Predicting Recovery Rates for Defaulting Credit Card Debt

Predicting Recovery Rates for Defaulting Credit Card Debt Angela Moore Quantitative Financial Risk Management Centre School of Management University of Southampton Abstract Defaulting credit card debt is growing in the UK. Not all of the debt will be collected in-house. At some stage the original lender may decide to sell off the debt to a collections agency. Prediction of the recovery rate for this debt can be used to assess how it should be valued. The distribution of the recovery rates of credit card debt sold to a collection agency can be quite different from that being collected in house because it is usually the case that this debt has already proved difficult to recover. In this study we build several models for predicting the recovery rate for a credit card debt that has been sold to a collections agency. We estimate the parameters of the model using real data. The results obtained and the structure of the model will be presented. 1. Introduction The Diners Club issued the first credit cards in 195, which were used to pay for food in restaurants anywhere that the Diners Club Card was accepted. Technically this was a charge card not a credit card because the entire balance had to be paid when the user was billed. American Express issued the first real credit card in 1958 followed by BankAmericard (now Visa) later that year. [1] The first credit card to be issued in the UK was the Barclaycard owned by Barclays Bank in 1966. [2] Over the last ten years, there has been a rapid rise in the popularity of plastic cards. The credit card industry is booming. In July 24, the UK broke through the symbolic 1 trillion barrier of out standing debt for the first time. [3] By 26 nearly a third of all consumer spending was on plastic cards. [4] In June 27 there were 66 million cards in the UK making 157.3 million transactions that month with a value of 12.3 billion. [5] Unfortunately with increased credit card use, many consumers fail to pay back the debt. There are many factors contributing to customer delinquency. These include poor financial management skills, the economy and ease of access to loans and credit cards. When a debtor becomes delinquent for 18 days (FSA definition) then the loan is considered to be in default. When this happens most lenders will try to collect the debt in house. However some companies use outside agents or will just sell off the debt. If the lender s collection department is unable to collect the debt, then they may also decide to use a collection s agency or just sell off the debt. The debt can be passed on several times, and can be collected up to six years after the last payment was made. [6] The amount of debt passed to debt collection agencies, exceeds 5 billion per annum. [7] This paper will look at the factor affecting the RR (Recovery Rate) of credit card debt, which has defaulted and been sold off to a debt collections agency. Using the variables available and regression analysis, a model will be introduced for estimating the RR for credit card debt sold to a collections agency. This model will also be tested against the real data. Because the debt sold to debt collection agencies will in the majority of cases be difficult to collect, this paper will first look at the factors a

logistic regression to targeting debtors who have a RR greater than zero. Before looking at a linear regression on debtors who have a RR of greater that zero, to predict their recovery rate. This paper is important on three counts. Firstly the introduction of the Basel New Accord in 27 means that the estimation of LGD (Loss Given Default) has become extremely important to the banking world. Therefore knowing what factors affect the RR (Recovery Rate) is important for calculating the LGD of borrowers. Secondly, knowing what factors affect RR can help with a lender s collection policy. Knowing which debtors are more likely to pay after they have defaulted, means that debt collectors can focus their attention on to these debtors to recover the debts as quickly as possible. Thirdly, being able to identify debtors who are more likely to pay during the selling and purchasing of debt, can aid in the pricing of the debt. 2. Case Study The data used for this study is from a debt collection agency working out of London. Their primary method of debt collection is telephone with written communication in support. The telephone is used because it can lead to fast recovery of debt, as it is a direct line of communication with the debtor and can result in a payment from the first conversation. The telephone is also very cost effective compared to face-to-face communication but is just as personal. There is also the element of surprise and the debtor and collector can negotiate to achieve a mutually satisfactory result. The ideal outcome for the collector is to receive payment in full on the first call. In order to achieve this they will often offer discounts or threaten legal action. If they discover that the debtor is unable to pay the full amount then the fall back positions are to set up a payment plan and to receive part of the payment in advance. In order to set up the correct payment plan, the collector should find out as much information as possible from the debtor. If the debtor refuses to pay or doesn t make the agreed payments then the debt collection agency will start County Court Proceedings. This will most likely result in a warrant of execution to retrieve the debt. Although the debt collection agency collects many different types of debt this paper is focused on credit card debt. This collection of debt has been bought by the company over a 2-month period and contains over 7, debts. The individual debts vary from a few pounds to over 4,. The debt sold to a collections agency will normally be debt, which has proven hard for the lender to collect in house. Since this is the case the distribution for LGD shows that the majority of the debt has not been paid. In fact over 8% of the debts have had no payments made on them at all. Figure 1, shows the LGD distribution for the real credit card debt over a 2-month period. Because most of the debtors have not paid anything back at all, this paper will concentrate on Recovery Rates instead of LGD.

LGD 7 6 5 4 3 2 1 1.95.9.85.8.75.7.65.6.55.5.45.4.35.3.25.2.15.1.5 LGD Figure 1, Distribution of LGD for Credit Card debt sold to a collections agency over a 2-month period 2.1 Variable Analysis The variables available for analysis are the debtors titles, country of residence, age, amount of debt, if contactable by telephone, length of time on books, and home ownership status. 2.2 Age The debtors range in age between 19 and 1, with the majority of debtors in the 25-35 bracket. The data does appear to suggest that the older the debtor is the more likely they are to have a recovery rate greater than zero. Figure 2 illustrates the proportion of debtors who s RR is greater than zero in each of the age brackets. Recovery Rate by Age 25 2 15 1 5 18-25 25-35 35-45 45-55 55-65 65+.25.2.15.1.5 whose RR> RR= RR> whose RR> Age Figure 2, Recovery Rate by Age 2.3 Title The data included the debtors title, with five classifications; Dr, Mr, Miss, Mrs and Ms, with over 5% of the debtors being men. Figure 3 illustrates the proportion of debtors who s RR is greater than zero in each of the classifications. As figure 3 demonstrates women are more likely to pay something than men and married women are the most likely with 23% of the debtors using the title of Mrs paying something to the collection agency. What is interesting is that debtors using the title of Dr are least likely to pay anything back.

Recovery Rate by Title 4 35 3 25 2 15 1 5 Average Dr Miss Mr Mrs Ms.25.2.15.1.5 whose RR> RR= RR> whose RR> Title Figure 3, Recovery Rate by Title 2.4 Homeownership Homeownership is divided into four classifications; family, solo ownership, joint ownership and tenant. If the debtor is known to reside in a property owned by a member of their family, but not themselves, then their homeownership is classified as Family. If the debtor resides in a property owned solely by them then their homeownership status is Solo. Joint status is recorded if the debtor and another own their residence and Tenant status if they are renting or the details are unknown. The vast majority of the debtors are recorded as Tenants, over 85%. Figure 4 demonstrates that debtors who are classified, as Tenants are least likely to pay anything and debtors who reside at a property that are jointly owned appear to be most likely to pay anything back. Presumably this is because they have not only a property to raise money with but also another person to help them raise the money. Recovery Rate by Homeownership 6 5 4 3 2 1 Family Joint Ownership Solo Ownership Tenant.35.3.25.2.15.1.5 whose RR> RR= RR> whose RR> Homeownership Figure 4, Recovery Rate by Homeownership 2.5 Country of Residence Debtors have been divided into four classifications for their country of residence, see figure 5; England and Wales, Scotland, Northern Ireland and Foreign. Although the vast majority (over 9%) of the debtors fall into the classification of England and Wales, over 1 debtors reside abroad and they appear to be harder to acquire the debt from. 2.6 Debt Amount The individual debts vary from a few pounds to over 4,. With the bulk of debtors owing between 5 and 1,. Figure 6 shows that the debt collection agency was especially successful in obtaining money from debtors who owed less than 1, with over 4% of them paying something towards their debt. However there are only 85 debts, which fall into this category.

Recovery Rate by Country of Residence 6.25 5 4 3 2 1.2.15.1.5 whose RR> RR= RR> whose RR> Average England & Wales Foreign Northern Ireland Scotland Country of Residence Figure 5, Recovery Rate by Country of Residence Recovery Rate by Debt Amount 25 2 15 1 5-1 1-5 5-1 1-15 15-2 2-5 5-5.5.45.4.35.3.25.2.15.1.5 whose RR> RR= RR> whose RR> Debt Amount ( ) Figure 6, Recovery Rate by Debt Amount 2.7 Telephone Information The data included which telephone numbers for the debtors were still active; they had up to five numbers for the debtors, which could include a mobile or work number. Figure 7 illustrates the number of active telephone numbers for the debtors and proportion who have a recovery rate of greater then zero. As would be expected the collection agency was least able to obtain money from the debtors which no telephone numbers. What is interesting is that it was not the debtors with a work number who were more likely to pay but the debtors with mobile numbers, with over 4% of the debtors paying something to the collection agency. Recovery Rate by Telephone 6 5 4 3 2 1 Telephone= Telephone=1 Telephone>1.25.2.15.1.5 whose RR> 25 2 15 1 5 Work No Work Mobile No Mobile.5.45.4.35.3.25.2.15.1.5 whose RR> RR= RR> whose RR> Figure 7, Recovery Rate by Telephone 2.8 Time on Books The collections agency bought the debt over a 2-month period. With the majority of the debt bought in the last eight months. As figure 8 shows, the longer the debt has been with the collections agency, the more likely it is that the debtors will pay something to the agency. The jump in the collections around the 1-month period is probably due to the collections agency acquiring a better book of debt. So they are

able to collect of the debtor more quickly. Since the time on books is an operational variable, it will not be included in the regression analysis. Recovery Rate by Time on Books 12 1 8 6 4 2 2 4 6 8 1 12 14 16 18 2.4.35.3.25.2.15.1.5 whose RR> RR= RR> whose RR> Time on Books (Months) Figure 8, Recovery Rate by Time on Books 3. Logistic Regression Model After reviewing the data in section two, it becomes quite clear that telephone information and debt amount are the two variables which have the greatest effect on the collections agency s ability to procure money from the debtors. So using Enterprise Miner in SAS to create a model using debt amount and telephone information the following results are obtained. Parameter DF Estimate Standard Error Wald Chi- Square Pr>ChiSq Standardised Estimate Exp(Est) Intercept 1-1.8929.932 412.34 <.1.151 No Work Telephone 1 -.1959.31 39.99 <.1.822 No Mobile Telephone 1 -.1582.247 41 <.1.854 Amount 1 1.6695.4723 2.1.1564 1.953 Amount 5 1 -.61.951.9949.999 Amount 1 1 -.2258.848 7.9.77.798 Amount 15 1 -.368.886.17.678.964 Amount 2 1 -.886.959.85.3556.915 Amount 5 1 -.1469.879 2.8.945.863 Number of Telephones 1.6115.247 615.19 <.1.3196 1.843 Table 1, Logistic Regression Results Table 1 shows the results from the logistic regression model. No Work Telephone is referring to debtors who do not have an active work telephone number on file. Since the estimate for this parameter is negative then, those who do not have a work phone are less likely to pay any of their debt back than those who do have a work phone. This is consistent with the data in figure 7, where debtors who have a mobile or a work telephone are more inclined to pay part of their debt back. Number of Telephones is referring to the number of numbers on the debtors record, up to five can be recorded. This estimate of.6115, explains that debtors with an active telephone number are more likely to pay back part of their debt than debtors without an active telephone number. This also consistent with the data in figure 7, which shows that debtors with no telephone numbers were least likely to pay back part of their debt. The amounts parameters are referring to the total original amount of debt. Debtors who owe between - 1 fall into the category Amount 1. Debtors who owe between 1.1-5 fall into the category Amount 5 etc. Table 1 shows that

the estimate, for debtors in the category Amount 1 is.6695 so they are most likely to pay back part of their debt. 4. Linear Regression Model Since there is such a large spike in the recovery rates at zero, because over 8% of the debtors have failed to pay back anything, linear regression will only be used to estimate the Recovery Rate for debtors who have paid part of their debt back. With most of the debtors not falling into this category, there is just over 12, debtors to estimate with. So only 7, of these debtors will be used for creating the model and the rest will be used as a holdout sample for testing the model. 4.1 Estimating an Ordinary Linear Regression Model The following variables were used: Is the debtor aged between 18-25 Is the debtor aged between 25-35 Is the debtor aged between 35-45 Is the debtor aged between 45-55 The debt amount owed Does the debtor have one or more active telephone numbers Does the debtor have an active mobile number Does the debtor have an active work number Does the debtor reside in a residence owned by a family member Does the debtor reside in a residence jointly owned by them and another Does the debtor reside in a residence owned by them solely Is the debtor s title Mr Is the debtor s title Miss Is the debtor s title Mrs Is the debtor s title Ms Using the linear regression model in SAS the results in table 2 were obtained. The model has a R-squared value of.197 and a Root Mean Squared Error of.32493. Figure 9 shows the predicted Recovery Rate against the real Recovery Rate. As figure 9 and table 3 both indicate, the mean of the predicted and the real Recovery Rates are very close but the standard deviation of the predicted is far smaller. This indicates that the predicted results are all clustered around the mean. Predicted Recovery Rate Predicted Recovery Rate.8.6.4.2 -.2.2.4.6.8 1 1.2 -.4 -.6 -.8-1 Real Recovery Rate Figure 9, Correlation of Linear Regression Results

Label DF Estimate Error t Value Pr> t Intercept 1.59798.9882 6.5 <.1 Age 18-25 1.9125.1613 5.66 <.1 Age 25-35 1.4455.1379 3.23.12 Age 35-45 1.2598.1332 1.95.511 Age 45-55 1.865.1416.61.5413 Debt Amount 1-4.2E-5 1.88E-6-21.38 <.1 One or more Telephones 1 -.1368.112-9.41 <.1 Mobile 1.1332.949 1.4.162 Work Number 1 -.486.16-4.6 <.1 Family Home 1 -.4719.165-2.86.43 Joint Homeownership 1-7.56E-5.1256 -.1.9952 Solo Homeownership 1.869.1897 4.25 <.1 Mr 1 -.16496.9821-1.68.931 Miss 1 -.19539.9859-1.98.475 Mrs 1 -.2612.9842-2.9.363 Ms 1 -.24914.9924-2.51.121 Table 2, Linear Regression Results Variable N Mean Standard Deviation Sum Minimum Maximum RR 5191.2913.34532 1511.12 1 Predicted RR 5192.2941.11264 1527 -.76715.59231 Table 3, Correlation of Linear Regression Results 4.2 Beta Distribution As well as the linear regression model a beta distribution model was created. Since the linear regression model assumes a normal distribution, and the data does not support this assumption, a beta distribution was assumed instead. This model assumes that the distribution of the data is Beta, not normal, so transforms the data from a beta distribution to a normal distribution, to use linear regression. Once linear regression has been applied the data is then transformed back. The same variables were used again. Variable N Mean Standard De via tion S um Minimum Ma ximum RR 5191.2913.34532 1511.12 1 rrpre d 5192.2758.849 1432.23125.29687 Table 4, Correlation of Linear Regression Results Assuming a Beta Distribution With the beta distribution, the R-squared value is.1161 and a Root Mean Squared Error of.17839. Table 5 shows the estimates for the model and figure 1 shows the predicted Recovery Rate against the real Recovery Rate. As figure 1 and table 4 both indicate, the mean of the predicted RR is close to the real RR. However the variance is far smaller than the real RR, so the predicted RR is clustered around the mean. The R-squared value was better than the linear regression model implying a better fit.

Label DF Estimate Error t Value Pr> t Inte rce pt 1.45883.5691 8.6 <.1 Age 18-25 1.5462.941 5.8 <.1 Age 25-35 1.3236.794 4.8 <.1 Age 35-45 1.1735.764 2.27.232 Age 45-55 1.679.81.84.416 De bt Amount 1-2.42E-5 1.6E-6-22.71 <.1 One or more Te le phone s 1 -.2955.642-4.6 <.1 Mobile 1.184.542 3.39.7 Work Numbe r 1 -.895.573-1.56.1186 Family Home 1 -.2389.944-2.53.114 J oint Home owne rs hip 1 -.27.717-3.77.2 Solo Home owne rs hip 1.766.1124.68.4955 Mr 1 -.9726.5657-1.72.856 Mis s 1 -.1126.568-1.98.475 Mrs 1 -.1853.5668-1.91.556 Ms 1 -.13985.5714-2.45.144 Table 5, Linear Regression Results Assuming a Beta Distribution Predicted Recovery Rate using Beta Distribution Predicted Recovery Rate.32.3.28.26.24.22.2.2.4.6.8 1 1.2 Real Recovery Rate Figure 1, Predicted Recovery Rate Assuming a Beta Distribution 5. Conclusions and Future Research This paper has looked at predicting the recovery rates (RR) for debt, which has been sold to a debt collections agency. As the data shows, the majority of the debt has not been collected. Less than 17% of debtors achieved a RR>. The data shows that the debt collections agency has had better results collecting from the older debtors (those aged 45 and over). Women were more likely to pay than men, especially married women. Interestingly too, debtors who have joint ownership of their home where more likely to pay part of their debt. Unsurprisingly debtors who did not own their own home were found to be the harder to collect from. Their country of residence, surprisingly made very little difference to whither they paid or not. The debt collection agency were very good at collecting from debtors who owed less than 1 or has a active mobile or work telephone number. Since the majority of the debtors failed to pay back any part of their debt, the linear regression model was only used on the debtors who had achieved RR>. Two regression models were used. One was the basic regression model and the other

assumed a beta distribution. Both regression models predicted the mean of the recovery rates to be very close to the real recovery rate. The beta distribution however gave a better R squared value and all of the predictions were positive because the beta distribution is positive where as the normal linear regression model had numerous predictions below zero. The most important aspect of this research is that it clearly demonstrates that some debtor properties like their age, marital status and homeownership have a clear effect on the recovery rate. In this case study the number and type of telephones and the debt amount had the greatest impact. It is useful to be able to predict the recovery rates of debtors because if you can predict the recovery rate for a book of debt then you can estimate the value of the debt. Since over 5 billion of debt is passed to collection agencies every year in the UK, correctly estimating the debt could have a big effect in the price that the debt is sold of for. Further research will investigate what impact, if any, that changes in economical conditions will have on the model. The consumer credit market is very venerable to changes in the economic situation both worldwide and in the UK. Further research will include estimating the value of the debt for sales purposes; this will look at converting the recovery rate into a monetary value. However calculating the value of debt requires the predicted recovery rate over the lifetime of the debt, which can be many years. This research has viewed the debt over a very short time span, and the final recovery rates will be very different from the results displayed here. References 1 Mary Bellis, Who invented Credit Cards? www.inventors.about.com 2 Wikipedia: credit card entry, http://en.wikipedia.org/wiki/credit_card 3 BBC News 29 th July 24 quoting the new Bank of England figures for debt 4 BBC Debit card spending roars ahead, 3 July 27, http://news.bbc.co.uk/1/hi/business/6265784.stm 5 British Banking Association http://www.bba.org.uk/bba/jsp/polopoly.jsp?d=149 6 The Limitations Act 198 7 Credit Service Association http://www.csa-uk.com/csa/faq.php