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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