MODELLING THE PROFITABILITY OF CREDIT CARDS FOR DIFFERENT TYPES OF BEHAVIOUR WITH PANEL DATA. Professor Jonathan Crook, Denys Osipenko

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1 MODELLING THE PROFITABILITY OF CREDIT CARDS FOR DIFFERENT TYPES OF BEHAVIOUR WITH PANEL DATA Professor Jonathan Crook, Denys Osipenko

2 Content 2 Credit card dual nature System of statuses Multinomial logistic regression Macroeconomics and cycles Panel data and regression Utilization rate modelling interst income Profitability modelling non-interest income Modelling examples Exposure at default prediction Resume and client behaviour

3 Credit card dual nature 3 Credit Card has dual nature: Payment tool and Loan Payment tool Credit card Convenie nt loan What is the confident definition for revolver? Positive outstanding balance during 3 months, 6 months,? If only once paid off full amount? Outstanding balance is stochastic value in the range from 0 to Limit. Clients is split up two group: revolvers and transactors Revolver user, who carry a positive credit card balance and not pay off the balance in full each month roll over Transactor user, who pay in full on or before the due date of the interest-free credit period Competent user do not incur any interest payments or finance charges Credit cards dual nature and profitability were investigated by: Crook, Hamilton, Thomas (992) Banasik, Crook, Thomas (200) Ma, Crook, Ansell (200) So, Thomas (2008) Cheu, Loke (200) Tan, Steven, Yen (20)

4 Logistic regression means the binary target. Multinomial regression uses more that two values target. Credit Cards Statuses 4 Inactive The main task to estimate the probability of transition from status to status on the client level. Default Delinquent Revolver (standard) Transactor Transition matrix (classic approach) is calculated on the portfolio/pool level The problem the number of statuses which account can transfer to is more than two (for example, revolver can be transactor, delinquent, stay revolver, or inactive)

5 Multinomial logistic regression 5 We need to predict the probability of transition to the certain state (0,, 2, ) Multinomial logistic regression is a regression model which generalizes logistic regression by allowing more than two discrete outcomes This kind of the models can show weaker results than ordinal logistic regression, but better than tree of conditional logistic Cumulative probability of the transition for two different statuses

6 Map of statuses 6 Account status Definition Risk assessme nt Revenue assessment Note closed Account is closed or inactive more than 6 months No No Exclude from analysis inactive transact or OB (-6M) = 0 and Turnover (-6M) = 0 OB (-6M) = 0 and Turnover (-6M) <> 0 No No R No OB TR PR TR No predicted revenue and risk (avg interchange rate + fees rate)*tr current OB > 0 and DPD = 0 Behaviour al Score Limit*IR*PR + Beh. and Revenue Rate Scorecards for B0 R TR Current delinque nt OB > 0 and DPD > 0 and DPD <=90 Behaviour al Score Delinq. R TR + Penalty? Beh. and Revenue Rate Scorecards for B-3 defaulte d OB > 0 and DPD > 90 LGD - Recovery is not revenue

7 Credit cards income sources 7 Status Interest Fees/Interchang e Penalty Non active Transactor -/+ + - Current (revolver) Delinquent Defaulted - - +/- Different income sources can be applied on different life-time stages Delinquent customer can bring an income, but not defaulted client

8 Credit Limit = 3000 Credit line Income Prediction 8 For interest income Utilization = Balance / Credit Limit IR_Income = Utilization Rate x Limit x IR For non-interest income (POS, ATM, Interchange etc.) POS Income = TR Debit_POS x POS_fees_rate Interchange = TR Debit_POS x Interchange_fees_rate Cash Withdrawal Income = TR_Debit_ATM x ATM_fees_rate 50% X IR = IR Income Interest Income from Balance: 500 UAH X 36% /2 = 45 UAH Monthly transactions: 000 UAH POS X 2% = 20 UAH 500 UAH ATM X 2,5% = 2,5 UAH Total Non_Interest Income = 32,5 UAH Total Income = 45+32,5 = 77,5 UAH

9 Rates Modelling 9 First approach logistic regression with binary transformation p i T logit pi ln w w x w x wp x p w x p i where p i is the probability of particular outcome; w 0...w p are regression weights; x...x p are characteristics. For UT rate is the share of balance - the weighted logistic regression with binarization. Parameters Outcome Binarization Parameters Outcome Weight X 0,75 X 0,75 X 0 0,25 Second approach Linear regression with Beta-transformation Distribution density function given via Gamma function It s possible to build a wide variety of distribution shapes

10 Macroeconomics and cycles 0 Unemployment Rate 0.0% 9.0% 8.0% 7.0% 6.0% 5.0% 2008/ /03 20/ % 40.0% 30.0% 20.0% 0.0% UnemplRate ln Unempl_mom 4.0% 3.0% 2.0%.0% 0.0% -0.0% -20.0% ln Unempl_qoq ln Unempl_yoy 0.0% -30.0% Macroeconomic indicators contain cycles and fluctuations. They have an impact on client behaviour as systematic factor

11 ln x Utilization rate, % Correlation of macro- and micro indicators 0.6 The most correlated Macro Indicators and UT rate Unemployment_lny oy UAH- EURRate_lnyoy CPIYear_lnyoy avgut avgut lag More or less stable correlation can be observed between micro characteristics (like utilization rate) and macro indicators. The correlation between deltas (changes) of indicators is more stable. 0

12 Panel data and panel 2 regression Types of the data in econometrics: Cross-sectional by economic items at the same point of time (without any relation to the time) Time series observation of the economic values ranked in time In practice often this two dimensions is joined: Independent join (not ranked in time) pooled data Data slices Balance Jan, Balance Feb as Balance row, Balance row 2 Panel data two-dimension array (cross-sectional data ranked as time series) Ranked Data slices - Balance Jan, Balance Feb as Balance t=, Balance t=2

13 Panel data advantages 3 Higher number of observations results increase in the levels of freedom, gives more efficient estimations Heterogeneity of the sample objects is under control Testing of the effects which is impossible to identify separately in cross-sections and time series Decrease in multicollinearity It s possible to build more complicated behavioural models and decrease the influence of the missing values and incorrectly measured observations

14 Panel linear regression 4 y uit it x T it u i t it it i index individual, t index time, β vector of regression coefficients, x it T transposed vector of observations independent characteristics. μ i, λ i non-observed individual and time effects, υ it residual idiosyncratic components. y it X it it Pooled model α и β intercept and slope is independent from observation and time Х it - vector of regressors (predictors) Approach with time slices is widely applied as industry standard, for instance, to create development and validation samples from the data set with not enough observation at the point in time or to take into account different seasons. Assumption: dependence between factors is stable in time correlation between observations is not taking into account But in practice it is not true!

15 Panel linear regression 5 Fixed effect model y it it ui X it vit i - individual intercept (specific effect) Intercept is varying across groups and/or times Error variance is constant Random effect model y u X i v it it u i v it - Random effect Intercept is constant Error variance is varying across groups and/or times

16 Utilization Rate Modelling 6 UT Regression equation: utilization rate depends from behavioural, application, macroeconomic characteristics, and also from utilization rate with time lag it UT i UT T T t 2 it2 4 i( tl) b bi, t a ai m, t l UT K k B L l A M m M φ, α, β, γ regression coefficients (slopes) B vector of behavioural factors (for example, average balance to maximum balance, maximum debit turnover to average outstanding balance or limit, maximum number days in delinquency, etc for some periods of time) A vector of application factors - client s demographic, financial and product characteristics like age, education, position, income, property, interest rate, etc. M vector of macroeconomic factors (GDP, FX, Unemployment rate changes, etc.) UT utilization rate

17 Interest Income modelling,, ) ( t m M m ai L l a K k t bi b T l l t i T l it M A B UT T UT T Average utilization rate for the period of T months Income = Avg UT() x IR ()x Limit() Average Income (-T) = Avg UT(-T) x IR x Average Limit (- T) Average Income for period of T months depends of average utilization rate, average credit limit and interest rate

18 Non-interest income modelling 8,, ) ( ln m t M m m ai L l a K k t ki k T l l t i M A B UT T P P st stage estimation of the probability that the client will use credit cards for POS/ATM transaction during the forecast period 2 nd stage income amount for the period,, ) ( t m M m m ai L l a K k t bi k T n n t i it M A B UT T POS φ, α, β, γ regression coefficients (slopes) B vector of behavioural factors (for example, average balance to maximum balance, maximum debit turnover to average outstanding balance or limit, maximum number days in delinquency, etc for some periods of time) A vector of application factors - client s demographic, financial and product characteristics like age, education, position, income, property, interest rate etc) M vector of macroeconomic factors (GDP, FX, Unemployment rate changes, etc)

19 Utilization rate and Income distributions 6% 4% 2% 0% 8% Utilization Rate Density Distribution for active accounts Utilization rate density may have an U-shape distribution, can be approximated, as option, by beta-distribution 6% 4% 2% 0% POS income (interchange fees) may have exponential distribution It s necessary to filter a lot of insufficient amounts and enormous outliers 35.00% 30.00% 25.00% 20.00% 5.00% 0.00% 5.00% 0.00% Average POS income amount Итог

20 Utilization rate by characteristics Ut Rate - Age Ut Rate - Education 70% 60% 50% 40% 30% 20% 0% 0% Ut Rate 70% 60% 50% 40% 30% 20% 0% 0% Ut Rate Ut Rate - Industry Ut Rate - Position 70% 60% 50% 40% 30% 20% 0% 0% Ut Rate 70% 60% 50% 40% 30% 20% 0% 0% Ut Rate

21 2 Example of utilization rate model coefficients estimation Parameter Estimates Pooled Random Effect Variable Estimate Standard Standard t Value Pr > t Estimate Error Error t Value Pr > t Intercept < <.000 UT to AvgUT < <.000 OBalance Avg To MaxOBalance < <.000 Tr_max_debit3_To_Limit < <.000 Age < <.000 Edu_ High Edu_ Secondary < <.000 Edu_ Special < <.000 Edu_ Two Degree/PhD < <.000 Marital_ Civil < <.000 Marital_ Divorced < <.000 Marital_ Married Marital_ Single < <.000 Marital_ Widow < <.000 position_ Employee position_ Manager < Position_ Other < <.000 position_ Technical < <.000 position_ Top < <.000 UAH_EUR Rate_ln yoy_lag3m < <.000 Unempl_ln yoy_lag3m < FDI_ln yoy_lag3m < <.000

22 Example of linear regression avg POS amount Variable Standard Estimate Error t Value Pr > t Intercept Limit <.000 customer_income <.000 other_income <.000 spouse_income <.000 UnemplRate_ Unempl_lnyoy_ UAH_EURRate_lnyoy_ b_avg_ut <.000 b_avg_ut b_avgob3_to_maxob b_trmax_deb3_to_limit <.000 b_trmax_deb3_to_avgob <.000 b_travg_deb3_to_avgob <.000 b_trmax_deb6_to_limit <.000 b_trmax_deb6_to_avgob b_travg_deb6_to_avgob <.000 b_trsum_deb6_to_trsum_crd <.000 b_deltaut3to b_ut_to_avgut <.000 b_avgnumdeb b_avgnumdeb <.000 b_deltanumdeb3to b_max_dpd <.000 b_max_dpd b_delbucket <.000 Variable Estimate Standard Error t Value Pr > t Edu_Secondary <.000 Edu_Special <.000 Edu_TwoDegree <.000 Marital_Civ Marital_Div Marital_Mar 0... Marital_Sin Marital_Wid position_empl 0... position_man <.000 position_oth position_tech position_top <.000 sec_agricult sec_constr sec_energy sec_fin <.000 sec_gov sec_industry sec_manufact sec_mining sec_service sec_trade SSE MSE R-Square 0.305

23 23 Example of linear regression POS amount Estimated function: Avg POS transaction amount

24 Profitability ratios Income part of the ratio: Interest Income = IR x Limit x Utilization Rate Non-Interest Income = POS Income + ATM Income Two approaches of profitability calculation denominator: Average Outstanding Balance real profitability Credit Limit profitability on allocated sources Profitability = (Interest Income + Non-Interest Income) / Average Outstanding Balance Or Profitability = (Interest Income + Non-Interest Income) / Credit Limit

25 Credit Limit = 3000 Exposure at Default estimation 25 Expected Loss EL = PD x LGD x EAD +40% +200 at Default Point Exposure at Default for credit card: EaD L UR L UR CF 50% CF (conversion factor) the percent (share) of the additional usage of remaining credit line at the default point. The credit conversion factor (CCF) converts the amount of a free credit line and other off-balance-sheet transactions (with the exception of derivatives) to an EAD (exposure at default) amount. L credit limit Some investigations of EaD - Jacobs (2008), Qi (2009) 500 CF = 200/500 = 80%

26 26 Utilization rate and Profitability estimation in Credit Limit Strategy Segment Utilization Profitability 0.0%.0% 2.0% 3.0% 4.0% 5.0% 6.0% 7.0% 8.0% 9.0% 0.0% 0.2% 3% 5% 5% 0% 0% 0% 0% 0% -5% -5% -5% -5% 2 6.3% 5% 0% 5% 5% 5% 5% 0% 0% 0% 0% -5% -5% 3 8.0% 7% 0% 0% 0% 0% 5% 5% 5% 5% 0% 0% 0% 4 9.5% 9% 5% 5% 0% 0% 0% 0% 5% 5% 5% 5% 0% % % 20% 20% 5% 5% 5% 0% 0% 0% 0% 5% 5% % 2% 20% 20% 20% 20% 5% 5% 5% 0% 0% 0% 0% % 3% 25% 20% 20% 20% 20% 5% 5% 5% 0% 0% 0% % 4% 25% 25% 20% 20% 20% 20% 5% 5% 5% 0% 0% % 6% 30% 30% 30% 25% 25% 25% 20% 20% 20% 5% 5% % 8% 35% 35% 35% 30% 30% 25% 25% 25% 20% 20% 20% 78.7% 9% 40% 40% 35% 35% 30% 30% 30% 25% 25% 25% 20% % 2% 45% 45% 40% 40% 35% 35% 35% 30% 30% 25% 25% 3 9.9% 24% 55% 50% 50% 45% 45% 45% 40% 40% 35% 35% 30% % 25% 60% 55% 55% 50% 50% 45% 45% 45% 40% 40% 35% Credit Limit changes depends on the profitability and probability of default segment. Utilization rate illustrates the fact that credit line profitability doesn t depend on the utilization rate pro rata. PD

27 Resume Client Behaviour 27 Transactor Revolver Competent Reveolver Interest Income Low/ No High No Non-Interest Rate High Low Low Risk Level Low Moderate Moderate/ High Competent Revolver the worst client from the profitability point of view (but not the sales volume point of view) It s recommended to build strategies in the Card business with the risk revenue principle to maximize the profitability. Areas of application: Limit management segmentation by revolver/transactor risk limitation and usage motivation Pricing not only risk-based, but use motivation Marketing differentiate target groups Use of panel data helps to avoid the impact of time heterogeneity on model results

28 Thank you for your attention! 28 The Business School The University of Edinburgh Professor Jonathan Crook Denis Osipenko, Doctoral Student

THE COMPARATIVE ANALYSIS OF PREDICTIVE MODELS FOR CREDIT LIMIT UTILIZATION RATE

THE COMPARATIVE ANALYSIS OF PREDICTIVE MODELS FOR CREDIT LIMIT UTILIZATION RATE PROFESSOR JONATHAN CROOK DENYS OSIPENKO CRCCXIV, 26-28 August 215, Edinburgh Content 2 Objectives The utilization rate definitions