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Managing Credit Lines and Prices for Bank One Credit Cards
. Trench • . One Card Services, Inc., 3 , Wilmington, Delaware 19801 Bank One Card Services, Inc., 2500 Westfield Drive, Elgin, Illinois 60123
. Lau • Lizhi Ma •
Bank One Card Services, Inc., 3 , Wilmington, Delaware 19801

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School of Business, University of Connecticut, Storrs, Connecticut 06269 • • • •
We developed a method for managing the characteristics of a bank’s card holder portfolio in an optimal manner. The annual percentage rate (APR) and credit line of an account influence card use and bank profitability. Consumers find low APRs and high credit lines attractive. However, low APRs may reduce bank profitability, while indiscriminate increases in credit- lines increase the bank’s exposure to credit loss. We designed the PORTICO (portfolio control and optimization) system using Markov decision processes (MDP) to select price points and credit lines for each card holder that maximize net present value (NPV) for the portfolio. PORTICO uses account-level historical information on purchases, payments, profitability, and delinquency risk to determine pricing and credit-line changes. In competitive benchmark tests over more than a year, the PORTICO model outperforms the bank’s current method and may increase annual profits by over $75 million.
(Financial institutions: banks. Dynamic programming/optimal control: Markov, finite state.)
A retentive memory may be a good thing, but the ability to forget is the true token of greatness.
(19th century philosopher, not necessarily speaking about MDPs)
Suppose you are considering a large purchase. You carry three credit cards with different pric- ing, spending limits, and terms. Which card will you use? Will the credit line or the annual percentage rate (APR) on the cards influence your decision? In industry parlance, which card will be at the “top of your wallet?” Intense competition in the banking and credit-card industry makes the answers to such ques- tions extremely important. Credit issuers apply statis- tics and operations research to answer these questions. We applied modeling and optimization methods to the
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problem of awarding credit lines and changing APRs to customers.
Trends in the Credit-Card Industry
Credit cards have come a long way from their origin as charge cards, a convenient way of making pay- ments (without the option of drawing on a revolving line of credit). The first credit-card banks arose in the early 1980s. There are now more than 7,000 US credit- card issuers and 27,000 types of credit cards (Hanft 2000). Today, consumers can use their lines of credit for various payment and personal-financing needs. On the merchant side, it is hard to find businesses that do not accept credit cards; even grocery stores and the Internal Revenue Service (IRS) accept credit
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4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0
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7.0% 6.5% 6.0% 5.5% 5.0% 4.5% 4.0% 3.5% 3.0%
TRENCH, PEDERSON, LAU, MA, WANG, AND NAIR
Bank One Credit Cards
Figure 1: (a) Direct mail solicitations have shown a steady increase over the years. (b) Delinquencies and charge- offs have also increased recently (source: http://www.cardweb.com/cardtrak/news/2002/april/29a.html).
cards. Along the way, the industry has introduced many innovations, including chip-embedded smart cards, convenience checks, magnetic stripes for paper- less transactions, fraud-detection systems, real-time purchase-transaction processing, and rewards prod- ucts that grant cash or points for spending towards a variety of purchases, such as airline travel, telephone calls, and hotel stays.
With the mass marketing of credit, the average per- son in the US has 4.2 credit cards (Federal Reserve 2001). This level of market penetration has caused intense competition among issuers for new accounts. In 2000, firms sent out 3.54 billion direct mail solici- tations (McKinley 2001) for credit cards (Figure 1). In 2001, they are estimated to have sent 4 billion. In spite of the massive amount of targeted marketing, fewer than one in 100 credit-card prospects who are good risks from a lending perspective actually respond to these offers. Pricing is highly competitive in today’s environment, with zero-percent financing for periods of six months or longer common. Low-rate financing through other credit vehicles, such as home equity lines of credit, is also readily available.
At the same time, the worsening economy has adversely affected the profitability of many issuers, especially those who market to high-risk customers. Several major issuers have left the subprime market because of the high cost of customer defaults and bankruptcies. Two key measures of credit risk that
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drive bank profitability are the proportion of total dollars delinquent to total debt (delinquency rate) and the proportion of total dollars that have been placed in default to total debt (charge-off rate). In March 2002, customer-delinquency rates were 5.54 percent, and default or charge-off rates stood at 6.59 percent. These rates are near the record high levels (Figure 1) experienced in the 1990–1991 recession (http://www. cardweb.com/cardtrak/news/2002/april/29a.html).
In recent years, banks have continued to issue new credit cards and to increase the credit lines of exist- ing customers, and they have lowered their pricing (APRs) to remain competitive. Growth in available credit has more than kept pace with the rise in debt; consequently the open-to-buy (the difference between the credit line and debt) has been increasing (Con- sumer Federation of America 2001). During the same period, the average APR issuers charge on revolv- ing debt has declined (Figure 2). Issuers have also increased the number of offers with variable APRs relative to fixed APRs (Federal Reserve 2001).
Factors Influencing Profitability—
Product Dynamics
Credit card profitability is driven by customers’ spending and payment behavior and by the mechan- ics of the industry itself. When a customer makes a purchase, the issuer and the bank association (Visa or
Direct Mail Solicitations in Billions
Jan-01 Mar-01
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3,500 3,000 2,500 2,000 1,500 1,000
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Total Debt
20 19 18 17 16 15 14
1971 1976 1981 1986 1991 1996 2001
TRENCH, PEDERSON, LAU, MA, WANG, AND NAIR
Bank One Credit Cards
1993 1994 1995 1996 1997 1998 1999 2000
Figure 2: (a) Credit lines relative to the level of debt have increased over the years. The difference between the two curves, or the “open-to-buy,” has also steadily increased (source: Consumer Federation of America 2001). (b) The average APR on cards has been reducing steadily in recent years (source: Federal Reserve 2001).
MasterCard) charge the merchant a fee. For any debt left unpaid by the due date, customers pay interest. The unpaid balance is referred to as the revolving bal- ance, and the amount of interest paid is determined by the card’s APR. The customer is expected to make a minimum payment on the revolving balance each month, and if this payment is missed or arrives late, the issuer assesses a late fee.
The largest component of credit-card revenue is the interest paid on card members’ revolving balances. Most banks establish an APR for a credit-card account when the customer responds to an offer. For example, a customer may respond to an offer with a zero per- cent APR for six months and 12.9 percent APR effec- tive at the end of the discount period. However, if a customer becomes chronically delinquent, banks will often increase his or her APR.
Merchant fees (interchange) are usually the second most important source of revenue for a credit-card issuer. These fees are about 30 cents per transaction plus about 2.50 percent of the amount of the trans- action and are split between the issuer and a bank association (about 10 cents per transaction or sale and about 1.50 percent of the amount of transaction goes to the association). American Express charges a higher percentage, and retains all of the fees, because it is not part of a bank association.
Other main sources of profits are convenience checks, user fees, and membership fees. Banks market convenience checks to build card holders’ balances
and allow them to make purchases or transfer balances from other cards at interest rates lower than their base APRs. Banks assess fees for certain customer behaviors, such as making late payments or request- ing over-limit authorizations. Recently, late fees have become an important source of revenue. Since 1996, late fees have more than doubled from an aver- age of $13.28 to $29.84 (http://www.cardweb.com/ cardtrak/news/2002/may/17a.html), even as the grace period and other terms for levying fees are becoming more stringent. Finally, some card holders pay annual fees to receive such privileges as earning airline miles or credits towards future automobile or gasoline purchases.
Factors Influencing Profitability—
Customer Dynamics
Unless a bank charges a yearly fee for a credit card, it will earn no money until the customer uses the card to make purchases or payments, or to withdraw cash. A large part of issuers’ portfolios consists of inactive accounts. For example, a customer may open an account just to get the 10 percent discount on the first purchase. Or a customer may surf (transfer) a bal- ance into an issuer’s portfolio to take advantage of a six-month introductory APR rate on balance transfers, surf out at the end of the introductory period, and become inactive thereafter. Card issuers try to moti- vate customers to carry revolving balances (that is,
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Credit Lines and Debt in $Billion
Average Annual Percentage Rate

to only partially pay off new purchases and previ- ous balances). They do this by encouraging the cus- tomers to spend more and to carry balances on the bank’s card rather than a competitor’s, or by encour- aging them to transfer balances to the bank from competitors’ cards.
Customer attrition is a continual challenge for banks because of the intense competition for accounts. Competitors frequently tempt good customers away from their existing issuers by offering low APRs and other enticements. In addition to their direct efforts to retain customers (for example, making counteroffers), banks try to acquire new customers to replace those lost through attrition. To remain competitive, banks strive to ensure customer loyalty through pricing, proactive increases in credit lines, and such features as rewards incentives. However, overly aggressive pricing strategies can erode profit margins to unac- ceptable levels, and offers to induce loyalty, such as cash-back rewards, can be expensive to fulfill.
Finally, delinquencies and charge-offs can literally break the bank. The higher the credit line, the higher the balance a customer can accumulate before ceas- ing to make payments. When the bank finally charges off an account, it declares the customer’s entire bal- ance a loss, except for a fraction that debt collectors can recover. The bank needs the net income of many good accounts to offset the losses caused by a sin- gle default. One way banks can stimulate growth in balances and interest income is by increasing credit lines. Banks limit such policies because the increases in open-to-buy can increase losses.
Determining methods to improve profitability and manage credit loss requires sophisticated analysis and modeling. Bank One has teams constantly working on these issues to improve the products and services it offers to customers.
Bank One Card Services, Inc.
Bank One Card Services, Inc., a division of Bank One Corporation, is the third largest issuer of credit cards and the largest issuer of Visa cards in the United States. The company offers credit cards for consumers and businesses under its own name and on behalf of several thousand marketing partners. These partners
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include some of the leading corporations, universities, sports franchises, affinity organizations, and financial institutions in the United States. The company has 55 million card members and $64 billion in receiv- ables (www.bankone.com). Bank One earnings as a whole are significantly affected by the performance of Bank One Card Services, Inc.
In the Bank One Card Services organization, the decision technologies group plays an important role in developing ways to achieve management objec- tives. The dynamics of managing credit cards cause a tension between risk and revenue growth. For exam- ple, whereas the firm evaluates the marketing depart- ment on the number of new customers acquired and the cost of acquisition, it evaluates the risk depart- ment on how well it controls credit losses from such acquisitions programs. The optimization applications the bank implements must balance these objectives. Because it is at the center of the organization, the deci- sion technologies group can focus on solutions that are optimal for the company as a whole.
The decision technologies group includes experts in statistics, operations research, and information sys- tems. The group has developed and implemented sev- eral optimization models for acquiring new accounts, managing existing portfolios, and formulating test designs. Optimization staff members work with statis- ticians to collect data through experimental designs and to develop models that will provide input to the optimization models. They also work with infor- mation technology staff members to implement the models they develop.
The objective of every project the decision technolo- gies group works on is to apply its models to the portfolio after properly testing them. The group con- ducts rigorous benchmark tests to ensure that pro- posed approaches are indeed better than the existing methods and other available alternatives. It routinely evaluates and compares vendor offerings to make the best choices from available solutions. The group’s pri- mary mission is to focus on analytic solutions; often, it makes discoveries and develops new and useful techniques for the bank.
The credit-card business is rich in data, and the bank is driven by data in developing its tactics and strategies. With over 1.5 billion purchase transactions
TRENCH, PEDERSON, LAU, MA, WANG, AND NAIR
Bank One Credit Cards

annually, it houses many terabytes of data that cap- ture customer-payment and card-use history. It uses statistical testing extensively to develop and enhance products and techniques. In any given month, the bank creates, launches, and monitors hundreds of tests. This environment and the infrastructure the bank has created provide fertile ground for develop- ing, testing, and validating optimization models.
Genesis of PORTICO
The decision technologies group began the PORTICO (portfolio control and optimization) project in July 1999 when the bank asked it to evaluate approaches to improve the profitability of the bank’s portfolio. Our goal was to stimulate sales and balance accumulation on Bank One card products.
There are two basic ways the bank can improve cus- tomer profitability: Take unilateral action to promote the desired behavior, or take measures that require customers to make some initial response before they adopt the desired behavior. In the first category are such actions as changes in credit lines and pricing. The second category consists of such measures as mailing convenience checks or balance-transfer checks and offering additional products; customers must respond to these offers before the bank earns finan- cial benefits. Because of this distinction, it may be difficult to determine whether a unilateral action has produced the desired behavior. There is anecdotal evi- dence that increases in credit lines spur increased card use, but there is much countervailing evidence that many account holders ignore credit line increases. The effect of pricing changes is usually considered stronger, but because most price changes are increases to the APR, called repricing, the effect tends to be attri- tion or reduced card use.
When we were formulating approaches to increase customer profitability, the bank mailed notices of changes (usually increases) in credit lines along with convenience checks. Therefore, we considered systems that would help managers to make deci- sions about credit line changes, APR changes, and convenience-check offerings together. We developed a prototype optimization model for simultaneous actions to change credit lines and prices and to
mail convenience checks. We subsequently discov- ered that we needed two models, one for recurring convenience-check mailings, intended for short-term customer response, and one for the credit line and price models, intended to produce changes in cus- tomer behavior over time. We later used campaign optimization, based on projections of the likelihood of customers responding to offers, to handle checks and other response-sensitive offers. We initially focused on pricing and credit lines, which simplified the let- ter the bank would send to customers, because check offers must include explanations of terms and condi- tions. We wanted to send a letter to customers that clearly and positively explained that we were improv- ing the pricing or credit line of their current credit card.
Our strategy was to identify the actions the bank could take on pricing and credit lines to stimulate customer use of its card products. We further wanted to improve our communication of these actions to customers. For customers who received an increase in credit line, a reduced APR, or both, we would reinforce those benefits with a letter describing the changes and emphasizing the customer’s value to the bank. We also decided to focus on actions that would engender customer loyalty, card use, and ultimately, revenue growth. For this reason, we did not consider actions that would raise APRs or reduce credit lines.
Prior Research
Some literature covers methods for granting credit initially, but much less concerns the subsequent management of credit lines and pricing. Bierman and Hausman (1970) developed statistical models using a Bayesian approach and a Markov decision model for making decisions to grant credit. Dirickx and Wakeman (1976) and Waldman (1998), among oth- ers, extended this work. Rosenberg and Gleit (1994) surveyed credit-management methods. Little research has been published that relates to adjusting the base price of card products.
Of more immediate relevance to our work is the decision to periodically change credit lines and pric- ing. Evidence exists that banks use increases in credit line for existing card holders as a tactical marketing
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TRENCH, PEDERSON, LAU, MA, WANG, AND NAIR
Bank One Credit Cards

tool and routinely make such actions to encourage card use (Lunt 1992, Punch 1992). Soman and Cheema (2002) found that increasing credit lines is associated with increased spending among certain consumers. They hypothesized that these customers see the in- creased credit lines as a signal of their future earning potential, encouraging them to increase spending now. This line of reasoning supposes that these customers are under the impression that banks use sophisticated models to determine credit-line increases that incorpo- rate forecasts of customers’ future earnings potentials. Soman and Cheema (2002) tested this hypothesis in an experimental se

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