Applicability of generic linear scoring mosels in the U.S. credit-union environment

Although credit-scoring models represent a widely used managerialaid for large financial intermediaries, the vast majority ofU.S. credit unions—relatively small cooperatively ownedretail intermediaries, constrained by sample and funding limitations—haveyet to adopt such techniques. Lovie & Lovie (1986) havetheorized that the flat-maximum effect or curve of insensitivityassociated with linear scoring models could be advantageousin areas of applied prediction such as credit scoring. In thiscontext, we reported the relative predictive power of genericcredit-scoring models versus customized models in an earlierpaper (Overstreet et al. 1992). Unfortunately, these findingswere not readily adaptable to the credit-union industry dueto a dated sample with incomplete credit-bureau information.Consequently, from 1988 to 1991, we gathered a refined databasefrom which to further develop and field-test generic scoringmodels in the credit-union environment. The results reportedherein not only confirm, but amplify, the relative predictivepower of such models found earlier. Relative costs and benefitsof generic versus customized models are modelled for a representativecredit union. Future research directions are set forth in theconclusions.     

Analysis of the effectiveness of manufacturer-sponsored retailer gift cards in supply chains

Some manufacturers sponsor “free” retailer gift cards to be given to consumers who purchase their products. These gift cards are paid for by the manufacturer and are redeemable on all products at the retailer. We develop a model of such a supply chain. We analyze cases in which the gift cards’ redemption rate is constant or increasing in gift card value. The results indicate that in addition to the redemption rate and consumers’ valuation for gift card dollars, the profitability of manufacturer-sponsored gift cards depends on the average gross margin of the retailer and the type of purchases consumers make with gift cards. Furthermore, we show that under certain conditions, free gift cards will increase the expected profits of the retailer and manufacturer as well as decrease the retail price of the product. These conditions include a retailer with large average gross margin and consumers using gift cards to purchase products they would not buy with cash otherwise. Furthermore, all consumers, including those who do not redeem the gift card, are more likely to benefit from a reduced retail price when their probability of redeeming the gift card after purchase is equal to their estimated redemption probability at purchase time. We show the conditions under which gift cards are more profitable than cash mail-in rebates. We develop an incentive scheme to improve the performance of supply chains with gift cards.     

Credit card pricing and impact of adverse selection

Variable pricing is one way of improving the profitability of credit cards when the price is the interest rate to be charged. However, choosing the appropriate price for each risk grade of default is not straightforward, as one of the main problems is adverse selection, when the lender finds that the borrowers who actually take a specific offer have a higher default rate than expected. We show that modelling the choice of credit card by the borrower as an auction process means that the winner's curse can lead to adverse selection. By modelling the way lenders use the credit score of a borrower in their pricing decision we are able to show that there is a simple relationship between the actual probability of a borrower repaying and what the successful lender believes this probability to be, regardless of the distribution of the errors caused by adverse selection. This allows one to assess the impact on profitability of these errors.     

On the economic order quantity under conditions of permissible delay in payments

In this note, I amend Goyal's model by considering the difference between unit price and unit cost. I then establish an easy analytical closed-form solution to the problem. The theoretical results obtained here reveal the following two managerial phenomena. (1) In certain cases, the economic replenishment interval and order quantity decreases under the permissible delay in payments, which contradicts to Goyal's conclusion. It makes economic sense for some customers to order less quantity (or shorten the replenishment time interval) and to take the benefits of the permissible delay more frequently. (2) If a supplier wants to reduce his/her large level of inventory, then he/she should charge an excessive interest rate on his/her customer's outstanding amount after the credit term expires. Consequently, his/her customers will order to buy more quantity than the classical economic order quantity. As a matter of fact, these two managerial phenomena have been demonstrated in the decision making of using credit cards. For example, most credit card companies provide card holders 25 days of grace period, and charge 18–20% interest on the amount past due (ie, the second phenomenon). However, for a well-established credit card holder, he/she will take the benefit of 25 days of grace period constantly, but will not spend over his/her limit and face an excessive finance charge (ie, the first phenomenon).     

A profit-based scoring system in consumer credit: making acquisition decisions for credit cards

Consumer credit scoring is one of the most successful applications of quantitative analysis in business with nearly every major lender using charge-off models to make decisions. Yet banks do not extend credit to control charge-off, but to secure profit. So, while charge-off models work well in rank-ordering the loan default costs associated with lending and are ubiquitous throughout the industry, the equivalent models on the revenue side are not being used despite the need. This paper outlines a profit-based scoring system for credit cards to be used for acquisition decisions by addressing three issues. First, the paper explains why credit card profit models—as opposed to cost or charge-off models—have been difficult to build and implement. Second, a methodology for modelling revenue on credit cards at application is proposed. Finally, acquisition strategies are explored that use both a spend model and a charge-off model to balance tradeoffs between charge-off, revenue, and volume.     

The Effectiveness of Communication at Meetings: A Case Study

Meetings occupy over 30 per cent of the time of an executive and existing training in meeting behaviour was not considered to be effective. Methods used to analyse communication at meetings are described. A group of observers has been trained to assist chairmen in improving the usefulness of their meetings. Reductions of 20 per cent in the number of meetings and of 30 per cent in their duration have been achieved. Standard practices for meetings have been established. Training should be given to coherent groups in the organization rather than to individuals if changes in behaviour patterns are desired.     

Developing a measure of risk adjusted revenue (RAR) in credit cards market: Implications for customer relationship management

Current models of customer lifetime value (CLV) consider the discounted value of profits that a customer generates over an expected lifetime of relationship with the firm. This practice can be misleading in the financial services markets because it ignores the risk posed by the customer (such as delinquency and default). Specifically, in the credit card market, the correlation between revenue and risk is positive. Therefore, firms need to adjust a customer’s profits for the associated risk before developing a measure of customer lifetime value. We propose a new measure, risk adjusted revenue (RAR), that can incorporate multiple sources of risk and demonstrate the usefulness of the proposed measure in correctly assessing the value of a customer in the credit card market. The model can be extended to compute risk adjusted lifetime value (RALTV). We use the RAR metric to understand the effectiveness of different modes of acquisition, and of retention strategies such as affinity cards and reward cards. We find that both reward- and affinity-cardholders generate higher RAR than non-reward and non-affinity cardholders respectively. The ordering of different modes of acquisition with respect to RAR (in decreasing order) is as follows: Internet, direct mail, telesales, and direct selling.     

Credit scoring,augmentation and lean models

If a credit scoring model is built using only applicants who have been previously accepted for credit such a non-random sample selection may produce bias in the estimated model parameters and accordingly the model's predictions of repayment performance may not be optimal. Previous empirical research suggests that omission of rejected applicants has a detrimental impact on model estimation and prediction. This paper explores the extent to which, given the previous cutoff score applied to decide on accepted applicants, the number of included variables influences the efficacy of a commonly used reject inference technique, reweighting. The analysis benefits from the availability of a rare sample, where virtually no applicant was denied credit. The general indication is that the efficacy of reject inference is little influenced by either model leanness or interaction between model leanness and the rejection rate that determined the sample. However, there remains some hint that very lean models may benefit from reject inference where modelling is conducted on data characterized by a very high rate of applicant rejection.     

Credit risk assessment: a challenge for financial institutions

^** E-mail: vangeli3{at}eaee.gr This study explores financial credit risk assessment. This isan important issue because there is currently no standardizedmethod used by financial institutions for the assessment ofcredit risk. A critical evaluation of the most popular creditrisk assessment methods—the judgmental method, credit-scoringand portfolio models—highlights a number of limitationswhen used on their own. Several interviewees confirm that creditrisk assessment methods should be combined for effective creditrisk assessment. Accordingly, the study proposes a frameworkfor improving credit risk assessment, which combines the strengthsof these methods and copes successfully with their limitations.     

A multinomial tree model for pricing credit default swap options

Among the traded credit derivatives, the market interest in credit default swap options (CDSwaptions) is enormous. We propose a multinomial tree model to price Bermudan CDSwaptions. Our basic rationale is that we distribute the occurring probability for each node in a branch proportional to the probability density function of the assumed (normal) distribution. Through this approach, without the need of solving a large number of equations simultaneously, only the first four moments are required to build an arbitrarily large N-branches tree. We also demonstrate the detailed model implementation procedure including the valuation and the estimation of critical prices through an empirical example in Tucker and Wei (J Fixed Income 15(1):88–95, 2005). Numerical results show that, in the valuation, the proposed multinomial tree model is accurate and can significantly save pricing time under the same degree of accuracy as the binomial tree model. In the estimation of critical prices, the results are less accurate than those in the valuation, but the relative errors are acceptable.     

Estimation and status prediction in a discrete mover‐stayer model with covariate effects on stayer's probability

A discrete‐time mover‐stayer (MS) model is an extension of a discrete‐time Markov chain, which assumes a simple form of population heterogeneity. The individuals in the population are either stayers, who never leave their initial states or movers who move according to a Markov chain. We, in turn, propose an extension of the MS model by specifying the stayer's probability as a logistic function of an individual's covariates. Such extension has been recently discussed for a continuous time MS but has not been considered before for a discrete time one. This extension allows for an in‐sample classification of subjects who never left their initial states into stayers or movers. The parameters of an extended MS model are estimated using the expectation‐maximization algorithm. A novel bootstrap procedure is proposed for out of sample validation of the in‐sample classification. The bootstrap procedure is also applied to validate the in‐sample classification with respect to a more general dichotomy than the MS one. The developed methods are illustrated with the data set on installment loans. But they can be applied more broadly in credit risk area, where prediction of creditworthiness of a loan borrower or lessee is of major interest.     

The optimal ordering policy of the EOQ model under trade credit depending on the ordering quantity from the DCF approach

This paper discusses the optimum order quantity of the EOQ model that is not only dependent on the inventory policy but also on firm’ credit policy. Here, the conditions of using a discounted cash-flows (DCF) approach and trade credit depending on the quantity ordered are discussed. We consider that if the order quantity is less than at which the delay in payments is permitted, the payment for the item must be made immediately. Otherwise, the fixed trade credit period is permitted.     

The effectiveness of support for students with non-traditional mathematics backgrounds

This article describes an initiative introduced at LoughboroughUniversity by SIGMA, a Centre for Excellence in Teaching andLearning (CETL), to support physics students who were mathematicallyless well-prepared than their counterparts. The article outlineshow students were identified as being less well-prepared. Thesestudents were taught in a separate group, using different materialsand a different teaching style, but the same assessment methodswere used for both groups. An evaluation of the success of thisinitiative is made by comparing the results of the less well-preparedstudents receiving support in 2005–06 with those of theless well-prepared students (taught in the mainstream group)in 2004–05. A key outcome of this comparison is an increasein the pass rate from 48% to 67%.     

Modelling the evolution of credit spreads using the Cox process within the HJM framework: A CDS option pricing model

In this paper a simulation approach for defaultable yield curves is developed within the Heath et al. (1992) framework. The default event is modelled using the Cox process where the stochastic intensity represents the credit spread. The forward credit spread volatility function is affected by the entire credit spread term structure. The paper provides the defaultable bond and credit default swap option price in a probability setting equipped with a subfiltration structure. The Euler–Maruyama stochastic integral approximation and the Monte Carlo method are applied to develop a numerical scheme for pricing. Finally, the antithetic variable technique is used to reduce the variance of credit default swap option prices.     

Credit risk estimation using payment history data: a comparative study of Turkish retail stores

Our paper presents a comparative study applying logistic regression and multiple criteria decision analysis tools to the operations of wholesalers to assess the credit risk of their retailers using payment history data and to cluster the risky customers by ranking their risk levels. Our sample comprises approximately 6,000 retailer customers and 600.000 transactions of one of the major wholesalers of Turkey. Our findings emphasize the importance of using payment history and some non-financial factors data for predicting the creditworthiness of a firm.     

Credit risk optimization using factor models

We study portfolio credit risk management using factor models, with a focus on optimal portfolio selection based on the tradeoff of expected return and credit risk. We begin with a discussion of factor models and their known analytic properties, paying particular attention to the asymptotic limit of a large, finely grained portfolio. We recall prior results on the convergence of risk measures in this “large portfolio approximation” which are important for credit risk optimization. We then show how the results on the large portfolio approximation can be used to reduce significantly the computational effort required for credit risk optimization. For example, when determining the fraction of capital to be assigned to particular ratings classes, it is sufficient to solve the optimization problem for the large portfolio approximation, rather than for the actual portfolio. This dramatically reduces the dimensionality of the problem, and the amount of computation required for its solution. Numerical results illustrating the application of this principle are also presented. JEL Classification G11     

The assignment of credit limits with a behaviour-scoring system

Received on 1 July 1991. Behaviour-scoring systems for authorizations enable the riskof a customer defaulting to be quantified. These risks mustbe incorporated into a credit strategy which assigns creditlimits and makes authorization decisions in the most effectivemanner. This paper introduces the concept of marginal risk whichhas proved a useful tool in defining credit limit strategiesfor a mail-order company. Behaviour scores for authorizations are similar to credit applicationscores in that they predict the overall risk of a customer defaulting.If a cut-off risk can be established, then the optimal strategywould appear to be to withhold credit for customers exceedingthis risk and to grant unlimited credit for the remainder (thisis analogous to application strategies). The notion of grantingunlimited credit is often commercially unacceptable (particularlyif customers are to be informed of their credit limits!) andso strategies which give all or nothing are of limited valueand need further refinement. In order to overcome this problem, the concept of marginal riskhas been devised. The marginal risk is the risk of the ‘last£’ of an account being defaulted. This reflectsthe fact that small-balance customers may well pay off theircurrent balance only to default on larger subsequent purchases.Although the overall risk of customers with a given behaviourscore defaulting is relatively constant, their marginal riskwill vary according to their outstanding balance. This paperexplores the relationships between marginal risk and overallrisk and between marginal risk and outstanding balance. A modelwhich summarizes these relationships is proposed, and contoursof equal marginal risk are built on the basis of this model.These contours provide strategies for allocating credit limitswhich are both practical and optimal for a well formulated cut-offrisk and which suggest that the probability of defaulting isnot the best criterion for allocating credit limits. The results of the application of this approach will be demonstrated.Some of the problems that have been overcome are discussed,as are some of the outstanding problems.     

Modelling the profitability of credit cards by Markov decision processes

This paper derives a Markov decision process model for the profitability of credit cards, which allows lenders to find an optimal dynamic credit limit policy. The states of the system are based on the borrower’s behavioural score and the decisions are what credit limit to give the borrower each period. In determining which Markov chain best describes the borrower’s performance, second order as well as first order Markov chains are considered and estimation procedures developed that deal with the low default levels that may exist in the data. A case study is given in which the optimal credit limit is derived and the results compared with the actual outcomes.     

A new index of creditworthiness for retail credit products

This paper introduces a novel family of indexes to describe borrowers’ creditworthiness in retail credit products, both for fixed term loans and for open-ended products such as credit cards. Each index is the ratio at a given time of the net present value of actually received cashflows to the contractual ones. Some interpretations of the indexes are given and it is also described how to link them to the profitability of the credit financial operation. For open-ended products, a competing risks survival analysis methodology is proposed to estimate the cashflow returns and illustrated with a simulation.     

Risk factor analysis and portfolio immunization in the corporate bond market

In this paper we develop a multi-factor model for the yields of corporate bonds. The model allows the analysis of factors which influence the changes in the term structure of corporate bonds. More than 98% of the variability in the corporate bond market is captured by the model, which is then used to develop credit risk immunization strategies for corporate bonds of multiple credit ratings. Empirical results are given for the US market using data for the period 1992–1999.