks performace over profitability ad marketability. Two hypothetical DMUs, amely Bak A (DMU4 DMU6) ad Bak B (DMU16 DMU18), are 7 NBD Bacorp acquired First Chicago Corp. ad chaged its ame to First Chicago NBD Corp. Also, First Uio Corp., Fleet Fiacial Group, ad PNC Bak Corp. acquired First Fidelity Bacorp, Shawmut Natioal Corp., ad Midlatic Corp., respectively. However, data before acquisitio are ot available for the curret study Maagemet Sciece/Vol. 45, No. 9, September 1999

12 Profitability ad Marketability of the Top 55 U.S. Commercial Baks Table 4 Adjusted Efficiecy Levels for Selected Baks DMU2 BakAmerica Corp. Origial Level Adjusted Level Stage 1 Stage 2 DRS i Stage 2 Employees Assets ($ millios) Equity ($ millios) Reveue ($ millios) Profit ($ millios) Market Value ($ millios) Total Returs to Ivestors (%) Earig per share ($) DMU35 Firstar Corp. Origial Level Adjusted Level Stage 1 Stage 2 IRS i Stage 2 Employees Assets ($ millios) Equity ($ millios) Reveue ($ millios) Profit ($ millios) Market Value ($ millios) Total Returs to Ivestors (%) Earig per share ($) DMU50 Siget Bakig Corp. Origial Level Adjusted Level Stage 1 Stage 2 IRS i Stage 2 Employees Assets ($ millios) Equity ($ millios) Reveue ($ millios) Profit ($ millios) Market Value ($ millios) Total Returs to Ivestors (%) Earig per share ($) created to represet the result of the two acquisitios. Additivity is assumed i acquisitio, i.e., the iput ad output levels i Bak A ad Bak B are the summatios of the associated iput ad output levels for DMU4 ad DMU6, ad DMU16 ad DMU18, respectively. For example, the umber of employees i Bak A (72443) is the summatio of umber of employees i DMU4 (39078) ad DMU6 (33365). TRI ad EPS are relative umbers. To obtai a aggregated umber for TRI or EPS, we eed iformatio o total ivestmet ad profit after taxes. Ufortuately, the curret study does ot have access to data o total ivestmet. Therefore, we use the profit levels to combie the TRIs ad EPSs respectively. TRI j acquisitio 1 j TRI j1 2 j TRI j2, j A ad B. j j where 1 (Profit j1 /Profit j1 Profit j2 ) ad 2 (Profit j2 / Profit j1 Profit j2 ). Specifically, we cosider the covex combiatio of the levels of TRIs for the acquired baks. I this case, we have A , A , ad B , B Note that the profit levels are profits after taxes. Thus, we may derive the EPS for baks A ad B by EPS acquisitio j Profit j1 Profit j2 Profit j1 Profit, j A ad B j2 EPS j1 EPS j2 Table 5 provides the iput ad output data o the two hypothetical baks. We examie the effect of acquisitio o profitability ad marketability for two cases. (Note that DMU16 is a CCR-efficiet bak i Stage 1.) I Case I, we keep the origial CCR-frotier fixed, i.e., we keep the CCRefficiet DMUs (icludig DMU16) i the referece set. I Case II, we exclude DMU16 from the referece set. This affects the CCR-frotier i Stage 1 but ot i Stage 2, sice DMU16 is a CCR-iefficiet DMU i Stage 2. Thus, for marketability, we oly eed to cosider Case I. Table 5 reports the results. I Case I, the CCR scores of the two hypothetical baks are almost the same. I both stages, o obvious efficiecy gai results from the acquisitio. (Note DMU16 is oe of the referet baks.) I Case II, removal of DMU16 results i better profitability for both baks A ad B. I both cases, DMU30 is i the referece set for the evaluatio of Baks A ad B. 3.5 Cotext-Depedet Performace We have idetified best-practice/performace for profitability ad marketability ad examied/pre- Maagemet Sciece/Vol. 45, No. 9, September

13 Profitability ad Marketability of the Top 55 U.S. Commercial Baks Table 5 The Effect of Acquisitio o Performace BANK A Chemical Bakig Corp. (plus) Chase Mahatta Corp. New Level Case I Case II Stage 1 Stage 2 Stage 1 Employees Assets ($ millios) CCR Efficiecy CCR Efficiecy CCR Efficiecy Equity ($ millios) Reveue ($ millios) Referet baks Referet baks Referet baks Profit ($ millios) Bak 5 (1.41) Bak 13 (2.55) Bak 5 (1.34) Market Value ($ millios) Bak 16 (0.33) Bak 40 (6.70) Bak 17 (0.34) Total Returs to Ivestors (%) Bak 30 (3.94) Bak 30 (4.12) Earig per share ($) 4.38 BANK B Wells Fargo & Co. (plus) First Iterstate Bacorp New Level Case I Case II Stage 1 Stage 2 Stage 1 Employees Assets ($ millios) CCR Efficiecy CCR Efficiecy CCR Efficiecy Equity ($ millios) Reveue ($ millios) Referet baks Referet baks Referet baks Profit ($ millios) Bak 16 (1.96) Bak 13 (0.06) Bak 17 (1.51) Market Value ($ millios) Bak 30 (0.75) Bak 40 (6.42) Bak 30 (2.05) Total Returs to Ivestors (%) Bak 52 (0.35) Earig per share ($) Note. The umbers i paretheses represet optimal lambda values. scribed improvemets for idividual baks. Our suggestios for improvemet addressed the radial distace from a iefficiet bak to the best-practice frotier. However, we have ot examied the ifluece of similar or closely performig baks. Researchers of cosumer choice theory poit out that cosumer choice is ofte iflueced by cotext. For example, a circle appears large whe surrouded by small circles ad small whe surrouded by larger oes. Similarly a product may appear attractive agaist a backgroud of less attractive alteratives ad uattractive whe compared to more attractive alteratives (Tversky ad Simoso 1993). Cosiderig this ifluece withi the framework of the curret study, oe would ask what is the relative attractiveess of a particular bak whe compared to others i terms of profitability ad marketability? As i Tversky ad Simoso (1993), oe agrees that the relative attractiveess of bak x, compared to bak y depeds o the presece or absece of a third optio, say bak z (or a group of baks). Relative attractiveess is depedet upo the backgrouds costructed from alterative optios (baks). We first develop the followig DEA techique to costruct these differet backgrouds for measurig the attractiveess of a particular bak. Defie J 1 {DMU j, j 1,..., } (the set of all DMUs (baks)) ad iteractively defie J l 1 J l E l where E l {DMU k J l *(l, k) 1, ad all slacks o iputs ad outputs are zero}, where *(l, k) is the optimal value to the followig liear programmig problem: * l, k max l, k j,, l,k s.t. j y rj l, k y rk r 1,...,s; j f J l 1282 Maagemet Sciece/Vol. 45, No. 9, September 1999

14 Profitability ad Marketability of the Top 55 U.S. Commercial Baks j x ij x ik j f J l i 1,...,m; j 0 j f J l, (5) where x ik ad y rk represet the amouts of the ith iput ad the ith output of DMU k, ad j f(j l ) meas DMU j J l, i.e., f represets the correspodece from a DMU set to the correspodig subscript idex set. Whe l 1, Model (5) becomes the origial outputorieted CCR model ad E 1 cosists of all the efficiet DMUs. Whe l 2, Model (1) gives E 2 the set of efficiet DMUs after exclusio of the origial efficiet DMUs. Ad so o. We call E l the level-/best-practice frotier (BPF). I this maer, we idetify several levels of BPFs. 8 The followig algorithm accomplishes the idetificatio of these BPFs by Model (5). Step 1. Set l 1. Evaluate the etire set of DMUs, J 1 by (1) to obtai the Level 1 efficiet DMUs, set E 1 (the Level 1 BPF). Step 2. Exclude the efficiet DMUs from future DEA rus. J l 1 J l E l. Step 3. Evaluate the ew subset of iefficiet DMUs, J l 1, by (1) to obtai a ew set of efficiet DMUs E l 1 (the ew BPF). Step 4. Go to step 2. Stoppig Rule. J l 1 A, the algorithm stops. Thus employig Model (5) iteratively gives a stratificatio of the etire set of DMUs. From the algorithm, it is obvious that l goes from 1 to L, where L is determied by the stoppig rule, i.e., J L 1 A. Itis easy to show that the set of DMUs has the followig properties: Property 1. J 1 L l 1 E l ad E l E l A for l l ; Property 2. The DMUs i E l are eveloped by the DMUs i E l if l l; Property 3. Each DMU i set E l is efficiet with referece to the DMUs i set E l l for all 0 l l L. As described i Seiford ad Zhu (1996), the sets E l serve as evaluatio backgrouds (cotexts) for DMUs 8 The larger the value of l, the lower the efficiecy level. i E l, where l l. The attractiveess score of a specific DMU q ( x q, y q ) i a specific level E lo, l o {1,..., L 1} is defied as the optimal value to the followig liear programmig problem l o q max q j, q s.t. j y rj q y rq j f E lo j x ij x iq j f E lo 1,...,L l o r 1,...,s; i 1,...,m; j 0 j f E lo, (6) where the iteger gives the degree of attractiveess. The optimal value q lo ( ) is called the (output-orieted) -degree attractiveess of DMU q. Obviously, the smaller the value of q lo ( ), the more attractive DMU q is relative to the other DMUs. (See Seiford ad Zhu 1996 for a more complete discussio of the properties o q lo ( ).) 9 Note that q lo ( ) depeds o the particular evaluatio backgrouds E lo, ad Model (6) provides a measure of cotext-depedet performace. 10 Tables 6a 6b report the differet levels of BPF ad the first-degree attractiveess scores ( 1) for profitability ad marketability. First-degree attractiveess evaluates how distictive a bak s performace is compared to baks i the ext lower efficiecy level. For example, first-degree attractiveess for the baks i E 1 is determied i the cotext of the baks i E 2. There are six ad te levels of BPFs for profitability ad marketability respectively. Nie baks (DMUs 2, 34, 38, 45, 46, 47, 53, 54, ad 55) are i the last BPF level for profitability. However, the origial CCR scores for these last-level baks are ot all amog the worst. For example, 9 Model (6) ca be regarded as a CCR model i which the particular DMU uder evaluatio is excluded from the referece set. This is frequetly referred to as the superefficiecy DEA model. As a result, either lo q ( ) 1 or (6) is ifeasible. However, as show i Zhu (1996a) ad Seiford ad Zhu (1999c), (6) is always feasible. 10 It ca be see that (6) is differet from the model used i rakig efficiet DMUs i (Aderse ad Peterse 1993). Model (6) measures attractiveess of the efficiet DMUs agaist iefficiet DMUs, whereas the Aderse ad Peterse model for rakig efficiet DMUs measures a efficiet DMU agaist all other DMUs icludig the remaiig efficiet DMUs. Maagemet Sciece/Vol. 45, No. 9, September

15 Profitability ad Marketability of the Top 55 U.S. Commercial Baks Table 6a Cotext-Depedet Performace o Profitability Level 1 Level 2 Level 3 Level 4 Level 5 Bak Score Bak Score Bak Score Bak Score Bak Score Average Table 6b Cotext-Depedet Performace o Marketability Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 7 Level 8 Level 9 Bak Score Bak Score Bak Score Bak Score Bak Score Bak Score Bak Score Bak Score Bak Score Average DMU48, with a CCR score of , is i Level 5, whereas, DMU2, with a CCR score of , is i the last level. We observe that CCR scores aloe do ot etirely characterize the performace of these baks. The stratificatio which results from DEA Model (5) provides a better idicatio of the structure of the set of baks. For profitability, DMU30, DMU29, DMU6, DMU33, ad DMU37 are the most attractive baks for each of the first 5 levels of BPF. However, the first-degree attractiveess scores for the baks i Level 3, Level 4, ad Level 5 BPFs are very similar. I cotrast, the first-degree attractiveess score for DMU29 idicates a large differece relative to the other baks i Level 2 BPF. Similarly, for marketability, DMU52, DMU42, DMU45, DMU41, DMU37, DMU22, DMU15, DMU23, ad DMU7 are the most attractive baks i each of the first 9 levels of BPF. Amog the origial CCR-efficiet DMUs, DMU52 has the lowest first-degree attractiveess score almost oe third of the average. Relative to the baks i the Level 2 BPF (evaluatio backgroud), DMU52 exhibits distictive performace o marketability, compared to the other CCR-efficiet baks. The average first-degree attractiveess scores i 1284 Maagemet Sciece/Vol. 45, No. 9, September 1999

16 Profitability ad Marketability of the Top 55 U.S. Commercial Baks Table 7a Level 1 Bak Effect of Acquisitio o Attractiveess Measure for Profitability 1st-Degree Attractiveess With Acquisitio 1st-Degree Attractiveess Without Acquisitio Score Referet Baks Score Referet Baks Chage (%) A (0.01), 15 (4.00), 29 (0.52), 40 (1.69) (0.54), 24 (0.18) (3.18) (1.16) A (0.01), 15 (0.46), 29 (1.00) (0.11), 18 (0.33), 19 (0.06) (0.38), 40 (2.18) (0.03), 24 (0.74) (0.08), 19 (0.23) (0.03), 24 (0.72) 0 Average Notes. 1. Bak 24 becomes the ew CCR efficiet DMU due to the removal of Bak 16. The 1st-degree attractiveess score for Bak 24 is The baks i level 2 BPF (with acquisitio) are DMUs A, B, 15, 19, 28, 29, 31, 40, ad The umbers i paretheses represet the optimal lambda values i the attractiveess measure (6). Table 7b Effect of Acquisitio o Attractiveess Measure for Marketability Level 1 Bak 2d-Degree Attractiveess With Acquisitio 2d-Degree Attractiveess Without Acquisitio Score Referet Baks Score Referet Baks Chage (%) (0.21), 31 (0.35) (0.21), 31 (0.35) (0.49), 31 (0.44) (0.49), 31 (0.44) B (0.06), 35 (0.49) (0.33), 51 (0.33) (0.98) (0.99) (0.15), 53 (0.87) (0.84) (0.52), 53 (0.39) (0.09), 49 (0.36), 51 (0.44) Average Notes. 1. The baks i Level 3 BPF (with acquisitio) are DMUs B, 11, 21, 31, 35, 38, 39, 41, 49, 51, ad The umbers i paretheses represet the optimal lambda values i the attractiveess measure (6). each level may be used as a measure of average radial distace betwee successive BPFs. For example, the average value of for Level 1 i Table 6a idicates that o average, the two output levels (reveue ad profit) may be decreased approximately by 73% before the Level 1 BPF reaches the Level 2 BPF. Thus the averages i Tables 6a ad 6b portray average performace differeces of profitability ad marketability betwee successive BPFs. If we cosider the secod-degree attractiveess for baks i Level 1 BPF (Stage 1), i.e., we set l 0 1 ad 2, the we have the optimal values to (5), (DMU1), (DMU5), (DMU10), (DMU16), (DMU17), ad (DMU30). Therefore, if Level 3 BPF is chose as evaluatio backgroud, DMU5 is the most attractive oe i profitability, ad the DMU30. Whereas if the Level 2 BPF is chose as evaluatio backgroud, we obtai the opposite result o DMUs 5 ad 30, i.e., DMU30 is the most attractive bak, ad the DMU5. This idicates that differet evaluatio backgrouds may yield differet results o cotext-depedet performace. Note that i Model (1), deletig or addig some iefficiet DMUs does ot alter the efficiecies of the existig DMUs. However, such actios will obviously affect the results from the attractiveess measure (6). I 3.3, we examied the effect of acquisitio o the performace of the baks ivolved i the acquisitio. Now, by (6), oe is able to study the effect of acquisitio o the relative attractiveess of the other baks. As described i 3.3, Baks 4 ad 6, ad Baks 16 ad 18, are respectively replaced by two hypothetical baks, A ad B. From Model (5), we obtai that, i Stage 1, A ad B are two ew members i the Level 2 Maagemet Sciece/Vol. 45, No. 9, September