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									                  Delinquency & Loss forecasting for Consumer (Auto) loan portfolio
                        with inclusion of Dynamic risk –Market & Operations

                                                    White Paper
                                           Business Process / Management

                                                      March 2009

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               This paper describes, along with classical approach of Roll Rate Forecasting,
               a new technique of constructing Delinquency and loss forecasts for
               consumer loan portfolio’s to improve the results. This new method captures
               three features observed in this scenario. The loans are not homogeneous as
               they originate from different credit quality; delinquencies are affected by
               macro-economic conditions of economy & Collections effort by the
               organization. This model represents the monthly movement of a loan
               between different stages of delinquency & effect of Market & Operational
               risk has been overlay on forecast results.

               Key Words:

               Loss forecast, Delinquencies, Roll Rate forecast, Collections, Macro-
               economic, Market risk, Operational Risk ,Regression, ARIMA, Trend,
               Seasonality, Auto Loan

               Paper Type:


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                   1. Application

                   Consumer credit delinquencies in the fourth quarter of 2007 reached their highest
                   levels since 1992, according to the American Bankers Association's Consumer Credit
                   Delinquency Bulletin. The composite ratio, which tracks eight closed-end installment
                   loan categories, raised 21 basis points to 2.65 percent of all accounts in the fourth
                   quarter (seasonally adjusted). James Chessmen, ABA chief economist, attributed the
                   rise largely to auto loan delinquencies. The auto loan category comprises about two-
                   thirds of all closed-end consumer installment loans. [1]

                   Auto Loan Performance Outlook:           Prime & sub prime auto loan losses (annualized
                   net losses) are expected to continue increasing in 2008 as well. Fitch's prime and sub
                   prime auto loss index levels could be above 2% and 11%, respectively, in the next 12
                   months. In the last six months of 2007, prime and sub prime loan losses began to
                   increase, after a declining trend the last five years. Prime losses ended 2007 at 1.34%,
                   up from 0.66% at mid-year 2007, while sub prime loans ended 2007 at 7.56%, up
                   from 3.9% at mid year. [2]

                   As automakers try to entice consumers with low- and no-interest financing on new
                   vehicles amid a slow economy and rising fuel prices, any company in the business of
                   making loans will, of necessity, require a forecast of future losses on these loans. As new
                   customers are booked, as account age, and as the environment changes, the expected
                   losses on a portfolio can vary greatly. The regulatory changes (Basel II) combined with
                   increasing pressure to accurately predict future earnings have pushed risk management
                   to the forefront of business strategy.

                   The objective of loss forecasting for management is to analyze the past performance
                   with respect to impact of marketing campaigns, credit policies and collection
                   strategies. These forecasts are also used to predict delinquencies and charge-off’s
                   from newer vintage for capacity planning for collections team, predict overall losses
                   to set aside reserves and planning to evaluate loss impact of new marketing &
                   collections plans.

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                   There are many different classical methods available with which to forecast losses
                   such as Traditional/Unconditional methods: Net flow Rate, Vintage loss curves,
                   Score distribution; Econometric /Conditional methods: Regression, Time Series, and
                   Wavelets; Simulation & scenario based forecasting: Monte Carlo simulation, What-if
                   scenario analysis.

                   All the techniques mentioned above aim to create forecasts of future payment
                   patterns/losses on a portfolio, using the payment history observed on the portfolio.
                   They are extrapolations of the payment behavior seen till date. They do not attempt to
                   model explicitly the macro-economic and social changes that clearly affect the level
                   of bad debts ( and overall portfolio performance).The other principle influence on
                   future levels of bad debt is that of policies and systems under the lender’s control –
                   for instance, collections strategies & policies. These are not incorporated explicitly in
                   the models mentioned above.

                   Auto loan performance is particularly sensitive to economic factors that affect the
                   ability of the consumer to repay debt, including the unemployment rate, the consumer
                   price index, personal income growth and Negative home price trends. Also
                   organization’s operational, i.e. collections & marketing, strategies also greatly reflect
                   on their portfolio performance. Apart from Classical forecasting method, this paper
                   talks about using Market & operational risk overlay on forecasts to predict close to
                   real-life values.

                   This approach forecasts the delinquency movements over month & overlay market &
                   operational risk contributions to forecast leading to many viable & accurate results.
                   This forecasting methodology apart from looking at portfolio trend and loan
                   originations quality also looks at market conditions / internal organization’s effort
                   which gives true picture of portfolio losses expected. Also, the effect of changing
                   economic conditions/capacity planning changes /policies changes can be studied on
                   overall portfolio delinquencies & losses & strategies can be build for minimizing the
                   same. This approach does allow sensitivity analysis. In each case, a mechanism
                   allows the model parameter to be adjusted .A judicious choice of parameters can
                   show how the portfolio would react to economic and managerial scenarios.

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                   2. Loss forecast – Dynamic Risk inclusion : Methodology

                   Delinquency & loss forecasts provide management with unit & volume projections.

                   2.1 Data Sources

                   Generally, longer histories are needed for financial models as an idea of variations in
                   payment patterns are necessary, to tune sensitivity analysis.

                   Corporate Data warehouse: Account level historical info (3-5 years), Acquisition and
                   performance data

                   Chronology logs: Credit policies, Collection strategies

               2.2 Segmentation

               Any forecast benefits greatly from the identification of groups of customers or
               accounts exhibiting different timing of lifecycle events and divergent responses to
               environmental conditions.

                   Portfolio intelligence, that is, knowing how the portfolio will perform under different
                   conditions and scenarios, gives the institution a better handle on capacity planning in
                   collections, a clear picture of economic capital requirements and resulting investment
                   decisions, and the ability to better forecast account groups used in securitization
                   branches. This next frontier in portfolio analysis ties sophisticated measures of
                   segment value directly to an ability to predict behavior accurately over the customer
                   lifecycle and across economic cycles.

                   Segmentation is an important step in forecasting, both from forecasting accuracy &
                   usability perspective. In this technique, the choice of portfolio segmentation for
                   forecasting is driven by preferences for familiarity or a corporate-reporting process
                   that emphasizes product or channel but analytically segmentation optimized for
                   forecasting in the realm of risk-adjusted profit, portfolio predictability, early warning,
                   and the pursuit of beneficial portfolio effects that reduce volatility and increase value
                   have been taken into consideration.

               2.3 Roll rate forecast

                   There should be sufficient data to build forecast. Detailed information is required
                   from the loan application as well as a snapshot of the key transaction and payment
                   behaviors across the life of each account. If possible, the data should be captured
                   across an entire economic cycle.

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                   To get the insight into trends, there are many industry driven ways of doing
                   forecasting as mentioned earlier.
                   Here in this technique, as we are doing a portfolio level forecast, Net flow rate –
                   forecast has been used to forecast the account movement from one bucket to another
                   delinquency bucket.

                   Net flow rate – Overview: [3]
                   A net flow rate is a forecast in which the flow of outstanding from one level of
                   delinquency (lower) to another (higher) is applied to the current portfolio outstanding
                   mix. This technique follows the flow from current through all the delinquency
                   buckets to charge-off.Net flow rates from bucket to bucket are calculated by dividing
                   each month’s delinquency bucket by the delinquency bucket from the prior month.

                   This methodology is of best use for segmented portfolio, each of which is separately
                   forecasted, then rolled up to portfolio level. In addition to producing the most
                   accurate monthly forecasts, the net flow methodology provides the highest degree of
                   detail and offers insights and diagnostics. By breaking losses down into component
                   flows, portfolio management can easily see where change is coming from.

                   Table 1: A brief structure Net flow rate calculations (numbers and dates do not
                   represent the data used)

                   With these net flow rates (Account level) available by month, we individually
                   forecast the net flow rates for next 18-24 months for each segments. One can use any
                   of time series forecasting methodology depending on availability of data points.

                   The basic idea is to get trend & seasonality break for these segments for different
                   delinquency buckets. Here, we have used Arima & Decomposition -time series
                   forecasting methods (MINITAB & SAS) to get trend forecasts for next 18 months net
                   flow rate & seasonality for different delinquency buckets.

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               2.4 Market risk

                   As we know, the portfolio delinquencies and charge-off are driven by macro-
                   economic conditions prevailing. In this dynamic risk based forecasting, we include
                   the macro-economic impact on forecasts from net flow rate.

                   Various macro-economic variables like bankruptcies, civilian unemployment rate,
                   housing starts affecting consumer payment behavior was studied to identify the
                   relationship with portfolio delinquencies & the best explanatory variables were used
                   in macro-economic variable based forecasting.

                   Table 2: To identify best explanatory macro-economic variables with respect to
                   portfolio delinquency (numbers and dates do not represent the data used)

                   The identified, highest correlated, macro-economic variables are used to build
                   multivariate regression model equation to predict roll rates for next 18 months. The
                   forecasted values of macro-economic variables (available on paid basis online) are
                   used to predict different delinquency bucket roll rates for each segment.

                   The R2, (correlation coefficient) obtained from these equation act as a sensitivity
                   factor to decide the contribution of macro-economic forecast & statistical forecast in
                   final output.

                   Mathematical notation (f-forecast):

                   MC Roll Rate (f) = Trend roll rate (f) + (Macro economic roll rate (f) – statistical
                   forecast (f))* Correlation coefficient (R2)

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               2.5 Operational risk

                   As macro-economic changes in economy shows high correlations with delinquency
                   movement in portfolio, similarly the operational changes of business also do have a
                   high impact on delinquency & losses.

                   Here, in this approach, we have looked at Collections operations effort in portfolio &
                   developed a statistical relationship between collections metrics like pen rate, number
                   of representatives & loan accounts movement across delinquency buckets.

                   Table 3: To identify best explanatory Collections operations metric with respect to
                   portfolio delinquency (numbers and dates do not represent the data used)

                   Similar to macro-economic forecast overlay, we identified the best metric & build a
                   model (linear/non-linear) to predict the delinquencies. Also, portfolio manger &
                   business knowledge should be utilized here to use the best metric which will help in
                   predicting right results.

                   Once we have equations, based on projected metric data & R2 (correlation
                   coefficient) we can build the Collections based roll rate forecast.

                   Mathematical notation:

                   Overall roll rate (f) = MC roll rate (f) + (Change in Collections based roll rate (f) in
                   consecutive months - Change in macro-economic roll rate (f) in consecutive
                   months)*correlation coefficient (R2-C)

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               2.6 Charge-off’s forecast

                   Charge-off in any portfolio is function of delinquency patterns in portfolio,
                   repossession policies, economic situation & other unforeseen reasons. Charge-off’s in
                   auto loan portfolio is divided into mainly four segments: Bankrutpcy, Repossession,
                   Skip & others. Each of these segments is homogeneous in their nature & model has
                   been created separately to get the accurate predictions.

                   The Bankruptcy based charge-off are independent of any trend from historical
                   bankruptcies accounted in that portfolio; that’s the reason here bankrupt accounts are
                   predicted by building a Linear relationship on Industry bankruptcies projections.

                   The Skip Charge-off’s are basically a function of accounts which are not able to be
                   traced in early stage i.e. XX dpd bucket of last month when accounts are called first
                   time as they become delinquent. So, the skip charge-off’s net flow rates are calculated
                   on last month’s XX dpd bucket & forecasts are built.

                   Similar , is the case of Repo charge-off/other charge-off ,depending on organization’s
                   policies on repossessions ,the relationship can be checked graphically of movement of
                   these charge-off accounts with delinquency buckets & forecast can be built in a
                   similar fashion.

               2.7 Assumptions: Sourcing ,Closures & Avg. Dollars

                   As we get forecasts for all delinquency & charge-off buckets roll rate month over
                   month movement for next 18 months, next objective is to get Accounts & associated
                   dollar value to it.

                   For accurate predictions, we’ll need projections for new accounts sourcing, closure
                   rate & avg. dollars calculation at each segment level. These data points have been
                   provided with organization here but it can be predicted as well using historical
                   information at segment level.

               2.8 Model : final overlap

                   Finally, all the forecasts are combined & an interactive model is built to provide a
                   forecast which provides much more accurate & sensitive data.

                   The final approach is built to decide the impact of market risk & operational risk on
                   different delinquency bucket & segments with respect to statistically significant
                   strategies and business decision. Here, the option is kept open for forecast users to
                   change the factor loading on forecast & can see the changes in forecast which is
                   useful in current changing market trends.

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                   The Net Flows forecasts are then combined with sourcing, closure rate, avg. dollars
                   and other assumptions to reach to final delinquency/loss ($) projections for coming 18

                   3. Auto Loan - Loss forecast : Example

                   The forecasting strategy mentioned above in the paper, is been used to predict the
                   delinquency/loss ($) behavior of auto loan portfolio. Below, is an example which
                   shows the practical usage of this method & evaluation of same.

                   The historical data available for this portfolio was for only last 24 months, so we have
                   kept 24 data points for usage in forecast model built & have back-forecasted for
                   validation purpose.

               3.1 Segmentation

                   The Auto loan portfolio is studied for segmentation on basis of acquisition scores, car
                   brand, product type & vintage type. The basic statistical rule is not to do forecasting
                   for segments <5 % of total population as that will lead to volatility in results. Also the
                   segments which are small but have similar delinquency/loss rate, forecast model of
                   one has been overplayed on another segment.

               3.2 Roll rate forecast

                   Statistically, for arima forecasting at least 30 data points are necessary to get right
                   results. As we don’t have sufficient data for arima, in this example we have used
                   decomposition multiplicative method of forecasting.

                   This method helps us to get the trend & seasonality separate & increase the accuracy
                   of forecast. While graphically checking the seasonality factors, they came out to be
                   significantly similar for all the segments for a particular delinquency bucket. So, in
                   this forecasts a common seasonality factors have been applied to segments for each
                   delinquency bucket.

                   Here, we have used Minitab software for getting trend equation & seasonality factors.

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                   Table 4: Minitab forecast example

                   3.3 Charge-off’s forecast

                   Here, Charge-off’s relationship have been studied with respect to different
                   delinquency buckets & charge-off‘s roll rate forecasts are derived.

                   Bankruptcy charge-off’s: As mentioned above, the bankruptcies are independent of
                   portfolio characteristic and have been forecasted independently. We have first
                   calculated the portfolio bankruptcy filling rate form historical available data & have
                   build regression model to forecast bankruptcy filling rate with respect to industry
                   bankruptcy projections( source: Global Insight) .

                   Repo charge-off: Here, in this portfolio, the repo charge-off’s shows to be following
                   trends of 60+ delinquencies bucket with lag2.

                   Table 5: Graphical representation to verify relationship b/w repo charge-off and 60+
                   delinquency bucket (numbers and dates do not represent the data used)

                                                                                                                                                                                                                                                    60+ lag2

















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                   Similarly Skip & other charge-off’s relationship have been identified with respect
                   to XX delinquency buckets & YY delinquency buckets respectively. These roll
                   rates, in turn are forecasted to get actual charge-off accounts.

               3.4 Market risk
               To overlay the market risk, the different macro-economic variables relationship with
               30-59 delinquency bucket as that bucket is most impacted by external environment of
               Economy. The most significant macro-economic variables, X1, have been used here
               to build a regression model to project 30- 59 delinquency roll rates for different
               segments. For eg:

                          30-59 = 0.797 - 0.175 X1                       R-Sq = 79.6% R-Sq(adj) = 76.2%

               3.5 Operational risk

                   Collections operations data is collected for historical period and studied with respect
                   to early stage delinquency bucket & late stage delinquency bucket. In this portfolio
                   forecast, the Y1 metric came out to be significant variable to predict collections effort
                   on early stage delinquency roll rates. So, here collections effort adjustment have only
                   be applied on early stage delinquency bucket, 1-30 & 30-59 days past due.

                   As per studying the relationship between roll rates & Y1, i.e., increasing the Y1
                   should decrease the roll rates, we build a non-linear regression equation to identify
                   the change in roll rates with respect to change in Y1 in collections operations world.

               3.6 Sourcing & Closure

                   The sourcing & closure information for portfolio was available with car flow
                   projections of the organization and have been used in forecast to get actual number of
                   accounts at each delinquency bucket level.

                   The Avg. Dollars have been taken as last 3 months average with respect to giving
                   higher weight to recency.

               3.7 Model : final overlap

               The overall 30-59 roll rates are calculated by utilizing all the overlaps which takes
               care of market & operational risk & flows through all delinquency buckets.

                       30 -59 roll rate (mc) = Statistical forecast (30-59) + (Macro-economic forecast
                              (30-59) - Statistical forecast (30-59)) * Correlation coefficient

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                   Similarly for collections overlap, we first identify change in roll rates over
                   consecutive months with respective change in Y1 & macro-economic variables. Then
                   this change is applied on delinquency buckets identified.

                       Final 30 -59 roll rate = 30 -59 roll rate (mc) + (change in mc forecast (30-59) *
                       (1- Correlation coefficient (collections) - change in collections forecast (30-59) *
                       Correlation coefficient (collections))* 30 -59 roll rate (mc)

                   Similarly this concept can be applied to other delinquency bucket where we want to
                   apply the market & operational risk factors.

                   Once final roll rates are projected then in turn corresponding accounts & dollars can
                   be project using car flow projections.

               3.8 Evaluation of Results

                   The validations done on these results with respect to individual statistical forecasts/
                   macro-economic forecasts shows that this approach gives results which are more
                   closer to actual numbers & also have features which can change the forecasting
                   procedure as per economy & operational conditions operating in environment.

                   Table 6: Evaluation of forecasting methods, results showing for 3 months (numbers
                   and data are not actual)

                   4. Summary

                   This paper proposes the dynamic risk based forecasting as it showed better results for
                   auto loan portfolio. Although conventional method could have been used in this
                   scenario but these common methods weren’t applicable since the loans are not
                   homogeneous with respect to credit quality, only a small window of data is available
                   with changing environment conditions.

                   The conventional method gives lot of emphasis on historical trend which is not true in
                   today’s culture, so this method comes out to be suitable as it takes care of recent
                   development with respect to market and operational changes in economy.

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                   1.   Gross, D and Souleles, N. (2002) An empirical analysis of personal bankruptcy

                        on delinquency. Journal of Financial Studies ,15(1),319-347

                   2.   Patterson, k (2000) An Introduction to Applied Econometrics: A Time series


                   3.   Sullivan, A.C. (1987) Economic Factors Associated with Delinquency Rates on

                        Consumer Installment debt. Credit Research Centre, Working Paper No 55 ,

                        Krannert Graduate School of Management

                   4. Salomon Smith Barney Guide to Mortgage-Backed and Asset-Backed
                        Securities By Lakhbir Hayre ,Published by John Wiley and Sons, 2002

                        ISBN 0471196908, 9780471196907

                   5. Econometrica By Econometric Society, JSTOR (Organization),Published
                        by Econometric Society, 1962

                   6.   Delinquencies up in 4th quarter: Publication: Northwestern Financial Review

                        Date: Thursday, May 1 2008




                   8.   Unleashing the Power : Driving Profits through Risk-Based Mortgage Collections

                        – Delloitte Financial Services

                   9.   Loss forecasting methodologies :

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               *Corresponding Author: Anubhavi Gupta, Sr.Consultant, GENPACT
               Email address:;

               Authors have a Post graduate degree in MS Operational Research & have
               been involve in risk management & analytical solutioning for retail finance
               products. She is a certified lean consultant & has been involved on various
               process improvement projects.

               She is currently working with a client on lean six sigma initiative based out
               of Chicago, IL in a Black Belt role.

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