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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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THREE ESSAYS ON RISK-ADJUSTED CUSTOMER LIFETIME VALUE AND
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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v
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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vi
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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vii
THREE ESSAYS ON RISK-ADJUSTED CUSTOMER LIFETIME VALUE AND
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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viii
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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xii
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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xiv
Table 5.5.Results from DEA VRS/Input-Oriented Model..89
Table 5.7.Results from the Tobit model...90
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1
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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2
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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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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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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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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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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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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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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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
VFvVINTvVFCvBFvBINTvBFCvPDv
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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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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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
VFvVINTvVFCvBFvBINTvBFCvPDv
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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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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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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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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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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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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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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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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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