Forecasng cusomer behavour n a mul-servce fnancal organsaon: a profably perspecve A. Audzeyeva, Unversy of Leeds & Naonal Ausrala Group Europe, UK B. Summers, Unversy of Leeds, UK K.R. Schenk-Hoppé, Unversy of Leeds, UK CREDIT SCORING & CREDIT CONTROL XI CONFERENCE Ednburgh, Augus 2009
Movaon & conrbuon Movaon Cusomer Lfeme Value: Key busness ool for cusomer managemen Gves he same focus hroughou he dfferen decson makng areas of he organsaon (Thomas, 2000) CRM: cusomer relaonshp managemen (Zehaml e al., 200) Inegral par of lendng decsons (Olver, 993, Fshelson-Holsne, 998, Fnlay, 2009) Cusomer segmenaon for servces dfferenaon & cos opmsaon (Zehaml e al., 200) Challenges n CLV esmaon n he mulservce fnancal ndusry: Muldmensonal naure of cusomer behavour (Donkers e al., 2007) Mulple non-ndependen purchases (Kamakura e al., 99, 2003; L e al., 2005)) Cusomers can easly swch beween producs & produc provders Conrbuon Propose a novel approach o CLV predcon based on adapve segmenaon Neghbourhood-based segmens capure homogenous cusomers wh smlar characerscs & pas behavour Approach can be appled o a range of predcve asks (e.g., produc purchasng decsons and purchase volumes) Approach mplemened for a UK real bank
Leraure Emprcal evdence for mulservce fnancal ndusry: curren complex servce-level models of cusomer behavour do no offer advanage over smple models usng aggregae daa (Donkers e al., 2007) Smple models: cusomer profably s consan over me or a lnear funcon of pas profably (Berger and Nasr, 998, and Malhouse and Blaberg, 2003) Complex models: Mulvarae prob (Kamakura e al., 99 and 2003) only -perod predcon can be made purchase volumes need o be predced separaely Markov Chan Mehodology (Morrson e al., 982, and Pfefer and Carraway, 2000) depends on exsence of a small number of meanngful segmens
τ General CLV model CLV = T τ = 0 ( R τ C τ ) ( q τ ) D τ AC 0 R τ C τ AC 0 D τ q τ - predced revenue from cusomer n perod gven he/she connues relaonshp wh he company n hs perod - drec cos of servcng cusomer n perod - cos of acquson of a new cusomer - dscoun facor n perod τ - projeced probably ha cusomer may ermnae hs/her relaonshp wh a company n perod τ, τ < T τ τ (Berger and Nasr, 998, Jan and Sngh, 2002, Renarz and Kumar, 2003, & Gupa e al., 2006, among ohers)
Adapve segmenaon approach Am o oban he condonal probably dsrbuon, y ( y,, ) τ τ = y M τ = 0,, 2,..., T x ( ) s a vecor of predcve varables: x = x,, x K I can nclude any elemens of he hsorc nformaon se for a cusomer avalable a me The condonal probably dsrbuons of observng he vecor x of dependen varables gven he curren cusomer sae : p ( y + x ) ( y + 2 ) ( y + T ), p x,, p x - predcve dsrbuons Because he analycal form of he predcve dsrbuons s no known, we esmae hem emprcally usng an adapve segmenaon approach Assumpon: Cusomers wh smlar characerscs and pas behavour expeced o exhb smlar behavour n he fuure
Adapve segmenaon approach Fgure. Esmaon of he emprcal predcve dsrbuons wh 2 predcve varables Local Segmen Curren sae x of cusomer n me-perod Predcve dsrbuon of he p x dependan varable ( y + ) ( x ) 2 0 Jon predcve dsrbuon of he p x x + explanaory varables ( ) ( x ) 0 Pas cusomer daa x = x x, =,..., N x 0 ; (, ) 0 2 0
Adapve segmenaon approach Sze of he local segmen: small enough o ensure cusomer homogeney whn he local segmen suffcenly large o ensure robus forecass of fuure behavour Local segmenaon uses a smlary measure: D ( ) [ K = ( )] j j x,x 0 wk xk, xk, 0 k = 2 w k = Percenle ( x,0.975) Percenle( x,0.025) k, 0 k, 0 Weghs w k are used o normalze he explanaory varables wh dfferen measuremen scales Connuous dependen varables: he emprcal predcve dsrbuons used o esmae mean/ medan values and confdence nervals Cardnal dependen varables: a frequency of observng a cusomer wh a gven value gves as an esmae of he correspondng probably. The hreshold for a value forecas esmaed durng he model valdaon usng a ROC-analyss framework.
Mul-perod forecas Two-perod-ahead predcve dsrbuon Tau-perod-ahead ahead predcve dsrbuon: Mul-perod predcve dsrbuons esmaed emprcally: p p ( y x ) p( y 2 x x ) dx = p( y 2 x ) p( x x ) 2 =, dx ( y τ x ) = p( y τ x τ ) p( x τ x τ 2 ) p( x x ) dx τ dx x Random vecor smulaed from he one-perod predcve dsrbuon usng resamplng echnques (boosrap) or by samplng from an approxmang analycal dsrbuon (usng copulas or kernel smoohng) Usng he smulaed values from, he correspondng values of smulaed for he nex perod. The resulng par x +, y2 has jon probably dsrbuon p( y 2 x ) p( x x ). The margnalzaon over s acheved by y +2 poolng for all smulaed values of. x y 2 x + x +
Adapve segmenaon approach: Advanages over exsng mehods Works wh varous shapes of varable dsrbuon & wh dfferen correlaon srucures (no lmng assumpons mposed) Full nformaon, conaned n he varable probably dsrbuon, preserved Unlke Markov Chan & oher probablsc models usng cusomer segmens, our model adapvely seeks for homogenous cusomer segmens whou loss of nformaon The model can work wh paral nformaon &mssng varables producng a meanngful forecas for new cusomers The effec of errors & oulers n he raw company daa s mnmzed n our scalng
Opmsaon of compuaonal effcency ( x 2 ) 0 Pas cusomer daa ( x ) 0 x 0 ; (, = x x ) 0 2 0 x, =,..., N avalable n me-perod 0 Segmen sze s he same across all coarse segmens o ensure equal represenaon. Coarse segmen sze, N, chosen wh an objecve o mnmze he amoun of compuaon.
Objecves of valdaon: Model esmaon and valdaon choose a se of predcve varables evaluae he predcve performance of he model Model valdaon uses real cusomer daa of 467,789 cusomers of Naonal Ausrala Bank Europe over 2005-2008 Purpose of sudy & poenal problem: predc cusomer revenue as an oucome of cusomer behavour BUT: revenue values affeced by exernal facors even f cusomer behavour does no change over me, e.g.: sales margns change due o change n he BE base rae msmach beween he BE rae, coss of wholesale borrowng and neres raes on real fnancal producs Soluon: Focus on maxmzng he rank correlaon beween he predced and acual values Kendall s au s nsensve o any varable ransformaon whch does no change he orderng n he populaon. Model preserves he relave orderng n he dependen varable (he revenue from a cusomer) & accuraely predcs cusomers wh hgher fuure revenue versus cusomers wh less fuure revenue, even f he revenue value s affeced by exernal facors n fuure
Valdaon of one-perod-ahead forecas Acual versus predced cusomer revenue; logarhmc scale One-perod-ahead predcon
Valdaon of wo-perod-ahead forecas Acual versus predced cusomer revenue; logarhmc scale Two-perod-ahead predcon
Valdaon of one and wo-year-ahead forecas of cusomer revenue Model sascs: valdaon of one and wo-perods-ahead predcons of he revenue from ndvdual cusomers usng acual values of revenue n 2007 and 2008 correspondngly Concord an pars, Percen Dscord an pars, Percen Perods Kendall's Kendall's Somers Somers Mean Medan S. ahead τ Z Gamma D(R C) D(C R) error error Dev. One Perod 0.7 74.90 0.83 0.3 0.72 0.69 0.72 0.29 0.0 27.34 Two perods 0.62 66.06 0.78 0.7 0.64 0.6 0.64 2.59.89 35.0
Oher applcaons: predcng large jumps n revenue from a cusomer One-perod ahead forecas of bnomal varables: () ncrease n revenue above he mnmum hreshold ( jump up ), (2) decrease n revenue below he mnmum hreshold ( jump down ) and (3) change n revenue whn he hreshold ( sable ) Forecased varable Area Under Curve Accuracy Sable 0.9068 0.8488 Jump Up 0.8256 0.7566 Jump Down 0.900 0.8690 ROC curves for he one-perod-ahead predcon of cusomer behavour Sable : change n revenue whn he hreshold Jump up : ncrease n revenue above he mnmum hreshold Jump down : decrease n revenue below he mnmum hreshold 0.8 0.8 0.8 True Posve Rae 0.6 0.4 True Posve Rae 0.6 0.4 True Posve Rae 0.6 0.4 0.2 0.2 0.2 0 0 0.2 0.4 0.6 0.8 False Posve Rae 0 0 0.2 0.4 0.6 0.8 False Posve Rae 0 0 0.2 0.4 0.6 0.8 False Posve Rae
Concluson Propose an adapve segmenaon approach o he modellng of lfeme value for ndvdual cusomers n a mulservce fnancal organsaon Man Advanages: Model adapvely seeks o locae homogenous cusomer segmens whou loss of nformaon abou varable dsrbuons compromsng he accuracy of predcon Approach does no requre assumpons abou he shape of he varables dsrbuons or he correlaon srucure beween hem; The model can work wh paral nformaon and mssng values Model s valdaed and mplemened for a UK real bank Gves robus predcons usng a small number of predcve varables he revenues from ndvdual cusomers sgnfcan changes n revenues Valdaon usng 2008 daa, concdng wh he crss year n bankng, confrmed he robusness of our relave rankng approach Oher poenal applcaons: predcon of oher cusomer-relaed characerscs & behavour Provdes a powerful ool n he developmen of alored cusomer managemen sraeges (e.g., cusomer acquson and reenon)