WPC #ba/%´N{'hT=&p5tf[lf9//xCiah\oac| ,oc^b#UR "oA& ]`ʧ|w_DT#S,FY5M.`1"qخuq1<@byiî2)瑸p)fr1nfwk'χtabDogOZLuAҀz1rO}|RMډŅ^|* Cn]Yǎw̬,+BUq<NZ]FCF;LTp. ξο[m.h 1t4|P̏ުB婯|UN?_^n乸KƙM}-gtIVel9Kdʾj^9N>Mu/Q>Xr#! UN= % 04 ^ w@ 4 % 4 m6 0DM 0x A 0x 0D* U Nn 0N  M| H !"# 0P}&;&b'0j))4,. AS/02am46 0K7 D+7 89@;;o]>pdL CffaU*ʱfaa  D3ǴUNUNHUNsdWN4444t6d.@ غ> i B*?Vioqd B A D3 B-؊؊؊؊؊؊؊؊؊؊؊؊؊؊؊؊؊ 0P AQUU 0DHP LaserJet 5Si Mopier,,,,,,0(hH  Z6Times New Roman RegularX( U$  H$ %%D%%D%%D%%D%%\%!; f3|x% U($$  0  (92b$ U!     0  . ,-&OLE 2.0 Box <=8C HKKKK(((3$ U!       0  (#$  0  (hH  Z 6Times New Roman Regular(O$  $      3    _ԀTheoriginalDowDividendstrategy,asdescribedby_OHiggins_,formedportfoliosatthe  closeofthelastbusinessdayofthepreviousyear(seepage187ofBeatingtheDow).InKnowles  andPettysperturbationofthestrategy,portfoliosareformedatthecloseofthesecondbusinessdayoftheyear(seepage108ofTheDividendInvestor).Weformourportfoliosonthefirstbusiness  dayoftheyearinordertobeconsistentwiththeFoolishFourstrategy(seepage84ofTheMotley p Fool).  $      3    _ԀTheoriginalDowDividendstrategyas,describedby_OHiggins_,formedportfoliosatthe  closeofthelastbusinessdayofthepreviousyear(seepage187ofBeatingtheDow).InKnowles  andPettysperturbationofthestrategy,portfoliosareformedatthecloseofthesecondbusinessdayoftheyear(seepage108ofTheDividendInvestor).Weformourportfoliosonthefirstbusiness  dayoftheyearinordertobeconsistentwiththeFoolishFourstrategy(seepage84ofTheMotley p Fool).Level 1Level 2Level 3Level 4Level 5 C $      5    _ԀWeaccountforthediscrepancybetweenourFoolishFourshistoricalreturninTable1of  28percentandthe25percentreportedintheGardnersbookintwoways:first,weinclude1994,1995,and1996,andthelattertwowereverygoodformostportfolios,andsecond,wereinvestalldistributionsimmediatelywhereas,forreportingpurposes,theGardnersletcashdividendssitidleuntiltheyarereinvestedatthebeginningofthenextcalenderyear. $      10    _ԀSeeCarhart(1997)fordocumentationofthesurvivorshipbiasinmutualfunds. $      15    _Thetransformationis:^'IJ(`0 `E|0|7|0^   MotelyGardnersOHiggins CRSPXX.xxmonotonicallyIyengarMacKinlayMcQueenThorleyModiglianiDornbushBossons edsMittooNicholsDownes KarzDriggsFaneuil TNRBhomepageLeinweberRundewebsiteKnowles LeebSuperbowlVerbruggerebalancingWalmart USXdissipativeMalkielHalpernTurnbullPraxairmsm.byu.edu emp grmgrm.htmCarhartProbusOverfitting  $      4    _ԀThedifferencebetweentheFoolishFours28.03percentreturnandtheDow30's15.80  percentreturnisstatisticallysignificantatthe99percentlevel(tstatisticof3.05withasamplesizeof24).Thatis,wereitnotforthedatamining,wecouldbe99percentconfidentthattheFoolishFourpremiumdidnotarisebychance.  $      9    _ԀInamoreadvanced stupidtrick,Leinweber(1998)usesaninthdegreepolynomialto  perfectlyfiteightyearsoftheS&P500indexwithjustonevariable,years.Heconcludeshisstudy  withanappropriatewarning, Dontfallintothedatamine.Level 1Level 2Level 3Level 4Level 5  $      11    _TheMotleyFoolwebsiteanddatabasesactuallytrackahostofdifferentstrategies,most  withcolorfulnamesincludingTheDowDozen,DowRacers,Boring,andCombo,butalasnoFracturedFour.Wefindthisplethoraofstrategiesproblematicinlightofthepotentialfordataminingandportfolioprospecting.Level 1Level 2Level 3Level 4Level 5Level 1Level 2Level 3Level 4Level 5  $      16    _ԀTheannualtransactioncostsarecalculatedasfollows:     ` W'CD! `E` 77` 7W   ` W'UV! `E` 77` 7W߀BothoftheseestimatesareconservativesincesomerebalancingisrequiredeachyearintheDow30andFoolishFourportfolios,evenwhentheDJIAcompositionisstable.Inaddition,theFoolishfourwillrequirehalftradeswhenthedoubledupPenultimateProfitProspectchanges,butremainsinthe  p   FoolishFour.((3$ U!    1#Xd# X $      6    _ԀInTheMotleyFool,theFoolishFourstrategyisdescribedasasimplewayforinvestors  tobeattheDow.Subsequently,onthewebcite,theFoolishFourhasbeenlabeleda modelstrategy,nota realdollarstrategy.Nevertheless,manyofthe realdollarstrategiesaresimplyderivativesoftheFoolishFour.Whethera modelor realdollarportfolio,forourpurposes,theFoolishFourisanexcellentvehicletodiscussdatamining.www.fool.com/DDow/1997/  $      12    _Suspiciousreadersmayquestionourchoiceofthetwooutofsampletests.Didweengage  in reversedatamining,searchingforoutofsampleteststhatexhibitedtheweakestpossibleresults  fortheFoolishFourportfolio?Wecanonlyassurereadersthatwedidnot.Theprevious24yearswasouronlychoiceofatrueourofsampletestwithoutcollectinginternationalequitydata.JulywaschosenasthealternativestartingmonthbecauseitismidyearandthusthemonthfurthestawayfromJanuary.  $      8    _ԀPeterCoy(1997)discussesdatamininginabroadercontextincludingTheBibleCode,  cancerhotspots,andclinicaldrugtrials.Amongtechnicaltraders,dataminingiscalled optimization.Thistermreferstothepracticeoffindingthebestpossibleparametervaluesofatradingruleoverasethistoricaltimeperiod.  $      13    _ԀOuradjustmentsforrisk,transactioncosts,andtaxesareinthespiritoftheGardners  appropriateandinsightfulinsistenceintheirAppendixBthattheinvestmentindustryreportreturnsafteraccountingforalltransactioncostsandthencomparetheseadjustedreturnstothemarketreturn. M -, dc  $      1    _ԀDataminingstudiesinclude:XXXXJensenandBennington(1970),Black(1986,1993),#XXXX}#XXXXMerton  (1987),#XXXX#XXXXIyengarandGreenhouse(1988),LoandMacKinlay(1990),Mayer(1997),Leinweber  (1998),KramerandRunde(1998),andSullivan,_Timmermann_,andWhite(1998aand1998b),and_Dimson_ԀandMarsh(1998)#XXXXV#.  $      7    _Otherresearchers,includingLoandMacKinlay(1990)andSullivan,_Timmermann_,and  White(1998aand1998b),callintergenerationalmining datasnooping,andshowhowsuccessiveusesofthesamedatasetbyinterdependentresearchersleadstoinappropriateconclusions. W $      6    _ԀInTheMotleyFool,theFoolishFourstrategyisdescribedasasimplewayforinvestors  tobeattheDow.Subsequently,onthewebsite,theFoolishFourhasbeenlabeleda modelstrategy,nota realdollarstrategy.Nevertheless,manyofthe realdollarstrategiesaresimplyderivativesoftheFoolishFour.Whethera modelor realdollarportfolio,forourpurposes,theFoolishFourisanexcellentvehicletodiscussdatamining.Level 1Level 2Level 3Level 4Level 5( $ Figure  1  'dxd  $      2    _John_Slatter_,thenananalystforPrescott,Ball&_Turben_,alsoproposedthedividendstrategy  anddocumenteditsperformancesometimeinthelate1980's(seeJohn_Dorfman_sAugust11,1988  WallStreetJournalarticle).  $      14    _ԀInTheMotleyFool,theGardnerssuggestthatafterinvestingintheFoolishFour,some  moresophisticatedinvestorsmaywanttoenhancereturnsbybuyingselectsmallstocksandshortingotherstocks.ThesetwoadditionalstrategieswouldprovidesomeofthediversificationlackingintheFoolishFourportfolio.23*OLE*  $      17    _XXXXEvidenceofinvestorlearninghasbeenfoundinotherareasofinvestingbyNicholsand  Brown(1981),HalpernandTurnbull(1985),MittooandThompson(1990),andMcQueenandThorley(1986).#XXXX`#ԀWenotethattheMotleyFoolsannouncetheirintendedtradesanddonotparticipate  in_frontrunning_.However,aswithanyrulebasedstrategysuchastheFoolishFour,outsiderscould,andapparentlydid,anticipatethechangesintheportfolioandprofitfrom_frontrunning_.WPC@@>>>>!>>     0''   Arial-----"Systemn-'-  0-'-  0- "- $MMs s M "-MMs s M "-Ms s s $$99MMs s  "---'--- w ---'--- v M---'--- s M- "-  FFCC&&//(j(jss--kTkT]]>>xxnn@'@'|b|bYYLLiimm|5|5ppii---'--- v M---'---  0---'---  0---'---  0  2 I 0* 2 1* 2 2* 2 ]3* 2 4* 2 5* 2 r6* 2 #7*---'---  0---'---  0  2 -15** 2 -10** 2 3-5* 2 c0* 2 5* 2 10** 2 15**---'---  0-----'--- w 0  2   Event Day2%**6*%----'---  0-----'---   Arial-2 !Cumulative Excess Return (%)-----'---  0---'---  0--'  0 '  'WPWin 6.0/OLE 1.0 Prefix Information MarkerExcel.Sheet.8Vࡱ>  ! 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  } =C<<C($$   1  U!   _  XXMiningFoolsGold#XXW# p GrantMcQueenandStevenThorley*February1999Abstract7ThispaperisalightheartedversionofourdataminingarticleappearingintheMarch/April1999issueofthe%%FinancialAnalystsJournal%%.%%WeinvestigatethepopularMotleyFoolFoolishFour  portfolioasacasestudyindatamining"thepracticeofdevelopingtradingstrategiesbysearchingthroughdatabasesforcorrelationsandpatterns.TheperformanceoftheFoolishFourportfolioisdocumentedandusedtoillustratethemistakeninferencesthatcanplagueanyinvestmentresearchproject.UsingtheFoolishFourcasestudy,weshowthatdataminingcanbedetectedbythecomplexityofthetradingrule,thelackofacoherentstoryortheory,theperformanceofout-of-sampletests,andtheadjustmentofreturnsforrisk,transactioncosts,andtaxes.Finally,wedocumentthattheFoolishFourandDowTentradingruleshavebecomepopularenoughtoinfluenceselectedstockpricesattheturnoftheyear.   `     h       %%*BusinessManagementDepartment,MarriottSchoolofManagement,BrighamYoungUniversity.Wewishtothank_Dianna_ԀBlack,DwightBlood,RogerClarke,KayeHanson,GaryKarz,andSallyTaylorfortheirhelpfulcomments.TheHaroldF.SilverFundatBYUprovidedfinancialsupportfordatabasesandresearchassistants.TheauthorsalsoreceivedfinancialsupportfromtheGoldmanSachsandtheDriggsfellowships,andfromFaneuilResearch.Sendcorrespondenceto:StevenThorley,MarriottSchoolofManagement,BrighamYoungUniversity,666TNRB,Provo,UT846023141,Voice(801)3786065,Fax(801)3785984,email:steven_thorley@byu.edu  -@)+   !MiningFoolsGold% Prologue  ` 0 0 (# (#0h(#(#0h(#h(#Whatfoolsthesemortalsbe.p(#(#    `     h   AMidsummersNightsDream `    Asreadersofthepopularbusinesspress,wearerepeatedlyconfrontedwithstoriesofsuccessfulinvestingstrategies.Everynowandthen,oneofthesestrategiescultivatesafollowingofdisciples,generatesabestsellingbusinessbook,andpropagatesalifeofitsown.OnesuchinvestmentstrategyistheMotleyFools FoolishFour,introducedinTheMotleyFoolInvestment 0  Guidein1996,itsassociatedAmerica_OnLine_Ԁforum,andTheMotleyFoolInternethomepage  whichwentonlineinAugustof1994.Inthebook,authorsDavidandTomGardnerreportthatfrom1973through1993theFoolishFourportfoliohadanaverageannualreturnof25.5percentcomparedtoonly11.2percentforthe30stocks(Dow30)intheDowJonesIndustrialAverage(DJIA).BeatingtheDow30byanaverageofmorethan14percentayearovertwodecadesisaphenomenalfeat.Thisamazingaccomplishment,combinedwiththeGardnerbrothersacerbicandamusingwriting,propelledthebooktothetopoftheNewYorkTimesbestsellerlistwithsimilarascensionsfortheInternetsiteandassociatedproductssuchasthesyndicatednewspapercolumn.  IntheGardnerswritings,theuseofthename Fools(capitalF)derivesfromShakespearesFoolsorcourtjesterswhooftenweretheonlymembersoftheroyalcourtwhodaredtoconfoundconventionalwisdomwithplainandsimpletruth.UsingthisFoolishtraditionofwisdomwrappedinaveneerofwitandwhimsy,theGardnersgivemuch#%#%$%$%neededfinancialadviceandexposemanyoftheself%%%%&%&%servingpracticesoftheWallStreetWise.WithapologiestoShakespeare,wepaytributetotheGardner'%'%s(%(%stylewiththehighestformofflattery,andattempttowritewithShakespeareanwit+%and+%with)%the)%*%inthe*%requisitefiveacts. -P(+ ! !8XXdXXd8 !    Inthispaper,weaddresstheissueofdataminingandquestionwhethertheGardnershave  discoveredinvestmentsgoldenchaliceorjustminedfoolsgold.WearenotparticularlyinterestedintheGardnersFoolishFourforitsownmerits.Rather,weareinterestedinusingthispopularinvestmentstrategyasavehiclefortwopurposes:first,toremindreadersaboutthepitfallsofdatamining;andsecond,toreadyremediesdesignedtohelpavoidthesepitfalls.  Dataminingisthepracticeoffindingforecastingmodelsbysearchingthroughdatabasesforcorrelations,patterns,ortradingrules.Aftersearchingoverenoughvariablesorrulessay,onehundredaresearcherwillfind,justbychance,aboutfivethatarestatisticallysignificantatthe95percentconfidencelevel.Dataminingbecomesparticularlyproblematicwhenthefinalpatternisproclaimedsignificantwithoutprovidingthenumberofunsuccessfulminingattempts.Discussionsofdataminingarenotnew;nevertheless,webelievethattherecentexplosionofdataavailabilityandthelowcostofcomputingpowermakeourinvestigationavaluableandtimelyreminder.( #  1      ׀ P   InActIwedocumenttheapparentFoolishFoursuccessinordertouseitforillustrativepurposeswhendiscussingdatamining.InActIIwediscussthepotentialpitfallsofdataminingwhendecidingbetweenrealityandcoincidence.InActIIIweprescribefourantidotestothesedataminingpitfalls.InActIVwediscusstheconsequencesofinvestorlearning,andweconcludeinActV. p&!$ Ї ActI.TheFoolishFour 0  0h(#(#0h(#h(#Whatsinaname?Thatwhichwecallarosebyany(#(#    `     h   otherwordwouldsmellassweet.   `     h   RomeoandJuliet p Scene1:AFoolishGenealogy  TheFoolishFourisaninvestmentstrategytoutedbyDavidandTomGardnerintheir_best,%,%-%-%selling_Ԁbook,TheMotleyFoolInvestmentGuide:HowtheFoolsBeatWallStreetsWiseMenand  p  HowYouCanToo,(hereafterTheMotleyFool)andontheirpopularwebsite,www.fool.com.Our P  interestinthisstrategyispedagogical:weneedacasestudytodiscussdataminingpitfallsandantidotes.ThebestwayforustoexplaintheFoolishFouristotrackitshistoricaldevelopmentorgenealogy,startingwiththeFoolishFoursgreatgrandfather,theDowDividendapproach.8  Greatgrandfather,DowDividend:TheDowDividendapproach(alsoknownasthe  DogsoftheDow)sortstheDJIAstocksbytheirdividendyieldsatthebeginningofeachyearandthenbuysanequallyweightedportfolioofthetenhighestyieldingstocks.ThisstrategywaspopularizedbyMichael_OHiggins_bookwithJohnDowns,BeatingTheDow,firstpublishedin1991.. #  2      P   8  Grandfather,DowFive:TheDowFivestrategycallsforanadditionalsortoftheten 0 DowDividendstocksbypriceand,eachyear,buyinganequallyweightedportfolioofthefivelowestpricedstockswithinthetenhighyieldingset.ThisstrategyisalsointroducedinBeatingtheDowandthemovetofivestocksisdiscussedinKnowles % # andPettysTheDividendInvestor,firstpublishedin1992.`'"%   8  Father,DowFour:TheDowFourrefinestheDowFivebydroppingoutthelowest  pricedstockintheDowFive,atweaktotheDowFivementionedby_OHiggins_ԀbutinstitutionalizedbytheGardnersinTheMotleyFool.p   8  Son,theFoolishFour:TheFoolishFournotonlyeliminatesthelowestpricedstock, P  butalsodoublesuponthesecondtotheloweststock.ThisunequalweightingstrategywasinstitutionalizedbytheGardnersbasedon_OHiggins_discussionofthesecondtothelowestpricedstockcalledthe PenultimateProfitProspect.    Thus.%,.%theFoolishFourfollowerwould,atthebeginningofJanuaryeachyear,fashionafourstockportfoliofromthefivelowestpricedofthetenhighestyieldingDowstocks.Thefourstockportfolioexcludestheverylowestpricedstock,thencallsfora40percentweightonthesecondtothelowestpricedstockand20percentweightsontheremainingthreestocks.InTheMotleyFool, P theGardnersreportthatfortwodecades,from1973to1993,theFoolishFourreturnedanannualaveragereturnof25percentandthatit shouldgrantitsfansthesame25percentannualizedreturnsgoingforwardthatithasservedupinthepast(page104).Wehaveonlyminorquibbleswiththehistoricalpartofthisclaim(25percentreturns),butduetothedatamininginvolved,wetakeexceptiontothelatterpart(thesame25percentannualizedreturnsgoingforward).SceneII:TheHistoricalDatàXXXX  InTable1wereportannualreturnsandsummarystatisticsforreturnsonanequallyweighted P(#& portfolioofallthestocksintheDJIA,theDow30,and#XXXXB(#XXXXallfourgenerationsoftheroyalfamily(the 0*%( DowDividend,theDowFive,theDowFour,andtheFoolishFour)aswella#XXXX;)#XXXXԀnewmemberofthe ,`'* family,theFracturedFour,thatwe_discusse_ԀinthenextAct.#XXXX*#ReturnsontheDJIAindexarenot  includedinthetablebecausetheindexignoresdividends.XXXXԀThefirmsincludedintheDJIAatthe  beginningofeachyeararebasedontheMay28,1996WallStreetJournalspecialreport 100Years p oftheDJIA.Dividends,prices,andreturnsarefromtheUniversityofChicagosCenterforResearchinSecurityPrices(CRSP)tapes.  Weformportfoliosusingtheclosingpriceonthefirstbusinessdayoftheyearandholdtheportfoliosuntilthecloseofthefirstbusinessdayofthefollowingyear./%/%/%/% #  3      ׀Whencalculatingreturns, @  weimmediatelyreinvestcashdividendsinthestockthatpaidthem.TheCRSPreturnsthatweusealsoincludenonstandarddistributionssuchaswarrantsanddividendspaidinsharesofanothercompany.ThesedistributionsarealsosoldimmediatelyandreinvestedintheDowstockthatpaidthem.InrarecaseswhereaDJIAstockceasestotradebeforetheendoftheyearduetoamergeroracquisition,weinvesttheproceedsforthestockintheCRSPtotalmarketportfoliountilthefollowingyear.#XXXXG+#XXXXThemajordifferencesbetweenourCRSPbasedreturnsandthereturnsbasedon 0 theWallStreetJournaldatafoundinTheMotleyFoolandBeatingtheDowaresummarizedin ` AppendixA.However,wenotethatourconclusionsarenotmateriallyaffectedbythesourceofrawdata.OurmotivationforusingtheCRSPdataratherthanprinteddatasourcesistoallowforoutofsampletestswithouthavingtogatherpricesanddividendsbyhand.  Thedividendyieldsusedtoformportfolioseachyeararebasedonthebeginningofyear $" price(i.e.,closingpriceonthefirstbusinessdayoftheyear)andtheannualizedvalueofthelastordinaryquarterlydividend.Thus,wechoosestockswiththehighesttrailingdividendyields.InTable1,wereportresultsfor24yearsofdata,1973to1996.The1973startingperiodmatchesthestartingperiodusedbytheGardners.Tous,the1973startdateseems,atbest,whimsicaland,atworst,theworkofdatamining.Hence,inActIVwealsoperformanoutofsampletestwithaseparate24yearperiod,1949to1972.The1996endingperiodisbasedontheavailabilityofCRSPdataatthetimeofourresearch(June1998).  Table1reportsthattheDow30portfoliohadanaverageannualreturn(arithmeticmeanofthe24annualreturns)of15.80percentandastandarddeviationof17.29percent(seethefirstcolumnofTable1).TheFoolishFourportfoliohadbothahighermeanandstandarddeviation,28.03and26.97percent,respectively(seethefifthcolumn). #  4      ׀TheFoolishFourstrategyhasbeen p spectacular;28percentperyearonaveragewithnoheavypicking!P #  5      ׀TheDowDividend,DowFive, P andDowFourstrategiesmeanreturnsincreasedmonotonicallyfromtheDow30totheFoolishFour,justasifeachsuccessiveportfoliowasabetterinvestmentstrategythanthepreceding portfolio.Ofcourse,thismonotonicimprovementinhistoricalmeanreturnscouldalsobetheresult @ ofsuccessiveroundsofdatamining.2%*2%2%"2% #  6      ׀#XXXX+0#ԀAretheGardnersgallantgeniusesguidingustowardgenuine   gems,oraretheymerelymundaneminersmanipulatingustowardmediocremendacitythatisthequestion.(Wecallthiswordmining). ActII.TheGoldenChalicevs.FoolsGold 0  Wiselyandslow;theystumblethatrunfast.0 (#(#    `     h     RomeoandJuliet  p    Asresearchers,weareunabletofullyanalyzethesignificanceofastrategythatworkedinthepastwithoutknowinghowmanystrategieswereexploredunsuccessfully.ThisinabilityincludesunsuccessfulstrategiestriedbytheGardnersthemselves(whichwecallintragenerationalmining)  andunsuccessfulstrategiestriedbypriorinvestmentadvisorssuchasMichael_OHiggins_ԀorKnowlesandPetty(whichwecallintergenerationalmining)XXXX)@ #  7      .Theinabilitytoassessthe  significanceofatradingrulefoundafterextensivecollectivesearchinghasbeendubbedthe filedrawerproblembyIyengarandGreenhouse(1988)and dataminingbyMerton(1987),Black(1986,1993),andLoandMacKinlay(1990).%  #  8      ׀Essentially,thetruestatisticalsignificanceof  p successfulinvestmentstrategiescanbeassessedonlyafterquantifyingthenumberofunreportedorunpublishedfailuresgatheringdustinthefiledrawersofstockmarketanalysis,traders,andresearchers.Becausewedonotknowthedegreeofdataminingthatledtothisone successfulrule,wecannotdirectlyaccessitssignificance.Blacks(1993)commentsonthedisappearanceofthe sizeanomalyseemanappropriatecaution:8  Whatthissoundslikeisthatpeoplesearchedoverthousandsofrulesuntiltheyfoundonethatworkedinthepast.Thentheyreportedit,asifpastperformancewereindicativeoffutureperformance.Aswemightexpect,inreallifeoutofsampledata,theruledidntworkanymore.    #XXXX>#  TheGardnersseemtounderstandtheprincipleofdatamining,atleastinitsintragenerationalform,andexposethepracticeusingthelabel backtestinginsteadof datamininginthefollowingaccount(seepage264ofTheMotleyFool)ofStephenLeebsMasterKey  investmentstrategywhichpromisedincrediblereturns:8  Howwasthis MasterKeyinvented?Backtesting.Inotherwords,usingpastresults,somebodyessayedtodevelopaformulathatsucceededinidentifyingtheoptimaltimestobuyandsellstocksoverthepasthistoryofthemarket.Beginningwithabasicpremiseforwhentobuyandwhentosell,theresultingformulawouldthenbetweakedanytimeitdidntwork.Letssaythebacktesterformulatedthingsthisway:BuyonMondays,sellonTuesdays.HewouldthenbeginbacktestinguntilhehitasnaginwhichitwasactuallybettertobuyonTuesdayandthensellonMonday.LetssaythatfirstsnagcameinAugust1994.Thebacktesterwouldthentweakthebacktestedformulatosay, BuyonMondaysandsellonTuesdays,exceptinAugust1994whenyoubuyonTuesdayandsellonMondays.Andsoon.Onceyougobackfarenoughandinventenoughexceptions,youcanendupdevisingaperfectmarkettimingformula.Unfortunately,youwouldhavewastedyourtime;suchaformulahasnopredictivevalueorusefulapplication(otherthantounscrupulousadvertisementcopywriters.)    TotheGardnerswesay: Mischief,thouartafoot.IsswitchingMondaysforTuesdaysthatfarremovedfromswitchingfromfivetofourstocksbydisdainingthelowestpricedhighyieldingstockwhilesimultaneouslydoublinguponasimilarstockthatonlysellsfortwobitsmore?Prithee, ,`'* shouldntweplaybyonesetofrules?  Giventhenumberofcreativepeopleworkingintheindustry,thefloodofdata,andtheexplosionofcheapcomputingpowerandcannedstatisticalsoftware,wewouldbesurprisedifaleatoryhistoricalpatternsinstockreturnswerenotregularly discovered.Givenenoughmonkeys,typewriters,andtime,eventuallyamonkeywillproduce: Friends,Romans,countrymen,lendmeyourears!Furthermore,theprobabilityoffindingsuchalinewouldincreasesubstantiallyifsocietyrewardedthefinderwithpower,prestige,andthechoiceofanendowedchairatawellknownschoolofbusiness,aWallStreetbonusbigenoughtoendowsuchachair,ortheproceedsfromabestsellingbook.  Toillustrateourpoint,wetookashotatthedatamininggameourselves.Vestedinoursteeltoedbootsandhardhats,wetumbledfromourivorytowerandslitheredintotheshaft.JustasMichael_OHiggins_ԀnoticedthatthehighyieldingstocksintheDJIAhadhighsubsequentreturns,andjustasKnowlesandPettynoticedthatthefivehighestyieldingstocksperformedparticularlywell,andjustasAnnColeman,editoroftheWeeklyFool,noticedthattheverylowest5%5%6%6%pricedstock ` performedpoorly,andjustas Gazingonthenumbersaminutemore,aFoolfurthernotesthatthesecondlowestpricedstock...providedunbelievablereturnsoverthepasttwodecades(seepage85ofTheMotleyFool),we,too,noticedsomething.WenoticedthatallfouroftheFoolishFour "  stockstypicallydidwellinevenyearsbutnotoddyears.Thus,inthespiritoftheFools,weformedourownnewmemberoftheDowDividendclan,thecrownprinceofthefamilywecallthe FracturedFour.InourFracturedFour,weproscribeholdingtheFoolishFourstocksinequalweightsinevenyearsandbuyingonlythesecondtotheloweststock(PenultimateProfitProspect)inoddyears.Lookhither,OyeFools,theFracturedFourearnedanaveragereturnof34.82percent ,`'* (seeTable1),nearly35percentayearwitha24yeartrackrecord!JustastheFoolishFourbeatitsgreatgrandfather,theDowDividend>%,>%byabout8percentperyear,theFracturedFourinturnbeatitsfather,theFoolishFour,byalmost8percentperyear.Andwediditinjustonegeneration(or p sowesay).TheKing(FoolishFour)isdead,longlivetheKing(FracturedFour).  Now,incaseyoumissedthepoint:donttrythisathome.OurpurposeindescribingtheFoolishFourandintroducingtheFracturedFourisnottoevaluateaspecificstrategyortogiveinvestmentadviceofourown,buttoevaluatethepitfallsofdatamining.OurhopeisthattheFracturedFourissoobviouslytheproductofintergenerational(andperhapsintragenerational,wewonttell)miningthatitdriveshomethepoint: successfulinvestmentstrategies,eventhosethathavebeen successfulfor24years?%,?%mayturnouttobefoolsgold,notagoldenchalice. ActIII.AntidotesforDataMining 0  SomethingisrotteninthestateofDenmark.P(#(#    `     h   !Hamlet @   Datamininghappens.Praytell,nowwhat?Inthefollowingfoursceneswegivesomesuggestionsdesignedtohelpinvestorsrecognizethesignsof,andthentestfor,mining. Scene1.WarningSigns "    Themoststraightforwardwarningsignofdatamining,ifacknowledgedbytheinvestigator,isahighnumberofvariables.DavidLeinweber(1998),inhissatiricstudyF%,F%StupidDataB%B%C%C%D%mD%E%ME%in@%ing@%A%erA% p&!$ Tricks,minestheUnitedNationsG%G%databaseandfindsthatbutterproductioninBangladeshcan P(#&  predict75percentofthevariationintheStandard&Poors500stockindex.Searchingoverallthe 0*%( variablesintheUNdatabaseisadeadgiveaway. #  9      ׀TheGardnerscomment, But21percentgrowth   annuallywasntenoughforFoolsinouronlineforum,whobegantopickapartthehistoricalnumbers,aspiringtoconstructmoreprofitablemodelsH%H%(page84ofTheMotleyFool),I%I%shouldalso p raisearedflag.Intergenerationalminingmaybehardertorecognize,butafewwordssuchas notesor noticedJ%,J%thatbuildoneachothershouldraisesuspicions.Thesewordsindicatethatthenewgenerationofminersischoosingthedirectionforprospectingafterobservingthefindingsofpriorminerswhousedsimilardata.ExamplesofthesetelltK%eK%L%aL%lM%lM%N%eN%signsofintergenerationalminingincludeTheMotleyFools inhistext_OHiggins_Ԁnotesandouruseofthephrase wenoticedthat.   Takentogetherwithitsforefathers,ourFracturedFourportfoliohasatleastsearchedoverdividendyields,prices,years,numberofstocksintheportfolio,andweightingschemes.OnewondersO%,O%whatelsewastried?DidresearcherslookattheS&P500beforetheDow?Didtheyunsuccessfullysearchoverindustries,startingdates,P/Emultiples,saleslevels,numberofanalysts,lengthofdividendhistory,priorreturns,booktomarketratios,andlettersinthealphabet?Wedontknow;andthat,dearreader,isthepoint.  Arelatedproblemisnotknowinghowmanydifferentfundswereactuallystartedbyaninvestmentgroup.Datamininghasacleverunderstudywecall portfolioprospecting.Briefly,amutualfundfamilycould,withoutfanfare,startseveralsmallfunds.Threeyearslateroneofthose fundswillhaveunusuallyhighreturnsjustbychance,andwithalltheflagsandthetrumpetsitis $" hardnottofocusonthewinner. #  10      ׀ThusP%,P%portfolioprospectingaperniciousgameoflosers   concealedandwinnersrevealedyieldsanotherwarningsign.Inlightoftheportfolioprospectingproblem,thereportsbyGaryKarzsandMark_Hulbert_Ԁmakeussuspicious.Theyreportthat,earlyon,theGardnersstartedandstoppedseveralfunds.OneFoolishportfoliocalled RunningWiththeMarketwasclosedaftersixmonthsofpoorperformance.Reportedly,anotherportfoliostartedbytheGardnersslightlyunderperformedthemarketin1994,andthisportfoliodidnotmakethejumpfromtheirprintednewslettertotheirbookoronlineserviceQ%.Q%(See_Hulbert_Ԁ(1998)andKarzsinvestmentsite,4Lte O  5  www.investorhome.com/fools.htm6gOgThre  7teg4OteO  5  6WhOkhThre  7tehԀalongwiththeFoolishresponseat   www.fool.com/pr/htm).R%R%Furthermore,theactualmakeupoftheFoolishFourhasrecentlychanged.  OurdescriptionoftheFoolishFourisfromthe1996bookandwasthedefinitionwhenwestartedthisarticle.Butalas,thisdescriptionisnolongervalid.On30December1997,DavidGardnerannounceda policychangefortheFoolishS%S%T%T%Fourmodel(seewww.fool.com/DDow/1997/DDow971230.htm).Atweakbyanyothernameisstillatweak.Inthis 0  policychange,outwentdoublingupbutincameequalweightsandanewdoublerankingsystem(bydividendyieldandbyprice)whichonlyrarelyexcludesthelowestpricestock.ThisnewFoolishFourwasformerlycalledTheUnemotionalValueorUV4. #  11      ׀Givenourrecentdiscussionofwarning   signs,thefollowingexplanationforthetweak,givenontheFoolswebsite,needsnoexplanation. Whytheswitch?HistoryshowsthattheUV4hasactuallydonebetterthantheoldFoolishFour $" (see4#et"O  5  www.fool.com/DDow/1997/6mOmThre  7et nDDow971230.htm).  Scene2.NoStory  Thelackofanymotivefortweakingarule,besidesthefactthatitworksbetterhistorically,isanotherdataminingwarningsign.Avalidtradingstrategymusthaveaplausibletheoryorstoryastowhythestrategyworks.Ontheonehand,theFoolishFoursgreatgrandfather,theDowDividendportfolio,canbejustifiedasanapplicationofvaluestyleinvesting.Thestoryisthatsomestocksfalloutoffavorinthemarketplace,perhapsasanoverreactiontobadnews,andthatthesestocksareavailableatlowerthanfairprices.Acomparisonoffinancialratioslikedividendyield,P/E,ormarkettobook,hasthepotentialtorevealundervaluedsecurities.Ofcourse,onehastowonderatthesimplisticwaythevaluestyleofinvestingisappliedintheDowDividendportfolio(i.e.,onlylookatthethirtyDJIAstocksandalwaysbuyexactlyten),butatleastacoherenttheoryforlookingatdividendyieldexists.  Ontheotherhand,asimplecomparisonofrawsharepricesbetweendifferentsecuritiesisnonsensicaltheonlydifferencebetweena$20anda$10shareisastocksplit.Evenifsortingbyrawsharepricewasgroundedinlogic,theparadoxofchoosingbetweenthetwolowestU%U%V%V%pricedstocksremains.Whattheorypartitionsthesetwoverysimilarstocks,differingbyonlyafewcentsinprice?Whatmakesoneaperpetuallooser,notworthyofpurchase,andtheotherapersistentwinner,worthyofanextraproportion?Whatisthejustificationfora40percentproportion,besidesminingthehistoricaldata?HavewecompletelymissedthegrandunifyingGoldilockstheoryofstockprice(nottoolow,nottohigh,butjustright)?Beware,dearreader,ofaplayfullofoddcoincidenceswithoutaconvincingplot.ThefamousNFL/AFLSuperbowltradingrulewasminedbysports ,`'* mindedtradersinthe80's,anditalso workedfordecades,butonlyafterthefact.  Inhisbook,AgainsttheGods:TheRemarkableStoryofRisk,PeterBernsteincautions  againstnotonlysimple,butalsocomplextradingrulesvoidofthenecessarystoryortheory.8  Likenesstotruthisnotthesameastruth.Withoutanytheoreticalstructuretoexplainwhypatternsseemtorepeatthemselvesacrosstimeoracrosssystems,theseinnovationsprovidelittleassurancethattodayssignalswilltriggertomorrowsevents.Weareleftwithonlythesubtlesequencesofdatathattheenormouspowerofthecomputercanreveal(page334).      Unlikeagoodstoryinaplay,agoodstoryinatradingstrategyisanecessarybutnotasufficientconditionforatradingstrategytohavevaluegoingforward.Onceitssuccessisspotlighted,evenastrategywithasuitablestorywilllooseitsstingonceitisseen.ThepropensityforsuccessfulstrategiestoloosepredictivepowerisonemanifestationofthedreadedEfficientMarketHypothesisfromfinancialeconomics.Economistsassertthatpublicinformationaboutastock,suchasthefactithasahighdividendyield,isquicklyandaccuratelyincorporatedintoitssharepriceasinvestorsbuyandsellonthatinformation.Intheextremeformofthistheory,themarketpriceisalwaysthebestpossibleestimate(basedonpubliclyavailableinformation)ofastockstruevalue.Ifthemarketpricecorrectlyincorporatesallpublicinformation,thennostockisabetterinvestmentthananyother,andmostofusmightaswellinvestinanindexedmutualfund.  FightingagainsttheEfficientMarketHypothesiscanbefoolhardy.Thehypothesisisselfhealing.Anomaliesmakeitstronger.Eachtimeacombatantilluminatesachinkinitsarmor,thisveryfindleadstocompetitionamongothercontestantswhicheliminatestheanomaly.Welaughattheoldjoke,butevenifW%theW%Foolsclaimthatpeoplefind100dollarbillsinthecanyonsofManhattan,theymustconcedethatthebillswouldnotbeonthesidewalkforlong.Leeand  +p&) Verbrugge(1996)observethatempiricalflawsinthetheoryactuallycausethetheorytobecomemorerobust.Theycomment: Thosewhodothemosttoensurethattheefficientmarkettheoryremainsfundamentaltoourunderstandingoffinancialeconomicsarenotitsintellectualdefenders,butthosemountingthemostseriousempiricalassaultsagainstit.  OnedoesnotneedtobeamarketefficiencyextremisttodismisssimpletradingrulesliketheFoolishFour,evenifitdidhaveaplausiblestory.Whilethestockmarketmaynotbeperfectlyefficient,competitionamongthemillionsofindividualandinstitutionalinvestorsintheUnitedStateswilleliminatethevalueofsimpletradingstrategiesoncetheyaremadepublic.Ultimately,theonlypotentialvalueofasimpletradingrulepublishedinabestsellingbookistoexploitthosewhofollowit.InActV,wewillshowthatexploitationmayinfactbehappeningwithrespecttotheFoolishFour.Scene3.OutofSampleTests  Warningsignsandthelackofareasonabletheoryleadustoamoreconcreteantidotetomining:testingthestrategyoutofsample.ContinuingwiththeFoolishFourillustration,ifowninghighyieldlowprice(butnottoolow)stocksisrewarding,shouldntthisstrategyworkinthe1950'sand1960's,aswellasinthe1970'sand1980's?ShouldntitworkinJuly,aswellasJanuary?ShouldntitworkinEuropeandAsia,aswellasintheU.S.?Truthdoesnotchangeeverytimeweturnthecalenderorcrosssomearbitrarylineonamap.Realtruthshouldhavelegs.Withtruthsrobustnessinmind,wetesttheFoolishFourstrategybytravelingoutofsampleintwodirections.First,inordertomatchtheGardnerssamplesize,welookatthe24years,1949to1972,justpriortotheinsampleperiod.Second,usingtheinsampleyears,1973to1996,weinitiatetheFoolish ,`'* FourstrategyonthefirstbusinessdayeveryJuly(i.e.,midyear)ratherthanthefirstbusinessdayofJanuary.Ifoursuspicionsbasedonwarningsignsandthelackofaconvincingstoryareright,theFoolishFourshouldnotbeattheDow30bythelargepremium(12.23percentperyear)foundinsample.$ #  12       P    InTable2wereportthe1949to1972resultsfortheFoolishFourandtheDow30.Overthisoutofsampleperiod,theDow30portfolioreturned14.11percentayearonaverageandtheFoolishFourportfolioreturned14.43percent.TechnicallytheFoolishFourdidbeattheDow30outofsample,but0.32percentmaynotbeworthwritinghomeabout.InTable2wealsoreporttheresultsofinitiatingtheFoolishFourstrategyatthecloseofthefirstbusinessdayinJuly,andholdingitforayearbeforerebalancing.Thus,thistestisonlypartiallyoutofsample,sinceweareinsamplewithregardstofiscalyears,1973to1996,butoutofsamplewithregardstotheanniversarydayofranking,buying,andselling.WhenlabelingtheresultsinTable2,wedesignatethe12monthperiodendingthefirsttradingdayofJuly1996,asfiscalyear1996.Usingthismidyearapproach,theDow30averaged14.35percentwhereastheFoolishFouraveraged17.30percent.This2.95percentdifferencemaybeworthwritinghomeabout;butforsooth,itisafarcryfromthe12percentminedusingJanuarydata,andmaynotbeworthwritingabookabout.BewaretheidesofJuly.  AthirdpotentialoutofsampletestistolookatreturnssincetheFoolishFourwasdiscovered.Unfortunately,withonlyafewyearssincethebookspublication,afullstatisticaltest $" ispowerless.Forwhatitisworth,wecanlookat1994tothemiddleof1998(thetimewepennedthistome)asanecdotalevidence.In1994,theFoolishFourlostmoneyinayeartheDow30wasup.Thenin1995,1996and1997,theFoolishFourbeattheDow30.Sofar(asoftheendofJune1998),theFoolishFourhasnotfairedwellin1998,uponly4.5percentwhereastheDow30isup14.2percentasreportedbytheFools(seewww.fool.com/DDow/DowReturns.htmforupdates.) 0    Insummary,inourlongestandcompletelyoutofsampleresults,the1949to1972period,theFoolishFourandtheDow30hadalmostidenticalreturns.InourquasioutofsamplemidyeartesttheFoolishFourbeattheDow30byabout3percentayear.Andthepost1993anecdotalevidencefindsthattheFoolishFourbeattheDow30inthreeofthelastfiveyears.TotheGardnerscredit,theFoolishFourprobablybeatthemajorityofactivelymanagedfunds.ButtheFoolishFourisnotatremendoustravelerandisrathertimidinnewterritory.ItdidnottrouncetheDow30bythedoubledigitstypicalonitshomestage.Aswediscussnext,however,eventhe12percenthomestagepremiumistenuous,sincejudgingstrategiesbytheirunadjustednominalreturnscanbetricky. Scene4.Risk,TransactionCosts,andTaxes @   XXXXAlthoughtheanalysisinTable1,andtoamuchlesserextentTable2,showsthattheFoolish   FourportfoliohadhighermeanreturnsthantheDow30,italsoshowsthattheFoolishFourhadhigherrisk(asmeasuredbythestandarddeviation.)Inaddition,followingtheFoolishFourstrategyrequiresmanymoretradesthanfollowingtheDow30strategy.Finally,byconstruction,alargerportionoftheFoolishfourreturncomesintheformofdividends,whichhadataxdisadvantageduringmuchofthesampleperiod(priorto1987andsince1993.)WenowadjusttheFoolishFourresultsforitshigherrisk,morefrequenttransactions,andtaxdisadvantagesfollowingtheworkof ,`'* McQueen,Shields,andThorley(1997).& #  13          SharpsportfolioperformancemeasurecanbeusedtocorrectorpenalizetheFoolishFourportfolioforitshigherdegreeofrisk.Withonly4stocksintheportfolio,anda40percentweightonjustonestock,asubstantialamountofunsystematicriskremains,resultinginahigherstandarddeviationthanthebetterdiversifiedDow30portfolio./P #  14      ׀Usingthe1973to1996Treasurybillannual 0  meanof7.18percent,theFoolishFoursreturncanbetransformedtoariskadjusted20.55percent(withastandarddeviationof17.29percent,similartotheDow30portfolio).  #  15      ׀Thisadjustmentis @  akintoinvestingabout64percentofonesmoneyintheFoolishFourportfolio,with36percentinTreasurybills.AddingthisproportionofTreasurybillstotheoverlyriskyFoolishFourportfolioresultsinanadjustedportfoliowithastandarddeviationexactlyequaltotheDow30,facilitatingafaircomparison.Withoutadjustmentsforrisk,thedifferenceinthetwoportfoliomeansis12.23percent(28.0315.80)#XXXX^#XXXX.However,theFoolishFourriskadjustedreturnisonly20.55percent,and P thedifferenceshrinksto4.75percent(20.5515.80).Thus,riskaloneexplainsmostoftheFoolishFourin-samplepremiumovertheDow30portfolio.AsimilarcomparisonoftheFoolishFourto ` itsGreatGrandfather,theDowDividendportfolio,showsasmalldeclineintheriskadjustedmean  return.Inotherwords,therehavebeennoimprovementsinriskadjustedperformancesincetheoriginalDowDividendportfoliowasdiscovered.Apparently,theminerswerelookingforhighreturns,notlowrisk.  Wenowturnourattentiontotransactioncosts.ThestocksintheDJIAhavebeenrelativelystable.ThemostrecentchangewasMarch1997,whenTravelersGroup,HewlettPackard,Johnson&Johnson,andWal*MartreplacedWestinghouse,Texaco,BethlehemSteel,andWoolworth.Thenextmostrecentchangewas6yearsearlier(May1991)whenCaterpillar,J.P.Morgan,andWaltDisneyCompanyreplacedNavistarInternationalCorporation,PrimericaCorporation,andUSXCorporation.Infact,foroursampleperiod,anaverageofonly0.50outof30firmschangedintheDJIAeachyear.Comparatively,thefirmsintheFoolishFourportfoliowerequitevolatile.Onaverage,2.39outofthe4firmschangedeachyear,resultinginalargetransferofwealthfromtheFoolstotheWallStreetWise.Remember,lowcostonlinetradingisarelativelyrecentphenomenon.Ifweassumea1.00percentonewaytransactioncost,1.20percentoftheFoolishFourswealthislosttotransactioncostsinatypicalyear,whereasonly0.03percentoftheDow30'svalueislostindissipativetrading. #  16      ׀Aftertransactioncostsareaccountedfor,theriskadjusted4.75   percentFoolishFourspremiumfurtherdecreasestoonly3.58percent(19.3515.77.)Inthetwooutofsampletests,theFoolishFourspremiumiseithernearlynilorworse,negative.  NextweconsidertwoDow30taxadvantagesforanindividualwithamultipleyearholdingperiodandassetsoutsideofanIRA.First,capitalgainsaretaxedonlywhenthegainisrealized.BecausetheDow30resultsinfewertransactions,itallowsforlongertaxdeferment.Second,dividendsaregenerallytaxedatahigherratethancapitalgains;yetX%,X%bydefinition,theFoolishFourdeliversmoreofitsreturnintheformofdividends.Withtheexceptionofthe1987to1990taxyears,capitalgainshavereceivedfavorabletaxtreatment.  AformalanalysisoftheDow30'stwotaxadvantages(longerdefermentandlowertaxrates)woulddependonanindividualsmarginaltaxrateandyearbyyeartaxlawchanges,particularlythecapitalgainslaw.Yet,afterweadjustforriskandtransactioncosts,amere3.58percentpremiumremainsfortheFoolishFourstrategy.WebelievethatmostofthisdifferencewouldhavebeencapturedbytheIRS.  LikeMacbethstriadof thunder,lightening,andrain,thetriplethreatofrisk,transactioncostsY%,Y%andtaxescandodamagetonominallyprofitablestrategies.BurtonMalkiel(1998,page36)conclusionZ%sZ%isquiteconclusive: Investorsshouldbeverywaryofanyschemethatpromisesunusuallylargereturnsbasedonpastpatternsofstockreturns.Relativetoabuyandholdstrategy,theonlybeneficiariesarelikelytobeyourbroker,thetaxcollectorandbookauthors.#XXXX# $"  P(#&  ActIV.FoolingtheFools 0  0h(#(#0h(#h(#O,sir,towilfulmen,theinjuriesthattheythemselves  procuremustbetheirschoolmasters. (#(#    `     h   !KingLear    RegardlessofwhethertheFoolishFourisaproductofcoincidenceorreality,thegoldenchaliceorfoolsgold,acaveatregardinginvestorlearningiscalledfor.Marketparticipantsarenotfools.EventhestarchedshirtandsuspendersgangonWallStreethaveagileintellectsandsharppencils.IfsomeinvestorsnoticethatFoolsflocktotheFoolishFourstockseachJanuary,thentheseinvestorswilldesignasimpleruletofleecethem.Inaformoffrontrunning,aninvestorcouldbuy,say,inlateDecember,thestocksmostlikelytobeintheFoolishFour.Then,onthefirstbusinessdayofJanuary,watchastheFoolishFourfollowersbidupprices.Ofcourse,ifthesefleecersregularlyboughtinlateDecembertotakeadvantageoftheFools,theytoocouldbecomethetargetsofnewfrontfrontrunners,who,inturn,wouldfeedthefrontfrontfrontrunners,andsoon.Inthisfashionofinvestorlearning,anypublicizedpatterninreturnsshouldbearbitragedawaybythewolvesonWallStreet.  InFigure1,withdatasincethestrategywaspublicized(1994to1997),weshowevidencethatthepopularityoftheFoolishFourstrategy,togetherwiththeDowDividendstrategy,isinfactlargeenoughtoaffectmarketprices.CumulativeexcessreturnsareplottedovertimewithdayzerobeingthefirstbusinessdayinJanuary.ThegraphprovidesweakevidenceofabnormalbuyingstartingaboutfiveorsixdayspriortotheofficialproscribedFoolishFourstartingday.Then,onthefirstdayofthenewyear,pricesclearlyjump.Consequently,attheendofthefirstdayoftrading, strictfollowersoftheFoolishFourstrategyendupbuyinghigherpricedstocksandmissouton @)$' severalpercentagepointsofpotentialreturn.SomebodyhasbeenfoolingtheFools.`%_1`%`%<`% #  17      _Ԁ     AninterestinganecdoteregardinginvestorlearningistherunupinpricesontheFoolishFourstocksbeforetheopeningbellonthefirsttradingdayin1998.Forexample,EastmanKodakclosed1997at$609/16[%,[%andopened1998at$621/8andInternationalPaperclosed1997at$431/8andopened1998at$45.AnyonefollowingtheFoolishFourstrategyonthefirsttradingdayin1998clearlygothurt.Then,ontheirwebsite,theGardnersreportedtheloweryearend\%\%]%]%closingpricesasthebasisforbeginningthenewyearwhentheseprice^%s^%werenotavailabletofollowerswhodutifullyboughtonthefirstbusinessday.Marry,somedisciplesweredisillusioned(seewww.fool.com/ddow/1998/DDow980105).   V.TheFinalAct 0 0 (# (#0h(#(#Wisdomcriesoutinthestreets,andnomanregardsit.ph(#h(#    `     h !HenryIVpart1 `   Whathavewelearned,orhasourplaybeenmuchadoaboutnothing?Firstofall,usingThe @ MotleyFoolsFoolishFourmodelportfolio,welearnedsomethingaboutthepitfallsofdatamining.  p Welearnedthatbydiggingthroughenoughdataortradingrules,onewillfindsomethatworkjustbychance.Infact,withinafewminutesoflookingatthedata,wewereabletomineanuggetofourown:theFracturedFour,whichhadahistoricalaveragereturnof34.82percentover24years.Shouldwestartanews_%_%letter,writeabook,andsetupawebsite?Aucontraire;wewillremainunknownlegendsinourmine.OurFracturedFourwillnotworkwelloutofsample.Itisatleast % # theproductofintergenerationaldataminingoverindexes,dividendyields,prices,years,numberofstocksintheportfolio,andweightingschemes.Nooneknowswhatothervariables,rules,orpatternshavebeenminedbypriorprospectors.Thus,wehavelearnedthatbecauseofubiquitousminingactivity,all successfulinvestmentstrategiesaresuspect.  Second,armedwithoursuspicion,wehavelearnedsomewaystoavoiddataminingstempest.Vigilanceforwarningsignsisagreatstartingpoint.Themorevariablesinvolved,the `  morelikelythestrategyworkedjustbychance.Also,rulesthatarebuiltupontheshouldersofpriorsuccessfulrulesareguiltyofintergenerationalmining.Next,letreasonbeyourguide.Havinga   plausibleandreasonabletheoryc%ofc%whythestrategyworkedisfarmoreimportantthanjustknowingthatitdidwork.Havinganappreciationoftheverycompetitivenatureofinvesting(EfficientMarketHypothesis)isessential.Remember,inonesense,themarketpricerepresentsthecollectivewisdomofallinvestors.Therefore,theoriesorexplanationsbasedondumb,lazy,ormyopicmarketparticipantsarenottobetrusted.Then,testingsuccessfulstrategiesoutofsamplecanbe 0 enlightening.Truthshouldhavelegs.A truetradingruleshouldbeabletotraveltoothertimeperiodsandothercountries.Finally,neverbeimpressedwithunadjustednominalreturns.Manytradingrulesthatyieldhighnominalreturnscomeataprice.Lookforthehiddenpricetagsofhigherrisk,highertransactioncosts,andhighertaxes. "    Third,wehavelearnedthatallisnotwellthatendsnotwell.Anypopularinvestmentruleorstrategywillfallvictimtoitsownsuccess.Asevidencethatamultitudeofforty_niners_Ԁwillbedescendingonafewminesismadepublic,frontrunningminersandmerchantswillmaneuvertoprofitfromthemigrationand,intheprocess,_marginalize_Ԁthemine.Theownersofdataminesoftenfindapparentanomalies.Evenso,afterworkersdiginvirginterritory,andaftertheowners,brokers, ,`'* IRS,andfrontrunnersstripofftheirshare,whatpartofthemineisleft?YouguesseditTheShaft!  Weendonamorepositivenote.AlthoughwehavebeenunkindtotheGardnersFoolishFourmodelstrategy,wearenotcallingforabilliondollarbonfireofbestsellingbooks.WefindmuchoftheGardnersadvicetobeaccurate,timely,andfun.Advicefoundintheirsecondbook, P  YouHaveMoreThanYouThink,(i.e.,stopgambling,savemore,investlongterminstocks,avoid 0  highcommissions,enjoylife)issorelyneeded.WealsoresonateandjoinwiththeGardnersdrumbeatcallingformorefinancialeducationinprimaryandsecondarypubliceducation.Wewouldrecommendthaty%,y%aspartofp%n%thatn%p%q%thq%t%q%iq%t%r%q%rq%r%s%es%u%iu%s%rs%financialeducationv%,studentsbetaughtthedangersofdataminingv%w%inthateducationw%x%.x%  p   AppendixAAfterimplementingthevariousDividendInvestorstrategiesusingtheCRSPdatafiles,wecomparedourresultstothosereportedinahistoricaldatasetsoldonTheMotleyFoolswebz%z%site.Thefourmajordifferencesbetweenthetwosourcesare:1)Inourreturns,allcashdividendsarereinvestedimmediately,whereas,inTheMotleyFools 0  returns,cashdividendsareheld,withoutinterest,untilthefirstbusinessdayofthefollowingyear.2)Inourreturns,allwarrants,dividendsintheformofothercompanysstock,andothernoncashdistributionsaresoldoffandtheproceedsarereinvestedinthedistributingstock.InTheMotley @  Foolsreturns,thesenoncashdistributionsarehelduntilthefirstbusinessdayofthefollowingyear. 0  Forexample,inmid1992eachshareofUnionCarbidedistributedanothershareofPraxair.OurreturnsimmediatelysellthePraxairshareandreinvesttheproceedsinUnionCarbide,whereasThe  MotleyFoolsreturnsholdPraxairuntilJanuary5th1993.  3)BothourreturnsandTheMotleyFoolsreturnscalculatedividendyieldsasfourtimesthemost  recentordinarydividenddividedbythefirstbusinessdaysclosingprice.However,onseveraloccasionstheCRSPsclassificationof ordinarydiffersfromTheMotleyFoolsclassification. p 4)WefoundthatTheMotleyFoolsreturnshaveasmallnumberoferrorsincludingdataentry P errors,noncashdistributionerrors,andDJIAmembershiperrors.Anexampleofeachtypeoferrorfollows:0  TheCRSPtapesandtheWallStreetJournalbothreportthatonMonday,January3,1977,  p StandardOilofCalifornias(nowChevron)closingpricewas$405/8,notthe$587/8reportedinTheMotleyFoolsdataset.Incident{%al{%ly,StandardOilofIndianadidcloseat$58 P 7/8andStandardOilofIndianawaslistedjustbelowStandardOilofCaliforniaintheWall @ StreetJournal.0(#(# 0  In1991,USXsplitintotwosecurities.AnexistingUSX_stock|%|%holder_ԀreceivedonefifthofashareofanewclassofstockcalledUSXU.S.SteelGroupforeacholdUSXshare.USXsharesoutstandingwerethenevenlyexchangedforUSXMarathonGroupstock.Thus,theoldsharewasdividedinto0.2sharesofUSXU.S.SteelandonefullshareofUSXMarathon.TheMotleyFoolsreturnsarebasedonashareholderreceivingonefullshareof % # USXU.S.,notthe20percentofashareactuallydistributed. 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TheDangersofDataDrivenInference:TheCaseofCalendarEffectsinStockRet~%r~%u%r%ns.LondonSchoolofEconomics,FinancialMarketsGroup,DiscussionPaperNo.304,1998b.  % #   Table1HistoricalReturnsandSummaryStatisticsforVariousDowDividendPortfolios1973to1996F*q67 ddd Xdd Xdd X(#(#q,Z,Z,Z,Z,Z,Z,Z+  ," `  (@,?+ 4 <DL!X?Year 'x 3@ @'Dow30 'x  3@ 'DowDividend 'x  3 @'DowFive 'x  3@ @'DowFour 'x 3@ 'ЀFoolishFour 'x 3 'FracturedFour ?5x 3 ( (?73 ' 3 'Є10.03 ' 3 '4.92 ' 3 '20.97 ' 3 '28.07 ' 3 '31.73 ' 3 '46.39 ?5 3 ( (?74 ' 3 'Є15.49 ' 3 '1.46 ' 3 'Є3.67 ' 3 '6.28 ' 3 '3.73 '  3 '6.28 ?5 !3 ( (?75 '  "3 '49.46 '  #3 '60.78 '  $3 '73.69 '  %3 '78.33 '  &3 '93.61 '  '3 '154.73 ?5  (3 ( (?76 '( )3 '31.53 '( *3 '35.23 '( +3 '41.15 '( ,3 '41.72 '( -3 '44.57 '( .3 '41.72 ?5( /3 ( (?77 '@ 03 'Є13.30 '@ 13 'Є1.90 '@ 23 '0.49 '@ 33 'Є1.24 '@ 43 '0.28 '@ 53 '6.36 ?5@ 63 ( (?78 'X 73 '0.92 'X 83 '2.77 'X 93 '3.08 'X :3 '8.88 'X ;3 '7.43 'X <3 '8.88 ?5X =3 ( (?79 ' p >3 '12.96 ' p ?3 '11.57 ' p @3 '8.18 ' p A3 '13.49 ' p B3 '8.98 ' p C3 'Є9.08 ?5 p D3 ( (?80 '8E3 '24.17 '8F3 '31.04 '8G3 '46.37 '8H3 '46.10 '8I3 '48.47 '8J3 '46.10 ?58K3 ( (?81 'PL3 'Є2.16 'PM3 '6.11 'PN3 '1.03 'PO3 'Є3.65 'PP3 '2.40 'PQ3 '26.59 ?5PR3 ( (?82 'hS3 '22.16 'hT3 '23.46 'hU3 '30.91 'hV3 '44.25 'hW3 '54.07 'hX3 '44.25 ?5hY3 ( (?83 'Z3 '34.62 '[3 '38.87 '\3 '35.84 ']3 '33.53 '^3 '33.74 '_3 '34.57 ?5`3 ( (?84 'a3 'Є0.46 'b3 '6.96 'c3 '10.09 'd3 '14.12 'e3 '11.86 'f3 '14.12 ?5g3 ( (?85 'h3 '31.33 'i3 '30.49 'j3 '40.02 'k3 '41.75 'l3 '38.64 'm3 '26.20 ?5n3 ( (?86 'o3 '23.95 'p3 '33.96 'q3 '24.46 'r3 '29.04 's3 '30.24 't3 '29.04 ?5u3 ( (?87 '0v3 '17.89 '0w3 '10.11 '0x3 '12.67 '0y3 '2.65 '0z3 '3.41 '0{3 '6.46 ?50|3 ( (?88 'H}3 '19.14 'H~3 '24.23 'H3 '21.42 'H3 '20.83 'H3 '21.51 'H3 '20.83 ?5H3 ( (?89 '`3 '31.10 '`3 '29.81 '`3 '12.20 '`3 '8.18 '`3 '9.45 '`3 '14.55 ?5`3 ( (?90 '(x3 'Є7.24 '(x3 'Є7.82 '(x3 'Є14.93 '(x3 'Є12.65 '(x3 'Є13.15 '(x3 'Є12.65 ?5(x3 ( (?91 '@3 '29.60 '@3 '35.49 '@3 '62.58 '@3 '69.48 '@3 '92.80 '@3 '186.11 ?5@3 ( (?92 'X 3 '12.72 'X 3 '11.85 'X 3 '31.08 'X 3 '43.72 'X 3 '40.44 'X 3 '43.72 ?5X 3 ( (?93 'p!3 '18.76 'p!3 '25.39 'p!3 '34.04 'p!3 '41.13 'p!3 '41.24 'p!3 '41.69 ?5p!3 ( (?94 '"3 '3.93 '"3 '3.44 '"3 '6.89 '"3 '1.50 '"3 'Є6.08 '"3 '1.50 ?5"3 ( (?95 '#3 '37.55 '#3 '39.32 '#3 '33.08 '#3 '44.27 '#3 '40.09 '#3 '23.38 ?5#3 ( (?96 '$ 3 '26.08 '$ 3 '29.95 '$ 3 '29.83 '$ 3 '34.05 '$ 3 '33.28 '$ 3 '34.05 ?5$ 3 ( (? '% !3 ' '% !3 ' '% !3 ' '% !3 ' '% !3 ' '% !3 ' ?5% !3 ( (?Average ''(# '15.80 '&8"3 '20.31 '&8"3 '23.40 '&8"3 '26.41 '&8"3 '28.03 '&8"3 '34.82 ?5&8"3 ( (?StandardDeviation J@)0%  ףp=J1@17.29 ףp=J1@J17.29 mc5(@$3  ףp=J1@17.29  ףp=J1@ 0@16.500@m16.50 mc5(@$3 0@16.50 0@ q= ף4@20.69q= ף4@m20.69 mc5(@$3 q= ף4@20.69 q= ף4@ Hz6@22.78Hz6@m22.78 mc5(@$3 Hz6@22.78 Hz6@ Q:@26.97Q:@m26.97 mc5(@$3 Q:@26.97 Q:@ @F@44.50@F@m44.508XR XXXPFD(@$3 @F@44.50 (  @F@ P#XX X8XR# ,( Ї  (Table1continued)jNote:Theportfoliosareformedusingtheclosingpricesandtrailingdividendyieldsonthecloseofthefirstbusinessdayofeachyear.Theportfoliodefinitionsare:Dow30:0 ` 0 ` (#` (#anequallyweightedportfolioofall30stocksintheDowJonesIndustrial `  Average(DJIA)  (# (# DowDividend:0 anequallyweightedportfolioofthetenDJIAstockswiththehighest 0  dividendyield  (# (# DowFive:0 ` 0 ` (#` (#anequallyweightedportfolioofthefivelowest%%%%pricedstocksintheDow P  DividendPortfolio  (# (# DowFour:0 ` 0 ` (#` (#anequallyweightedportfolioofthefourhighest%%%%pricedDowFivestocks  (# (# FoolishFour:0 ` 0 ` (#` (#aportfoliooftheDowFourstockswith20percentweightonthethree  highest%%%%pricedstocksand40percentweightonthelowest%%%%pricedstock  (# (# FracturedFour:0 theDowFourinevenyearsandthe penultimateprofitprospectinodd  years p (# (# >XXXX  Table2  OutofSampleHistoricalReturnsandSummaryStatisticsfortheDow30andFoolishFourPortfolios̀1949to1972,January     p 1973to1996,July p #XXX>XĪ#*9: ddZZZZZZZ67(#(#,Z,Z,Z,Z,Z,Z,Z+  ," P  (@,?+ 4 <DL!X?Year 'h 3@ @'Dow30 'h  3@ 'FoolishFour 'h  3 ' 'x  3 @'Year 'h 3@ @'Dow30 'h 3@ 'FoolishFour ?5h 3 ( (?49 ' 3 '22.38 ' 3 '30.05 ' 3 ' ' 3 '73 ' 3 'Є4.38 ' 3 '2.09 ?5 3 ( (?50 ' 3 '28.93 ' 3 '35.72 ' 3 ' ' 3 '74 ' 3 'Є2.40 '  3 'Є19.32 ?5 !3 ( (?51 ' "3 '21.33 ' #3 '30.48 ' $3 ' ' %3 '75 ' &3 '23.65 ' '3 '21.45 ?5 (3 ( (?52 ' )3 '13.72 ' *3 '15.88 ' +3 ' ' ,3 '76 ' -3 '23.08 ' .3 '23.26 ?5 /3 ( (?53 '0 03 '2.17 '0 13 'Є14.39 '0 23 ' '0 33 '77 '0 43 '1.73 '0 53 '11.76 ?50 63 ( (?54 'H 73 '55.17 'H 83 '68.76 'H 93 ' 'H :3 '78 'H ;3 'Є7.94 'H <3 'Є8.66 ?5H =3 ( (?55 '`>3 '24.14 '`?3 '19.08 '`@3 ' '`A3 '79 '`B3 '7.53 '`C3 '14.73 ?5`D3 ( (?56 '(xE3 '9.20 '(xF3 '10.49 '(xG3 ' '(xH3 '80 '(xI3 '10.75 '(xJ3 '13.41 ?5(xK3 ( (?57 '@L3 'Є7.79 '@M3 'Є15.99 '@N3 ' '@O3 '81 '@P3 '19.58 '@Q3 '23.55 ?5@R3 ( (?58 'XS3 '42.45 'XT3 '52.04 'XU3 ' 'XV3 '82 'XW3 'Є14.55 'XX3 '9.11 ?5XY3 ( (?59 'pZ3 '17.51 'p[3 '11.53 'p\3 ' 'p]3 '83 'p^3 '60.68 'p_3 '53.99 ?5p`3 ( (?60 'a3 'Є3.70 'b3 'Є5.65 'c3 ' 'd3 '84 'e3 'Є2.68 'f3 '4.23 ?5g3 ( (?61 'h3 '23.18 'i3 '25.07 'j3 ' 'k3 '85 'l3 '26.71 'm3 '31.42 ?5n3 ( (?62 'o3 'Є7.09 'p3 'Є13.45 'q3 ' 'r3 '86 's3 '37.75 't3 '39.81 ?5u3 ( (?63 ' v3 '21.87 ' w3 '14.18 ' x3 ' ' y3 '87 ' z3 '32.57 ' {3 '51.13 ?5 |3 ( (?64 '8}3 '19.41 '8~3 '23.64 '83 ' '83 '88 '83 'Є5.96 '83 'Є15.59 ?583 ( (?65 'P3 '17.06 'P3 '28.71 'P3 ' 'P3 '89 'P3 '18.15 'P3 '24.49 ?5P3 ( (?66 'h3 'Є15.42 'h3 'Є24.89 'h3 ' 'h3 '90 'h3 '18.74 'h3 '5.33 ?5h3 ( (?67 '0 3 '22.09 '0 3 '37.11 '0 3 ' '0 3 '91 '0 3 '5.80 '0 3 '7.14 ?50 3 ( (?68 'H!3 '10.36 'H!3 '11.00 'H!3 ' 'H!3 '92 'H!3 '18.56 'H!3 '5.35 ?5H!3 ( (?69 '`"3 'Є10.15 '`"3 'Є14.52 '`"3 ' '`"3 '93 '`"3 '13.48 '`"3 '31.37 ?5`"3 ( (?70 'x#3 '8.00 'x#3 'Є11.07 'x#3 ' 'x#3 '94 'x#3 '6.03 'x#3 'Є3.30 ?5x#3 ( (?71 '$3 '7.96 '$3 '14.35 '$3 ' '$3 '95 '$3 '29.22 '$3 '41.12 ?5$3 ( (?72 '% 3 '15.87 '% 3 '18.14 '% 3 ' '% 3 '96 '% 3 '28.34 '% 3 '47.35 ?5% 3 ( (? '&"3 ' '&"3 ' '&"3 ' '&"3 ' '&"3 ' '&"3 ' ?5&"3 ( (?Average '($ '14.11 ''(#3 '14.43 ''(#3 ' ''(#3 'Average ''(# '14.35 ''(#3 '17.30 ?5'(#3 ( (?StandardDeviation J@* & (\0@16.01(\0@J16.01 mc5)0%3 (\0@16.01 (\0@ Q6@22.62Q6@m22.62 J@5)0%3 Q6@22.62 Q6@ J ')0%3 'StandardDeviation J@* & )\0@16.91)\0@J16.91 mc5)0%3 )\0@16.91 )\0@ Gz3@19.83Gz3@m19.83PFD)0%3 Gz3@19.83 (  Gz3@ P  +'   Figure1FoolishFourEventStudy(1994to1997)g>m 09)%`|0H `..EUHHE 6m (#(#                            (#(#ThisgraphplotsaveragecumulativeexcessreturnsontheFoolFoolishFourPortfoliofor15daysbeforeandaftertheeventday.TheeventdayisthefirsttradingdayinJanuaryofeachyear.DailyreturnsarecalculatedinexcessoftheCRSPtotalmarketreturnonthatday.  % # _%@11AppendixB(NotcurrentlyinPaper)  Afterresidentsinasmalltownwereswindledina_Ponzi_Ԁscheme,abankputthefollowingsatiricposterinitswindow.Designedasapublicserviceremindingcitizenstobecautious,thesignhadtoberemovedafterfrequentseriousinquirieswerereceived.*5X;` ddZZZZZZZ9:(#(#,dd +   @   XX$@--%FreeMoney?$#XX +F#Ԉ   p\K<,(`~1 MO `VEF IOO p                                            yQA1-lzP `E m$XX m$XyyRA1-lz/*  `EJ# X XJ# XyOwnyourowncatfarmandearnfreemoneysellingfurpelts.What,youask,willyoufeedthecats.Wholerats.Thatsright,ownaratfarmnextdoor.Andwhat,youask,willyoufeedthe h Jh J  rats.Skinnedcats.Feedthecatstotheratsandtheratstothecatsandgetthepelts2 XXForFree#XX 2K#," l% "  h Jh J ,   ,'|"" >XXXX  Table3(NotCurrentlyinPaper)  AnnualMeanPercentageReturnsandStandardDeviationsfortheDow30̀andFoolishFourPortfolioswithAdjustmentsforRiskandTransactionCostsBL   `     h InSample   p OutofSample p      `     h 1973to1996   p 1949to1972   x 1973to1996 P     `     h January   p January   x July  @   YXFoolishFourMeanReturnmm#m#28.03-xx2x214.43**<*AA 17.30  p  Dow30MeanReturn  mm#m#15.80-xx2x214.11**<*AA 14.35 P  NominalDifference  mm#m#12.23-xx2xss30.32**<*A~~B 2.95#XXX>X#L#>XXXXԈ 0  RiskAdjustedDifferencemm#mhh$4.75-xx2x1121.80**<*A~~B 1.46#XXX>XR#%>XXXX%     b b b RiskandTransactionCostmm#mhh$3.58-xx2x1122.97**<*A~~B 0.29  AdjustedDifference YYNote:0  NominaldifferenceequalstheFoolishFourreturnminustheDow30return.Risk ` adjusteddifferencecorrects(usingSharpesratio)thenominaldifferenceforthedifferencesinriskbetweentheFoolishFourandtheDow30strategies.RiskandtransactioncostadjusteddifferencecorrectsthenominaldifferenceforriskandtransactioncostsassociatedwiththeadditionalportfoliorebalancingthattheFoolishFourstrategyrequireseachyear.  (# (# %#XXX>XQS#_