three essays on risk-adjusted customer lifetime value and returns to search

8/12/2019 Three Essays on Risk-Adjusted Customer Lifetime Value and Returns to Search

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THREE ESSAYS ON RISK-ADJUSTED CUSTOMER LIFETIME VALUE AND

RETURNS TO SEARCH

by

Shweta Singh

APPROVED BY SUPERVISORY COMMITTEE:

___________________________________________Ram C. Rao, Co-Chair

___________________________________________B.P.S. Murthi, Co-Chair

___________________________________________Brian T. Ratchford

____________________________________________Nanda Kumar


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Copyright 2008

Shweta Singh

All Rights Reserved


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To my dear parents, Dr. B.K. Singh and Niloo Singh, to my dear husband, Sumit Singh,

to my lovely daughters, Sneha and Supriya Singh, and last but not the least my sister,

Shubhra Singh, brother-in-law Amit Singh, and sister-in-law Dr. Maulshree Singh. I have

learnt a lot from you all. My parents showed me that kindness towards others and hard

work never goes waste, and how to give to others without expecting anything in return.

My husband showed me that theres nothing impossible in this world. If you set your

mind on something you can achieve it and more. He has been my constant rock who has

never let me fall down. My sister through her life experiences has showed me that by a

positive outlook towards life one can persevere over anything. She has showed me that it

is okay to fall down but you get right back on your feet, a stronger person, and a better

person. My daughters never cease to amaze me with their wonderful outlook towards life.

They are by far my biggest achievement in life. I thank all of you for your everlasting

love, support and encouragement at every stage of my life. I have reached this milestone

because of you.

I love you all very much!


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RETURNS TO SEARCH

by

SHWETA SINGH, B.A, M.B.A, M.S.

DISSERTATION

Presented to the Faculty of

The University of Texas at Dallas

in Partial Fulfillment

of the Requirements

for the Degree of

DOCTOR OF PHILOSOPHY IN MANGEMENT SCIENCE

THE UNIVERSITY OF TEXAS AT DALLAS

August, 2008


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ACKNOWLEDGEMENTS

I would like to express my most sincere gratitude, appreciation, respect and

admiration for my entire committee, Dr. B.P.S. Murthi, Dr. Ram C. Rao, Dr. Brian T.

Ratchford and Dr. Nanda Kumar.

I would like to extend my utmost regard for Dr B.P.S. Murthi for his encouragement,

guidance, inspiration and support throughout my doctoral study at The University of Texas at

Dallas. Without his help, this dissertation would have been impossible. He has worked with

me on each of the three essays, providing a sturdy board to bounce off ideas. Thank you, Dr.

Murthi, for always being there and for everything. No matter how mundane the question,

you answered each and every one of them and with utmost patience. You have been a true

mentor. You never lost faith in me but helped me continuously grow as a teacher and a

researcher. You never cease to amaze me with your astuteness and ability to think on the feet.

You have trained me in such a way that when stuck with a research problem, I just ask

myself how you would have proceeded under those circumstances and the answer to the

question always saves the day!

Dr. Ram C. Rao is an icon in his research area and I feel greatly humbled that I have

had the opportunity to complete my dissertation under his supervision. He is one of those

people that can look at your work and give a suggestion or an angle that leaves you

speechless and thankful at the sheer brilliance and novelty of it. Thank you for going over

and beyond your role as a mentor to always give me the most sound advice and support. You


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were key in getting me into the program and I am a much better person for it. Your constant

encouragement helped me every step of the way.

My admiration and respect for Dr. Brain T. Ratchford is boundless. He has taught me

that true humbleness comes from true greatness. One thing that has always stuck with me

about him is that he never passes judgment. He lets you find your own niche and just

provides a supporting environment so that you can excel in it. His doors are always open for

his students, always ready to offer help. My third essay was possible due to his kind

generosity. The data used in the essay belongs to Dr. Ratchford and he worked right along

with me every step of the way to make this paper a good one. Thank you for always keeping

such an open mind and listening.

Last but not the least; I am also indebted to Dr. Nanda Kumar for his valuable,

ingenious comments and helpful suggestions. He has always been there to guide me and

encourage me and I have never really had to think twice before approaching him because of

the sound advice he has given me each and every time. He even coached me before my

campus interviews at the American Marketing Association and his input greatly helped me in

acing the interviews. Thank you, Dr. Kumar for being a constant support.

May 2008


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RETURNS TO SEARCH

Publication No. ___________________

Shweta Singh, Ph.D.The University of Texas at Dallas, 2008

Supervising Professors: Dr. Ram Rao, Co-Chair,Dr. B.P.S Murthi, Co-Chair

ABSTRACT

This dissertation is made up of three essays. In essays 1 and 2, we show that valuing

customers on the basis of the cash flows that they generate for the firm can be misleading. In

the market for credit cards, the correlation between risk and revenue is both positive and

high. Moreover, when faced with a situation in which there are multiple sources of revenue

and risk, managers need a metric to evaluate customers. We identify three sources of revenue

for a credit card company- interest, interchange, and fee incomes, and seven types of risk a

customer can potentially pose to a firm- probability of default, betarisk in each revenue

measure and volatility in each revenue sources. In essay 1, we use fractional programming to

provide a single index of risk-adjusted revenue (RAR) for each customer. In essay 2, we use

an alternative efficiency frontier approach, stochastic frontier approach to calculate Risk-

Adjusted Lifetime Value (RALTV) for each customer. We use the metrics RAR and RALTV

scores to understand the effectiveness of acquisition modes and retention strategies such as


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reward cards and affinity cards. Our findings indicate that even though reward cardholders

and affinity cardholders are less profitable for a firm than non-reward and non-affinity

cardholders, they tend to perform better on both, the RAR and RALTV metrics because of

the low risk they pose to the firm.

The third essay deals with consumer search for information and measuring the returns to

search. In the past, results regarding the gains to search have been unclear and measures of

returns to search have either been subjective or limited to price reductions. In this essay, we

provide a more comprehensive approach to measuring returns to search. We measure returns

to search in terms of the ability of consumers in buying a better quality product. We use Data

Envelopment Analysis (DEA) to estimate our conceptual model of returns to search. Our

findings indicate that Internet users and more experienced and educated consumers tend to

make more efficient choices while consumer efficiency goes down with age.


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TABLE OF CONTENTS

ACKNOWLEDGMENTS ...................................................................................................vABSTRACT ...................................................................................................................... viiLIST OF FIGURES .......................................................................................................... xiiLIST OF TABLES ........................................................................................................... xiii

CHAPTER 1 ADJUSTING FOR RISK .............................................................................11.1 Motivation ....................................................................................................11.2 Overview of the credit card industry ...........................................................61.3 Research issues ..........................................................................................101.4 Literature Review.......................................................................................12

1.4.1 Credit card literature.......................................................................121.4.2 Existing CLV models .....................................................................131.4.3

Papers dealing with risk .................................................................15

1.5 Data description .........................................................................................16

CHAPTER 2 RISK ADJUSTED REVENUE: ITS IMPLICATIONS FOR CUSTOMERRELATIONSHIP MANAGEMENT .................................................................................19

2.1 Modeling Approach ...................................................................................192.1.1 Revenue streams .............................................................................192.1.2 Risk measures .................................................................................19

2.2 Data Envelopment Analysis and DEA model ............................................232.3 Input Oriented CRS DEA Models for determining RAR scores ...............262.4 Identifying the Best customers: Who are they? ......................................29


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CHAPTER 3 RISK-ADJUSTED LIFETIME VALUE: A NEW APPROACH TOVALUING CUSTOMERS ................................................................................................31

3.1 Introduction ................................................................................................313.2 Modeling Approach and Results ................................................................32

3.2.1 Revenue ..........................................................................................323.2.2 Risk.................................................................................................32 3.2.3 CLV model and results ...................................................................343.2.4 Model for calculatingP (alive)......................................................363.2.5 SFA model and results ...................................................................383.2.6 RALTV model and results .............................................................40

3.3 Comparing RALTV and traditional CLV measures ..................................41

CHAPTER 4 CONTRIBUTIONS, CONCLUSIONS, LIMITATIONS AND FUTURERESEARCH...43

4.1 Contributions to existing literature ............................................................434.2 Conclusions, limitations and future research .............................................43

CHAPTER 5 RETURNS TO SEARCH AND ITS DETERMINANTS .........................475.1

Motivation ..................................................................................................47

5.2 Literature review ........................................................................................495.3 Theoretical Model of Consumer Search Efficiency ...................................53

5.3.1 Conceptual framework ...................................................................535.3.2 Data Envelopment Analysis ...........................................................555.3.3 Linking DEA and Conceptual Model.............................................57

5.4 Dataset........................................................................................................58 5.5 Results from the DEA model .....................................................................605.6 Relating Efficiency to search .....................................................................645.7 Results from the Tobit model ....................................................................695.8 Conclusions, limitations and future directions...........................................70


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APPENDIX A - FIGURES ................................................................................................72APPENDIX B - TABLES ..................................................................................................77REFERENCES ..................................................................................................................91VITA


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LIST OF FIGURES

Number Page

Figure 1.5a. Descriptive statistics- Frequency Plot of different sourcesof revenue for a creditcard company..72

Figure 1.5b. Descriptive Statistics - Frequency Plot of modes of acquisition....73

Figure 1.5c. Descriptive Statistics - Frequency Plot of Reward cardholders.73

Figure 1.5d. Descriptive Statistics - Frequency Plot of Affinity cardholders.74

Figure 1.5e. Descriptive Statistics - Frequency Plot of type of cards 74

Figure 5.4. Pie Chart of share of different Information Source......75

Figure 5.6. A Model of Returns to Search..76


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LIST OF TABLES

Number Page

Table 1.1A. Correlation between risk and profits....77

Table 1.1B. Correlation between risk and CL..77

Table 1.5A. Descriptive Statistics of Relevant Variables for 36 months.78

Table 1.5B.Descriptive Statistics of Relevant Variables for 24 months..79

Table 2.1.2.Logit Output for Probability of Default for 36 months.80

Table 2.3.Results from DEA CRS/Input-Oriented Model81

Table 2.4.Logit Output for identifying the Best customers82

Table 3.2.2.Logit Output for Probability of Default using 24 months data.....83

Table 3.2.5.Results from SFA model...................................................................................84

Table 3.2.6.Logit output from RALTV model.85

Table 5.4.1A.Descriptive Statistics of variables used in essay 3.86

Table 5.4.1A.Types of Information sources Used...87

Table 5.4.1C.Type of Car Bought87

Table 5.4.2A.Regression output for dependent variable,Consumer Reportsquality ratings, for all classes of cars combined...88

Table 5.4.2B.Separate regression output for dependent variable,Consumer Reportsquality ratings, for each class of cars88


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Table 5.5.Results from DEA VRS/Input-Oriented Model..89

Table 5.7.Results from the Tobit model...90


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CHAPTER 1

ADJUSTING FOR RISK

1.1 Motivation

Recent times have witnessed a growing interest in the customer relationship

management (CRM) and customer lifetime value (CLTV) areas by both researchers and

practitioners alike. This trend is partly attributable to the fact that more and more firms find

at their disposal, today, an overwhelming amount of customer data and are looking for new

and innovative ways to mine this data to obtain managerially useful insights. Also, as more

firms struggle to find solutions to their costly yet perpetual problems of customer acquisition

and retention, they find themselves searching within their own customer databases to look for

answers. It has been estimated that it costs firms six times more to acquire new customers

than to retain their old ones. Hence, firms need to better manage their existing customer base

to the extent that they are able to identify not only their key segment of customers but also

the segment in the mass market they want to go after.

Financial industries like credit card companies constantly have to search for more

effective ways to attract new customers who are good risks and at the same time try and

minimize their expected loss from the customers who are bad risks. Aggressive marketing

efforts have led to a deeper penetration of the pool of high risk customers. The correlation

between risk and revenue is both positive and high. In the credit card industry, customers are

often classified into two types: the class of customers who make their payments on time and

payoff their balance in entirety every month and the class of customers who use the credit


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card for borrowing purposes and have a revolving balance on which they pay finance charges

and fees. It is the second class of customers who are a source of both risk and revenue for the

credit card companies since a profitable customer is one who carries a large balance on

his/her credit card and pays a higher rate of interest. These cash strapped customers are also

more risky as they could default and cost the company quite a lot of money. In this context

traditional measures of lifetime value are inadequate as they do not control for risk.

Traditionally, customers have been valued on the basis of how much cash flow they bring to

the firm. However, in financial service industry, the customers who contribute the most to the

profitability of a firm are also the most risky. If the riskiness of a customer is not taken into

account, firms may overestimate the overall value of that customer. According to Gupta,

Hanssens et al (2006), Locally optimal decisions regarding the acquisition and development

of customers may in some cases be globally suboptimal from the broader business

perspective. For example, in some financial services settings (e.g., credit cards), current CLV

measurement practices that focus on the expected value of a customer may predict that high-

risk customers are more valuable than low-risk ones. Acting on this information, the

marketing manager will focus on acquiring these high-risk customers. However, the financial

markets expect the firm to have a portfolio of customers that comprises a mix of low- and

high-risk customers. Locally optimal behavior by the marketing manager may therefore be

suboptimal for the firm.

We fill the gap in the literature by developing measures of risk adjusted revenue

(RAR) and risk-adjusted customer lifetime values (RALTV) that we hope will be useful in

guiding managers in financial service sector to better target and retain profitable customers.

We use dataset from a major credit card company to develop and estimate our model and also


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make inferences about the impact of RAR and RALTV on a customers overall value to the

firm. This is managerially important since, most of the time managers have at their disposal a

limited budget and one of the key issues they face is how to allocate this budget among

alternative assets. With the RAR and RALTV scores that define each customer, managers

will have a better idea of how to efficiently allocate the scarce resources. Valuing customers

on the basis of the cash-flow that they generate can be misleading. According to Jain and

Singh (2002), Loyalty of unprofitable customers is not good for a firm. However, in this

paper we show that even though certain customers are less profitable, they are still valuable

for the firm since they are less risky. After adjusting for risk, we find that these otherwise

less profitable customers score high on both the RAR and RALTV metrics and thus prove to

be valuable to the firm.

We develop seven measures of risk in this paper: probability of default, volatility in

interchange income, volatility in interest income, volatility in fee income, betarisk in

interchange income, betarisk in interest income, and betarisk in fee income. We define the

probability that a customer will default as the account being delinquent for 90 days at a

stretch. The probability of default measure of risk is calculated using the Logit model as a

function of a customers transaction history, marketing activities on part of the firm, and

demographic variables. In the past, one of the predominant areas of research in the credit

card industry have involved developing behavioral scoring models that identify the level of

risk associated with the existing customer base of a credit card company. Calculating the

probability that a customer will default on his payments or probability that a customer will

commit fraud has been the focus of these studies. Rosenberg and Gleit (1994), Thomas

(2000), and Till and Hand (2003) provide excellent reviews of the models used in the


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literature for behavioral scoring of credit card customers. Volatility measures the standard

deviation of a customers pattern in making transactions, incurring finance charges and fees

separately. This captures the idea that even though the average returns of two customers are

the same, a company would prefer a customer who provides a steadier stream of revenue. We

use this measure as a surrogate for a customers share of wallet. Erratic spending habits and

long spells of silence from a customer have implications for number of times the customer is

using the firms credit card as opposed to that of its competitors. Betarisk of a customer

measures correlation with the portfolio of customers as a whole. Beta is calculated byregressing the customer's return against the entire portfolio of customer. Dhar and Glazer

(2003) were the first to suggest the use of customer beta as a measure to calculate the

riskiness of customers. Their beta model is used to capture the uncertainty of the cash flow

generated by customers.

We also identify three sources of revenue for the credit card company: interchange

income, interest income and fee income. Customer profit in the financial services industry is

driven from three primary income streams, interest income, interchange income, and fees.

The most significant component of profit is interest income, which results when customers

do not pay their total outstanding balance in full at the end of each billing period, but instead

opt to carry a portion of their balance over to the following billing period. Approximately

78% of the total account revenue is derived from interest on outstanding balances (Min &

Kim 2003). In our dataset, approximately 72% of the revenue comes from interest income.

Interchange income is derived from the small percentage that the firm earns on every

customers retail transaction. The final income stream is cardholder fee income. While many

accounts no longer carry an annual fee, fees remain a significant and growing source of


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customer income. In addition to annual fees, firms charge fees for negative customer

behavior such as over-the-limit fees, late payment fees, and returned check fees. Americans

paid an estimated $30 billion in financial service fees in 2004; an increase of 18% over 2003

(CardTrak 1/13/05). Fees have become an increasingly important source of income for firms

as a result of increased competition that lowered annual percentage rates and increased

aggressive promotions.

Table 1.1A provides the correlation between profits and the seven measures of risk,

while table 1.1B provides the correlation between CLV and our risk measures, respectively.

As is evident from both the tables, the correlation between risk and return is both high and

positive.

In essay 1, the seven measures of Risk and three measures of Revenue are then used

in a DEA (Data Envelopment Analysis) model to come up with a single RAR score for each

individual customer. DEA is commonly used to evaluate the efficiency of a number of firms.

While a typical statistical approach is characterized by a central tendency approach and

evaluates consumers relative to an average consumer, the DEA is an extreme point method

that compares each consumer with only the best consumers. DEA is especially useful in

our context due to its ability to handle multiple inputs and outputs and does not require an

assumption about the functional form relating inputs to outputs. The scores are then used to

segment customers into most profitable and least profitable after adjusting for the risk

they pose to the firm. We then identify the factors that discriminate between the two

segments. We use the input-oriented constant returns to scale (CCR) model o calculate the

RAR scores. The model is discussed in more detail under the models section in chapter 2.


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In essay 2, we use Stochastic Frontier Analysis (SFA) to create our customer efficient

frontier. SFA is an econometric technique that allows for stochastic errors. Unlike DEA

which is a non-parametric technique, SFA is a parametric approach that estimates a profit

function assuming that the error term has two independent components (Aigner et al, 1977;

and Meeusen and Van Broeck, 1977). While one component captures technical inefficiency,

the other captures statistical noise such as random effects of measurement errors or external

shocks. Technical efficiency refers to the ability of each customer to obtain the maximum

output from a given set of inputs. Technical inefficiency is zero for the value-maximizing

customer, i.e. the customers that lie on the efficient frontier, but is strictly positive for

customers that lie below this frontier.

The output variable in our SFA model is the customer lifetime values while the input

variables are the three measures of risk. Estimation of the efficient frontier generates

individual level efficiency scores that we refer to as Risk-adjusted lifetime value or RALTV.

Hence, we define RALTV in terms of the maximum CLV that a customer represents to a

firm for given levels of risk. The RALTV scores are then used to explore the impact of

acquisition and retention strategies on RALTV. We want to see whether our results in essay

1carry over once we incorporate the costs of servicing customers.

1.2 Overview of the credit card industry

Financial institutions are increasingly measuring and managing risk from credit

exposures at the portfolio level, in addition to the transaction level

Wilson (McKinsey and Company, 1998)


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In an age where cash is being replaced by plastic and technology, credit cards are one

of the most popular and growing mediums used for the purposes of both transaction and

borrowing worldwide. Consumers use credit cards for two purposes, either for the

convenience it offers or for borrowing funds that gives them the flexibility of deferring

payment to a future date while making up for their temporary liquidity shortfalls. From a

customers point of view, credit cards provide two primary benefits - as a medium of

convenient exchange and as a source of short-term or intermediate term revolving credit

(Garcia 1980). Whichever the purpose, the credit card industry in recent times has witnessed

an exponential boom in its usage. On one hand, the profits accruing to credit card companies

have been on the rise but the flipside of this increase is the tremendous increase in the portion

of the total outstanding consumer credit attributable to revolving charge accounts (Kinsey,

1981). According to a recent survey by Demos and the Centre for Responsible Lending,

seven out of ten low- and middle-income households reported using their credit cards as a

safety net by using their credit cards to pay for car repairs, basic living expenses, medical

expenses or house repairs. The average credit card debt carried by a low- and middle-income

household in America is $8,650 (The Plastic Safety Net: Demos and the Center for

Responsible Lending).

Unlike bank loans which are secured loans, credit card loans are often unsecured

loans. Thus, the degree of risk associated with credit card lending is much more since

repayment depends primarily on the borrowers capacity to repay. Asymmetry of information

makes this risk even more pronounced since credit card holders have better information than

the card issuersabout their ability and willingness to repay the loan that they take. Thus,

given the risk associated with credit card lending, it is essential for credit card companies to


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identify the sources and types of risk associated with the customers they acquire and the ones

who are already part of their existing customer base.

In addition to the credit risk that is posed by the individual customers, credit risk also

exists in the overall portfolio of customers that a credit card company has. Thus, there is a

need to evaluate portfolio performance and profitability by taking into account the different

types of risks posed by the portfolio. At any given point in time, each firm manages a

portfolio of customers rather than a single customer. In marketing, one can think of managers

faced with a portfolio of customers and the problem of how to better manage them in order to

strike a balance between risk and return. It is true that customers are a potential source of

revenue for a firm but in truth there is some kind of risk attached to each one of these

customers. This is especially true of the credit card industry. The average American today

carries around 11 credit cards and has roughly $9000 in credit card debt. The riskiness of a

credit card holder in terms of the probability that he/she will default is rising in the amount of

the credit card debt he/she carries.

In the financial sector, the correlation between risk and return has been established to

be positive. In the consumer market for goods and services too, this positive correlation

carries over. According to Dhar and Glazer (2003), customers constitute a major source of

cash flows of a firm, which in turn makes them risky assets. They differ with respect to the

size and volatility of the cash flows they generate for the firm in question. The authors

contend that since the biggest generators are often the most risky, it helps to hedge the

portfolio with some steady customers.

In the face of intense competition, credit card companies are looking for new and

innovative means to better serve their existing customers so as to enhance their loyalty and


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increase their satisfaction level. An immediate outgrowth of such strategies is continued

retention of these customers that translates into increased profits for the firm (Reichheld,

1996). The increased profits can result from either an increased spending by the loyal

customer, low operating costs required to serve these customers, customer referrals made by

the customer or the price premium that can be elicited from these loyal customers.

Two of the most commonly employed retention strategies used by credit card

companies are reward card and affinity card programs. According to the creditorweb.com, a

reward card offers you the opportunity to earn different types of reward based on your usage

of a particular reward card, while an affinity card is a branded credit card that is co-issued

by a bank and the organization whose logo appears on the card with the intention to co-

market the card to the organization's customers or members in hopes of enticing them to

carry the card. Some of the most common reward are cash-back rebates, airline frequent

flyer credits, gas rebates, and discounts at specific stores and entertainment venues. Some of

the common affinity cards that exist today include charity credit cards where a donation is

made to a particular charitable organization whenever the card is used or the sports team

affinity card, aimed at supporters of a particular football team or other sporting club.

Both reward and affinity cards are aimed at increasing sales, strengthening customer

relations and enhancing their loyalty to the firm, as also increasing the duration of their stay

with the firm. All these together should translate into higher profits for the firm. However,

previous work in the credit card industry has shown that reward cardholders and affinity

cardholders tend to be less profitable than non-reward cardholders and non- affinity

cardholders, respectively (Steffes, Murthi and Rao 2005). Given the costs associated with

implementing reward and affinity cards, this result comes as a surprise. We are therefore


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interested in re-visiting this issue from a different perspective, i.e.by incorporating risk into

traditional customer lifetime value models. We are interested in seeing how results change

once we have adjusted for the different sources of risk.

1.3 Research issues

In creating measures of risk-adjusted revenue and risk-adjusted lifetime value for

each customer, we are interested in answering the following questions.

How to adjust for multiple sources of risk?

Which is the most important risk to be considered?

Who are the customers that are able to produce the maximum revenue for a

given level of risk or vice versa?

How does retention strategies affect risk adjusted revenue (RAR) and risk-

adjusted lifetime value (RALTV)?

Do different modes of acquisition affect RAR and RALTV?

Which approach, between traditional CLV and RALTV models, does better in

terms of identifying the true value of a customer?

To help answer our first three questions, we use two competing frontier approaches to

measure the productive efficiency of customers. Productive efficiency is used to measure

distance to a revenue frontier in case of essay 1 and the profit frontier in case of essay2. A

firms objective is to maximize its revenue/profits while at the same time keeping risk posed


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by customers to a minimum. For a credit card firm, the revenue/profit frontier is created by

customers that are able to produce the maximum revenue/profit for a given level of risk. We

use frontier functions for two reasons. Firstly, we are able to estimate customer-specific

efficiency in achieving the firms objective. Secondly, the frontier approach is capable of

handling the multiple sources of risk that a customer poses to the firm.

In answering the research questions 3 and 4, we take the RAR and RALTV measures

from our DEA and SFA models, respectively and divide the customers into groups based on

their risk-adjusted values (we use median split). We then use a logit model to find out the

impact of a firms acquisition and retention strategies, customer demographic characteristics

and transactional activities such as amount of balances carried forward, frequency of

purchases etc., on customer risk-adjusted values.

We also want to compare the traditional CLV and RALTV measures to identify the

measure that is a better predictor of the true value of a customer. Our dataset spans 36

months and around 1679 customers. We use the first 24 months data for estimating our

models of CLV and RALTV. The remaining 12 months data are used for validation purposes.

Among the 1679 customers in our dataset, there are some customers whose accounts have

been closed due to non-payment of their balances. We take different cut-off points (such as

top 50, 25, 10 percentiles) to identify the customers who have been classified as being the

most valuable by our CLV and RALTV measures, respectively. We then use the validation

dataset to identify the total number of actual defaulters who have been identified as valuable

and to calculate the total loss resulting from these defaulters. As suspected, the traditional

CLV measure tends to overestimate the value of a customer. Traditional CLV measures

identify those customers who give high returns to the firm to be the most valuable. However,


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they do not take risk into account and hence, given the positive correlation between risk and

return, often identify the most risky customers to be the most valuable ones. We find that

among the top fifty percent of the customers that have been identified by traditional CLV

measures, in our validation period, thirty of them turn out to be actual defaulters. In terms of

dollar amount, the loss given default from these customers totals $$240384. Alternatively,based on our RALTV scores, none of top fifty percent customers turned out to be actual

defaulters in our validation dataset leading to a loss of $ 0. We carried this analysis using

different cut-off points such as the top 25% and the top 10% but our results remained the

same. Although the number of actual defaulters decreased as we increased our percentile

range, however, the consistent result was that traditional CLV models continued to identify

the most risky customers as the most valuable ones.

1.4 Literature Review

1.4.1 Credit card literature

Previous research on credit cards has predominantly focused on three areas: credit

scoring models, behavioral scoring models, and customer profiles. Credit scoring models are

specifically geared toward the decision of whether or not to grant credit, while behavioral

scoring models focus on identifying risk (e.g., fraud, default) in the existing customer

portfolio. Excellent reviews of the models employed in credit scoring and behavioral scoring

are provided in Rosenberg and Gleit (1994), Hand and Henley (1997), Thomas (2000), and

Till and Hand (2003).


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1.4.2 Existing CLV models

An enormous number of papers have been written on calculating customer lifetime

values and its implications for a firms marketing efforts. Alternatively, the literature on the

need to adjust for the riskiness of consumers is in an evolving state. However, papers that

have shown the empirical relevance of adjusting for customer risk in calculating the true

value of the customer continue to remain sparse and few. Essays 1 and 2 are an attempt to fill

this gap in the CLV literature. Due to lack of substantial papers that deal with the issues of

customer risk-adjusted lifetime values, we will first provide a broad overview of the literature

related to traditional CLV models, followed by a couple of papers that we feel are related to

the current work.

Recently, the focus has shifted from a Product-centric approach to a Customer-centric

approach. The view that customers represent the assets of a firm whose value should be

quantified, has led to a greater emphasis on CLV models (Dwyer 1997; Colombo and Jiang

1999; Mulhern 1999; Reinartz, and Kumar 2000; Venkatesan and Kumar 2004; Pfeifer,

Haskins, and Conroy 2005) and papers that deal with a firms marketing strategies and their

implications for customer profitability (Thomas 2001; Gupta, Lehman and Stuart 2004;

Rust, Lemon, and Zeithaml 2004; Reinartz, Thomas and Kumar 2005). According to Jain and

Singh (2002), CLV models are a systematic way to understand and evaluate a firms

relationship with its customers. Jain and Singh (2002), Berger, and Nasr (1998), Kumar,

Ramani, and Bohling (2004), and Gupta, Hanssens, Hardie et al (2006) provide an excellent

overview of the different models used to calculate Customer Lifetime Value.

A related concept that has received much attention is customer base analysis. The

models developed in papers that deal with Customer Base Analysis (Schmittlein, Morrison


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15

level of risk and therefore the cash flows that these customers generate are discounted at the

same rate. Secondly, since the basic CLV model has been derived from the CAPM (Capital

Asset Pricing Model) in Finance, it adjusts for all sources of risk through a single discount

rate, without identifying and quantifying the different sources of risk that affect the value of a

customer.

1.4.3 Papers dealing with risk

Two papers in the literature that closely resemble the logic followed in this paper are

the works by Dhar and Glazer (2003) and Ryals and Knox (2005). Dhar and Glazer (2003)

were the first to put forward the view that customers are risky assets and firms need to

account for the unpredictability of their customers in a similar manner as do investors in their

treatment of stocks. At the heart of their analysis lies the view that just as investors have, at

any given point of time, a well-diversified portfolio, firms too need to hedge in their mix of

customers to protect themselves from the unpredictability of some customers. Their analysis

suggests that firms are better off adding to their existing portfolio, those customers that

stabilize their overall risk. If a firms customer portfolio is highly risky, then the addition of

non-risky customers would balance the portfolio. A well-diversified portfolio of customers

can maximize a firms overall returns. Ryals and Knox (2005) use data from the insurance

industry on twelve key accounts to calculate the economic value of a customer. They

consider two types of risk that a customer poses to a firm- the probability of filing a claim

and the probability of retention. The net earned premiums is first multiplied to the claims

risk, added to other sources of revenue from that customer, multiplied to the probability of

retaining the customer minus the cost of serving the customer and then adjusted by the firms


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16

weighted average cost of capital to arrive at the economic value of the customer. Since the

risk measures used in the paper are probability measures, it is easy to multiply them and get

an estimate of expected revenue or the economic value of the customer. However, when the

risk measures are not probability measures, adjusting for them is not such a straightforward

exercise. We, thus, need a method which is capable of handling different types of risk

irrespective of the units in which they are measured. Also, Dhar and Glazer consider only

one type of risk, i.e. betarisk. Here, we propose seven types of risk that a customer can

potentially pose to a firm and also propose an existing methodology which is capable of

handling these different risk measures.

1.5 Data description

Our dataset covers a three-year time period representing approximately 1700 accounts

all starting their relationship with a financial services provider at the same time. The

customers were initially acquired through four modes. The majority of the customers were

acquired through directmail (52.35%), followed by telesales (29.88%) directselling (10.76%)

and the Internet (7%). In the face of stiff competition, in order to enhance the loyalty of their

existing customers credit card companies commonly use two types of retention strategies-

reward cards and affinity cards. Within our sample, nearly 82% of our customers carry

affinity cards and roughly 21% carry reward cards. Four types of credit cards were issued to

the customers. Platinum cardholders make up the bulk of the customers (77.65%), followed

by standard cardholders (16.71%), quantum cardholders (3.94%), and gold cardholders

(1.71%). Data on the demographic profile of the customers also includes their occupation

type and age. The average age of the customers in the sample is around 44 years.


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17

Apart from the demographic characteristics of the customers, the dataset is also rich

in providing and calculating transactional details such as number of purchases, amount of

purchases, balances carried in each period, the credit line extended to each of these customers

etc. In tables 1.5A and 1.5B, we report the descriptive statisticsof the variables of interest for

36 months and 24 months, respectively, while figure 1.5 contains the frequency plots of

categorical variables of interest. From table 1.5A we can see that on average customers paid

$ 1182.75 in finance charges over the period of 36 months, $ 238.62 in interchange income,

followed by $ 232.75 in fees. Thus, while finance charges accounted for nearly 72% of the

revenue generated for the firm, interchange income and fees accounted for around 15% and

14% respectively. The average frequency of transactions made by the customers is around

138. There also exists considerable volatility in the interest income, interchange income and

fee income paid by the customers.

Nearly 8% of the customers defaulted on their payments for consecutive ninety days

which is not easy to ignore. Given, that in reality the number of customers a credit card

company has run into millions, 8% of a million customers translates into a huge number of

defaulters. The mean value of credit line extended by the firm is around $14,000. One of the

dilemmas faced by credit card companies is the balances that customers carry on their

account. On one hand, since finance charges are their main revenue source, increasing

balances translate into increasing revenues. On the other hand, large amounts of balances

also increase the riskiness of a customer since there is always a possibility that the customers

can default and run away with the money, thereby costing the firm a lot of money. In ourdataset, on average customers carry a balance of around $ 2,900on their card.


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Since the data used in essays 1 and 2 are the same, we provide a common section that

deals with data description in chapter 1.The mean values provided above have been

calculated for the entire 36 months period. However, since essay 2 uses 24 instead of 36

months of data to estimate our revenue, risk, CLV and RALTV measures, some of the key

variables used in essay 2 will differ from the values calculated in essay 1.Thus, in tables 1.5A

and 1.5B we provide the mean values for relevant variables for the 36 months and 24 month

periods separately.


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19

CHAPTER 2

RISK ADJUSTED REVENUE: ITS IMPLICATIONS FOR CUSTOMER

RELATIONSHIP MANAGEMENT

2.1 Modeling Approach

2.1.1 Revenue streams

There are three main streams of revenue for credit card companies:

a. Interchange income: total transaction amount that generates interchange fees

(generally 1-2% of dollars amount spent). The average interchange income for the 36

month period is around $ 239.

b. Interest income: total finance charges which result from balances carried by the

customer. The average interest income for the 36 month period is around $ 1182.

c. Fee income: total fees charged by the bank for delayed payments and defaults. The

average fee income for the 36 month period is around $ 232.

2.1.2 Risk measures

Given the need to adjust for risk, in this section we propose and model the following

types of risk.

Volatility: This is the standard deviation in each revenue measure over time. This

captures the idea that even though the average returns of two customers may be the same, a

firm would value the customer that provides a more stable return.


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20

222 ))(()()))((( XEXEXEXE == (EQ 2.1)

Where, E(X) is the expected value of X

We consider volatility of three types:

1. Volatility in Interest Income The calculated average volatility in interest income

is 23.09

2. Volatility in Interchange Income - The calculated average volatility in

interchange income is 12.69

3. Volatility in Fee Income - The calculated average volatility in fee income is 11.23

Betarisk: This measure of risk analogous to the beta measure in financial markets

captures the correlation of a customers returns to that of the entire portfolio of customers. It

is a measure of the systematic risk of a single instrument or an entire portfolio. Systematic

risk implies the risk of holding the portfolio. In our context, one can think of the risk

accruing to the credit card firm as that of holding the entire portfolio of customers.

Systematic risk cannot be diversified by a firm. All the customers together make up the

market portfolio for a firm. The market portfolio is assigned a beta of 1.0. A beta greater

than 1 implies that the customer returns are moving up and down more intensely than that of

the portfolio. On the other hand, if the portfolios returns move up and down more intensely

than the customers returns then the customers beta will be less than 1. We calculate beta in

the following way:

)(

),(

mt

mtiti

RVar

RRCov= (EQ 2.2)


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Where, i is the Betarisk, itR is the return/revenue generated by customer i at time t and

mtR is the return/revenue generated by customer the entire portfolio of customers/market

at time t. Both itR and mtR are calculated using simple returns. Beta greater than 1

indicates that the customers returns fluctuate more than that of the portfolio while a beta

less than 1 indicates that the portfolios returns are fluctuating more than that of the

individual customers. A customer with a beta less than zero implies that he/she has a

risk-return ratio that is moving opposite to that of the portfolios risk-return ratio or trade-

off.

We identify Betarisk from each source of revenue as:

4. Betarisk from Interest Income The calculated average betarisk from interest

income is 0.90

5. Betarisk from Interchange Income - The calculated average betarisk from interest

income is 1.05

6. Betarisk from Fee Income - The calculated average betarisk from interest income

is 0.95

Our seventh and final measure of risk is,

7. Probability of default - This is the probability that a customer will default on payments.

We define default as nonpayment of minimum balance for 90 days. We use the Logit model

to calculate the probability of default of a given customer. The average probability of default

is 0.08. These models are primarily used to model the relationship between discrete

responses and a set of explanatory variables. In our case, the entire sample of customers were

divided into two groups using the above definition of a defaulter, where 1= defaulter and 0=

non-defaulter. Suppose Y is the binary response variable taking on the value 1 or 0, x is a


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vector of explanatory v

(Y=1|x)), then,

p

ppLogit)1

log)( =

=

= + 1 Direct Mail+ 2

+ 6 Age+ 7 Average B

+ 10 Platinum+ 11 Stand

+ 15 Preferred Professio

+ 19 Education+ 20 Mili

Where, is the intercept

We included the follo

Modes of Ac

Modes of Ret

Average Bala

month period

Age: Age of t

Average Freq

the 37 month

Types of Car

Credit Line:

the customer

riables, and p is the response probability be

x'+

Tele Sales+ 3 Internet+ 4 Affinity+ 5 Rewar

lance+ 8 Average Frequency+ 9 Quantum

ard+ 12 Retired+ 13 Homemaker+ 14 Self-Emp

als+ 16 Skilled Labor+ 17 Unskilled Labor+

ary+ 21 Unemployed+ 22 Creditline (E

parameter and is the vector of slope param

wing explanatory variables in our Logit model:

uisition: Direct Mail, Tele Sales, Internet, and

ntion: Affinity cards and Reward card holders.

nce: Average Balance carried by a custome

e customer

ency: Average number of transactions made

eriod

s Carried: Standard, Gold, Platinum, and Quant

aximum amount of credit that the credit card

22

ing modeled (p= Pr

d

loyed

18 Student

2. 3)

ters.

irect Selling

throughout the 37

y a customer within

um

company extends to


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23

Occupation Types: Professionals, Educators, Preferred Professionals,

Homemaker, Retired, Self Employed, Skilled Labor, Unskilled Labor, Student,

Military, Unemployed.

Output from our default model is given in table 2.1.2 of the appendix. A look at the

model fit statistics and R-square indicate that our model has good predictive power. Results

indicate that as credit limit increases, probability of default goes down, which is consistent

with industry belief that a credit limit is much more than a cutoff point for spending. It's a

reflection of how a particular credit card company gauges your credit worthiness and your

likeliness to charge away on their card. In general, the better your credit, the thicker your

credit lines tend to be (source: moneycentral.msn.com/content/Banking/creditcardsmarts).

However, as average balance on the card increases, the default probability goes up. By

industry standards, charging more than 30% of ones credit limit has an adverse effect on the

default probability. Risk is increasing in the amount of average balance carried by customers.

Our findings also indicate that people who are self-employed are more likely to default as

compared to professionals while students are considered as good risks. We find that

customers who are affinity card holders are nearly 30% less likely to default as compared to

non-affinity card holders and as average frequency in transactions decreases, the default

probability increases. Default probability also decreases with age which is a consistent

finding in the credit card literature (Greene, 1992; Gross and Souleles 2002; Stavins, 2000).

2.2 Data Envelopment Analysis and DEA model

DEA is a linear programming formulation that defines a nonparametric relationship

between multiple outputs and inputs. DEA is used extensively in operations research to


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24

measure the relative efficiency of decision-making units (Banker, Charnes, and Cooper

1984), for the evaluation of educational programs (Charnes, Cooper, and Rhodes 1978),

hospitals (Banker, Conrad, and Strauss 1986), retail sales units (Mahajan 1991), and a firms

managerial skills (Murthi, Srinivasan, Kalyanram 1996)

The simple DEA program is formulated as a fractional programming problem and is then

reduced to a linear programming problem that is easy to compute. Given that there are I

customers, each with certain inputs and outputs, the relative efficiency score of a test

customer k is obtained by solving the following model that was proposed by Charnes et al.

(1998):

Maximizekvfkvkvfckbfkbkbfckp

kfkkfc

VFvVINTvVFCvBFvBINTvBFCvPDv

FwINTwFCw

++++++

++

intint

int

Subject to 1intint

int ++++++

++

ivfivivfcibfibibfcip

ifiifc


FwINTwFCw

Ii ,....,1=

and, 0,,,,,,,,, intintint > vfvvfcbfbbfcpffc vvvvvvvwww (EQ 2.4)

Where,

Iis the number of customers that a firm has,

iFC is the income from finance charges from customer i,

iINTis the interchange income from customer i,

iFis the income from fees paid from customer i,


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25

iPD is the probability that customer i will default,

iBFC is the betarisk from interest income from customer i,

iBINTis the betarisk from interchange income from customer i,

iBFis the betarisk from fee income from customer i,

iVFCis the volatility in interest income from customer i,

iVINTis the volatility in interchange income from customer i,

iVFis the volatility in fee income from customer i,

vfvvfcbfbbfcpffc vvvvvvvwww ,,,,,,,,, intintint are the positive weights given to interest income,

interchange income, fee income, probability of default, betarisk from interest income,

betarisk from interchange income, betarisk from fee income, volatility in interest income,

volatility in interchange income and volatility in fee income, respectively. In EQ 2.4, = a

non-Archimedean element smaller than any positive real number (we take =.000001).

The positive weights are given by the solution to the programming problem. The subscript i

refers to a particular customer that is being evaluated. The element ensures consistency

with the desired prioritized optimization in the non-Archimedean specification and the actual

value of does not have any practical significance. The above program finds the weights

that maximize the ratio of the weighted outputs to the weighted inputs of a customer subject

to the condition that all such ratios of the customers are less than or equal to one. In that

sense, DEA measures the efficiency of a customer in relation to that of the set of customers

that use the same inputs to obtain the same outputs. DEA is able to segregate the efficient

customers from the inefficient customers based on whether or not they lie on the Pareto-

efficient frontier. The distance of a customer from the efficient frontier gives a measure of


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26

its relative inefficiency. Banker and Morey (1986) extend DEA to control for returns to scale

and the effect of environmental variables outside the managers control that might affect

efficiency (also see Banker and Thrall, 1992).

The fractional program given in EQ 2.4 can be represented by the linear programming

equation (EQ 2.5) below.

Maximizekfkkfc FwINTwFCw ++ int

Subject to 1intint =++++++ kvfkvkvfckbfkbkbfckp VFvVINTvVFCvBFvBINTvBFCvPDv

[ ] 0intintint

++++++

++

ivfivivfcibfibibfcip

ifiifc


FwINTwFCw

i

and, 0,,,,,,,,, intintint vfvvfcbfbbfcpffc vvvvvvvwww (EQ 2.5)

The above program is runI times to calculate the relative scores of all customers. In general,

a customer with a relative score of 1 is deemed efficient and with a score of less than 1is

deemed inefficient.

Thus, the efficiency score in the presence of multiple inputs and multiple outputs can

be represented by EQ 2.6:

inputsofsumweighted

outputsofsumweightedEfficiency = (EQ 2.6)

2.3 Input Oriented CRS DEA Models for determining RAR scores

In EQ 2.5, by maximizing the weighted average of the returns to that of the risk, we

are obtaining an index of risk adjusted revenue (RAR). We consider the input oriented

Constant Returns to Scale (CCR) model to calculate the RAR scores.


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27

An efficiency measure quantifies in one way or another distance to the efficient

frontier of the technology. We use the Radial distance. This measure (a.k.a. Debreu-Farrell-

measure, or radial part of the CCR/BCC measure) indicates the necessary improvements

when all relevant factors are improved by the same factor equiproportionally. Its oriented

versions have nice price interpretations (cost reduction/revenue increase).

The DEA program identifies for every inefficient customer, a set of corresponding

efficient customers as benchmarks for improvements. For the Input Oriented and Constant

Returns to Scale (CCR model) the benchmarks can be obtained from the dual problem in EQ

2.7 below.

,

* min=

Subject to:

0

0

0

0

0

0

00

0

0

0

FF

INTINT

FCFC

VFVF

VINTVINT

VFCVFC

BFBF

BINTBINT

BFCBFC

PDPD

k

k

k

k

k

k

k

k

k

k

(EQ 2.7)

Where, is the input reduction rate or * the efficiency score as represented by equation

2.6. The higher values of * imply higher efficiency,

is a nonnegative vector

EQ 2.7 is solved in two stages by first minimizing, then fixing = * .


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The output from the DEA model is presented in table 2.3 in the appendix. Apart from

identifying the most efficient group of people, DEA also provides three additional and

significant pieces of information- Benchmarks, Slacks and Weights. DEA estimates relative

RAR score, i.e. how well each customer does relative to the best customers. These scores

vary between 0 and 100% in case of the input-oriented CRS model. The average RAR score

for the customers in our sample is 62%. Best customers are those who do well on all

dimensions. These customers are used as benchmarks against whom the rest of the

customers are compared and their RAR scores calculated. The number of times a best

customer is used as a benchmark helps discriminate among the group that has been identified

as the best. In our model, the average number of times the efficient customer is used as a

benchmark is 129 times. If a customer is found to be the best performer on one particular

dimension, he/she will be identified as the best even though they may not do well on the

other dimensions. However, such customers will not be used as a benchmark to calculate the

RAR scores for the rest of the customers. The higher the frequency with which a particular

customer appears as a benchmark, the more likely it is an exemplar of good performance on

all dimensions. A branch whose efficiency rating is based fairly evenly on all its outputs and

inputs can be said to show well-rounded performance. A 100% efficient branch with well-

rounded performance is relatively efficient when all aspects of its performance are taken into

account rather than just a small subset of them, (Thanassoulis et al, 1987).

DEA assigns weights to the different input and output variables to calculate the scores.

These weights are derived directly from the data and are chosen so that a best set of weights

are assigned to each customer, i.e. the resulting input-to-output ratio for each customer is

maximized relative to all other customers when these weights are assigned to these inputs


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29

and outputs for every customer. A look at table 2.3 indicates that the input oriented model

assigned the maximum mean optimal weights to interest income, followed by interchange

income and fee income in the case of outputs and maximum mean optimal weights to

volatility in transactions followed by volatility in interest income and volatility in fees.

Slacks measure the shortage (*+S ) or excess (

*S ) in inputs and outputs that are needed

to achieve the optimal level. Slacks have managerial relevance since they provide managers

with the knowledge of how to make the lesser efficient customers more efficient or Pareto

efficient, as defined by the customers who fall on the efficiency frontier. The input-oriented

CCR model identified the highest excess mean for volatility in interchange income, followed

by volatility in interest income and BetaRisk in interest income. Although the DEA output

provides slack values for individual customers, due to space limitations, the mean slacks

values are presented for each of the input and output variable. For each customer, it provides

how much that variable needs to be increased (in case of shortage) or decreased (in case of

excess) in order for the customer to achieve the optimal RAR score.

2.4 Identifying the Best customers: Who are they?

Once we have the RAR scores for all the customers, we divide the customers into two

segments using median split. The top 50 % are classified into Segment 1 (the risk adjusted

profitable segment) and the remaining 50% are put in Segment 2 (the risk adjusted

unprofitable segment). We then use the Logit model to ascertain the discriminating variables

between these two segments. The output from the Logit model is presented in table 2.4. The

results indicate that modes of acquisition and retention strategies have significant impact on

Risk-adjusted Revenue. Customers with Reward cards and Affinity Cards are more likely to


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30

belong to the risk adjusted profitable segment. This result more than the others reveal the

importance of adjusting for risk in calculating the overall value of a customer. Based on

revenue accruing from interest income and fee income (that account for the majority of the

firms profits) alone, customers with affinity and reward cards appear to be less profitable for

the credit card company. However, once we adjust the revenue for risk, we find that while

affinity cardholders are 57% more likely to belong to the risk-adjusted profitable segment

than do non-affinity cardholders, reward cardholders are 82% more likely to belong to the

risk-adjusted profitable segment than do non-reward cardholders. A closer look at the mean

values for the risk measures of the affinity and the reward cardholder reveals the reason

behind this finding. While the affinity and reward cardholders may not be the biggest

generators of revenue for the credit card company, they tend to do better than non-affinity

and non-reward cardholders on the RAR scores because of the minimal level of risk that they

pose to the firm.

Our results also shed light on the profitability of the different modes of acquisition.

Customers who are acquired through Internet are more likely to belong to the risk adjusted

profitable segment, followed by those acquired through the direct mail, and through telesales

as compared to the customers acquired via direct selling. Some of the other results indicate

that as average balances and average frequency of purchases increase, the likelihood of

belonging to the risk adjusted profitable segment increases. A look at the types of occupation

reveals that students are more likely to belong to the risk adjusted profitable segment .We use

the professional segment as the base for assessing the difference between the different types

of occupation based on the RAR scores. Among the different types of cards, the standard and

gold cards appear to do better than quantum cards.


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31

CHAPTER 3

RISK-ADJUSTED LIFETIME VALUE: A NEW APPROACH TO VALUING

CUSTOMERS

3.1 Introduction

Essay 1 presented in chapter 2 was an exploratory attempt to identify the different

sources of risk that a customer represents and incorporate it in a model of revenue to come up

with an index of Risk-adjusted revenue (RAR). Essay 2 is an extension of essay 1 in the

following ways. The DEA approach used is a deterministic model that does not account for

stochastic errors and quite susceptible to outliers and random noise. To ensure our results are

robust, we use a competing efficiency frontier approach in the second essay called the

stochastic frontier approach (SFA). SFA is an econometric technique that allows for

stochastic errors. It is a parametric approach that estimates a profit function assuming that the

error term has two independent components (Aigner et al, 1977; and Meeusen and Van

Broeck, 1977). While one component captures technical inefficiency, the other captures

statistical noise such as random effects of measurement errors or external shocks. Technical

efficiency refers to the ability of each customer to obtain the maximum output from a given

set of inputs. Technical inefficiency is zero for the value-maximizing customer, i.e. the

customers who lie on the efficient frontier, but is strictly positive for customers who lie

below this frontier.

In essay 1, the output variables used in the DEA model were the three revenue

measures. However, in essay 2 we calculate the costs of servicing customers and estimate


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32

customer lifetime values (CLV) for each customer. The output variable in our SFA model is

the customer lifetime values while the input variables are the seven measures of risk that we

proposed in chapter 2. Estimation of the efficient frontier generates individual level

efficiency scores that we refer to as Risk-adjusted lifetime value or RALTV. Hence, we

define RALTV in terms of the maximum CLV that a customer represents to a firm for given

levels of risk. The RALTV scores are then used to see whether our results from the previous

approach carry over.

Since we are also interested in finding out which approach (traditional CLV or

RALTV measures) does better in terms of estimating the true value of a customer, we divide

our dataset spanning 36 months into two parts. The first 24 months data are used to estimate

the revenue, risk, CLV and RALTV measures and the remaining 12 months data is used for

validation purposes. We find that the traditional CLV measure tends to overestimate the

overall value of a customer that translates into large amounts of losses for the credit card

firm.

3.2 Modeling Approach and Results

3.2.1 Revenue

We calculate the revenue accruing from each customer as the sum of cash inflows from

interest income, interchange income and fee income. The average revenue of the firm during

the first 24 month period is $ 1028.75.

3.2.2 Risk

The seven risk measures remain the same as the ones we identified in chapter 2.

However, here the risk measures have been calculated using 24 months data.


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1. Volatility in Interest Income The calculated average volatility in interest income

is 18.90

2. Volatility in Interchange Income - The calculated average volatility in

interchange income is 11.85

3. Volatility in Fee Income - The calculated average volatility in fee income is 10.20

4. Betarisk from Interest Income The calculated average betarisk from interest

income is 0.94

5. Betarisk from Interchange Income - The calculated average betarisk from interest

income is 1.06

6. Betarisk from Fee Income - The calculated average betarisk from interest income

is 0.81

7. Probability of default - The average probability of default is 0.08 which is the

same as in chapter 2. The output from the above model is presented in table 3.2.2

of the appendix. We find that among the different modes of acquisition, customers

acquired through direct mail have lower probabilities of default as compared to

those acquired through directselling. Our findings also indicate that affinity

cardholders are less likely to default as compared to non-affinity cardholders.

While self-employed customers are more likely to default, students are less likely

to default as compared to professionals. From the transactional data we find that

as the average balance on accounts increases, chances of default also increases.

However, increases in frequency of purchases and credit line are associated with

lower default. Also, the probability of default goes down with customer age.


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Credit card companies often borrow money from their lending banks in order to extend credit

to their customers. The lending bank charges an interest rate that varies. The credit card

company incurs this interest on any unpaid or outstanding balances carried by their

customers. Using federal rates data for the period of analysis, we are able to impute the cost

of borrowing for the credit card company for each time period. The average cost of

borrowing for the 24 months period is around $197.

Using EQ 4, we calculate CLV values for all the customers in our sample. The

average revenue generated by the customers is around $1029. The average CLV is

approximately $559.

3.2.4 Model for calculatingP (alive)

In EQ 4, the termp (active)is calculated using the Pareto/NBD model proposed by

Schmittlein, Morrison and Colombo (1987) and subsequently Schmittlein and Peterson

(1994). We need to account for a customers probability of being active since under non-

contractual settings especially, customers do not notify the firm explicitly about their

intention to terminate the relationship. This behavior is called silent attrition or churn.

Unaware of this decision, the firm continues to spend large amounts of money on these

customers. Using past purchases as a predictor of future purchases erroneously assumes that

the customer is still active.

Schmittlein, Morrison and Colombo (1987) extended the basic NBD model to

estimate the probability that a customer is active at a given time and predict the future

number of transactions. Their model (Pareto/NBD) accounted for the drop-out rate (). In

deriving their model, they make the following assumptions:


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37

While alive, a customer makes transactions according to a Poisson process with

rate

Each customer remains alive for an exponentially distributed duration with death

rate

Purchase rate is distributed gamma over the customers with parameters r and

Death rate is distributed gamma over the customers with parameters s and

The purchase rate and the death rate are distributed independently of each

other

The key contributions of this model are the equations for calculating the probability

of being active and the expected future number of transactions. This model uses three pieces

of information from a customers past purchase history - total number of transactions (x), the

time period when the last transaction was made (t) and total number of periods of data

available for a particular customer (T) to calculate the probability that a customer is active

in a given time period, P (alive | r, s, , , X=x, t, T). Here r, s, , are the parameters that

are estimated using Method of Moments (MOM).

Schmittlein and Peterson give the desired probability for < as

P (alive | r, s, < , X=x, t, T) =

where a2= r + x + s; b2= r + x; c2= r + x + s + 1; z2(y) = ( - ) / ( + y) and F (a, b; c; z) is a

gauss hyper geometric function (Abramowitz and Stegun, 1972). It can be computed either

using numerical integration or algorithms in Luke (1977).

( )( )

++

+

+

+

+

++

++

+

))(;;,(

;;,

1

2222

2222

TzcbaFT

T

tzcbaFt

T

t

T

sxr

s

xr

sxr


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38

Recently, NBD type models have become quite popular and have assumed a great

deal of importance due to their proficiency in answering some significant managerial

questions. Reinartz and Kumar (2000) and Reinartz and Kumar (2003) use the Pareto/NBD

model to answer some managerially relevant questions regarding relationship marketing and

calculate the probability of being active as an input to calculate profitability and customer

lifetime values. Reinartz and Kumar (2003) used data from a U.S. general merchandise

catalog retailer to replicate the estimation of the Pareto/NBD model used by Reinartz and

Kumar (2000) to acquire the parameter estimates that were used subsequently to calculate

customer lifetime durations.

The current work uses the Pareto/NBD model to estimate each customers probability

of being active at time t, which is a key component of our model of customer lifetime value.

3.2.5 SFA model and results

The first stochastic frontier production model was independently proposed by Aigner,

Lovell and Schmidt; and Meeusen and van den Broeck in 1977. It has traditionally been used

to model production functions and estimate the technical efficiency of firms. Excellent

reviews of the applications can be found in papers by Forsund, Lovell, and Schmidt (1980),

Schmidt (1986), Bauer (1990), and Greene (1993). SFA models have been estimated using

both cross-sectional and panel data. In the current research we use cross-sectional data to

estimate our SFA model of risk-adjusted lifetime value.

The standard stochastic frontier model is specified as:

iii xfy += ),(


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39

Where, iy is the observed output, ix is a vector of inputs and is a vector of unknown

parameters. The composed error term i is specified as

iii uv = , 0iu

The first error component is independently and identically distributes as ),0(~2ui Nv and

captures the effects of statistical noise such as random effects of measurement error and

external shocks. The second error component captures technical inefficiency which can be

measured as the deficiency in output away from the maximal possible output that is

represented by the stochastic efficiency frontier. The non-negativity constraint 0iu ensures

that all observed outputs either lies on the efficient frontier or below it but never above it.

The error component iu can be assumed to have different distributions- exponential

(Meeusen and van den Broeck 1977); half-normal Battese and Corra 1977); truncated normal

(Stevenson 1980); and two parameter gamma (Greene 1990).

We use the Cobb-Douglas functional form to estimate our SFA model. The Cobb-

Douglas frontier for our model of RALTV can be written as:

),()_ln(

)_ln()_ln()int_ln(

ar_ln()_ln()_ln()ln(

7

654

3210

ii

i

uvfeesvolatility

feesvolatilityfeesvolatilitycomeerchangeinbetarisk

financechbetariskfeesbetariskdefaultyprobabilitCLV

++

+++

+++=

(EQ 3.2)

where, the output variable is the individual level CLV that we calculated using EQ 3.1 and

the input variables are the seven risk measures. The error terms iv and iu are assumed to be

distributed normal and half-normal, respectively. Technical efficiency is calculated by

following the methodology presented in Battese and Coelli (1992),


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)exp( ii uTE = (EQ 3.3)

Estimation of the efficient frontier generates individual level efficiency scores that we

refer to as Risk-adjusted lifetime value or RALTV. By construction, the efficiency scores lie

between the values 0 and 1, with the customers that lie on the efficient frontier having a score

of 1 and those that lie below the frontier having scores greater than or equal to 0 but less than

1.Hence, we define RALTV in terms of the maximum CLV that a customer represents to a

firm for given levels of risk. The average RALTV score of the customers in our dataset is

0.62.

We use a computer program frontier 4.1 to estimate our SFA model. It provides

maximum likelihood estimates of the parameters of the Cobb-Douglas stochastic function.

Asymptotic estimates of standard errors are calculated along with individual and mean

RALTV estimates.

The output from the SFA model is given in table 3.2.4 of the appendix. Our results

indicate that all the risk variables except betarisk in fees and probability of default are

significant. Our log likelihood is -3054.43. The log-likelihood from the Ordinary Least

Squares (OLS) model was -0.3499.

3.2.6 RALTV model and results

Our output from the SFA model is risk-return trade-off metric that we term risk-

adjusted lifetime value or RALTV. Using the RALTV scores we divide the customers into

two groups on the basis of the median value of the scores the high and the low segments.

We use a logit model to assess the impact of the credit card firms acquisition and retention

strategies as also the demographic characteristics and transactional patterns on the risk-

adjusted customer lifetime values. The explanatory variables used in our logit model of


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RALTV are dummy variables to capture reward cardholders, affinity cardholders, the

different modes of acquisition, the different types of credit cards; demographic characteristics

such as customer age, occupation type; credit limit/line extended to the customer; and

transactional patterns captured by variables such as average balance carried on the account.

The results from our RALTV model is given in table 3.2.7 of the appendix. Our main

findings are that reward cardholders and affinity cardholders tend to have higher RALTV

than non-reward cardholders and non-affinity cardholders, respectively. Among the different

modes of acquisition, customers acquired through the Internet, followed by directmail have

higher RALTV as compared to customers acquired through directselling, while telesales

customers perform the worst. Occupation and card types do not have any impact on the

RALTV scores. Also, RALTV scores increase with increases in a customers average

balance and frequency of purchases while customer RALTV decreases with increases in the

credit limit extended to customers.

3.3 Comparing RALTV and traditional CLV measures

Traditional CLV models tend to value customers based solely on the cash flows that

they generate for a firm. However, in financial services industry like credit card companies,

the correlation between risk and return is very high. In such cases, traditional CLV models

can lead to overestimation of the overall value of the customer (Gupta et al 2006). After

adjusting for the different types of risk a customer potentially poses

three essays on risk-adjusted customer lifetime value and returns to search

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