the development and optimisation of a client …

The Development and Optimisation of a Client Portfolio

THE DEVELOPMENT AND OPTIMISATION OF A CLIENTPORTFOLIO

David YorkeUMIST

United Kingdom

Sydney McLarenUMIST

United Kingdom

ABSTRACT

The paper begins by tracing the development of the portfolio concept from its initial application in finance to its recent employment to client base analysis [Yorke and Droussitis (1994)]. The resulting literature review highlights that the current client portfolio models do not provide a means by which to rationalize the client base for optimality and resource allocation. The authors propose such a method. The developed model is also dynamic in recognition that corporate requirements of its potential and existing clients alters as the firm faces new challenges in the market place and in its evolutionanry process.

PORTFOLIO THEORY

Markowitz (1952) is the acknowledged pioneer of the portfolio concept. He argued that it was possible to determine from the plethora of investment instruments the best mix of investments which would yield the optimal return for the investor. He went on to suggest that holding a diversified mix of investments was more judicious than investing in a single stock or instrument. Markowitz proposed that two factors were sufficient to

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David Yorke • Sydney McLaren

determine this efficient mix, namely: expected return from the investment and the degree of risk associated with the instrument (subject to acceptability to the investor). The Markowitz's model was dichotomic in that two perspectives to investments could be considered:

1) investments could be made in light of the minimum risk consistent with a given level of return;

2) maximum expected returns for a given level of risk was the governing consideration.

Aside from the assumptions concerning investors expectance, Markowitz made simplifying assumptions about the marketplace. Principal amongst these were:

1) there was a perfect market immune from the vagaries of random market forces;

2) there was no time lag in acquiring or disposing of assets;

3) the sole constraint limiting acquisition or divestment was the investor's perspective.

Markowitz advocated that investors must be willing to make investment decisions after evaluating the two parameters of risk and returns. Limiting features to the Markowitz analytical technique were:

1) the technique required an exhaustive data base of historical information wherein the number of observations should be greater than the number of activities being studied;

2) the technique was time consuming and costly to implement even when computers were used to carry out the analysis owing to the fact that investment opportunities had to be compared with each other prior to a decision being taken.

Kahane (1977) offered an improvement on the Markowitz technique by using the Sharpe Single Index method (see Sharpe 1963). Through his model Kahane was able to surmount the above shortcomings as well as incorporate marketing concerns which has the potential to influence investment and divestment

66 8 University of Karlsruhe


activities. Instead of viewing the subject industry purely from a financial perspective Kahane analyzed it in terms of an investment and product portfolio, defining the optimal product and investment mix for a company.

Though Kahane was the first to quantitatively define an optimum product mix for an existing product portfolio, the analytical method was limiting in that decisions concerning portfolio profile are determined by comparative analysis incorporating a single index formed by determining two variables whose relationship to each other is undefined. Furthermore, the method gives no guidance:

1) as to new opportunities which could be explored nor tells whether the company has the capacity to pursue additional ventures;

2) concerning resource allocation amongst the elements of the existing portfolio nor for pursuit of future opportunities.

Ansoff and Leontiades (1976) adopted a qualitative approach to product portfolio determination. They favoured corporate reorganization along production or market segment lines (strategic business areas) stating that the forecasted long term benefits can be determined by various mathematical models available through literature review on the topic. However, caution was given that due to the limitation of the product life cycle concept limited success will be attained by using most of these mathematical tools. The treatise, however, did not go as far as to state how to select a portfolio such that short and medium term corporate objectives could be realised.

Hedley (1976) using the experience curve concept advanced the argument that as a consequence of the learning curve effect, competitors with high market shares in segments relative to their rivals should be able to develop the lowest cost position and hence the highest and most stable profits. Thus, according to Hedley, stable profit is a function of the experience curve and market growth in a sector. This is the underlying philosophy

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upon which the BCG product portfolio model is built [Hedley, (1977)]. The BCG's thesis is that stable profits, cashflow and growth are attained primarily by securing increased market shares. This ethos is supported by well documented evidence [Schoeffler et al (1974); Buzzell et al (1975)]. However, there have been dissenting views concerning the wisdom of pursuing market shares as a means of competitive advantage. Fruhan (1972) warns against this practise by citing examples of companies which have pursued this line to their detriment. The PIMS study [Schoeffler et al (1974)] also concedes that the value of market shares is not significant as a competitive tool to some industries. Day (1977) points out conditions under which market share acquisition may not lead to a competitive advantage.

Further shortcomings of the BCG matrix are:

1) the method does not indicate the constituents and profile of an optimal mix;

2) the method gives no guidance as to how the classification of various product is achieved;

3) the concept of commercial risk is ignored;

4) consideration of resource constraints and allocation is ignored;

5) the method forces complex issues to be determined along two decision parameters one of which is questionable.

Alternate product portfolio models have been proposed by others [Wind and Mahajan (1981); Hoch (1980); Alien (1979); Wright (1978); Wind and Claycamp (1976)] but all suffer from the weakness that they are largely descriptive and not capable of being used for analysis. Also they each fail to answer the question as to the profile of what an optimal portfolio.

Within the last fifteen years marketing theorists have begun to employ the concept of portfolio theory to a customer base [for example, Fiocca (1982)]. In the marketing adaptation the client instead of the product line or area of opportunity was the focus of the analysis. The thesis is that marketers by application of

670 University of Karlsruhe


the portfolio theory can assess any customer against marketing and corporate objectives and devise appropriate marketing strategies. A two dimensional multi-staged grid system is the common method of analysis, the positioning of the various client accounts within the grid(s) giving an indication of the existing mix of clients [Campbell and Cunningham (1983); Shapiro et al (1987); Yorke and Droussiotis (1994)].

Canning (1982) proposed a "customer value analysis", or CVA, methodology through which "client value" and "requirement of the customer" were the measures used to determine the development of marketing plans as well as the allocation of marketing resources to clusters of clients. Canning reasoned that if the supplier firm was able to determine the relative value of a client to its welfare then the supplier would be in a position to determine the magnitude of marketing effort justified in serving that client. Knowing the requirements to serve the said client points to ways in which the marketing budget can best be spent to meet marketing and corporate objectives. Clients with common values and requirements would be grouped and a marketing programme developed for that cluster of clients. In employing the methodology non-profitable clients would be identified and if necessary divested from the client portfolio. This would then release resources which could be allocated to more valued clients.

While the CVA as an analytical tool allows the ranking of clients, combining both profit and "beyond profit" characteristics to determine their value and the allocation of resources, the latter phase, resource allocation, is still a very subjective matter. Added to this there is still uncertainty as to the constituents of an optimal portfolio matrix and the concept of the inclusion of "tomorrow's client" is ignored.

Fiocca (1982) proposed a two-step customer portfolio analysis. In the first stage the client base is analyzed at a general level using as analytical variables the strategic importance of each account and the difficulty in its management. From this analysis those accounts needing more attention are identified for further


David Yorke Sydney McLaren

study. The second step, which uses the results from the first stage, involves an in-depth analysis of important client accounts. At this level the analysis takes the form of a two- dimensional graphical display of client accounts, plotting the client's business attractiveness against the perceived buyer- seller relationship. This, according to Fiocca, allows the analyst to assess strategies and profitability with respect to the account considered. Again the conceptual model is open to subjective application [Yorke & Droussiotis (1994)] and offers little help in determining optimal client mix and appropriate resource allocation to existing and future clients. Campbell and Cunningham's (1983) model also has similar shortcomings.

MODEL DEVELOPMENT

The literature review has highlighted that despite the advances in the conceptual development and application of the portfolio theory to client analysis researchers are yet to determine:

a) the optimal client mix by either qualitative or quantitative methods;

b) a method of quantitatively allocating resources to the respective client accounts;

c) a means of identifying what portion of marketing resources can be sensibly allocated to the pursuit of new opportunities;

The literature supports the ethos that clients are essential for the realisation of the corporate goals. As these goals must be dynamic so as to respond to changes in the marketplace it follows that the requirements from the client base also changes depending on the situation in which the company finds itself. Consequently, an understanding of the changing requirements of the firm is a necessary prequisite to formulating a client portfolio. Such an understanding is central to developing appropriate decision parameters against which to evaluate client attractivess or suitability. The organisational life-cycle



concept is a useful model for understanding these changing requirements if only to form a foundation for understanding the behaviour of organisations.

The organisational life-cycle theorm suggests that a firm will evolve through four phases during its corporate life, namely: introduction, growth, maturity and decline [Lippit and Schmidt (1967); Smith et al (1985); Pashley and Philippatos (1990)]. It is reasoned that as the firm evolves through the hierarchy of changes it adopts objectives commensurate with its stage of development [Mueller (1972); Kimberly (1979)] and sets goals which will assist in attaining, maintaining then surpassing each stage. The firm initiates an endogeneous examination of its structure [Miller and Friesen (1984)] and looks to its external environmental (the market place) in an effort to find possible opportunities for growth [Greiner (1972); Adizes (1979)]. The macro-economics of the market place also influences this search for growth and thus will influence the client selection variable. These two therefore lead us to arrive at the following hypothesis regarding decision variable for client inclusion to the portfolio.

HI: Decision parameters (DP) which define the ideal client for a firm are a function of the stages of organisational development as defined by the organisational life cycle concept (OLC) and the prevailing macro-economic condition of the market place (MACRO). 1

Mathematically stated:

DP = f (OLC, MACRO)

The research question therefore relates to the composition of the optimal mix of clients in light of the dynamic corporate

In addition to the support provided by the literature this hypothesis repeatedly emerged from interviews with a number of senior managerial staff in different firms. The purpose of the interviews was to determine factors which influence the relationship between firms and their existing and potential clients.



objectives which are shaped by the inter-play between life-cycle evolutionary process and the economics of the market environment. Figure 1 depicts the graphical representation of HI.

The parameters for each cell are determined by management policy, that is, the cells reflect the attributes management feels clients should possess so that corporate goals can be realised. The parameters serve as the criteria against which new and existing clients are evaluated to determine appropriate marketing actions (establish, sustain or discontinue relationships). Depending on the market conditions, for example prosperity, and the corporate evolutionary stage (for instance, growth) such attributes may be: corporate growth, staff skill development, reputation enhancement and fulfilling managerial aspirations.2 It is necessary that the evaluation system allows for the possible partial overlaping nature of the attributes as well as the simultaneous interaction among them. A discriminant analysis technique is appropriate and can be used to classify the client base into two groups: those with whom a relationship should be established or continued; and those who should be divested from or not included in the portfolio. The discriminant analysis method ensures that the two groups are distinguishable by allowing a scoring index to be developed which reflects the diffenences between the groups. The scoring index also takes into account the necessary

2 These are a few of the attributes extracted from in-depth interviews with senior management personnel in a case study being undertaken by the authors in which the model is being empirically applied.



weightings of the parameters used in separating the groups.3 Equation 1 is the general form of the linear relationship between the factors where pK is the score, bn the parametric attribute extracted from the DP matrix (Figure 1) and pn the weighted coefficient.

pK - pi bi + (32 b2 + ......+ pnb n (1)

Each client (potential and existing ) will have a pK score, pKi . However, only those above a threshold score (pK* ) will be shortlisted for further marketing attention. Those scoring just below the cut-off point can be subjected to further investigations to aid divesture decisions. pK* is developed by the discriminant analysis method which ensures effective partitioning of the group.

Beyond the scoring mechanism it becomes necessary to allocate marketing resources to the selected accounts. An intuitively attractive method would be to allocate the resources to the highest scoring member repeating the process for the second highest scoring member and so on until resources are exhausted. However, there are at least three disadvantages to this simple approach. First, resource allocation by index scoring yeilds a sub-optimal solution [Freeman (1968); Moore and Baker (1969)]. Second, such a method fails to account for the disability of the candidate account to complement the existing client mix, that is, an account viewed in isolation may seem quite attractive

If the predictor variables t>i ... bn are independent then the ranking of the weighting factors P] .... pn will reflect the ranking of the first differences of the means between the two groups. The standardised weightings and the discrimant loading factors will also show the same order of ranking and hence the three conditions are used as a test for independence. In the absence of independence caution should be applied when interpreting the results of the analysis [Churchill (1991:885 -886)]. Further conditions for using discriminant analysis is that the predictor variables are intervally scored [Tull and Hawkings (1990)] and there must be a multivariate normal

distribution of the parameters within the segregated groups [Churchill (1991)]. There must also be equal dispersion and covariance structure of the groups. Mitchell (1993) details methods for executing the checks.



but when compared with other accounts may rate poorly or be incompatable with an existing portfolio. Third, the method fails to consider complex resources constraints. The (mixed) interger linear programming (ILP) method is a means by which to overcome these shortcomings. Such a method can model complex corporate constraints while being sensitive to managements' overall goals. The methodology is detailed in Winston (1993). The challenge, however, is to determine the coefficients to be used in the objective function of the ILP. These coefficients ought to indicate the likely responsiveness of the client to the marketing effort. Because of the inherent risk of uncertainty relating to human behaviour, i.e. the clients future actions, an acturial technique will be used to develop the coefficients.

The coefficients yi and y'j

Managements' objective is to maximize its expected returns from the marketing effort whilst being mindful of corporate and external constraints. The idea is to identify suitable candidate accounts then allocate resources among them. For our model let the objective function be:

Maximise ME = £ yi xi + £ YJ Yi (2) 4

ME = Expected productive marketing effort.

xi = Productive time resource allocated to account i.yj = Free resources available to pursue other (new)

profitable accounts.

Yi = The probability that the client account i will meet the corporate expectation, i.e., be a "good" or an "ideal" client.

4 For convenience the notation £ is used instead of the symbols Z"i=i or Z mj=i .

6 76 University of Karlsruhe


y'j = The probability of securing new account j through the firm's marketing efforts. This factor can be developed through managements' experience of operating within the sector.

yi is determined by formalising its relationship with pKi , the client score used to classify client accounts to the shortlist (pK > pK*). First, we assume that a positive correlation between the pK score and client attractiveness exists, that is, the greater the pK score the more attractive the client account. Having developed the respective pK scores the cumulative relative frequency distribution of these scores is plotted. A positive (upward) gradient curve is expected. The resulting curve is the plotted conditional probability distribution of a client being a "good" account given that the account's pK score is above the cut-off or pK* value. This conditional probability we shall define as y (Figure 2).

Organi sational Life Cycle Stages

Decline

Mature

Growth

Intro duction

• ai

• an

• ji • J2

0 1

• li • 12

• In

Prosperit Steady Recession y State



Macro-Economic State

Figure 1: The Decision Parameter (DP) Matrix

Y 1.0

pK Figure 2: The Y - pK Curve

ThusYx = P(G | pKi) where pKi > pK*

Table 1 illustrates the calculation of yiNoteworthy is the fact that despite scoring above pK* there is still the possibility that undesirable accounts will still be selected (Type II error) and be serviced. The converse also holds true, some potentially desirable accounts will be rejected because of low pK scores (pK < pK*), - Type I errors will occur. Consequently, the determination of an appropriate cut-off point is vital to the success of the scoring method. This in the first instance is determined when completing the discriminant analysis. The effectiveness of the cut-off point can be assessed by either the "maximum chance criterion" or the "proportional chance criterion" when testing the scoring model against a hold out sample [Mitchell (1993)]. In the event where the client base is small and all the sample is needed to develop the scoring equation Crask and Perreault (1977) suggest a suitable estimating procedure which can determine the prediction accuracy of the equation with minimum upward bais.



Constraints

The following types of constraints are considered: manpower (manhour) limitations; the marketing budget; minimum expected revenues for the marketing efforts expended; mandatory accounts to be services; necessary requisite accounts as an entry to other desirable clients; conflicting client accounts; and the option to select at least one project from a group comprising a diverse mix of potential accounts.

Table 1: Sample calculation of YI

pK Value

(1)

0.8

0.6

0.5

No. ofobservations

(2)

60

70

150

DesirableClientAccounts(3)

55

56

110

UndesirableClientsAccounts(4)

5

14

40

Ydesirable

(3) + (2)

55/60

56/70

110/150

Yundesirable

(4) + (2)

5/60

14/60

40/150

The personnel resource constraint is relatively straightforward to model. As xi is the resource allocation to the i th existing client account and yj is the free resource available to pursue other (new) accounts then

Z j- V •£" A /Q^ Xi ~r /. yj S: A. \"/

where A is the upper time limit on the resource. Similarly with regard to the marketing budget, if Oi is the charge-out or (cost rate) of resource xi to the cost centre, <E*j the corresponding rate for resource yj and B the budget cap then



Ojyj <B (4)

Revenue expectations from the respective existing client accounts are modelled thus:

Ci<(|>iXi<Ui (5)

where <j)i is the revenue rate from client account i for each unit of market time (effort) invested and Ci and Ui are the minmum and maximum revenues expected from the the account. (Revenues from potential clients accounts are omitted as there is little guarentee that income will be generated within the review period. However, management can decide to include this income stream provided they are fairly certain of securing a commission from the targeted client.)When addressing conflicting interests in potential accounts a binary coding is first used to aid the selection/rejection process; 0 for rejecting an account and I for accepting it, thus if Clients 1 and 2 are conflicting accounts:

Zl + Z2 < 1 (6)

zi, Z2 = 1 if account is to be accepted and 0 otherwise

is a sufficient model. The condition precludes the acceptance of both project but makes allowance for the rejection of both , i.e.,

1 + 0 < 1 means accept Client 1 but reject Client 20 + 1 < 1 means accept Client 2 but reject Client 10 + 0 < 1 reject both accounts1 + 1 < 1 is a condition violation

Pre-requisite projects (a case which may arise if a parent company's account cannot be secured unless a subsidary or a number of its subsidaries accounts are serviced) can be modelled using a similar binary coding. In the case of a parent and a subsidary account:



Z4 < Zs (7)

where zs is the subsidary account (Client 3) and Z4 the parent account (Client 4). Note that the condition allows for the possibilty that despite servicing the subsidary account the parent company's is not guarenteed.

0 < 1 Ghent 4 not secured (or is not acceptable to the portfolio) despite servicing Client 3

Mandatory accounts (which are from the pool of existing clients) are formulated thus:

zs = 1 (for example, Client 5 is mandatory) (8)

For a simple client list this switch is unnecessary, however, for an extensive list the switch can be used to change the status of a mandatory project to that which can be excluded from the portfolio by setting its value to zero. This saves the analyst(s) having to search the client list for the client-code(s) which have to be reassigned.In the event the marketer deems it necessary to pursue at least one potential account from the candidate pool of different constituent market segment the inequality below assists. For client accounts 6 and 7:

ZG + z? > lif two segments are considered (9) 1 + 1 > 1 means pursue both segments 1 + 0 > 1 means pursue one segment0 + 0 > 1 means ignoring both segments violates the

condition

Having developed the binary decision variables for selecting or rejecting potential projects it is necessary to incorporate these as constraints because failure to do this will result in incorrect and impractical solutions [Winston (1993)]. For the instances discussed the constraints below are necessary and sufficient to link yj and Zj.



yj > D3 zj (10) yj<Mj Zj (11)where j = 1,2...... .,n

Mj being positive coefficients sufficiently large so as not to effectively act to constrain the value of yj. To elucidate.

For zj = 0, yj < 0

there is no resource requirement because the project is not accepted. However,

Forzj=l,yj<Mj

Since Mj serves as a ceiling on yj it becomes important that Mj is not the limiting constraint on Zj when all other constraints are considered. Mj is set to be (at least) the largest value yj could attain under the other (real) constraints. Dj is the minimum effort which has to be expended on an account once it is actively being pursued.The final constraints are those of non-negativity (negative resource allocation is impractical) and defining whether xi and yj should have continuous or integer values. The decision will be influenced by the units to be used in the calculations (xi and yj as a measure of pooled team annual manhours or aggregated categorical manhours etc.) Commercial software packages are available to solve the mixed or pure ILP model.Combining the objective function with the constraint considerations forms the model to be optimized:



Maximise ME = £ •$ xi +1 y'j y; (2) subject to:Z Xi + Z yj ^ A (manhour budget) (3) Z Oi Xi + X $j yj ^ B (fiscal marketing budget) (4) (|)i Xi > Ci (min. revenues from chent i ) (5a)({K Xi < Ui (max. revenues from chent i ) (5b) zi + Z2 < 1 (conflicting projects) (6)z^ - zs < 0 (pre-requisite projects) (7)zs =1 (mandatory projects) (8)ze + z? > 1 (entering at least one new segment) (9)yj > Dj Zj (min. effort invested new account) (10)y, <MjZj (11)XB > Ds zs (mandatory account) (12)DJ , MJ > 0 and is set by the user (13)Zj =0orl (14)Xi, yj > 0 (i, j, =1, 2, 3, ... ) (15)

The solution of the model results in the composition of the optimal chent portfolio and the corresponding resource allocation to each account. Table 3 below shows a format for a hypothetical optimised portfolio. Graphs of the respective manhours allocation, costs to the firm for each client account and the corresponding expected revenues can be developed from the results of the table.

CONCLUSIONS

The proposed model adds to the theory of client portfolio development and analysis by offering a dynamic psuedo quantitative -qualitative methodology. The dynamic element is incorporated by the development of decision parameters which alter with the economic state of the marketplace as well as with the evolutionary growth of the firm. In developing these



parameters the firm's management team needs to be mindful of changing corporate ambitions and client traits which support these goals. A rational proactive approach is encouraged. Such an approach fosters the early development of pK* through which the analyst's client evaluation (judgement) skills are honed. From this exercise realistic YI , and perhaps more importantly, y'j factors are developed.The model also offers guidances regarding conditions under which revision of the portfolio becomes necessary. These are:

1) whenever there is an ecomomic change within the marketplace;

2) whenever the firm progresses (or regresses) to another stage of the life cycle curve; or

3) should both (1) and (2) occur.Because linear programming (LP) techniques are being used it is possible to conduct:

(a) Sensitivity analysis of the objective function to determine the range of values of yi and y'j within which the portfolio remains stable for one coefficient varing whilst the others remain constant. The benefit of this analysis is that it discourages the unnecessary re-analysis of the portfolio for tolerable changes in the respective client probability coefficient.

(b) Dual or shadow values for each resource constraint. These are the net unit worth of the change in a single resource constraint within a given range while the other resources remain unchanged. The values reflect the increase or decrease in the objective function for changes in the resource under consideration.



Table 3: Presentation of hypothetical results (column 5 depicts the optimised client portfolio)Index

(0

1

2

3

4

5

6

Name

UM

PSA

MoD

ICL

IBM

OVE

Type

E

P

E

E

P

E

Bus.

Educ

Cons

Def.

Chem

Comp

Engrg

Mhr

120

0

0

160

360

100

Rev(£) OOO's

12

0

0

10

25

26

Cost (£) OOO's

7

0

0

5

10

8

Y

0.6

0.4

0.6

0.7

0.5

0.7

Reason for rejection /selection

Preq. for Client 8

ConflictswithClient 7

Sub-optimal

Mandatory

Mandatory

Optimal

pKscor e

20

16

21

20

18

21

pK* = 16

Key: E - Existing client P - Potential Client Bus. - Principal area of business



If there is a violation of any condition for either (a) or (b) the portfolio is in need of re-analysis. The LP results will also yeild the magnitude by which resources are exceeded or under utilised to achieve the optimal mix of clients. Such information is useful to management in determining resource deployment and other operational matters.There are still further developments for the model. One possible area of fruitful research would be to reformulate the marketing problem using multiple objective linear programming or goal programming techniques. In this method a number of prioritorised goals are set as objective functions and these are optimized subject to constraint considerations. Another worthwhile area of endeavour would be to empirically validate the proposed model. The ease with which decision parameters are developed by management and the meaningfulness of the results would give further insight into the concept of client portfolio theory. From these findings the model can be developed to a stage where it can be used as an interface in knowledge based decision making systems.



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