Credit cards and mathematics

Summary: Credit card issuers use mathematical models to determine credit lines and interest rates, as well as to detect fraud and analyze offers.

Credit card issuers use statistical analysis in a wide variety of ways. Statistical models of risk help the banks decide whom to approve for card membership and what interest rate to charge. Models also help issuers manage the risks of their existing customers and detect fraudulent transactions. Credit card issuers use designed experiments to help decide which offers have the largest potential to be profitable. Typically, the bank tries out the new offer on a sample of people (while leaving others in a control group) before deciding whether the new offer will be successful if given to the entire customer base. Data mining techniques help banks look at customers’ past transactions in order to model future uses of the card and to help decide which customers are most likely to want which other products and services that the bank offers.

History

The first credit card was born when businessman Frank McNamara realized that he had forgotten his wallet at a New York City restaurant. After his wife rescued him by bringing cash to the restaurant, he vowed he would never face that embarrassment again. The Diners Club card was born a few months later in 1950 and became the first widespread alternative to cash. The first businesses honoring Diners Club purchases were charged 7% of each transaction (typical costs are now 2% to 5%), and subscribers were charged $3 per year.

Bank of America pioneered its BankAmericard program in Fresno, California, in 1958, and American Express issued the first plastic card in 1959. Carte Blanche was another early card. The idea of a credit “card” really gained momentum when a group of banks formed a joint venture to create a centralized system of payment. National BankAmericard, Inc. (NBI) took ownership of the credit card network in 1970 and for simplicity and marketability changed its name to Visa in 1976. (One reason for the name “Visa” is that it is pronounced nearly the same way in every language.) That year, Visa processed 679,000 transactions—a volume that is processed on average every four minutes today. The Visa system is currently able to handle a load of about 6800 transactions per second, a capacity nearly exceeded on December 23, 2005, during the height of the Christmas shopping season. Visa is the largest merchant network, although MasterCard, American Express, and others process many transactions as well.

The Fair Isaacs Company (FICO) has grown in parallel with the credit card industry. It was founded in 1956 by mathematician Earl Isaac and engineer Bill Fair with the idea that data, used intelligently, can be used to make better business decisions. The next year, Conrad Hilton hired FICO to design and implement a complete billing system for his Carte Blanche card. FICO next developed the methodology to “score” the credit rating of customers but was unable to sell the idea to credit card banks until the 1970s. By the early 1990s, nearly every credit card bank was using some form of credit card scoring to help decide which customers to approve for credit and at what price. In 1995, both Fannie Mae and Freddie Mac, the two largest mortgage brokers in the United States, recommended using FICO scores for use in evaluating U.S. home mortgages. Today, U.S. citizens can access their various credit scores through online credit bureaus and, in fact, the U.S. government developed a policy allowing consumers to find out their scores once a year for free.

Credit Scoring

Credit bureaus use statistical analysis on past transactions, as well as income and other demographic information, to generate a credit score, usually referred to as a FICO score. This number is on an arbitrary scale that generally runs from 350 to 850 (with slight variations). The three main credit bureaus are Experian, TransUnion, and Equifax. Credit scores on the same individual may differ among the credit bureaus because of slight variations in the statistical model used to generate the number and slightly different data reported to the various bureaus. In all cases, the credit score is a prediction of how likely a borrower is to pay back the loan. For credit card companies, the score is used to decide both whether to issue the card, and what price (annual percentage rate) to charge on a balance that’s carried over from month to month.

Data Mining

Credit card transactions, while vital to the running of the credit card bank, also contain information on the cardholder’s spending patterns. These databases are very large, containing the records of tens of millions of customers, and dozens to hundreds of transactions per record. Using statistical models (often logistic regression models), banks can use these vast data repositories to identify the customers who are predicted to have the highest probability of enrolling for a new product or service. These offers may be made via a number of different channels. The offer may be given while the cardholder is calling a call center (800 number) with an issue concerning his or her card (in which case, the statistical algorithm will notify the operator that this customer should get the specific offer), by e-mail, by an outbound telemarketing call, by a targeted ad that pops up while the customer is visiting the issuer’s Web site, or as direct marketing (so-called junk mail).

Experimental Design

To evaluate whether a new type of offer (the so-called “challenger”) will be more effective (as measured by higher enrollment, revenue, profit, or other criteria) than the current offer (the “champion”), banks often use statistically designed experiments. The simplest such experiment is randomized at two levels, also known as a champion/challenger design. In this design, a sample is selected at random from the entire customer database. A proportion of those are chosen as the control group. They receive the current offer (the champion), and the rest are chosen to receive the challenger. The data are then collected, and the differences in response between the two groups are evaluated. The design can be complicated by blocking (stratification) on card type, region, income, or other demographic variables. Designs can be complicated by adding more factors, more levels, and by asymmetries introduced by infeasible treatment combinations. In the credit card industry, analysis is also complicated by the fact that one cardholder may be getting more than one experimental treatment (offer) simultaneously from different groups within the same organization and from different organizations. Capital One Bank claims to run upward of 40,000 such experiments a year on its cardholders.

Bibliography

Box, G. E. P., J. S. Hunter, and W. Hunter. Statistics for Experimenters. 2nd ed. Hoboken, NJ: Wiley Interscience, 2005.

McNamee, Mike. “Credit Card Revolutionary.” Stanford Business 69, no. 3 (2001).

Paterson, Ken. “Credit Card Issuer Fraud Management.” Mercator Advisory Group, 2008. http://www.sas.com/new/analyts/mercator‗fraud‗1208.pdf