Valuing Customer Portfolios under Risk-Return-Aspects: A Model-based Approach and its Application in the Financial Services Industry

Transcription

1 Unversty of Augsburg Prof. Dr. Hans Ulrch Buhl Research Center Fnance & Informaton Management Department of Informaton Systems Engneerng & Fnancal Management Dscusson Paper WI-217 Valung Customer Portfolos under Rsk-Return-Aspects: A Model-based Approach and ts Applcaton n the Fnancal Servces Industry by Hans Ulrch Buhl, Bernd Henrch n: Academy of Marketng Scence Revew 12 (2008) 5, p Unverstät Augsburg, D Augsburg Vstors: Unverstätsstr. 12, Augsburg Phone: (Fax: -4899)

2 Valung Customer Portfolos 1 Valung Customer Portfolos under Rsk-Return-Aspects: A Model-based Approach and ts Applcaton n the Fnancal Servces Industry EXECUTIVE SUMMARY For dentfyng and selectng the most proftable customers n terms of the shareholder value, the Customer Lfetme Value (CLV) ganed broad attenton n marketng lterature. However, n ths paper, the authors argue that the CLV does not take nto account the rsk assocated wth customer relatonshps and consequently does not conform to the prncple of shareholder value. Therefore, a quanttatve model based on fnancal portfolo selecton theory s presented that consders the expected CLV of customer segments as well as ther rsk. The latter ncludes the correlaton among the segments. It s shown how mperfect correlaton among segments may be employed to maxmze the value of the customer portfolo. Snce portfolo selecton theory does not allow for the consderaton of fxed costs, t s extended by a heurstc method consstng of two algorthms, referred to as subtract - and add -approach. Keywords: customer proftablty, customer portfolo, customer segment valuaton, fnancal servces ndustry Academy of Marketng Scence Revew volume year no. month Avalable: Copyrght year Academy of Marketng Scence.

3 Valung Customer Portfolos 2 Valung Customer Portfolos under Rsk-Return-Aspects: A Model-based Approach and ts Applcaton n the Fnancal Servces Industry INTRODUCTION In compettve economes, the man goal of every company s to maxmze ts shareholder value (Lumby and Jones 2001, pp. 4 ff). The shareholder value s based on the concept of net present value (NPV), whch reflects the expected long-term proftablty of a company. Many authors, e.g. Gruca and Rego (2005), Gupta, Lehmann and Stuart (2004) and Hogan et al. (2002), argue that the fundament of a company s proftablty s consttuted by ts customers. Hence, the ncrease of shareholder value requres frst of all the ncrease of customer value (or as Rappaport notced ( ) wthout customer value there can be no shareholder value (Rappaport 1998). Ths nsght led to some fundamental changes n marketng theory as well as n corporate practce towards a customer-centrc vew and the emergence of Customer Relatonshp Management (CRM). CRM focuses on the valuaton, selecton and development of endurng customer relatonshps and on the allocaton of lmted resources to maxmze the value of a company. For dentfyng the most proftable customers, varous valuaton methods have been developed n theory and practce. Customer valuaton ganed wde acceptance n partcular n the fnancal servces ndustry: accordng to a survey of Mummert Consultng, comprsng 80% of German nsurance companes, the ncrease of customer value and customer loyalty has hgh prorty n strategc management (Forthmann 2004). A study n the bankng ndustry at the Unversty of Muenster reveals that 100% of the nvestgated banks consder customer value management as an nstrument to ncrease returns (Ahlert and Gust 2000). A customer valuaton concept that s (at frst sght) compatble wth the prncple of shareholder value s the Customer Lfetme Value (CLV). It gans broad attenton n marketng lterature (cp. Woodall 2003). The CLV takes nto account all expected future cash n- and outflows of a customer and calculates ther NPV. Although marketng lterature dscusses the concept of CLV n detal, t stll lacks practcablty, snce the estmaton of future proftablty s uncertan and thus nvolves the rsk of bad nvestments. The consderaton of rsk,.e. the devaton of cash flows from ther expected value, s therefore crucal for a rsk averse decson maker, but stll remans farly dsregarded n customer relatonshp valuaton (Hopknson and Lum 2001). We can beneft from exstng fnancal theory concepts f future cash flow rsk s to be taken nto account: captal markets nvestors hold portfolos consstng of dfferent asset classes wth dfferent rsk-return profles for balancng losses. Although the dfferences between customers and fnancal assets wth respect to the process of ther valuaton, acquston and retenton behavor are clear, both of them reveal smlar characterstcs. Ths allows transferrng fnancal theory concepts (e. g. Captal Asset Prcng Model (CAPM), Portfolo Theory and Real Optons) to support customer valuaton decsons (as shown by Cardozo and Smth 1983, Dhar and Glazer 2003, Fader et al. 2005, Haenlen et al. 2006, Hogan et al. 2002, Johnson and Selnes 2004, Levett et al. 1999, Ryals 2001, Ryals and Knox 2005, Slater et al. 1998). For the purchase and acquston of both fnancal assets and customers, nvestments have to be made. Therefore, t s ratonal to buy and acqure fnancal assets and customers respectvely, f the expected cash nflows from fnancal assets or customers exceed cash outflows of the transacton or acquston. However, as wth fnancal assets, some customers may offer a substantal CLV, but at the same tme ther cash flows may be unsteady and therefore more rsky, whereas the CLV of others may be comparatvely smaller, but more constant (Ford et al. 2003, p. 83). Due to those smlartes, customers can be regarded as rsky assets, too (Hogan et al. 2002). Accordngly, valuaton technques not only have to consder the proftablty of a customer segment, expressed by the CLV, but also the assocated rsks. Such rsks do exst durng the whole customer lfe cycle. If a frm wants to attract many customers n the acquston process, several customer relatonshps are perhaps not valuable (lke wth cherry pcker customers) and thus, nvestments to acqure these customers are not proftable at all. For nstance, the fnancal servce Academy of Marketng Scence Revew volume year no. month Avalable: Copyrght year Academy of Marketng Scence.

4 Valung Customer Portfolos 3 provder we consder n our case study acqures customers (academcs) at the end of ther studes (rght before fnal exams) and supports students by gvng them advces for ther applcatons (applcaton documents etc.) or by provdng tranngs for ther applcaton assessments. Thus, the provder nvests nto the relatonshps wthout knowng ther future development and value n detal. If a student does not make ts career as ntally predcted, these nvestments are lost,.e. only a few or no cash nflows are generated by the customer n the future. If ths apples to many customers, these rsks have to be consdered as a hgher devaton of the expected CLV of a customer segment. Such rsks also exst wthn the growth and penetraton stage of relatonshps. Ths means that a customer may entrely swtch to a compettor or he/she may establsh relatonshps to more than one frm. Both have mpact on the duraton and ntensty of customer relatonshps whch has agan drect mpact not only on the expected CLV but also on the rsk of a customer segment. Snce frms want to generate the hghest cash nflows wthn ths stage, rsks - especally exogenous (gven) rsks, whch are, for example, based on economcal (cyclcal downturn) or compettve changes (new compettors jon the market) - have to be consdered. Mostly, such changes can not be prohbted by frms. However, frms have to manage these exogenous rsks,.e. they should thnk about addng customers and customer segments to the customer base, whch - compared to other segments - generate lower but steader cash flows durng ther lfecycle and are more ndependent, for example, from cyclcal downturns. Furthermore, the stages of relatonshp reactvaton and recovery nclude rsks too, prmarly the rsk that nvestments are not proftable. If the probablty s hgh that many customers n spte of nvestments mgrate to compettors both expected CLV of a customer segment and rsks (hgher devaton of the expected CLV) are affected. Thus the frm has to dentfy for whch customers t s reasonable to nvest n - or not to take the rsk of a lost nvestment. Such aspects whch are mentoned exemplarly here have mpacts on the expected CLV, the related rsks and thus proftablty of a customer portfolo. Moreover, tradtonal customer valuaton concepts often concentrate on assessng ndvdual customers (Hogan, Lemon and Lba 2003). Thereby, they neglect the fact that the rsk of customer portfolos may be dmnshed by selectng customers wth varyng cash flow structures (Dhar and Glazer 2003). Hence, the man objectve of CRM should be to determne and value the customer base as a whole (and not only ndvdual customers). In ths paper we present a model for the composton of a customer portfolo, consstng of dfferent customer segments. The model s based on the fnancal portfolo selecton theory of Markowtz (Markowtz 1952 and 1959). It consders the reward of assets (customer segments) on the one hand and the rsk assocated wth them on the other. The rsk of assets ncludes ther ndvdual rsk (denoted as devaton of expected cash n- and outflows of a customer segment) as well as ther correlaton between each other. The Markowtz algorthm, however, excludes the exstence of fxed costs, whch may play an mportant role n the context of valung customer segments and customer portfolos, as we wll see. Some papers n fnancal portfolo optmzaton present algorthms for the ncorporaton of transacton costs that occur when purchasng or sellng assets, e.g. Best and Hlouskova (2005) or Kellerer, Mansn and Speranza (2000). However, the number of decson varables ncreases drastcally wth transacton costs and the optmzaton problem becomes even NP-complete n the case of fxed transacton costs. Therefore, we present a heurstc approach n the paper at hand that allows fndng a soluton to the portfolo optmzaton problem n consderaton of fxed costs, whch arse wth customer relatonshps, for a manageable quantty of customer segments. The paper s organzed as follows: the next secton gves a short overvew of recent approaches n customer valuaton consderng the expected CLV of customers as well as ther rsk. Subsequently, we present our customer portfolo model. In a frst step, we test an already exstng customer base for effcency and optmalty (n terms of the Markowtz portfolo selecton theory). In a second step, we derve the value of new customer segments for a customer portfolo. In ths case, we have to consder the fxed costs of the new segments, whch requre the development of the heurstc method. The conceptual decson model s followed by the applcaton of the approach, llustratng mplcatons for strategc marketng. Fnally, the results of the paper are summarzed and drectons of further research are dscussed. Academy of Marketng Scence Revew volume year no. month Avalable: Copyrght year Academy of Marketng Scence.

5 Valung Customer Portfolos 4 RECENT RISK-RETURN-APPROACHES IN CUSTOMER VALUATION If future cash flows were known wth certanty,.e. n a determnstc world, the valuaton of the customer base and of ts contrbuton to shareholder value would be rather smple: the NPV of the customer base would be the aggregaton of the cash flows (cash nflows mnus cash outflows) of the sngle customers, dscounted by the rsk-free rate. Hence, n order to maxmze shareholder value, the cash flows of the ndvdual customers would have to be maxmzed. However, although most of the research papers n the area of customer valuaton do not explctly dfferentate between the determnstc and stochastc world, t s generally agreed that cash flows depend on several factors that may cause devaton from forecasts and are therefore uncertan. Srvastava, Tasadduq and Fahey (1997) classfy these rsk factors nto three groups: external factors may be of macroeconomc nature, lke technologcal, poltcal, regulatory, economcal or socal changes. Furthermore, changes n the compettve envronment of the company affect customer behavor and n turn cash flows. For example, compettors may launch new products, change product prcng or use new dstrbuton channels. Fnally, marketng actons of the company tself n product and servce development, dstrbuton, prcng and advertsng and promoton may have an mpact on cash flows (see also Hogan et al. 2002; Ryals 2005; Venkatesan and Kumar 2004). However, n ths paper we wll focus especally on the frst two groups of (exogenously gven) rsk factors, snce they cannot be nfluenced drectly by the company tself and therefore are harder to be balanced n contrast to the last group. Furthermore, we focus on exogenous rsk factors, snce these factors have been pad less attenton n scentfc lterature too. A good example of the mportance of these rsks s the bg slump of ncomes n the nformaton technology sector and related sectors (e.g. nformaton technology consultng) due to the crash of the nternet economy some years ago. Companes focusng on customers n these sectors got n trouble because ther cash nflows decreased together wth the decreasng ncomes of ther clentele (cluster rsks), too 1. Therefore, these rsks should among other measures be dversfed for optmzng the customer portfolo under rsk-/return-aspects. Such a dversfcaton can also be accomplshed for dfferent, potental strategc programs and decsons (e.g. entry n a new market or developng a new product; cp. Woodruff 1997) of the company tself. If a frm develops, for nstance, two alternatve strategc programs based on ther busness and marketng objectves (for the stages n the tradtonal plannng process of marketng management see Brassngton and Petttt (2006), t has to estmate the mpact on cash flows of each customer segment (e.g. addtonal expected cash nflows wthn the new market) as well as rsks (e.g. n the sense of the devaton of the expected cash flows) of both programs n a subsequent step. Gven such programs and estmatons, we focus on valung and optmzng the customer portfolo for each program takng nto account dfferent customer segments and ther rsk-return-profle. Snce the future proftablty of customers and customer segments s uncertan, rsk averse marketers wll request a mnmum rate of return for nvestng n such rsky assets. Some authors therefore propose the usage of the weghted average cost of captal (WACC) of a company as mnmum rate of return. They argue that the WACC, whch s computed as the cost of debt multpled by the proporton of debt fundng and the cost of equty multpled by the proporton of equty fundng, reflects the true cost for the company to get money from fnancal markets (Lumby and Jones 2001, pp. 419 ff.). Snce customer segments may be seen as rsky assets, too, t s clamed that the WACC may be used as dscount rate n the CLV (Kumar, Raman and Bohlng 2004; Hogan et al. 2002). Only f the return of a customer segment exceeds the costs of captal, the segment creates shareholder value (Ryals 2002). However, for acceptng a customer segment that ncreases rsk n the portfolo, t s argued that one demands a hgher return and the cost of captal rses. Ths means that decson makers are supposed to be rsk averse. In consequence, a constant dscount rate of the WACC n CLV calculaton does not reflect the customer segment-specfc rsk n a proper way. Rsker customer segments are overvalued and segments provdng lower but steader cash flows durng ther lfecycle are dscrmnated aganst. Hence, t s emphaszed that the WACC has to be adjusted to the ndvdual rsk of a customer segment by settng t hgher the more a segment contrbutes to the rsk of the whole customer base. The research n recent 1 Snce cash outflows lke e.g. costs of personal, nformaton systems or buldngs could not been reduced to the same extent, the cash flows and thus the CLV decreased as well. Academy of Marketng Scence Revew volume year no. month Avalable: Copyrght year Academy of Marketng Scence.

6 Valung Customer Portfolos 5 CRM lterature shows that the CAPM of fnancal portfolo theory s manly proposed and used to calculate a rsk-adjusted dscount rate n customer valuaton (Dhar and Glazer 2003; Hogan et al. 2002; Hopknson and Lum 2002; Ryals 2001; Gupta, Lehmann and Stuart 2004). The CAPM s based on the assumpton that nvestors are rsk averse,.e. they ask a larger reward for carryng hgher rsk. Furthermore, t mples that all assets carry two dfferent types of rsk that have to be dstngushed: systematc and unsystematc rsk. The systematc part s market-wde and therefore affects all assets. Examples are changes n nterest rates, ncomes, busness cycles, etc. The unsystematc part of rsk, however, s related to a sngle asset or a lmted number of assets. The CAPM shows that t can be elmnated by holdng a well-dversfed portfolo, whereas the systematc rsk cannot be dversfed away. Hence, nvestors requre a rsk premum for acceptng t. The systematc rsk of assets s not measured by the varance of return, but by ts covarance wth market return. The rato of the covarance between asset and market and the varance of the market reveals the Beta value of the nvestment. The Beta of the market s equal to one, an asset beng rsker than the market has a Beta larger than one, and a less rsky asset a Beta smaller than one. Furthermore, the CAPM assumes the exstence of a rsk-free nvestment. Investors hold a combnaton of the rsk-free asset and the market portfolo, whch s a portfolo consstng of all rsky assets avalable, wth each asset held n proporton to ts market value relatve to the total market value of all asset. It depends on ther ndvdual rsk averson how much they actually nvest n the rsk-free asset. Furthermore, f we use the term market portfolo n the meanng of the one market portfolo for all nvestors further assumptons are necessary. Frst, all nvestors have the same nvestment opportunty set (.e. for example each company can acqure, mantan and enhance the same customer segments). And second, all nvestors have homogeneous expectatons about the rsk-return-profle of each nvestment opportunty (.e. each frm have homogeneous expectatons about the rsk-return-profle of each customer segment beng n the opportunty set). We come back to ths aspect n the followng. Wth the help of the CAPM, we may determne the return of each rsky asset beng part of the market portfolo n the equlbrum of captal markets. It s a combnaton of the premum for acceptng the systematc rsk assocated wth the rsky asset and the return on the rsk-free asset. The relatonshp between systematc rsk and return for each rsky asset s lnear and may be gven by the securty market lne (SML) n (2.1) (Copeland, Weston and Shastr 2005, pp. 151): (2.1) E r ) = r + β ( E( r ) r ), ( f m f where E(r ) s the expected return on nvestment, β denotes the systematc rsk of asset. r f represents the rsk-free rate of return, whereas E(r m ) refers to the expected return on the market portfolo. It s argued that the SML may be used to adjust the specfc WACC of any rsky nvestment alternatve,.e. also n the context of relatonshp valuaton. For ths reason, the Beta value of a customer segment reflects the systematc busness rsk of the segment and the systematc fnancal rsk of the company tself (Lumby and Jones 2001, pp. 424 ff.). Consequently, the NPV of the customer segment would be (under the assumpton of tme nvarant costs of captal) gven by the expected cash flows, dscounted by the n segment-specfc rsk-adjusted WACC ( CF, denotes the cash nflows of customer segment n perod t, whereas CF, represents the correspondng cash outflows): out t t T n out CFt, CFt, (2.2) CLV = t= 1 ( 1 + r + β ( E( r ) r )) f m f t. The hgher the rsk of a customer segment, the hgher the rate of return shareholders wll requre for nvestng n that customer segment. The SML of equaton (2.1) at a Beta of one reflects the average WACC that may be mapped n a rsk-return-dagram. Ryals (2001; 2002) argues that, accordng to ther specfc Beta, some of the customer segments wll le below the average WACC n the dagram and hence destroy shareholder value, whereas others wll be above the average, creatng shareholder value. Academy of Marketng Scence Revew volume year no. month Avalable: Copyrght year Academy of Marketng Scence.

7 Valung Customer Portfolos 6 To calculate the value of the customer base as a whole, the CLV of the ndvdual customers may be aggregated snce the Beta values for all assets are lnearly addtve (Copeland, Weston and Shastr 2005, p. 153). Therefore, the CAPM allows frst of all for the determnaton of the customer value on an ndvdual level, wheren the return and the rsk of a customer are taken nto account. Furthermore, the value of the customer base and ts contrbuton to shareholder value may be derved. However, the CAPM shows some drawbacks n the context of valung customers and customer segments that wll be outlned brefly (see also Hogan et al. 2002): (1) Frst of all, the calculaton of the Beta value of customer segments requres the defnton of the market portfolo whch - as mentoned above - s the portfolo consstng of all assets avalable, wth each asset held n proporton to ts market value relatve to the total market value of all assets. Snce all companes or marketers n general do not have homogeneous expectatons about the rsk-returnprofle of each customer segment (e.g. because each company manages ts own customer relatonshps at the moment of the decson,.e. two companes estmate the rsk-return-profle of the same customer segment dfferently), the determnaton of one market portfolo for all companes s very dffcult or often not possble at all. As a result, Ryals (2001) as well as Dhar and Glazer (2003) defne the market portfolo n the area of CRM as the company s current customer base. Takng the company s current customer base as market portfolo s theoretcally approprate only f the value of an already exstng customer portfolo should be analyzed and therefore all requred data exst (restrctve case). However, the applcaton of CAPM n relatonshp management seems to be dffcult, f decsons should be taken about addng or deductng a customer segment to or from the exstng portfolo. The rsk premum for the market - and thereby for the customer base - must reman constant for determnng the segment-specfc rsk (Huther 2003, p. 127). Changng the composton of the customer portfolo by addng or subtractng a customer segment wll change ts return and thus ts rsk premum as well as the varance of return, though. Wthout knowng the varance of the market portfolo, the Beta value of the new customer segment cannot be determned. However, the Beta s crucal to adjust the WACC for rsk n the calculaton of the customer segment-specfc CLV. So, the determnaton of the market portfolo as well as the Beta value whch reflects the systematc rsk s really dffcult n the context of valung customer segments. Addtonally, even f we correctly determne both the market portfolo and the beta value, the current customer base s a result of self-selecton by customers, too. Thereby t wll not reflect a completely dversfed and rsk balanced portfolo n the sense of CAPM. Therefore, the CAPM s practcally not applcable. Another shortcomng of the CAPM s as mentoned the assumpton of homogeneous expectatons of all marketers. Ths assumpton s crucal for the exstence of the market portfolo and the equlbrum on captal markets (Copeland, Weston and Shastr 2005, p. 148). The equlbrum on captal markets, on the other hand, requres that all nvestment alternatves are part of the market portfolo wth ther correct market prce (Huther 2003, p. 130). Translated nto the customer valuaton context, ths requres that the values of all customer segments have to be gven for determnng the value of the customer base, whch agan s a prerequste for the valuaton of the dfferent customer segments. Consderng ths, CAPM s not an adequate method for valung customer portfolos. (2) In addton to these conceptual drawbacks, the exclusve consderaton of the systematc rsk related to the Beta value of a customer segment mples that the rsk averse decson maker can completely dversfy the unsystematc rsk away. Ths assumpton requres that, n case of an unforeseeable event (e.g. recesson, nflaton or the crash of the dot.com marketplace a few years ago), only one or a very lmted number of customer segments are affected. Ther cash flow devaton may be balanced by the steady cash flows of other segments, then. Therefore, the cash flows of dfferent segments have to be negatvely correlated. As we dscussed at the begnnng of ths secton, cash flows depend on several factors that may nfluence each customer segment to a dfferent extent. On the whole, however, ther cash flows wll tend to move n the same drecton,.e. correlaton mght be mperfect but postve (Ryals 2001). In consequence, the correct determnaton of the rskness of a customer segment has to consder the systematc as well as the unsystematc part of rsk. Hogan et al. (2002) argued n the same way by dscussng the drawback of customer valuaton models and Academy of Marketng Scence Revew volume year no. month Avalable: Copyrght year Academy of Marketng Scence.

8 Valung Customer Portfolos 7 CAPM to ncorporate the nfluence of envronmental effects (e.g. macroeconomc changes, mpact of competton). For nstance, they descrbed that durng recessons, customers become more prce senstve (Hogan et al. 2002). Ths crcumstance reduces among other thngs sze of wallet but not for each customer and customer segment to the same extent. I.e. that the sze of the wallet of dfferent customer segments wthn a portfolo are correlated. Such unsystematc rsks can cause serous cash flows and proft collapses. However, CAPM does not consder unsystematc rsks whch make t hard to use n the context of customer segment valuaton. (3) Wth the assumpton of completely dversfed portfolos, the CAPM furthermore gnores the fact that even wth postve but mperfect correlaton, marketers may proft from rsk dversfcaton. Snce customer segments do not react n exactly the same way on exogenous factors, the rsk of a portfolo may decrease. In consequence, portfolo value may be ncreased. Summng up, we state that the ssue of rsk n the context of relatonshp valuaton s addressed only n a few research papers. To the best of our knowledge, none of them explctly defnes the rsk preference of the decson maker. Ths s, however, a prerequste for an approprate consderaton of rsk n customer valuaton. If a marketer s for example assumed to be rsk neutral, the rsk of devatng cash flows does not have to be consdered at all. Furthermore, the dervaton of the Beta value of the customer segments s treated only very superfcally, so that the practcal applcaton of the models dscussed above seems rather dffcult. Although the basc CAPM has been advanced n the last decades (e.g. Hansen and Rchard 1987; Merton 1973; Söderlnd 2006), for nstance, to account for ntertemporal decsons and condtonng nformaton (n the context of customer valuaton such approaches can be used to consder manageral flexblty), the dscusson shows that the underlyng (basc) assumptons are assocated wth some serous drawbacks. The followng secton presents a model for customer portfolo management, whch s based on the portfolo selecton theory of Markowtz (1952; 1959). It wll be shown that some of the prevously dscussed dsadvantages of the CAPM n the context of CRM can be avoded by applyng the portfolo selecton theory: (ad 1) For portfolo selecton theory, t s not necessary to assume homogenous expectatons and defne the market portfolo (or the Beta value) n order to determne the rsk-return-profle of customer segments. In fact, a company can estmate the cash n- and outflows of each customer segment based on ts own ndvdual expectatons and ts current customer base. Ths may be used for the evaluaton of addng or subtractng a customer segment to or from the frms customer portfolo as well as for determnng a new customer portfolo (shown n the secton Composton of a new customer portfolo). Furthermore, t s necessary to consder, for nstance, fxed costs (e.g. acquston costs) f a new customer segment may be added to the portfolo. For that reason we adapted the Markowtz algorthm by two novel heurstcs wthn ths paper. (ad 2) Instead of consderng only the systematc rsks of a customer segment, the portfolo selecton theory takes nto account all rsks. Ths s a major advantage snce the nfluence of envronmental effects and especally macroeconomc changes (see Hogan et al. 2002) are represented by unsystematc rsks. E.g., (lnear) dependences between changes of the ncomes of dfferent customer segments (caused by a recesson and thus a reduced sze of wallet) can be represented mostly by correlatons between customer segments. Snce no approprate approaches n the context of customer segment valuaton exst to manage unsystematc rsks, we focus on these mportant rsks n order to optmze new and exstng customer portfolos. (ad 3) By means of the portfolo selecton theory, effects of rsk dversfcaton through mperfect postve correlaton between customer segments can be analyzed (CAPM gnores the fact as mentoned above that even wth mperfect correlaton one can realze dversfcaton effects). Thus marketers may proft from rsk dversfcaton through selecton of the optmal customer portfolo based on the set of effcent portfolos (customer portfolos whch are not domnated by at least Academy of Marketng Scence Revew volume year no. month Avalable: Copyrght year Academy of Marketng Scence.

9 Valung Customer Portfolos 8 one other portfolo). The choce of the optmal portfolo depends on the ndvdual rsk averson, whch can be derved from the preference relaton of the decson maker. Another advantage of the model whch s presented n the followng s that t supports the marketer s abltes to dfferentally deploy nvestments to each customer segment. Two types of nvestments can be dstngushed. Frstly, nvestments that may be assgned to a specfc customer segment, although stll ndependent of the number of customers, are treated as drect fxed costs (e.g. development of an nformaton system, whch s used for a specfc customer segment). However, those nvestments that may be assgned to customers of a specfc customer segment and are therefore dependent on the number of customers (e.g. costs of drect customer contact or addressng new customers), are referred to as drect varable costs. Based on ths dstncton t s possble to analyze whch nvestments lead to whch beneft of the optmal customer portfolo. Furthermore, n the presented model, market entry and ext barrers may be consdered by mnmum and maxmum restrctons of the sze of customer segments. Thus, the model consders the fact that due to entry barrers some segments cannot be acqured to the desred extent and other segments cannot be scaled down due to ext barrers respectvely. Summng up, t wll be shown that the applcaton of the portfolo selecton theory n customer relatonshp valuaton allows for clear mplcatons on the composton of the customer portfolo, accordng to the expected CLV of the dfferent customer segments and the rsk assocated wth t. Furthermore, we wll derve the monetary value per capta of the customer base. The aggregaton of the customer value per capta to the value of the customer base as a whole s mportant to enhance comparablty of shareholder value and customer value. However, the focus of ths paper s to develop a decson model that gves clear ndcatons for the composton of the customer base on the bass of the prncples of shareholder value. Assumptons CUSTOMER PORTFOLIO VALUATION MODEL The applcaton of portfolo selecton theory and the dervaton of a sutable valuaton method requre a few assumptons about the dstrbuton of cash flows and the behavor of decson makers. These are brefly presented n the followng. (A1) The number of customer segments = 1,,n, wth maxmum market sze M > 0, n the exstng customer portfolo of a company s n at tme t = 0. These are assumed fxed over the whole plannng horzon t = 1,,T. The customer portfolo of all segments together conssts of N IN customers at tme t = 0. The portfolo shares w of the segments, gven by the rato of the number of customers n segment and the total number N of customers n the portfolo, are the decson varables of the portfolo optmzaton n t = 0 for the whole plannng horzon. The portfolo shares are at least zero and sum up to one,.e. (3.1) n w = 1 = 1, w 0 { 1,..., n}. For all t {1, T} from t-1 to t, N changes by the gven growth rate 2 g, wth g (-1; ). The parameters N, M and g are assumed feasble,.e. on the global level (3.2) N M for g ( 1;0] n = 1, 2 The analyses can easly be extended to the case of segment-specfc growth rates g, wth = 1,,n, f the per capta vew, normalzed to the number of customers at tme t = 0, s stll kept. Thus we can ncorporate dfferently growng and shrnkng segments nto the analyses. Academy of Marketng Scence Revew volume year no. month Avalable: Copyrght year Academy of Marketng Scence.

10 Valung Customer Portfolos 9 N (1 + g) T n = 1 M for g ( 0; ) From assumpton (A1) t follows that on the customer segment level, we receve the upper bounds the portfolo shares (3.3) w = for g ( 1;0] M, N M w = T N (1 + g) for g 0; ( ). From the nequaltes n (3.2) and the equatons n (3.3) t follows for the upper bounds s greater or equal to one: (3.4) w 1. n = 1. w for w that ther sum Therefore, we may note that the feasble ntervals for the portfolo shares w of the customer segments are w [0;mn{ w ;1}] for all {1,,n}. Each segment yelds the cash nflow CF,t n, whch s the average perodc revenue per capta at tme t, wth t {0, T}, as well as the average cash outflow per capta CF,t out. The latter s the total of drect varable costs, whch depend on the number of customers n the segment. These costs result from acquston, servce and advsory as well as transacton costs. The calculaton of the segment-specfc cash outflow does not, however, nclude those costs that ndeed can be assgned to a certan customer segment, but do not depend on the number of customers. Hence, these drect perodcal fxed costs F,t of segment at tme t, wth t {0, T} are ndependent of the number of customers n segment and arse prmarly due to contractual commtments before tme t = 0. 3 These contan, for nstance, costs for rented buldngs, leasng costs or lcense fees for nformaton systems. Drect fxed costs may amount to an mportant sze, but f the respectve segment {1,,n} (wth w 0) s part of the exstng customer portfolo, ts fxed costs have to be treated as sunk costs, and therefore have no mpact on the portfolo optmzaton. However, ther NPV per capta n the respectve segment, whch s normalzed to the number of customers n the segment at tme t = 0 - rrespectve of the growth rate g -,.e. (3.5) NPV ( F ) T ˆ 1 F =, w N (, t t= + ) t 0 1 r where r f denotes the rsk-free rate, has to be taken nto account should a new portfolo be arranged, e.g. an exstng portfolo should be enlarged by a new customer segment. Indrect perodcal fxed costs IC t, lke management costs, overhead and admnstraton costs, whch are ndependent of the number of customers n the customer portfolo as well, are dffcult to allocate to specfc customer segments. Nevertheless, for creatng shareholder value, ther NPV per capta, also normalzed to the number of customers at tme t = 0,.e. f 3 Drect fxed costs, whch arse at tme t {0,, T} and are not a consequence of contractual commtments before t = 0, wll be neglected at frst. Later, t wll be shown that these costs, whch are relevant for the portfolo decson even n the case of an exstng customer portfolo, may be ntegrated nto the model as well. Academy of Marketng Scence Revew volume year no. month Avalable: Copyrght year Academy of Marketng Scence.

11 Valung Customer Portfolos 10 (3.6) T 1 IC NPV ( ICˆ) =, N t t= ( + ) t 0 1 r f should at least be covered by the value per capta of the customer portfolo. (A2) (3.7) (3.8) For every customer segment, wth {1,,n}, the average per capta net cash flow Q s gven by Q = ( q ~ 0,, q ~ 1,, K, q ~ T, ). The components q ~ t, are the average net cash flows per customer n customer segment and represent the delta of cash n and outflows at tme t {0, T}: n out q ~ t, = CFt, CFt,. ~ are assumed to be ndependent and dentcally dstrbuted random varables, whch are gven q t, at the decson tme t = 0, as well as the drect fxed costs F,t of segment and ndrect fxed costs IC t. The average per capta Customer Lfetme Value CLV of segment, whch s also normalzed to the number of customers n segment at t = 0, s gven by the expected NPV of Q, n consderaton of the perodcal growth rate: T E q t ( ) ( ) t E CLV ( ~, ) µ = ( ) = 1+ g. t t r = 0 1+ f For the followng model, we defne the expected return per capta µ of customer segment as E(CLV ) at tme t = 0, as s done n equaton (3.8). Hller and Heebnk (1965) showed that f the net cash flows are supposed to be ndependent and dentcally dstrbuted random varables, t may be concluded that the expected return per capta µ s asymptotcally normally dstrbuted. On the bass of assumptons (A1) and (A2), the expected NPV per capta of the customer portfolo E(CLV PF ), shortly denoted as µ PF, may be calculated as the sum of the weghted NPV of all segments µ : (3.9) µ PF = E( CLVPF ) = w E( CLV ) = w µ. n = 1 The decson maker has to choose an approprate customer portfolo now, accordng to hs rsk preference. Ths s, a rsk neutral decson maker consders only the expected portfolo return µ PF n hs decson and therefore ams to maxmze the shares of the customer segments wth the hghest µ n the portfolo. A rsk averse decson maker, however, takes the rsk of the portfolo return nto account as well. Ths s summarzed n the prncple of Bernoull, whch reasons that decson makers am to maxmze the expected utlty of an alternatve rather than ts expected return. n = 1 (A3) It s assumed that the rsk averse decson maker ams to maxmze the utlty per capta of the portfolo alternatves. The rsk of the expected return per capta of customer segment s quantfed by the standard devaton σ = Var CLV ). The rsk σ PF of the expected portfolo return ( per capta nvolves the standard devaton σ of the portfolo segments as well as ther covarance Cov j,.e. σ PF = n n = 1 j= 1 wσ w σ ρ. The correlaton coeffcents ρ,j, whch are supposed to be j j j smaller than 1,.e. correlaton s mperfect, are gven n tme perod t = 0 and are constant over the plannng horzon. For all possble values x assumed by the random varable CLV PF, ther utlty s gven by u x =1 e. ax (3.10) ( ) Academy of Marketng Scence Revew volume year no. month Avalable: Copyrght year Academy of Marketng Scence.

12 Valung Customer Portfolos 11 The parameter a denotes the Arrow-Pratt measure that ndcates the ndvdual level of rsk averson. A ratonal preference relaton that meets assumptons (A2) and (A3),.e. n case of normally dstrbuted random varables, the utlty functon gven n (3.10) and compatblty wth the Bernoull-Prncple, s gven by the followng equaton: a 2 (3.11) Φu ( µ PF, σ PF ) = µ PF σ PF = U PF Max! 2 The parameters μ PF and σ PF both depend on the portfolo shares w of the dfferent customer segments, whch have to be chosen so that Φ u (μ PF,σ PF ) s maxmzed. Agan, the parameter a represents the Arrow- Pratt measure. In the context of relatonshp valuaton, a/2 s defned as a monetary factor that reflects the prce per unt of rsk,.e. the reward asked by a rsk averse decson maker for carryng the rsk σ PF (Huther 2003, p. 155). Snce the portfolo shares w of the dfferent customer segments sum up to one, the expected portfolo utlty U PF s a monetary per capta amount. Valuaton of an exstng Customer Portfolo In ths secton, we wll optmze an exstng customer portfolo on the bass of the portfolo selecton theory, wheren the customer segments are gven, but not ther optmal portfolo shares w (Markowtz 1952; 1959). We wll frstly derve µ PF and σ PF of all effcent portfolo alternatves and secondly determne the optmal portfolo. The analyss consders the expected return per capta µ of all customer segments as well as ther varance σ 2 and covarance Cov j. The fxed costs F,t of segment are not taken nto account n the optmzaton for the reasons explaned above. The comparson of the exstng customer portfolo and the optmal portfolo shows whch customer segments have to be enlarged or rather dmnshed n order to ncrease shareholder value. Startng pont of the portfolo selecton theory s a rsk averse decson maker, who chooses between effcent portfolos,.e. portfolos wth hgher expected return accompaned by hgher varance and portfolos wth lower expected return and varance. Furthermore, he wll only select a portfolo PF, whch s a feasble portfolo,.e. all portfolo weghts are part of the feasble nterval of w [0; mn{ w ;1}] and the portfolo shares sum up to one. However, t may be reasonable to nclude mnmum restrctons for the portfolo shares of the dfferent customer segments as well. For nstance, f a customer segment s strategcally mportant, snce customers of ths segment act as reference clents (socal effects) on the market or the segment s needed to enter a market. Thus, we wll consder lower bounds w ( 0;mn { 1; w }) for the portfolo shares n the analyss, too, so that the feasble nterval for the portfolo shares s gven by w w ;mn{1; w }]. [ To derve the set of effcent portfolos, we mnmze the portfolo varance at every level of portfolo return. If the returns of the dfferent segments are mperfectly correlated, the overall portfolo rsk s smaller than the sum of the ndvdual varances of the customer segments. Therefore the more assets or customer segments are n the portfolo, the better portfolo rsk can be dversfed (Markowtz 1959). However, ths s only true f the segments are postve mperfectly correlated. In the case of negatve correlaton the drect opposte takes place. Negatve correlatons may arse, f the great many of customer segments wthn the portfolo lead for nstance to a bad mantanng and enhancement of customer relatonshp (e.g. overwork of sales). I.e. the targetng on specfc customer segments changes for the worse and a larger portfolo wth more segments leads to an sgnfcant ncrease of portfolo rsks (furthermore, ths may also lead to a decrease of the CLV of the customer segments resulted though, for nstance, bad and not ndvdualzed customer servces). Such effects have to compare wth dversfcaton effects resultng from mperfect, postve correlatons, whch already exst n most cases (cp. Ryals 2001). Academy of Marketng Scence Revew volume year no. month Avalable: Copyrght year Academy of Marketng Scence.

13 Valung Customer Portfolos 12 The selecton of the optmal portfolo out of the set of effcent ones depends on the ndvdual rsk averson, whch s represented by the ndfference curve n a ( µ σ PF 2, PF )-dagram. It can be derved from the preference relaton gven n equaton (3.11). The pont of tangency of the ndfference curve and the effcent fronter represents the locus of the optmal portfolo at the gven rsk preference. If t s optmal to reduce the customer portfolo by segment, ts portfolo weght wll consequently be w = 0 n the pont of tangency. Wth the expected return and varance of the optmal portfolo, ts utlty can be calculated by equaton (3.11). Fnally, the utlty per capta of the optmal portfolo has to cover the average NPV of drect and ndrect fxed costs per capta to create value for the company. Although these costs are sunk costs n the case of an exstng customer portfolo, the company creates value only f the portfolo utlty exceeds all fxed costs. Therefore, we have to weght the drect fxed costs per capta of the segments of equaton (3.5) wth ther respectve portfolo share w. 4 The Markowtz algorthm thus allows the determnaton of the average utlty per capta of a customer portfolo wth a gven number of customer segments. Furthermore, we derve exact portfolo weghts wth respect to an ndvdual utlty functon and therefore management can decde whether the portfolo share of customer segment should be enlarged or dmnshed. Whch benefts can fnally be drawn from the applcaton of the model? In most cases an already exstng customer portfolo of a company resulted from uncoordnated decsons made n the past,.e. from sporadc, uncoordnated acquston efforts, concdental acqustons, as well as from self-selecton by consumers who base ther ndvdual decsons on avalable offers and optons. In practce, the necessty of a strategc customer management, ncludng the structure of a company s customer portfolo n terms of the above mentoned rsk factors s often underestmated. On the one hand, the model can be useful to make these rsks more transparent and quantfable (e.g. cluster rsks due to strongly correlated segments). On the other hand, acquston efforts can be used to reduce such (cluster) rsks by means of mperfect correlaton of the expected cash flows of dfferent customer segments. If such cluster rsks can be avoded, a rsk averse decder would usually weght the segment wth the hghest stand-alone utlty (only cash flows and standard devaton) most hghly. By analyzng a customer portfolo n terms of ts rsk return profle, dependences on future nvestments n acquston, servces or advsory of customers become more transparent. Therefore, t can be advantageous to nvest n servces of a customer segment a, whch has a smaller expected average CLV per capta than another segment b, f the correlaton of segment a to the portfolo s lower than the one of segment b. Rsk dversfcaton s the reason for ths effect. Ths does not only apply to sngle nvestments but also to potental, dfferent sets of nvestments. In a smlar way large companes try to dversfy market rsks by ther dfferent busness dvsons for generatng constantly hgh revenues, ndependent from economc cycles. Ths apples not only for customer portfolos of small and medum szed enterprses but also for large-scale enterprses. Whle mnmum and maxmum restrctons n the model can be defned, both exstng market entry barrers and ext barrers can be consdered. In practce companes often cannot accomplsh an acquston of the focused customers of a segment to the optmal extent. Regonal markets, for nstance, n whch they were not represented untl now cannot be entered due to exstng entry barrers. The same apples to market ext barrers,.e. an enterprse wants to reduce the number of customers of an unproftable segment n the long run. For both cases, mnmum and maxmum restrctons can be determned for the partcular 4 Wth the weghtng of drect fxed costs per capta of segment, the portfolo share w n equaton (3.5) s cancelled out. Hence, the NPV of drect fxed costs can be dvded by the total number of customers N at tme t = 0 and therefore s a constant amount rrespectve of the segment s share w. For reasons of better nterpretaton and analyss, however, the fxed costs of segment are n the frst step normalzed to the number of customers n the respectve segment, who actually cause the fxed costs. Academy of Marketng Scence Revew volume year no. month Avalable: Copyrght year Academy of Marketng Scence.

14 Valung Customer Portfolos 13 segments. Thereby the best possble composton of the customer portfolo can be calculated consderng rsk-/return-aspects. A further ssue addresses opportunty costs. If the model proposes the reducton of the portfolo weght of an exstng segment, then opportunty costs of not makng sales to the customers of ths segment wll seem to be rather hgh. Ths may especally be the case when ths opportunty costs are compared to e.g. the low costs of malng sales offers to these customers. Two aspects should be consdered: Frst of all the low costs of such a customer contact are already consdered n the respectve cost parameters of the segment (drect fxed costs by the parameter F,t and drect varable costs by the cash outflow varable CF,t out ). It can be concluded that the optmal customer portfolo was already calculated based on ths data. Furthermore the money nvested n the above mentoned customer contact s bounded (gven a realstcally lmted budget whch s also expressed by the lmted range of the customer base) and s so mssng somewhere else. That s, n ths case opportunty costs e.g. for another segment could arse, too. The model compares both knds of opportunty costs. Therefore the resultng soluton takes nto account that the next dollar should be nvested n the new segment nstead of the exstng segment to optmze the rsk- /return-profle. Takng nto account those opportunty costs, the lost proft would be larger assumng the cash flows can be correctly assgned to a certan customer segment f the enterprse does not nvest n the new segment. Composton of a new Customer Portfolo Suppose the stuaton of a newly establshed frm, whch has not acqured any customers yet. Accordng to fnancal resources and the workng capacty of the company, the management of the company s able to determne a number of customers that can be served. However, t s stll unclear, whch customer segments should be consdered, and how they should be weghted n the portfolo. For the dervaton of the new portfolo, we have to slghtly modfy assumpton (A1) substtutng the upper part of (A1) by the followng (A1 ). (A1 ) The number of potental customer segments = 1,, n on the market s n at tme t = 0, wth maxmum market sze M > 0, whch s fxed for the plannng horzon. The number of segments n the customer portfolo and the portfolo shares w of these segments are now the decson varables of the portfolo optmzaton n t = 0, n consderaton of the mnmum restrctons w and maxmum restrctons w. Snce all customer segments are new n the portfolo, ther fxed costs F,t must not be treated as sunk costs and now have to be consdered n the analyss. Fxed costs are ndependent of the portfolo weghts w, and therefore they are not taken nto account n the optmzaton algorthm that was used n the prevous secton. In order to obtan the optmal soluton for a new customer portfolo, consderng fxed costs, a complete enumeraton of portfolo combnatons requres, for n potental target groups or customer segments, the calculaton of the utlty of (2 n -1) portfolos. In the case of, e.g. 20 customer segments, the utlty of 1,048,575 portfolos has to be derved. Snce ths procedure s enormously tme and thereby cost consumng, ths secton ams to develop a heurstc method that requres less computng tme to fnd a soluton. Moreover, n practce t mght be of hgher strategc mportance as to whether an exstng customer base should be reduced or enlarged ncrementally by takng a customer segment out of or nto the portfolo. Therefore, the presented model allows for an ncremental valuaton of the customer segments. The model conssts of two algorthms, henceforth referred to as subtract -approach and add -approach, whch may be appled for the decson. Snce both algorthms are heurstcs, ther results do not necessarly have to be the optmal solutons. However, f both procedures derve the same portfolo, we mght take ths as an ndcaton that we have possbly derved the optmal soluton. In the followng, we wll refer to ths portfolo (whch s the result of both procedures) as approxmate soluton to the optmzaton problem. In general, however, the two algorthms do not lead necessarly to the same result. In ths case, the decson maker wll choose the portfolo wth the hgher utlty. Academy of Marketng Scence Revew volume year no. month Avalable: Copyrght year Academy of Marketng Scence.