# Loyalty Rewards and Gift Card Programs: Basic Actuarial Estimation Techniques

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4 be used would be dependent on the accounting standads unde which the pogam opeates. In pactice, thee is a geat divesity of names fo these things but fo claity and simplicity we will standadize them in this pape.. Total Cost in Rewad Pogams In its most basic fom, a ewad pogam s total cost can geneally be boken out into thee components: a cuency component, a edemption ate component, and a cost component. Points x Redemption Rate x Cost pe Point = Total Cost (.) This geneic equation will be used in a vaiety of applications. Geneally the fist item, the cuency, points, o miles, is a known value. In fact it is typically the only numbe known at the time that an analysis is pefomed. The edemption ate epesents the pecentage of points which ae expected to be utilized o edeemed by the pogam membes. The cost pe point epesents the economic value of each point given that such point will be edeemed. This fomula can be used in balance sheet contexts whee an analyst is inteested in valuing eithe the accued costs o the associated defeed evenue of a pogam. The fomula can also be used in income statement contexts whee the analyst is inteested in valuing eithe the incemental cost of an issued awad o the incemental defeed evenue at point of sale. When consideing the fomula above, it is impotant to maintain a common basis fo all thee components. Fo example, one should not apply a edemption ate expessed as a pecentage of issued points to an outstanding point balance. In the subsequent sections we will discuss the edemption ate and cost pe point components of the model in futhe detail. Casualty Actuaial Society E-Foum, Summe 0 4

5 3. REDEMPTION RATE ESTIMATION APPROACHES One of the key components of nealy evey loyalty ewad o gift cad pogam is the edemption ate. The edemption ate is also fequently the single most challenging component to estimate. Developing a functional and pedictive edemption ate model can be an execise equiing significant time and effot. In many instances the degee of difficulty can be geatly inceased by data quality and availability issues o, on the opposite end of the spectum, ovewhelmingly lage quantities of data that ae difficult to manipulate and oganize. Redemption ates ae geneally expessed as a function of one of two diffeent bases; as the pecentage of the points that ae outstanding (points that have neithe been edeemed no fofeited) as of the valuation date o as a pecentage of the cumulative amount of points issued to date to pogam membes. As such it is impotant to keep in mind the basis on which edemption ates ae expessed. Thee ae specific qualities by which evey edemption ate must abide. Redemption ates, when expessed as a pecentage of cumulative points issued, must always be bounded by a minimum of zeo and by a maximum of unity. This can be intepeted to mean that thee can neve be moe point edemptions in the futue than the numbe of points issued to date o outstanding as of the evaluation date, and that thee can neve be negative edemptions, in aggegate. A situation whee histoical edemption ates ae below zeo o geate than unity would likely be due to data anomalies o exceptional situations elated to a pogam s T&C that need to be bette undestood and coected befoe moving fowad with the pojection of ultimate edemption ates. Beakage is fequently a facto of inteest. Beakage epesents the potion of points issued (o outstanding) that will neve be edeemed. Points that ae boken will eithe fofeit out of the pogam o sit domant until the pogam itself ceases to exist. The exact fate of the boken points is detemined by the T&C of the pogam. The beakage ate is, by definition, the complement of the edemption ate. Theefoe, unity less the edemption ate epesents the beakage ate. Because of the simple elationship between edemption and beakage ates, we will focus on the edemption ate heeafte with the knowledge that we can eadily convet the edemption ate into the beakage ate as needed. It should be noted Casualty Actuaial Society E-Foum, Summe 0 5

6 that while out of the scope of this pape, an analyst may be equied to conside applicability of elevant laws elating to escheat popety and how these laws may potentially affect the pope teatment of beakage. The appoaches fo estimating an ultimate edemption ate fo loyalty ewad and gift cad pogams illustated in this pape povide an estimate of the ultimate edemption ate expessed as a pecentage of cumulative points issued as of the valuation date of the analysis. This edemption ate on issued points can be conveted to a edemption ate on outstanding points, if needed. In addition, it should be noted that thee ae altenative appoaches which may be moe appopiate given a pogam s stuctue, data availability, o othe easons that could be compaably easonable to the methods contained in this pape. 3. Point Issuance Peiod Method The Point Issuance Peiod method is built on the pemise that points can be tacked fom the peiod in which they wee eaned by membes until thei ultimate edemption o domancy/fofeitue, and that the lifecycle of a point fom olde issuance peiods can be applied to points issued in subsequent peiods. While it can be exceedingly difficult fo a pogam s sponso to tack individual points and to come up with meaningful pedictions of how, o even if, the points will be used, gouping points by issuance peiods can make the undelying pocess statistically moe pactical and povide accuate aggegate estimates. Constucting Point Redemption Tiangles The fist step to this method consists of constucting histoical point edemption tiangles. Redeemed points ae gouped by issuance peiod, and cumulative point edemptions associated with that issuance peiod (at multiple evenly spaced evaluations) ae obtained in ode to effectively tack how histoical edemptions ae elated to time since the oiginal issuance peiod. Constucting tiangles in this manne is analogous to constucting a cumulative loss development tiangle, but instead of using an accident peiod we use an issuance peiod. t In the tiangle below, R i epesents the cumulative numbe of edeemed points, out of the total points issued in issuance peiod i at time t. Casualty Actuaial Society E-Foum, Summe 0 6

7 Issuance Evaluation Age Peiod 3 4 0X 3 R 0 X R 0 X R 0 X R 0X 3 R 0 X R 0 X R 0 X 0X3 R 0 X 3 R 0 X 3 0X4 R 0 X X We divide the cumulative point edemptions fo each issuance peiod by the espective numbe of points that wee issued in that peiod to geneate a cumulative edemption ate tiangle. In the tiangle shown below, t i epesents the cumulative numbe of edeemed points issued in peiod i at time t divided by the total numbe of points issued in that issuance peiod. It should be noted that the issued points in each issuance peiod ae effectively fozen so that the denominato acoss each ow is constant. Issuance Evaluation Age Peiod 3 4 0X 3 0 X 0 X 0 X 0X 3 0 X 0 X 0 X 0X3 0 X 3 0 X 3 0X4 0 X X Thee ae two pimay benefits to immediately conveting the edeemed points into edemption ates. Fist, this emoves the effect of changing volumes of issued points between issuance peiods and it also nomalizes the edemption activities between peiods making them moe easily compaable. Second, this appoach focuses diectly on edemption ates fom the outset of the analysis, which allows the analyst to immediately veify the bounday conditions so that edemption ates can neithe exceed unity (i.e., 00%) no be below 0%. Casualty Actuaial Society E-Foum, Summe 0 7

8 Estimating Ultimate Redemption Rates Using the edemption ate tiangle that was developed in the pevious step, it should be immediately clea that one can apply standad actuaial pojection methods (such as the chain ladde appoach) to obtain estimates of the ultimate edemption ates by issuance peiod. Thee is geneally no significant diffeence in methodology between estimating ultimate edemption ates on issued points and estimating ultimate losses in an insuance application, though thee can be diffeent consideations that an analyst may need to contemplate (e.g., loyalty pogams may equie consideation of pomotions and expansion of enollment into new classes of membes instead of insuance consideations of claim handling stability and changes in undelying mix of coveages). Standad actuaial pojection techniques on tiangula data ae coveed in many othe souces of actuaial liteatue and as such we will not expand on that topic in this pape. At the end of the analysis one should have a completed tiangle as is shown below. Issuance Evaluation Age Peiod 3 4 Ult 0X 3 4 ult 0 X 0 X 0 X 0 X 0 X 0X 3 4 ult 0 X 0 X 0 X 0 X 0 X 0X3 3 4 ult 0 X 3 0 X 3 0 X 3 0 X 3 0 X 0X4 3 4 ult 0 X 4 0 X 4 0 X 4 0 X 4 0 X 3 4 The ultimate edemption ates by issuance yea can be used as is fo each individual issuance yea o, altenatively, a single volume weighted edemption ate on all issued points can be calculated if the analyst is focused on the oveall ultimate edemption ate ( URR ) fo all points issued by a loyalty ewad o gift cad pogam. We note that this appoach can be successfully applied to loyalty ewad o gift cad pogams that include a point expiation policy in thei T&C. In cases whee issued points only emain valid fo a fixed peiod afte issuance, an analyst can quickly obtain the actual URR fo each issuance peiod. Such an expiation policy can significantly facilitate the URR estimation fo moe ecent issuance peiods since the ultimate peiod is defined by the pogam sponso. Casualty Actuaial Society E-Foum, Summe 0 8

9 Fo pogams without a point expiation policy, additional wok may be needed to obtain an estimated URR. Fo example, in many instances thee will be no histoical infomation available upon which to base futue expected point edemption activities beyond the most ecent evaluation date. Often, this is simply a esult of a ewad pogam not being sufficiently matue to have eached its point edemption ultimate in any histoical issuance peiod as of the evaluation date. Such an issue is compaable to detemining a tail facto in conventional loss development tiangles. In such instances an analyst may find that fitting a cuve that exhibits decay chaacteistics is the most appopiate method to apply. Obviously, multiple such cuves can be used to povide multiple pojections. In such instances, it is also ecommended that the analyst additionally apply a testing o anking appoach in ode to detemine which cuve might povide the best fit to histoical data. Fo a full numeical example of this method please efe to Appendix Aggegate Membe Join Peiod Method The Aggegate Membe Join Peiod method assumes that pogam membes cumulative edemption activity at any given time is elated to the time elapsed since the membes have joined the pogam. Membes ae typically combined into join peiod cohots so that points eaning o edemption activity ove the lifetime of the cohot can be elated to the age o matuity of the membes included in the cohot. Activities can be taced fom the date that membes fist enoll into the ewad pogam (join peiod) until thei ultimate lapse (i.e., fofeitue), depatue, o domancy. We will geneically efe to this as domancy, though the pogam-specific T&C will dictate if points actually do get fofeited out of membes accounts o not. In this method, the tiangle constuction includes membe join peiod cohot activity fo both domant and active membes. As a esult, any obseved changes in cumulative edemption activity between evaluation ages ae only attibutable to membes who emained active between evaluation peiods. Casualty Actuaial Society E-Foum, Summe 0 9

10 Constucting Point Redemption and Points Issued Tiangles The fist step to the Membe Join Peiod method consists of constucting histoical point edemption tiangles. Redemption tiangles in this method use cumulative membe point edemptions at vaious matuities. Multiple evenly spaced evaluations of the cumulative edeemed points ae obtained so that one can effectively tack how edemptions ae elated to time passed since the oiginal membes join peiod. This tiangle constuction, simila to the Point Issue Peiod appoach descibed ealie, is also analogous to constucting a cumulative loss development tiangle, but instead of using an accident peiod appoach we use a join peiod appoach. t In the tiangle below, R j epesents the cumulative numbe of edeemed points, out of the cumulative points issued to membes joining in peiod j, at time t afte the join date. Join Evaluation Age Peiod 3 4 0X 3 R 0 X R 0 X R 0 X R 0X 3 R 0 X R 0 X R 0 X 0X3 R 0 X 3 R 0 X 3 0X4 R 0 X X In the tiangle below, I t j epesents the cumulative issued points associated with membes who joined in peiod j, at time t afte the join date. Join Evaluation Age Peiod 3 4 0X 3 I 0 X I 0 X I 0 X I 0X 3 I 0 X I 0 X I 0 X 0X3 I 0 X 3 I 0 X 3 0X4 I 0 X X By dividing the cumulative edeemed point tiangle by the cumulative issued point tiangle we obtain the tiangle shown below, which epesents the cumulative edemption Casualty Actuaial Society E-Foum, Summe 0 0

11 ates ( ) fo membes, by join peiod. The cumulative edemption ates ae expessed as a t j pecentage of cumulative issued points. Unlike the Point Issuance Peiod method whee the points included in the denominato ae constant, the points included in this denominato continue to gow at each evaluation peiod, as long as at least one membe included in a join peiod cohot continues to be active in the pogam and eans moe points. Join Evaluation Age Peiod 3 4 0X 3 0 X 0 X 0 X 0X 3 0 X 0 X 0 X 0X3 0 X 3 0 X 3 0X4 0 X X Given this tiangle, an actuay can apply standad actuaial pojection methods to estimate the patten of futue estimated cumulative edemption ates at ultimate fo each join peiod. Pojected values coespond to the aeas within the boxed egion in the tiangle below. Join Evaluation Age Peiod 3 4 0X 3 0 X 0 X 0 X 0X 3 0 X 0 X 0 X 0X3 3 0 X 3 0 X 3 0 X 3 0X4 3 0 X 4 0 X 4 0 X X 4 0 X 4 0 X X 4 Teminal Redemption Peiod Consideations The Membe Join Peiod Method does not mathematically esolve itself to povide a clea cut-off whee the analyst can cease development. In fact, because of the cuve-like natue of the undelying cumulative data, mechanical development could pepetuate indefinitely with this method wee an analyst to poject out to infinity. Theefoe, it is necessay to establish a teminal peiod (o matuity) out to which the pojection should be pefomed. In geneal, thee is no eason that the teminal peiod used cannot vay by join peiod. Casualty Actuaial Society E-Foum, Summe 0

12 An actuaial analyst should conside multiple factos befoe establishing a teminal edemption peiod fo the edemption ate pojection. Geneally, consideations include, but ae not limited to: Cuent pogam Tems & Conditions Expected futue changes in pogam Tems and Conditions Membe, o points, domancy pattens and tends Relative contibution of point activities associated with membes at each espective expected domancy peiod Additionally, an actuay should discuss the issue with the pogam sponso s management in ode to ensue a thoough undestanding of the pogam befoe implementing a specific matuity at which to end development. Lastly, it should be mentioned that in some instances, an analyst may want to avoid pojecting out to the estimated time of domancy fo the last active membe(s) in a join yea in the Membe Join Peiod method (i.e., the time at which all membes ae domant). The eason is that, wee one to do this, the edemption ate povided by the model could oveestimate the tue edemption ate since that estimated time would implicitly account fo points which would not yet have been eaned as of the time of the evaluation. This would be inconsistent with the natue of establishing liability estimates as of a detemined evaluation date fo the points outstanding as of that date. Fo a full numeical example of the Membe Join Peiod appoach please efe to Appendix Point Inventoy Method and Choice of Redemption Estimation Method It would be natual fo individuals to ty to daw compaisons between conventional inventoy systems and loyalty pogams. While such constuctions ae helpful in placing loyalty pogam opeations into a well established and undestood famewok of conventional inventoy systems, thee exists a notable diffeence between conventional inventoy and a loyalty pogam inventoy system. The pimay eason that the compaison is not pefect is due to the fact that tangible inventoy typically has a value that is geneally Casualty Actuaial Society E-Foum, Summe 0

13 quantifiable via actual tansactional evidence at the time of acquisition o manufactue (i.e., the cost of puchasing o poducing an item included in the inventoy is known) wheeas the value of an issued and unedeemed point in a loyalty ewad pogam will not actually have a known cost until the date that that point is actually edeemed (if eve) sometime in the futue. Nevetheless, constucting an inventoy system that woks fo both financial epoting puposes and as a tool fo the analyst estimating the associated liability can still be a vey useful endeavo. Basic Oveview of Inventoy Systems Inventoy systems in loyalty pogams have simila stuctues to conventional inventoy systems. Below is a bief summay of the types. - Fist In, Fist Out: In this method, the oldest points owned by a membe ae the fist to get withdawn. - Last In, Fist Out: In this method, the newest points owned by a membe ae the fist to get withdawn. 3- Aveage Weighted Cost Method (a.k.a. Piggy Bank Method): In this method, the time at which a point is issued is ignoed and points go in and out of membes accounts iespective of when they wee issued (eithe because these dates ae intentionally disegaded o due to actual database constaints making them unavailable). As such, it is not possible to identify the exact issue time of any specific point and theefoe, it is neithe possible to identify the time of issuance fo any point that was edeemed o fofeited. In essence, evey point is completely impossible to distinguish fom evey othe point. Nevetheless, the aveage futue cost and aveage time of edemption can still be detemined. Geneally such a point inventoy system is constucted specifically to focus on membe point balances at any given time athe than to focus on the seies of tansactions that esult in a given balance. Inventoy Systems and Redemption Rate Estimation While thee is no specific ule as to the best edemption ate appoach to be used fo each inventoy system, o even which inventoy system should o should not be used, we believe that some methods moe natually accommodate the diffeent inventoy systems and make Casualty Actuaial Society E-Foum, Summe 0 3

14 analyses moe tactable and moe easily explained. Fo example, the Point Issuance Peiod appoach geneally woks well unde a FIFO system. Howeve, the eviewing analyst may fequently be equied to conside issues which fall outside the scope of this pape befoe constucting o ecommending any specific inventoy system fo a given pogam. 3.4 Undestanding Redemption Rate Bases and Thei Application As noted peviously, edemption ates can be expessed in tems of eithe pecentage of outstanding points o pecentage of issued points. Both measuements ae potentially of inteest to an actuay and to a pogam sponso s management team. Up until this point, we have focused on estimating edemption ates stated on a points issued basis. Since thee is a quantifiable elationship between the two bases, one can geneally convet between the two as needed. Typically, edemption ates expessed as pecentage of issued points ae utilized in an income statement context, eithe fo defeed evenue o expense ecognition calculations as they occu though the accounting peiod. Convesely, edemption ates expessed as a pecentage of outstanding points ae typically used in a Balance Sheet context, eithe fo detemining unpaid liabilities o in estimating cumulative defeed evenue at the financial epoting date. Conveting Redemption Rate on Issued Points to Redemption Rate on Outstanding Points Fo the Point Issue Peiod method, the total edemption ate on outstanding points can be detemined using the following equation: OS, T i Ult T T I R I R / i i i i i (3.4.) The above equation can be intepeted as edemption ate on outstanding points fo issue peiod i is the poduct of the total ultimate edemption ate on issued points fo issue peiod i and the cumulative issued points less those points that have aleady been edeemed as of the evaluation date. This is then divided by the total outstanding points as of the evaluation date, which is itself equal to the total issued points less the total edeemed points. T epesents the evaluation date. Casualty Actuaial Society E-Foum, Summe 0 4

17 concept of "fai value" of a point to customes. This can be significantly diffeent fom the value that a pogam sponso believes to be easonable to use when estimating its outstanding liability, unde cuent US GAAP accounting standads. Since the objective of this pape is not to take a "deep dive" into the accounting wold, we will not discuss this issue any futhe. Howeve, an analyst should conside this issue and seek appopiate guidance when detemining the value of a point. Any fowad looking estimation of the potential cost of a point o of the value of a point equies a solid undestanding of the past, a thoough undestanding of expected futue changes, and a deep knowledge of the T&C of the pogam. The value of a point at time of issuance is a function of the value that the point will have at the time that it will actually be edeemed. In instances whee the value is constant ove time thee is no need to estimate that value (so long as the value is known today). When the value vaies, howeve, the value of a point at time of issuance is not likely to be the same as when that point is going to be edeemed. Unde these conditions, we can build a famewok that accommodates many potential scenaios of vaying values o costs. The basic pupose of the appoaches outlined in this pape is to detemine the expected cost o value of a point at the time of issuance in ode to include this vaiable in the cuent liability estimate. 4. Effectively Constant Cost/Value Pe Point Model Single Redemption Option This is the tivial example whee the value to the membe o cost to the company emains constant, o at least effectively constant, ove time. While, in this context, constant is elatively self-explanatoy, effectively constant deseves moe explanation. When we efe to effectively constant, we efe to the fact that even though the cost o value of the ewad will change ove time, it is not expected to change between the issuance of the ewad pomise (i.e., the points) and the expected edemption of the points in etun fo that ewad. In such instances the value o cost of the pomised deliveable goods today, is the best indicato of the futue cost o value. Casualty Actuaial Society E-Foum, Summe 0 7

18 4. Vaying Cost/Value Pe Point Model Single Redemption Option In many instances, the cost o value of a ewad could vay ove time in a manne that is easonably estimable. Examples of such situations ae plane tickets o hotel oom ewads, both of which ae impacted by elatively pedictable seasonal changes as well as geneal inflationay pessues. To incopoate changes in cost o value of points ove time into a pedictive famewok we can ceate a simple model. The model equies the following assumptions: ) A edemption patten, whee t is the pecentage of total point edemptions n t occuing in peiod t, and whee. 0. t ) An estimation of the costs o values that ovelap with the point edemption patten, t whee we define c as the cost o value of points edeemed at time t. With these two items an analyst can estimate the cuent aveage cost pe point as: 4.3 Multiple Redemption Options n t t c (4..) t This appoach essentially adds an exta level of complexity to the peceding method. This method includes a thid component, i.e., the utilization. This is stated in tems of the elative pecentages of all points that ae expected to be edeemed on each edemption option, in each futue peiod. This component eflects the fact that most ewads pogams offe multiple edemption options to thei membes. The objective is to captue the mix of futue point edemptions acoss a basket of goods that is available to membes. Once the utilization component has been defined, an analyst can apply this component to expected futue cost o value of each available awad type in each futue peiod to obtain the cuent weighted aveage cost pe point edeemed in each pospective peiod. In this way, the analyst can combine the estimated mix of edemptions with the espective costs associated at each expected time of edemption to obtain the total aveage cost o value pe point edeemed in the futue. Fo example, hotel pogams often allow thei membes to use thei eaned points to edeem fo hotels, ailine tickets and othe mechandise. Ailine pogams fequently allow Casualty Actuaial Society E-Foum, Summe 0 8

19 thei membes to edeem fo fee flights and miscellaneous mechandise. In many instances, the cost o value of the multiple edemption options may vay significantly when viewed in a by-point basis. While membes usually decide how to use thei points based on thei individual needs, that decision has a diect impact on the costs incued by a loyalty pogam sponso. Some ewad options can be significantly moe costly to a pogam than othes and theefoe it is cucial fo any pogam to have a good undestanding of its customes expected edemption behavio. The model equies the following assumptions; ) A edemption patten, whee t is defined as the pecentage of total point n t edemptions occuing in peiod t, and whee. 0. ) Estimation of costs o values fo each edemption options that ovelap with the point edemption patten, defined c t q as the cost o value of each edemption options at time t fo edemption option q. 3) Utilization pecentage, defined as edeemed at time t, fo edemption option q. k u.0 at each t, whee k is the total numbe of edemption options. q t q t t u q, which epesents the pecentage of total points t u q can vay ove time, howeve, With these thee items an analyst can estimate the total aveage cost pe point as: k n t t t cq uq (4.3.) t q 4.4 Additional Consideations in Cost/Value pe Point Models Redemption Patten The edemption patten can be estimated using eithe of the edemption ate methods descibed in Section 3. Altenatively, othe estimation appoaches not coveed in this pape may be used. Since edemption pattens can be expessed as eithe a pecentage of outstanding points o a pecentage of issued points, cae should be taken by the analyst to ensue that the appopiate patten is estimated and applied in a manne that is consistent with the intended pupose. Casualty Actuaial Society E-Foum, Summe 0 9

21 pogams whee membes can change membeship levels (upgade o downgade) due to thei ecent activities within thei pogam. Some potential segmentation citeions that ae often used ae: Membeship level/categoy, Poduct type, Aveage spend by membes, and/o Geogaphic location. This list is by no means intended to be compehensive but athe a selected numbe of options which may be consideed by the analyst. 5. Data Quality Many pogams have been in opeation fo seveal decades and, fo all intents and puposes, pe-date the moden computing ea and compehensively managed database capabilities. As such, histoical data may not be complete o may simply not be available anymoe. Even in pogams that ae elatively young, the data may exhibit seious shotcomings o distotions. As a esult, thee may be limitations as to how the data can be povided to an analyst and, doubts may exist egading data integity. Given the impotance of data in actuaial analyses, it is impotant to make consideation of what is needed fo the analysis and compae that to what is actually available fom the pogam. In some cases, analytical decisions will be made based on data availability athe than theoetical optimization. In such instances, an analyst should conside and communicate to vested paties how data shotcomings may influence the estimated esults o incease the uncetainty aound the full undestanding of the pogam. 5.3 Changes in Pogam Tems & Conditions The Tems & Conditions of a pogam ae one of the single most impotant pats of a loyalty ewads pogam and they need to be well undestood befoe poceeding with an analysis of the estimated URR (o any othe component of such pogam fo that matte). In essence, the T&C ae the ules by which the membes and the pogam s sponso must abide (at least in theoy). It is impeative that the analyst gains a full undestanding of the T&C of any pogam that is unde eview. It is also impotant to undestand how stictly these ules ae actually applied by the pogam sponso. Casualty Actuaial Society E-Foum, Summe 0

22 Changes in T&C can ceate lage vaiations in a pogam s cost stuctue, membes edemption behavio, membeship pofile, and moe. In some instances, changes may impact the fundamentals of a pogam to the extent that an analyst s ability to ely on histoical data to suppot a URR analysis may be limited, at least without including significant adjustments to the oiginal data. Fom an insuance point of view, changes in T&C can often be compaed to legislative changes that affect all insuance policies in foce (o even etoactively apply to all policies eve witten). These changes can fundamentally change the ules of the game to the extent that the past s emegence may povide only limited assistance in pedicting the futue. An actuaial analyst would likely apply some adjustment techniques to the histoical data pio to using it in an analysis. Simila adjustments can be made to histoical point accumulation o edemption activities. An analyst must be able to anticipate how a change (defined) can impact an analysis to avoid poducing biased URR esults. 5.4 Maketing As touched upon biefly above, maketing decisions (e.g., point pomotions) can intoduce lage shifts o spikes in membe behavio and theefoe can have an impact on actuaial analyses. In addition, it is not uncommon that these maketing campaigns will influence only potions of the membeship populations, wok in calenda yea manne (i.e., acoss entie diagonals when actuaial tiangles ae used) o have effects that wee vey diffeent fom the intended outcome. As such, an actuay should wok closely with a pogam s maketing depatment to undestand the upcoming plans o campaigns, if possible. Moe impotantly, the insights that can be gained fom quantitative analysis of the pogam can povide useful feedback to a company s maketing depatment as to the effectiveness (and costs) of vaious maketing pogams. Casualty Actuaial Society E-Foum, Summe 0

23 In fact, the confluence of maketing and fundamental data analysis to moe deeply undestand costs and ewads is an aea that the authos believe to be a natual extension of the ideas contained in this pape. 5.5 Seasonal Effects Many pogams ae heavily impacted by seasonal effects. Fo example, ailine tickets typically tend to cost moe in summe months than in the fall o sping. Anothe example is that cedit cad companies typically issue significantly moe points in the holiday season due to the lage inceases in spending by membes. As such it is impotant to undestand how seasonal effects influence a ewad pogam fom both a membe pespective as well as fom the sponso s pespective. The good news fo an analyst is that it is likely that these effects ae consistent yea afte yea, which should help gain a pecise undestanding of thei timing and thei potential impact on calenda yea esults. This would also be helpful infomation when pefoming a patial yea analysis, with a oll-fowad appoach to the upcoming yea-end evaluation date. As with any actuaial analysis elying on histoical data, data consistency though time is a key component of a loyalty ewads analysis. Casualty Actuaial Society E-Foum, Summe 0 3

24 6. CONCLUSION The expansion in the univese of loyalty pogams has opened a new oppotunity fo actuaies to expand the application of thei taditional insuance pactice body of knowledge into anothe aea of expetise. The quantitative famewok developed by actuaies and the associated actuaial pojection methods ae exceptionally well suited to addess these nontaditional topics. While this pape focused on basic estimation techniques and thei application to loyalty ewads and gift cads pogams, we acknowledge that moe advanced techniques (including pedictive modeling methods) might also be successfully applied to the questions and poblems bought to us by these pogams. We puposely decided to exclude that discussion fom this pape in ode to maintain ou focus on the moe basic appoaches. It is always exciting to ventue into a new space and attempt to answe new questions. We hope that with this pape we will help the actuaial community continue its pogession and emain at the foefont of these new challenges. Casualty Actuaial Society E-Foum, Summe 0 4

26 coesponding to 0X at 36 months is calculated using the total incemental edemptions ( = 69) fo that issuance peiod as of the evaluation date. The next step is to divide the cumulative edeemed points fo each issuance peiod by the cumulative issued points fo each espective issuance peiod to obtain the cumulative edemption pecentages at each evaluation peiod. The esult of this is shown on Appendix 7., Table D. This table is the esult of dividing Table C by Table A. As an example, the 55.% on Table D is deived by dividing the 69 points edeemed at 36 months by the 5 points oiginally issued in that peiod. Step 4 Poject Ultimate Redemption Rate We can poject the ultimate edemption ate using one of many commonly accepted actuaial pojection methods. Fo this example, we have opted to use an exponential cuve fitted on motality basis edemptions fo ou ultimate pojection. The benefit of this method is that we can use the cuve to povide us with an estimate that extends beyond the oldest available data point (in this case actual data only extends to 48 months). The estimate of the tail potion is paticulaly impotant in this hypothetical example because we have assumed in this example that thee can be no fofeitues of value in this pogam. As such, edemptions can theoetically happen beyond ou latest data point, and pehaps significantly fathe. The fist step fo the exponential cuve fit is to convet ou cumulative edemption pecentages into incemental edemption pecentages. This can be seen on Appendix 7., Table E. We additionally ceate a tiangle of the cumulative amount that has not been edeemed at any given matuity (done by subtacting the cumulative edeemed pecentages fom 00.0%) The esult is shown in Appendix 7., Table F. We then calculate the motality ate by dividing the incemental pecentage edeemed in a given peiod by the cumulative unedeemed at the beginning of that peiod. Motality ates ae shown on Appendix 7., Table G and coesponds to Table E divided by Table F. We calculate the aveage motality at each matuity (fo example aveage motality ate at 4 months is 6.6% which is equal to [4.7% + 8.4% + 6.7%]/3). In this example we have chosen to fit an exponential decay Casualty Actuaial Society E-Foum, Summe 0 6

27 function to the aveage motality ates, though numeous othe extapolation techniques could be used. Table H of Appendix 7. shows the esult of this execise..having estimated a motality cuve we can then poject out the ultimate edemption ate fo late matuities. Table I, on Appendix 7. shows the full pojection of ultimate edemption ates fo each issuance peiod. Fo example, the pojection of cumulative edemption pecentage of 53.8% fo 0X4 at 36 months of matuity is calculated as (00.0% %) x.% %. Having just estimated the ultimate edemption ate on issued gift cad value, we can easily convet this into the edemption ate on outstanding value, if needed (please see Appendix 7.4 fo an example of this convesion). 7. Aggegate Membe Join Peiod Appoach - Numeical Example Below we outline a simple case study example of how to obtain the estimated URR, expessed as a pecentage of total issued points, fo a hypothetical hotel loyalty pogam. Step Undestand the pogam This example pogam involves a hotel loyalty pogam whee membes ean points on evey puchase that they make at a paticipating popety. These eaned points can then be edeemed in the futue fo hotel ewads. All membes leave the pogam within thee yeas of thei oiginal date of enollment. Step Obtain Data The key data elements equied fo this appoach ae as follows: Cumulative issued and edeemed points, by join peiod at fixed inteval peiods - These ae shown on Appendix 7., Tables A and B, espectively. Step 3 Manipulate Data into Usable Fomat Taking the aw data elements, we can divide the cumulative edeemed points shown on Table B by the cumulative issued points shown on Table A. The cumulative edemption ate Casualty Actuaial Society E-Foum, Summe 0 7

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