optimallyletitrain

ORIGINALBEITRAGDOI10.
1365/s41056-016-0015-0ZImmobilienkonomie(2016)2:103–120PredictingandmeasuringcustomerlifetimevaluesforapartmenttenantsJianWang·MurtazaDas·AmarDuggasaniReceived:3June2016/Accepted:4November2016/Publishedonline:8December2016TheAuthor(s)2016.
ThisarticleisavailableatSpringerLinkwithOpenAccess.
AbstractItisofgreatbenetforanapartmentcommunitytopredictthecustomerlifetimevalue(CLV)foreachtenant.
Thispredictioncanbeusednotonlytoidentifythemostprotableresidents,butalsotomakebetterpricingdecisions,especiallywhenoptimizingrenewalrentsforexpiringleases.
CLVhasbeenstudiedextensivelyinmanyindustriessuchasserviceandretail.
However,toourknowledge,thereisnoliteraturespecicallyaddressingtheestimationofCLVforapartmenttenants.
Inthisstudy,weproposeanapproximateapproachtopredictingthelifetimelengthandvalueforapartmenttenantsaswellastheirrenewalprobabilities.
Themodelwasestimatedandtestedbasedonarealdatasetfrom68apartmentcompaniesintheUS.
Theresultingpredictionaccuracywasparticularlysatisfactoryforthetenantswhodidnotreneworonlyrenewedonce.
KeywordsCustomerlifetimevalue·Apartment·Realestate·Prediction·Leases1IntroductionIncreasingly,companiesareviewingcustomersintermsoftheirlifetimevalue.
Intheapartmentindustry,thecustomerlifetimevalue(CLV)foratenantmeasuresthetotalvalueofthetenantforanapartment.
CLVcalculatesthelifetimevaluethatatenantcontributesduringthetenant'sentirestayintheapartment.
Inaddition,thelifetimelengthforthetenant'sentirestayisanimportantcomplementarymeasurementtoCLV.
Itisadvantageousforanapartmentcommunitytopredictthelifetimelengthandvalueforeachtenant.
ThispredictioncanbeusednotonlytoidentifytheJ.
Wang()·M.
Das·A.
DuggasaniTheRainmakerGroup,4550NorthPointParkway,Suite400,Alpharetta,GA,USAE-Mail:jwang@LetItRain.
comK104ZImmobilienkonomie(2016)2:103–120mostvaluabletenants,butalsotomakebetterpricingdecisions,especiallywhenoptimizingrenewalrentsforexpiringleases.
Apartmentsareoneofthemostimportantcategoriesofcommercialrealestate.
Intherentalbusinessofrealestate,tenanciesarecreatedwhenthelandlordandthetenantenterintoarentalorleaseagreementthatconveysapossessoryinterestintherealestatetothetenant(Crane2016).
Therearebasicallytwotypesoftenancy:commercialtenancyandresidentialtenancy.
Commercialtenantsandresidentialtenantssharesomecharacteristics,e.
g.
,bothofthemareleasingsomepropertyforause,buttheydifferinseveralaspects.
Forexample,thepurposesofcommercialtenantsleasingabuildingareusuallyassociatedwithabusinessoperationlikeastoreoranofce,whilethoseofresidentialtenantsaretiedwithapersonalresidencysuchassingle-andmulti-familyhousing.
Therentalsquarefootageforacommercialtenanttendstobe,onaverage,largerthanthatforaresidentialtenantresultingindifferenttenantvalues.
Apartmentsandapartmentcommunitieshereafterarelimitedtobetheresidentialtenancyformulti-familyhousing.
Apartmentcommunitiesbelongtotheserviceindustry,buttheyhavetheirowncharacteristics(Wang2008).
Forexample,thedurationofatenantiscontinuous.
Beforeaprospectivetenantmovesintoanapartment,thepersonsignsanewleasewhichspeciestheunittoberented,themove-indate,thechosenleaseterm(i.
e.
,thenumberofmonthstostay),themonthlyrentforthechosenleaseterm,aswellasotherterms.
Beforetheleaseisabouttoexpire,thetenantwillbeofferedasetofrenewaloptionsconsistingofdifferentleasetermsatvaryingrents.
Ifthetenantchoosestocontinuehisstayintheapartment,hewillrenewtheleasebysigninganotherleasefromtheleasetermsandrentsoftherenewaloffer;otherwise,hewillmoveoutoftheapartmentbythetimewhenthecurrentleaseexpires.
Thisrenewalprocesswillberepeateduntilthetenantmovesout.
Tenantsrarelymovebacktothesameapartmentaftermovingout.
Thisislargelybecausetheymayhaverelocatedtoadifferentcity,movedtoanotherapartmentcommunity,boughtahouse,etc.
Becauseofthisuniquecharacteristicofcontinuousresidency,thelifetimeofatenantforanapartmentisdenedasthecontinuousdurationbetweenthetimeswhenthetenantrstmovesinandwhenhenallymovesout.
Duringalifetime,thetenantwillsignoneormoreleases,wheretherstleaseiscalledanewlease,andanysubsequentleasesarecalledrenewalleases.
Therefore,thelifetimelengthandvalueofthetenantarecalculatedasthetotallengthofleasetermsandtheaccruedrents,respectively,fromalltheleasesthatthetenanthassignedduringalifetime.
Sincetenantsarenotallthesame,theirleasesarenotnecessarilythesamethusleadingtodifferentlifetimelengthsandvalues.
Inthisstudy,weproposeanapproximateapproachtopredictingandmeasuringthelifetimelengthandvalueforapartmenttenantsaswellastheirrenewalprob-abilities.
Thispaperisorganizedasfollows:Sect.
2presentsareviewofrelatedliterature.
Sect.
3describesadatasetofactualleasingtransactions.
Thisdatasetisdividedintotwosampledatasetstoestimateandtestanapproximateapproach,whichisproposedinSect.
4.
InSect.
5,weprovideanempiricalestimationoftheproposedapproach,followedbymeasuringaccuracies.
Finally,Sect.
6concludesthispaperwithsuggestionsforfurtherresearchandimprovement.
KZImmobilienkonomie(2016)2:103–1201052LiteraturereviewThereexistmanyvariantsofCLVdenitions,buttheyhavesimilarmeanings.
Forinstance,CLVforacustomerisoftendenedasthepresentvalueofallfutureprotsgeneratedfromthecustomer(GuptaandLehmann2003).
ResearchonthepredictionofCLVhasbeenperformedmainlyforretailandserviceindustries.
BecauseCLVsarecloselyrelatedtotheconsumerbehaviors,variousmethodsforestimatingCLVshavebeensuggestedacrossindustries(Faderetal.
2005).
InmeasuringCLVforacustomer,acommonapproachistoestimatethepresentvalueofthenetbenettothermfromthecustomerovertime(generallymeasuredastherevenuesfromthecustomerminusthecosttothermformaintainingtherelationshipwiththecustomer).
Typically,thecosttoarmiscontrolledbytherm,andthereforeismorepredictablethantheotherdriversofCLV.
Asaresult,researchersgenerallyfocusonacustomer'srevenuestreamasthebenetfromthecustomertotherm.
DifferentmodelsformeasuringCLVresultindifferentestimatesoftheexpec-tationsoffuturecustomerpurchasebehavior.
Forexample,somemodelsconsiderdiscretetimeintervalsandassumethateachcustomerspendsagivenamount(e.
g.
,anaverageamountofexpenditureinthedata)duringeachintervaloftime.
Thisin-formation,alongwithsomeassumptionsaboutthecustomerlifetimelength,isusedtoestimatethelifetimevalueofeachcustomerbyadiscountedcash-ow(DCF)method(BergerandNasr1998).
ResearchonCLVmeasurementhassofarfocusedonspeciccontexts.
Thisisnecessarybecausethedataavailabletoaresearcherorarmmightbedifferentunderdifferentcontexts.
Twotypesofcontextaregenerallyconsidered:non-contractualandcontractual(ReinartzandKumar2000,2003;Borleetal.
2008).
Anon-contractualcontextisoneinwhichthermdoesnotobservecustomerdefectionandtherelationshipbetweencustomerpurchasebehaviorandcustomerlifetimeisnotcertain(Faderetal.
2005).
Acontractualcontext,ontheotherhand,isoneinwhichcustomerdefectionsareobserved,andalongercustomerlifetimeimpliesahighercustomerlifetimevalue(Thomas2001).
Ourproblemtendstofallinthecontractualcontext.
Whenaprospectmovesinoratenantextendshisstayinanapartment,hewillsignorrenewaleasewiththeapartmentcommunity.
Whenhedecidestomoveout,hewillinformtheapartmentcommunityabouthisdecision.
However,theapartmentcommunitydoesnotknowatenant'slifetimelengthandvaluecompletelybeforehehasphysicallymovedout.
Thisisbecauseateachpointinthetenant'slifetime,theapartmentcommunityisnotcertainwhetherthetenantwilldefaulthisleasebymovingoutearlier,howmanymoretimesthetenantwillrenew,whatleasetermsthetenantwillselect,andwhatrentsthetenantiswillingtopay.
Inthisregard,thetenant'slifetimelengthandvalueareuncertain.
Thereisawealthofpublicationsrelatedtorealestate.
However,toourknowl-edge,noneofthemspecicallyaddressestheestimationofCLVforapartmenttenants.
Asdenedearly,theCLVofatenantresultsfromtheaccruedrentsfromoneormoreleasesthatthetenantsignsduringhislifetime.
HowtherentsaresetwillthusimpacttheresultingCLV.
Ontheotherhand,theaggregateamountofCLVsfromallindividualtenantsconstitutesthegrossrentalrevenuethattheapartmentwillreceive.
ThisamountshouldreectsomekindofvaluesthattheK106ZImmobilienkonomie(2016)2:103–120apartmentpropertypossesses,e.
g.
,the"highestandbestvalue"which,accordingtoMillerandGeltner(2004),isdenedasthereasonablyprobableandlegaluseofvacantlandorimprovedproperty,thatisphysicallypossible,appropriatelysup-ported,nanciallyfeasible,andwhichresultsinthehighestvaluekatthedateoftheappraisal.
AsanattempttoobtainsomeinsightsabouthowtoapproximateCLV,itishelpfultounderstandhowtherentsandvaluesofanapartmentaredetermined.
Rentsettingisanimportantandfundamentaldecisionthatapartmentownersandoperatorshavetomakefrequently.
Intraditionalapartmentmanagement,rentsareoftensetwiththeobjectiveofmaximizingoccupancyandreturnoninvestment.
Rentsarenormallydeterminedbysuchfactorsasphysicalcharacteristicsofaprop-erty,itscurrentvacancyrateandcompetitivepositioninthemarketplace,alongwithmanagers'priorexperience(Wang2008).
SirmansandBenjamin(1991)performedanextensiveliteraturereviewaboutthesettingofapartmentrents.
Forexample,Simansetal.
(1989)examinedtheeffectsofvariousfactorsonrent,inwhichthefactorsthattheystudiedincludeamenitiesandserviceslikecoveredparking,modernkitchen,andmaidservice,occupancyrestrictionssuchasnopetsallowed,trafccongestion,proximitytowork,accesstopublictransportation,andsoon.
PagliariandWebb(1996)builtaregressionmodeltosetrentalratesbasedonrentconcessionsandoccupancyrates.
Inmodernapartmentmanagement,rentsareoftensetwiththeobjectiveofmaximizingtotalrevenue.
Forexample,apartmentrevenuemanagement(RM)proposestooptimizetherentsbyoptimallybalancingdemandandsupplyintheconsiderationofcompetitorrentssuchthattotalrevenuewillbemaximized(Wang2008).
Inapartmentvaluation,ontheotherhand,appraisers,investors,taxassessorsandotherrealestatemarketparticipantsaremainlytheoneswhoareinterestedinestimatingthevaluesofproperties.
Forexample,whenmakingincomeorDCFcalculationofanapartment,anappraisermaytakeintoaccountthelifetimevalueofaleaseaswellasmanyotherfactorsthatinuencethevalues.
Hisobjectiveistoestablishthemarketvalueofapropertythataccountsforthemostprobablepricethatwouldbepaidforthepropertyundercompetitivecondition(AdetiloyeandEke2014).
Thevaluationofrealestatehasbeenstudiedextensively.
Thereexistvariousvaluationmodelssuchascostapproach,incomecapitalizationapproach,hedonicmodels,andsoon,forestimatingdifferenttypesofvalues.
AdetiloyeandEke(2014)giveathoroughreviewontherealestatevaluation.
Forinstance,anappraisermayusethecostapproachtoestimatethemarketvaluebysystematicallyestimatingthecostofproduction(MillerandGeltner2004).
Forapartmentpropertiesofrealestate,inparticular,therearealsomanyresearches.
Zietz(2003)summarizestheempiricalandtheoreticalstudiesformultifamilyhousing.
Asanexample.
BibleandGrablowsky(1984)observethatmultifamilyhousingcomplexeslocatedwithinrestorativezoningneighborhoodsincreaseinvalueatahigherratethancomparablecomplexesinneighborhoodsthatarenotsubjecttorestorativezoningcodes.
Thevaluationofrealestate,ingeneral,andapartments,inparticular,issometimesperformedbyapplyingnancialtheory.
Realestateinvestmentscomprisethemostsignicantcomponentofrealassetinvestments.
Itisarguedthatrealestateandnancialassetssharesimilarcharacteristics(Damodaran2012).
Forinstance,theaccruedrentsofaleasecontractandthereturnofabondorastockrepresentKZImmobilienkonomie(2016)2:103–120107theexpectedcashowsonarealestateandanancialasset.
Theirvaluesaredeterminedbythecashowstheygenerate,theuncertaintyassociatedwiththesecashowsandtheexpectedgrowthinthecashows.
Sinceresearchonnancialinstrumentsisgenerallyfaraheadrealestateresearch,manyrealestateresearchershavethereforeappliedgeneralnancialtheorytothevaluationofrealestate.
Thereisastreamofliteraturerelatingrealestatetonancialassets.
Forexample,Mc-ConnellandSchallheim(1983)pricedleasesandleaseoptionsusingBlackScholesoptionpricingtechniques.
WendtandWong(1965)comparetheinvestmentperfor-manceofcommonstocksandapartmenthouses.
TheycomparetheDCFofFHA-nancedresidentialprojectswith76randomlyselectedindustrialstocks.
Theyob-servethatbecauseofthespecialrealestatetaxadvantages,after-taxreturnsonequityinvestmentsinapartmenthousesaretwicethatofstockreturns,butafter-taxratesofreturnsvarysignicantlyoverdifferentperiodsoftimeandacrossdifferentproperties.
Inrentsettingandvaluation,thevariablesinvolvedaremore"exogenous"inthesensethattheyaremoregenericandrelatedtothecharacteristicsandconditionsofthepropertyandmarketwheretenantsreside.
Toalargeextent,thesevariablesplayanimportantroleinestimatingtheaveragerentandaveragevalueofatenant,andthusthecorrespondingaverageCLV.
BecauseCLVsarespecictoindividualtenants,othervariablesthataremore"endogenous"shouldbetakenintoaccountsothatwecanbetterunderstandtheCLVsonapersonallevel.
Endogenousvariablesarethosethataremorespecicandrelatedtothecharacteristicsandbehaviorsofindividualtenantssuchaslifeexpectancy,purchasingpower,creditworthiness,householdchange,productpromotion,defaultrisk,leaseterm,numberofrenewaltimes,andsoon.
Forinstance,wealthiertenantsmayhaveahigherCLVbecausetheycanbetterendurerentincreasesorperiodsofunemployment.
AtenantmayincreasehisCLVbymovingtoalargerunitofthesameapartmentcommunitywhenhisfamilyisgrowing.
Inaddition,hisCLVcouldalsoincreasebecauselargerfamiliesmovelessfrequentlyleadingtohigherrenewalprobabilities.
Also,ahigherdefaultriskincreasestheoddsofmovingoutearlierthananticipatedtherebydecreasinghisexpectedCLV.
Inanattempttoincreasetheexplanatorypowerofastatisticalmodel,onemaytrytoincludeasmanyvariablesasdesired.
Inpractice,however,thereareseveralissuesbydoingso.
First,theresultingerrorofsuchattedmodelmayincreasedisproportionately.
Second,itisdifcult,ifnotimpossible,andexpensivetoaccessalldesireddata,particularly,theendogenousdataaboutpersonaldemographics.
Third,itisnoteasytointerpretamodelwhentoomanyvariablesareincluded.
Asaresult,inthisstudy,wefocusedourattentiononasmallsubsetofvariablesthatarerelatedtoleases.
Ourintentionistoemphasizetheunderlyingmethodologyoftheproposedapproach.
3ThedatasetThedatasetconsistsof77,536historicalleasesfrom62,643tenantswithleasedatesrangingfromMarch4,1995toApril22,2015.
ItwasprovidedbyTheRainmakerK108ZImmobilienkonomie(2016)2:103–120Group(www.
letitrain.
com),arevenuemanagementsoftwarecompanyprovidingpricingsolutionsformulti-familyhousingandgamingcasinoresortsindustries.
Thisanonymizeddatasetwasselectedfromthehistoricaltransactionsof795communitiesbelongingto68apartmentmanagementcompaniesacrosstheUnitedStates.
Foreachtenantinthedataset,weknowhiscompletehistoryofleasingtransactions,i.
e.
,totalnumberofleasesthathehassigned,andtheterm,monthlyrent,startdateandenddateofeachsignedlease.
Inthisdataset,sincetherearemoreleasesthantenants,wecaninferthatsometenantshavesignedtwoormoreleasesduringtheirstays.
Inaddition,thisdatasetalsohas77,536setsof12renewaloptionsthatwereofferedtothetenantswhenaleasewasabouttoexpire.
Eachrenewaloptionspeciesarentforeveryleasetermrangingfrom1to12months.
Atenanthaseitherchosenoneofthe12renewaloptionstorenew,orhehaschosennottorenewbymovingout.
Fromthedataset,wecancomputetheactuallifetimelengthandvalueforeachtenant,whichareequaltothetotalnumberofmonths,andthetotalamountofrentsthathehaspaidduringhisstay.
Furthermore,wecanalsocomputetheresiduallifetimelengthandvaluefortheremaininglifetimeateachpointinalifetime.
Thisdatasetcanthusbeusedtoresemblearealisticcontextunderwhichateachpointinthelifetimeofatenant,weassumethattheapartmentcommunitydidnotknowhowmanymoretimesthetenantwouldrenew,whatrenewalleasetermsthetenantwouldchoose,andwhatmonthlyrentsthetenantwouldpay.
Bydoingso,wewouldbeabletocomparethepredictedlifetimelengthsandvalueswiththeactualones.
Twosamplesarerandomlydrawn(withoutreplacement)fromthisdataset.
Therstsample,referredtoastheestimationsample,contains62,049leasesfrom50,181tenantsrepresenting80%ofallthetenants.
ThissamplewillbeusedtoestimatetheparametersofamodeltobeproposedinSect.
4.
Thesecondsample,referredtoasthevalidationsample,includes15,487leasesfrom12,462tenantsrepresentingtheother20%ofthetenants.
Thissamplewillbeusedtopredictandmeasurethreedependentvariablesofprimaryinterest:theresiduallifetimelength,theresiduallifetimevalue,andtherenewalprobability,respectively,foreachtenantduringalifetime.
Table1summarizessomedescriptivestatisticsforthevariablesoflifetimelength,lifetimevalue,numberofrenewals,andleasetermsobservedacrossallofthetenantsintheestimationsampledataset.
Forexample,onaverage,atenantstaysforabout14.
3monthsmakingarevenuecontributionof$15,352.
Theaveragenumberofrenewalsis0.
5timeswithanaverageleaseterm9.
8months.
Table1SummaryStatisticsLifetimelength(months)Lifetimevalue(dollars)Numberofrenewals(times)Leaseterms(months)Mean14.
315,3520.
59.
8Std.
Dev.
7.
710,5760.
73.
1Median1212,375112Min146401Max48138,655512KZImmobilienkonomie(2016)2:103–120109Fig.
1TenantsbyLifetimeLengthLifetimelengthstnanetfoegatnecreP0.
00.
10.
20.
31020304050Fig.
2TenantsbyLifetimeValueLifetimevalue(times$1000)stnanetfoegatnecreP0.
000.
020.
040.
060.
0850100150Figs.
1,2and3displaythehistogramplotsoflifetimelength,lifetimevalue,andnumberofrenewals,separately.
Theyshowsignicantheterogeneityacrossthetenants.
Specically,Fig.
1showsthedistributionoflifetimelengthsrangingfrom1to48months.
Itcanbeseenthatthepeakoccursaround12monthsrepresenting40%oftenants.
Thisisconsistentwiththemedianof12monthsinTable1,meaningthatthemajorityoftenantssignasingleleasewithaleasetermof12months.
K110ZImmobilienkonomie(2016)2:103–120Fig.
3TenantsbyNumberofRenewalsNumberofrenewalsstnanetfoegatnecreP0.
00.
20.
40.
60.
8123456Fig.
4AverageLifetimeLengthandAverageLeaseTermbyNumberofRenewals101520253035)shtnom(htgnelemitefilegarevAAverageleaseterm(months)45678910012345NumberofrenewalsAvglifetimelengthAvgleasetermFig.
2showsthedistributionoflifetimevalues.
InthisFigure,althoughdetailsarenotshown,thelifetimevaluesrangefrom$500to$138,600,amongwhichmorethan60%oftenantshavealifetimevalueof$10430ormore.
Fig.
3showsthatthenumberofrenewalsspansfromzerotovetimes.
Thedetailshavenotbeenreportedhere,butmorethan64%oftenantsdidnotrenewatall,around26%oftenantsrenewedonce,andtheremaining10%oftenantsrenewedtwoormoretimes.
KZImmobilienkonomie(2016)2:103–120111Fig.
5AverageLifetimeValueandAverageRevenuebyNum-berofRenewals1520253035)0001$semit(eulavemitefilegarevAAveragerevenue(times$1000)46810012345NumberofrenewalsAvglifetimevalueAvgrevenueTherenewalbehavioroftenantsdeterminestheirlifetimelengthsandvaluesaswellasthenumbersofrenewals.
Inthispaper,twoterminologiesofnumberofrenewalsandrenewaltimesareusedthroughout.
Numberofrenewalsisdenedasthetotalnumberofrenewalleasesthatatenanthassignedinalifetime,whilerenewaltimesasthenumberoftimesthatatenanthasbeenmakingarenewaldecisionatsomepointtimeinhislifetime.
Bythisdenition,totalnumberofrenewaltimesforatenantisequaltothenumberofrenewalsplusone,becausethetenantwillnotrenewatthelastrenewaltimes.
Fig.
4displaystheaveragelifetimelengthandaverageleasetermbynumberofrenewals,wherethenumberofrenewalsofzeroisforthetenantswhoonlysignedanewleaseanddidnotrenewatall.
Itshowsthattheaveragelifetimelengthincreasesovernumberofrenewalsthatisequaltoorlessthanthree.
Thisseemsintuitivebecausewewouldexpectthatthelargerthenumberofrenewals,thelongerthelifetimelength.
However,thelifetimelengthstartstodecreaseoverthenumberofrenewalsthatislargerthanthree.
Thissaysthat,onaverage,thelifetimelengthofatenantdoesnotnecessarilybecomelargerasthenumberofrenewalsincreases.
Aplausibleexplanationisthattenantstendtosignshorterleasetermswhentheyrenewmoretimes.
Thedecreasingtrendofaverageleasetermsovernumberofrenewalstendstosupportthisexplanation.
Fig.
5exhibitstheaveragelifetimevalueandaveragerevenuebythenumberofrenewals.
Itshowsthattheymaintainsimilarpatternsastheaveragelifetimelengthandaverageleaseterm.
Fig.
6illustratestheaverageresiduallifetimelengthsandvaluesbyrenewaltimes.
Theresiduallifetimelengthandrevenueofatenantatarenewaltimesarecalculatedasthesumsofleasetermsandrevenuesfromthecurrentandanyfutureleases.
Asexpected,bothresiduallifetimelengthandrevenuedecreaseoverrenewaltimes.
Becausethemaximumnumberofrenewalsis5intheestimationsampledataset,thesevaluesbecomezerosattherenewaltimesof6.
K112ZImmobilienkonomie(2016)2:103–120Fig.
6AverageResidualLife-timeLengthandValuebyRe-newalTimes0.
00.
51.
01.
52.
0)shtnom(htgnelemitefillaudiseregarevAAverageresiduallifetimevalue($)0500100015002000123456RenewalTimesAvgresiduallifetimelengthAvgresiduallifetimevalueFig.
7RenewalRatesbyRe-newalTimesetarlaweneR0.
000.
050.
100.
150.
20123456RenewaltimesExistingtenantsOriginaltenantsFinally,Fig.
7displaystworenewalratecurvesbyrenewaltimes.
Therstrenewalratecurveisdenedasthefractionofthetenantswhowereactive(i.
e.
,stilllivingintheapartment)atagivenrenewaltimesandhaddecidedtorenew.
Specically,attherstrenewaltimes,about20%oftenantschosetorenew;atthesecondrenewaltimes,about18%oftheremainingtenantschosetorenew;andsoon.
Bythelastrenewaltimes,alloftheremainingtenantshadmovedout.
Ontheotherhand,thesecondrenewalratecurveisdenedasthefractionoftheoriginaltenantswhochosetorenewatarenewaltimes.
Itshowsthattherenewalratesofthiscurvedecreasemonotonically,meaningthatthenumberofremainingactivetenantsKZImmobilienkonomie(2016)2:103–120113becomessmallerasrenewaltimesincreases,andthateverytenantwouldmoveoutbythelastrenewaltimes.
4ModelThelifetimelengthandvalue,andrenewalprobabilityofanactivetenantarede-terminedbytherenewaldecisionsofthetenant.
Whenthecurrentleaseisabouttoexpire,thetenanthastwochoices.
Hecanchooseeithertorenewforaparticularleasetermatanofferedrent,ortomoveout.
Therenewaldecisionwillimpactthetenant'sresiduallifetimelengthandvalue.
Fig.
8illustratesadivisionofanactivetenant'slifetime.
InFig.
8,thelifetimeofanactivetenantisdividedintothreeperiods:past,currentandfuture.
Apastperiodrepresentsthetimelengthofleasetermsofallpreviousleasesthatthetenanthaseversigned.
Acurrentperiodrepresentsthetimelengthoftheleasetermofthecurrentlease.
Afutureperiodrepresentsthetimelengthofleasetermsofanyfutureleasesthatthetenantmayrenewduringtheremainderofthetenant'slifetime.
Furthermore,Fig.
8illustratesapartitionofthethreeperiodsintoanumberofconsecutivesegments,eachofwhichcontainsasetofleasingoptionsrepresentedbyarrows(directededges)connectedwithcircles(vertices).
Adashedarrowrepresentsaleaseoptionthatwasofferedoristobeoffered,whileasolidarrowrepresentsanactualleasethatthetenanthassigned.
Twocirclesattheendsofanarrowdenotethestartdateandenddateofalease.
Underthisillustration,eachsegmentinthepastandcurrentperiodshasoneandonlyonesolidarrow,whilethesegmentsinthefutureperiodhaveonlydashedarrows.
Givenanyactivetenanti,denoteLiandViasthetenant'slifetimelengthandvalue.
Atanytimepointtinthetenant'scurrentperiod,LicanbedecomposedasLiDLi;p.
t/CLi;c.
t/CLi;f.
t/,whereLi;p.
t/,Li;c.
t/andLi;f.
t/representthelifetimelengthsforthepast,currentandfutureperiods,respectively.
Accordingly,VicanalsobedecomposedasViDVi;p.
t/CVi;c.
t/CVi;f.
t/,whereVi;p.
t/,Vi;c.
t/andVi;f.
t/representthelifetimevaluesforthepast,currentandfutureperiodsatt.
Forbothpastandcurrentperiods,Li;p.
t/,Vi;p.
t/,Li;c.
t/andVi;c.
t/areallknown.
Theydonotchangeovert,andcanbecalculateddirectlyasthesumsPastCurrentFutureLifemeFig.
8VisualDepictionoftheDivisionofaLifetimeK114ZImmobilienkonomie(2016)2:103–120ofleasetermsandrevenues(i.
e.
,leasetermstimesmonthlyrents)fromalltheleasesinthepreviousandcurrentperiods,respectively.
Forthefutureperiod,Li;f.
t/andVi;f.
t/representtheresiduallifetimelengthandvaluefromanyfutureleasesthatmightbesignedaftert.
Bothofthemareunknown,andneedtobeestimated.
Forthesakeofbrevity,Li;f.
t/andVi;f.
t/willbecalledlifetimelengthandvalueattintheremainderofthepaper.
WenowproposeanapproachtoapproximatingLi;f.
t/andVi;f.
t/.
Denoteasadiscreterandomvariablecorrespondingtotherenewaltimesatt,forwhichmaytakevaluesof1;:::;N,whereNisthemaximumrenewaltimestobeallowed.
Table1showsthatthemaximumnumberofrenewalsis5inourdataset,implyingthatND6becauseeverytenanthadmovedoutbythesixthrenewaltimes.
Also,denote….
/Dl;j.
/1313asarenewalprobabilitymatrix,orcalledastransitionmatrix,atrenewaltimes,wherel;j.
/isdenedastherenewalprobabilityfromthecurrentleasetermltotheleasetermjofapossiblerenewallease,forl;jD0;1;:::;12.
Itisnotedthatwhenleasetemjisequalto0,itmeansthatthetenantchoosestomoveout.
Whenleasetemlisequalto0,thereisnopracticalmeaning.
ThereasonthatweintroducethenotationoflD0hereisjustamatterofalgebraicconvenience.
Specically,for,!
ri.
s/arenotknownandneedtobeestimated.
Intheliteraturereview,wementionedthatthereexistanumberofwaystoestimate!
ri.
s/.
Itisbeyondthescopeofthispapertodiscusshowtoestimate!
ri.
s/.
Tosimplifyourapproximation,wewillsimplyreplacetheval-uesof!
ri.
s/fors>bytheaveragerenewalrentsfromthehistoricalrenewaloffers.
Next,wedescribetheestimationof….
/.
Inpractice,thedeterminationof….
/iscomplicated,anditisinuencedbymanyfactorsincluding!
ri.
s/.
Tosimplifyourestimation,weassumethat….
/satisedtheMarkovproperty.
Specically,l;j.
/areassumedtodependonlytherentsandleasetermsofthecurrentleaseandapossibleleasetoberenewed.
Theyarenotdependentonthestatesofanypreviousleasesthatprecededthecurrentlease.
Inthisregard,foranyrenewaltimess>forwhichtherenewaloptions!
ri.
s/arenotknown,wewillapproximatel;j.
s/byusingtheempiricalestimateofrenewalprobability;fortherenewaltimessDinwhichtherenewaloptions!
ri.
/areavailable,wewillapproximateli;j.
/byusingMultinomialLogit(MNL)model.
MNLisavariantofcustomerchoicemodels(Train2009).
Therenewalprobabilityli;j.
/canbeapproximatedbybli;j.
/DeVi;j.
li;ri;ri;j.
//1CP12j0D1eVi;j0.
li;ri;ri;j0.
//whereridenotestherentofthecurrentlease,andVi;jli;ri;ri;j.
/autilityfunction(orcalledrepresentativeutility)atobtainedbychoosingtheleasetermj.
Vi;jli;ri;ri;j.
/measurestheperceivedbenetofrenewingaleasetermjoverchoosingtomoveout.
WeassumethatVi;jli;ri;ri;j.
/islinear-in-parameter.
Namely,Vi;jli;ri;ri;j.
/Daj.
/Ci;j.
/bj.
/Chi;j.
/cj.
/,wherethecoefcientsofaj.
/,bj.
/andcj.
/areunknownparameterstobeestimated,andi;j.
/andhi;j.
/arealternativespecicvariablesderivedfromli,riandK116ZImmobilienkonomie(2016)2:103–120Table2EstimatesofMNLParametersforD1and2D1D2D1D2ba1–4.
3*(0.
17)–4.
6*(0.
37)bb7–3.
6*(0.
48)–5.
0*(0.
99)ba2–3.
8*(0.
11)–3.
8*(0.
19)bb8–4.
5*(0.
59)–4.
9*(1.
25)ba3–3.
9*(0.
10)–3.
7*(0.
18)bb9–4.
2*(0.
60)–5.
0*(1.
31)ba4–4.
6*(0.
14)–4.
4*(0.
26)bb10–2.
4*(0.
29)–1.
6*(0.
60)ba5–5.
2*(0.
19)–4.
8*(0.
29)bb11–4.
2*(0.
51)–2.
5*(1.
23)ba6–3.
2*(0.
04)–3.
2*(0.
09)bb12–3.
1*(0.
20)–2.
7*(0.
49)ba7–4.
5*(0.
07)–4.
8*(0.
17)bc11.
4*(0.
42)2.
3*(0.
48)ba8–5.
1*(0.
09)–5.
2*(0.
20)bc21.
1*(0.
16)1.
4*(0.
24)ba9–5.
0*(0.
09)–5.
4*(0.
22)bc31.
2*(0.
14)1.
5*(0.
23)ba10–3.
4*(0.
03)–3.
3*(0.
07)bc41.
3*(0.
27)1.
2*(0.
49)ba11–4.
9*(0.
07)–4.
9*(0.
15)bc51.
3*(0.
43)1.
7*(0.
74)ba12–3.
1*(0.
04)–3.
3*(0.
08)bc61.
3*(0.
07)1.
3*(0.
12)bb1–4.
5*(0.
57)–2.
9*(1.
16)bc71.
7*(0.
17)2.
5*(0.
30)bb2–2.
7*(0.
42)–2.
3*(0.
74)bc82.
1*(0.
22)0.
6(1.
02)bb3–2.
9*(0.
41)–2.
9*(0.
72)bc91.
8*(0.
23)2.
2*(0.
55)bb4–3.
4*(0.
59)–2.
8*(1.
09)bc101.
0*(0.
07)0.
7*(0.
14)bb5–3.
4*(0.
80)–4.
6*(1.
27)bc112.
2*(0.
10)2.
6*(0.
23)bb6–3.
6*(0.
25)–3.
7*(0.
51)bc121.
6*(0.
04)1.
4*(0.
10)*indicatesthatthe95%posteriorintervalforaparameterdoesnotcontain0ri;j.
/.
Specically,i;j.
/Dri;j.
/ri1representstherelativerentchangeoftherenewalrentri;j.
/overthecurrentrentri,andhi;j.
/isahabitformation(orinertia)describingwhetheratenanttendstochoosethesameleasetermasthecurrentonewhenrenewing,thatis,ifjDli,hi;j.
/D1;otherwise,hi;j.
/D0.
5Estimationandvalidation5.
1EmpiricalestimationsRenewalprobabilitiesli;j.
/wereestimatedbasedontheestimationsampledataset.
Asproposedearly,whenrenewalrents!
ri.
/areofferedforsome,li;j.
/canbeapproximatedviatheestimationofMNLparameters;when!
ri.
/arenotavailable,li;j.
/willbeapproximatedempirically.
Inthisestimationsam-ple,morethan90%oftenantsdidnotreneworjustrenewedonce,whichisnotuncommonforapartments.
Thissituationwillcausetheestimatesofli;j.
/tobeinaccuratefor3forwhichtheredoesnothaveenoughdata.
Toalleviatethisproblem,wewillapproximateli;j.
/usingMNLmodelforD1,2,andusingtheempiricalestimatesofprobabilitiesfor3.
Table2reportstheestimatesofMNLparametersbaj.
/,bbj.
/andbcj.
/forjD1;:::;12andD1,2.
Thenumbersinparenthesesaretheposteriorstandarddeviations,andthesuperscriptasterisks*indicatethatthe95%posteriorintervalKZImmobilienkonomie(2016)2:103–120117Table3EmpiricalEstimatesof….
/forD1123456789101112010.
080.
010.
000.
000.
000.
000.
000.
000.
000.
000.
000.
020.
9120.
020.
060.
010.
000.
000.
010.
000.
000.
000.
000.
000.
000.
9130.
010.
010.
050.
010.
000.
010.
000.
000.
000.
000.
000.
010.
9240.
020.
090.
070.
020.
000.
040.
000.
000.
000.
000.
000.
000.
7650.
010.
050.
050.
030.
010.
060.
010.
000.
000.
010.
000.
000.
7760.
020.
040.
020.
010.
000.
090.
010.
000.
000.
000.
000.
000.
8170.
000.
070.
100.
020.
010.
050.
030.
010.
010.
010.
000.
010.
6880.
010.
030.
010.
040.
030.
140.
030.
010.
010.
060.
010.
040.
5890.
000.
000.
010.
010.
000.
180.
060.
010.
010.
040.
010.
080.
59100.
000.
000.
000.
000.
000.
020.
000.
020.
020.
090.
000.
050.
80110.
000.
000.
000.
000.
000.
000.
000.
000.
000.
090.
050.
070.
79120.
000.
000.
000.
000.
000.
000.
000.
000.
000.
000.
000.
140.
86foraparameterdoesnotcontain0.
Thisisinterpretedasanindicatoroftheestimatebeingstatisticallydifferentfromzero.
Itcanbeseenthatthesignsofbaj.
/areallnegativeimplyingthattherewasalargertendencytomoveoutthantorenew.
ThisimplicationisdemonstratedinFig.
7also,inwhich,e.
g.
,morethan80%oftenantschosetomoveoutattherstrenewaltimes.
Thesignsofbbj.
/arenegativeaswell,meaningthatthelargertherenewalrentchangei;j.
/,thelessertheutilityVi;jli;ri;ri;j.
/.
Thisisconsistentwithintuitiveexpectation.
Finally,thesignsofbcj.
/arepositiveindicatingthatthereexistsahabitualinertiaamongtenants.
Namely,whenrenewing,atenanttendstorenewtothesameleasetermasthecurrentone.
Asanillustration,Table3showstheempiricalestimatesof….
/Dl;j.
/1213forD1.
The12rowsrepresentthepossibleleasetermsofacurrentlease,andthe13columnsthepossiblerenewalleaseterms,inwhichtherenewalleasetermofzeroagainrepresentsthemove-outoption.
Oneachrow,thesummationoftheprobabilityvaluesacrossthe13columnsisequaltoone,meaningthatatenantwouldeitherrenewwithoneof12leasetermsorchoosetomoveout.
Itagainshowsthat,asexpected,theprobabilitiesofmovingoutarelargerthanthoseofrenewing.
Inaddition,itcanbeobservedthatthediagonalentriesof….
/arenotalwayslargerthantheoff-diagonalentries.
Thisempiricalestimationdoesnotprovidestrongevidenceoftheexistenceofhabitualinertiaaswesawincoefcientestimateofbcj.
/inMNLmodel.
5.
2PredictionandvalidationWeappliedtheproposedapproachtopredictingthelifetimelengthandvalueaswellasrenewalprobabilityforeachtenantinthevalidationsample,whichconsistsof12,462pasttenantswithatotalof15,487leasesspreadingacross4renewaltimes.
Becausewealreadyknowtheactuallifetimelengthsandvaluesandrenewaloutcomesofthetenants,wealsotestedthepredictionperformanceofourapproach.
K118ZImmobilienkonomie(2016)2:103–120Table4Comparisonofactualandpredictedlifetimelengthandvalue,andrenewalprobability1234Lf.
/12.
1710.
698.
896.
52bLf.
/11.
84(3%)10.
66(0%)9.
56(8%)7.
12(9%)Vf.
/13,308.
0711,527.
739190.
057313.
97cVf.
/13,147.
28(1%)11,735.
46(2%)9907.
5(8%)8001.
93(9%)f.
/20%18%13%7%bf.
/20%(0%)18%(0%)17%(31%)17%(143%)ForD1;2;3;4,denoteLf.
/,Vf.
/andf.
/astheaveragesoftheobservedLi;f.
/andVi;f.
/,andrenewalprobabilityfromthevalidationsample,respectively.
Thatis,Lf.
/andVf.
/werecalculatedastheaveragesofactualleasetermsandrevenuesfromthecurrentandsubsequentleaseswithrespectto.
f.
/wascomputedasthepercentageoftenantswhowereactiveandhadrenewedat.
Accordingly,denotebLf.
/,cVf.
/andbf.
/astheaveragesofpredictedbLi;f.
/,bVi;f.
/andP12jD1bli;j.
/,respectively.
Table4summarizestheestimatesofLf.
/,bLf.
/,Vf.
/,cVf.
/,f.
/andbf.
/.
ThenumbersinparenthesesrepresentMeanAbsolutePercentageErrors(MAPE)betweenthepairsofLf.
/andbLf.
/,Vf.
/andcVf.
/,andf.
/andbf.
/,separately.
ItcanbeseenthatthepredictionerrorsforLf.
/,Vf.
/andf.
/wereverysmall(i.
e.
,MAPEs3%)forD1,2.
However,forD3,4,thepredictionerrorswerenotthatsatisfactory,particularlyforf.
/.
Themaincausewasbecause,asdescribedearlier,thedatawassparse(thereareonlylessthan10%oftenantswhohadrenewedtwoormoretimes).
Therefore,thisproblemofdatasparsenessledtoinaccurateestimatesforLf.
/,Vf.
/andf.
/forD3,4.
6ConclusionInthisstudy,weproposedanapproximateapproachtopredictingthelifetimelengthsandvaluesforactivetenants.
Wedividedasampledatasetintoestimationandvali-dationsamples.
Basedontheestimationsampledataset,weestimatedtherenewalprobabilities.
Wethenpredictedthelifetimelengthsandvaluesaswellasrenewalprobabilitiesforthetenantsinthevalidationsample.
Theresultingpredictionaccu-racyseemedtobesatisfactoryonlyforthetenantswhodidnotreneworrenewedonce.
Itshouldbenotedthatinthisarticle,lifetimelengthsandvaluesareforecastfortheactivetenantsintheapartmentsofUSmarket.
Asaconsequenceofthespecicsofthatmarket,thetransferabilityoftheresultsandapplicabilityoftheproposedmodeltootherjurisdictionsandculturesislimited.
Toimprovethepredictionaccuracy,thefollowingexplorationscanbeperformed:Inclusionofadditionalvariables:Inthisapproach,weonlyusefourvariables:currentleaseterm,renewalleaseterm,numberofrenewaltimes,andactual(orestimated)renewalrentoffers.
Ifaccessible,wecanconsidermoreendogenousKZImmobilienkonomie(2016)2:103–120119andexogenousvariablessuchasdemographicinformationofage,incomeandfamilysize,economiccondition,marketrents,migrationtendencybetweenstates,andsoon.
Utilizationofexistingdata:Thepredictionaccuracybecameunsatisfactoryatthetimewhendataamountwassparse,particularlyforhighernumberofrenewaltimes.
Toalleviatethisissue,asetofhierarchyrulescanbedesignedtopoolthedataofalowernumberofrenewaltimeforahighernumberofrenewaltime.
Althoughthereisnorigorousacademicproofabouthowmuchanimprovementcanbegainedbydoingso,thisdatapoolingtechniqueseemstobeprevalentinpractice.
Estimationoffuturerenewalrentoffers:!
ri.
/areunknownforanyfuturerenewaltimes,andneedtobeestimated.
Weestimateditwiththeaverageofrenewalrentoffersfromhistoricalexpiringleases.
Asanalternative,wecanconsidertouseothermethodssuchasDCFandRMmodels.
Alternativecustomerchoicemodels:TheMNLmodelthatisusedinestimatingtherenewalprobabilitiesispopularinpractice.
Ithasmanyadvantagessuchasbeingsimpletounderstand,andeasytouse.
However,itsometimessuffersfromaninherentassumptionofIndependenceofIrrelevantAlternatives(IIA)(MeyerandKahn1991).
ThisIIAassumptionpresumesthattenantswouldignorethesimilaritiesamongalternativeleasetermswhentheymakearenewaldecision,whichmightnotbealwaystrue.
Tomitigatethisissue,othercustomerchoicemodelssuchasNestedLogit(NL)model(McFadden1981)canbetakenintoaccount.
OneofchallengesofusingNLmodel,forexample,istocluster"similar"leasetermsintoagroup.
Doingthis"right"isnoteasyinpractice.
Someunsupervisedlearningtechniquesindataminingeldmightbeneeded.
Theresultsmayseemrudimentary,buttheycanstillprovideapartmentcommu-nitieswithsomeinsightfulknowledgeaboutthevaluesoftheirtenants.
AgoodestimateofCLVofthecurrenttenantscanbeanadditionalkeymetricinassess-ingthenancialvalueoftheapartmentpropertyincomparisontoothercompetingmultifamilyassetsorothersisterpropertiesinanowner'sportfolio.
Sincetheapart-mentindustryhasacompetitivemarketenvironment,tenantbehaviorsmightchangequicklyovertime.
Asaconsequence,thepredictionoflifetimelengthandvaluecan-notjustbeevaluatedonceandkeptunchanged.
Theyneedtobeupdatedregularlytoreectpossiblechangesintenantbehaviors.
AcknowledgmentsWewouldalsoliketothankthethreeanonymousreviewerfortheirsuggestionsandcomments.
WewouldalsoliketoshowourgratitudetoMs.
MarleneRinker,ourformercolleaguefromTheRainmakerGroup,forherrevisiononanearlierversionofthemanuscript,althoughanyerrorsareourownandshouldnottarnishheresteemedreputation.
OpenAccessThisarticleisdistributedunderthetermsoftheCreativeCommonsAttribution4.
0Interna-tionalLicense(http://creativecommons.
org/licenses/by/4.
0/),whichpermitsunrestricteduse,distribution,andreproductioninanymedium,providedyougiveappropriatecredittotheoriginalauthor(s)andthesource,providealinktotheCreativeCommonslicense,andindicateifchangesweremade.
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