The Intelligent Asset Allocator -...
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TheIntelligentAssetAllocator
TheIntelligentAssetAllocatorHowtoBuildYour
PortfoliotoMaximizeReturnsandMinimizeRisk
WilliamJ.Bernstein
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ISBN:978-007-139957-9
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Contents
Preface
Introduction
1.GeneralConsiderations
2.RiskandReturn
3.TheBehaviorofMultiple-AssetPortfolios
4.TheBehaviorofReal-WorldPortfolios
5.OptimalAssetAllocations
6.MarketEfficiency
7.OddsandEnds
8.ImplementingYour
AssetAllocationStrategy
9.InvestmentResources
AppendixA:BecomingYourOwnPortfolioAnalyst
AppendixB:CorrelationCoefficientsAmongAssetClasses
Glossary
Bibliography
Index
Preface
OnJuly31,1993,IcameacrossanarticleinTheWallStreetJournal(“YourMoneyMatters”series)whichexaminedtheperformanceofvariousassetallocationsfortheperiod1973–92.ThearticlewasbasedonresearchdoneattheT.RowePrice
mutualfundgroup.Thetechniqueusedwasquitesimple:imaginaryportfolioswereconstructedfromvariouscombinationsofU.S.largeandsmallstocks,foreignstocks,andU.S.bonds,andreturnsandriskswerecalculated.Thearticlepointedoutthatoverthe20-yearperiodstudiedvariousfixedmixesoftheaboveassetsoutperformedthesinglecomponentparts(as
wellasmostprofessionalmoneymanagers),withsignificantlylowerrisk.Iwasintrigued.T.RowePricekindlysentmethedataunderlyingtheircalculations,whichIanalyzed.Theresultswereastonishing—almostanyreasonablybalancedfixedcombinationofthefourassetsoutperformedmostprofessionalmoneymanagersoverthesameperiod.
Forexample,a“simpleton’sportfolio”consistingofonequartereachU.S.largestocks,U.S.smallstocks,foreignstocks,andU.S.high-qualitybondshadahigherreturn,withmuchlowerrisk,thanlargeU.S.stocksalone(representedbytheS&P500index).TheS&P500,inturn,performedbetterthan75%ofprofessionalmoneymanagersoverthesameperiod.
IwasfascinatedbytheT.RowePricedata;herewasasimpletoolforascertaininghistoricalassetallocationperformance—collectdataonthepriorperformanceofvariousassetclasses,and“backtest”returnsandrisks.Tomydisappointment,Icouldfindnoreadilyavailablesoftwarewhichaccomplishedthis;Iwouldhavetowritemyownspreadsheetfiles.Ibeganto
buy,beg,stealorborrowdataonawidevarietyofassetsoverseveraldifferenthistoricalepochsandbuildportfoliomodelsgoingbackasfaras1926.Thecalculationsperformed
byT.RowePriceandmyselfcontainedanimportantimplicitassumption:thattheportfolioswere“rebalanced”periodically.Rebalancingbecomesnecessaryaftera
whilebecausesomeassetsinaportfoliowilldobetterthanothers,andthiswillaltertheoriginalportfoliocomposition.Inordertorebalancetheportfoliobacktoitsstartingcomposition,someofthebetterperformingassetsmustbesold—andtheproceedsusedtopurchasemoreofthepoorlyperformingassets.Mostexperiencedinvestors
learnthatthekeytolong-termsuccessliesinacoherentstrategyforallocationamongbroadcategoriesofassets,principallyforeignanddomesticstocksandbonds.Theyalsounderstandthatmarkettimingandstockormutualfundpickingarenearlyimpossiblelongterm.Theyareatbestadistraction.Putanotherway,itisfarmoreimportanttocomeup
withtherightproportionofforeignstocks,U.S.stocks,foreignbonds,andU.S.bondsthanitistopickthe“best”stocksormutualfundsorto“call”thetopsorbottomsofthemarkets.(Asweshallseelater,nobodyconsistentlycallsthemarket,andalmostnobodypicksstocksormutualfundswithanypersistentskill).Ifyoufindthisdifficultto
believe,considerthefollowing:1987wasnotagreatyearfortheU.S.stockmarket.U.S.largecompanystocks(representedbytheS&P500)gainedonly5.23%thatturbulentyear,andsmallcompanystocksactuallylost9.3%.Ontheotherhand,foreignstocksgained24.93%.Theclumsiestforeignfundmanagerwouldhavebeatenthemostskillfulsmall-stockpickerthatyear.
In1992,theoppositewouldhaveoccurredwhenU.S.smallstocksgained23.35%andforeignstockslost11.85%.Finally,the1995–1998periodprovidedunprecedentedreturnsforthebiggestU.S.growthstocksbutbatteredalmosteverythingelse.Stillnotconvinced?Inthe
late1980s,GaryBrinson,anotedmoneymanagerand
financialanalyst,andhiscolleaguespublishedtwosophisticatedstatisticalstudiesof82largepensionfunds.Theyconcludedthatassetallocationaccountedforover90%ofthereturnvariabilityamongthefunds,withaless-than-10%contributionfrommarkettimingandactualstockandbondselection.Inotherwords,assetallocationpolicywas10timesasimportantas
stockpickingandmarkettimingcombined.Inrecentyearsmanyobservershavesuggestedthatthe90%figureistoohigh;perhapsassetallocationaccountsforonly50%ofreturnvariability.Suchargumentscompletelymissthepoint.Markettimingandsecurityselectionareobviouslyimportant.Theonlyproblemisthatnobodyachieveslong-termsuccessintheformer,andalmost
nobodyinthelatter.Assetallocationistheonlyfactoraffectingyourinvestmentsthatyoucanactuallyinfluence.Itisthustrulyastonishing
thatsomuchinkandairtimeiswastedonanalysts’predictionsofthedirectionofstockorbondpricesandonparticularstockandmutualfundrecommendations.Infact,whenMr.Brinson
himselfappearedonLouisRukeyser’sWallStreetWeekin1994almostallofhiscommentsweredirectedtowardmarkettimingandalmostnoattentionpaidtoassetallocationstrategy.Thegamblinginstinctisingrainedinhumannature,andfewcanresistspeculationoneventsthatcannotbeforeseen.Sohowdoyouarriveat
theallocationthatwill
providethemostreturnwiththeleastamountofrisk?Youcan’t.Butdon’tfeelbad,becauseneithercananyoneelse.NotevenMr.Brinson,whountilheretiredhadmoreassetsundermanagementthananyotherindividualontheplanet.Sure,youcanlookathistoricaldataandexaminewhathasworkedinthepast,butdon’tconfusethatwithwhatwillworkinthefuture.Laterweshalllookat
historicaldataandattempttoextractfromitusefulportfolioadvice,butthelessonsaresparse.First,stocksareriskierthancash.Second,inthefuturetheywillprobablyhavehigherreturnsthancash,butnotbyasmuchasinthepast,particularlytherecentpast.Third,portfoliodiversificationreducesrisk.Andlast,indexyourinvestmentswhereveryou
can.Infact,ifyoutireof
readingthisbookandsimplywantarecipeforaserviceableportfolio,considerthefollowingadvice:Purchasetheabove-mentioned“simpleton’sportfolio”consistingofindexfunds—onequartereachofU.S.largeandsmallstocks,foreignstocks,andashort-termU.S.bondfund.Index
fundshavebecomealmostascommoditizedascomputerchipsandgasoline,andtheyareavailablethroughmostlargefundfamiliesand“supermarkets.”IhighlyrecommendVanguard.Attheendofeachyear,rebalanceyouraccountssothateachofthefourpartsareagainofequalsize.That’sit.Settinguptheaccountshouldtakeabout15minutes,andtheannualrebalancingshould
alsotakeabout15minutes.Youcanforgetaboutinvestingfortherestoftheyear.Ifthenext20yearsareanythinglikethelast20,thenyouwilloutperformtheportfoliosof75%ofallprofessionalmoneymanagers.In1996,Iplacedthis
book’sfirsteditionon-lineandbeganwritingregularpiecesformywebsite,
EfficientFrontier(http://www.efficientfrontier.comThereactiontoitexceededmywildestexpectations.Thehungerofsmallinvestorsforinformationaboutassetallocationandportfoliotheorywasgratifying,buttheresponsethatIreceivedfrominvestmentprofessionalswascompletelyunexpected.Yes,Iwastold,weallknowhowimportantassetallocationis,butitsnutsandbolts—the
roadmap,ifyouwill—werenotatallobvious.ThemagicoftheInternetputmeintocontactwithdozensoffolkswhosharedmyfascinationwithportfoliotheory—somewell-known,manynot.Twomoreelectroniceditionsfollowed.Theserevisions,thedozensofwebsitepieces,andthemanydiscussionsaboutinvestingandportfoliotheorywhichfollowedformthebasisofthisprintedition.
Readerswillnoticeseveralchangesfromthepreviouselectronicversions.Firstandforemost,theemphasisonindexinghasbecomeevenstronger.I’vecometotheconclusionthatactiveportfoliomanagementisasucker’sgame.Althoughinsomeareas,likesmallstocks,REITs(realestateinvestmenttrusts),andforeignstocks,activemanagersappeartobedoingwell,this
outperformanceisillusory.I’veeliminatedmostofthesectionsdescribingthemanualcalculationofvariousportfoliostatistics—spreadsheetsandfinancialcalculatorshavemademanualtechniquesobsolete.Isupposethatitaddstotheunderstandingofstatisticalconcepts,suchasstandarddeviation,tobeabletocalculatethembyhand,butyou’llhavetolookelsewhere
ifyouwanttolearnhowtodothis.I’vealsoadoptedanewalgorithmforthecalculationofrebalancedportfolioreturnsandhappilyabandonedthespreadsheetoptimizationemployedinpreviousversions.Inthepastfewyears,the
investmentindustryhasembracedelectroniccommerceandmadeadizzyingvarietyoftoolsand
vehiclesavailabletotheinvestingpublic.Unfortunately,mostofitissomuchrope—fundsupermarkets,on-linetrading,andanenormousvolumeofsecurities“research”—withwhichmostinvestorswillhangthemselves.Butfortheprudentinvestor,benefitsabound.TheexplosionoftheInternethasbroughtaplethoraofusefulservicesandmadethebrightestminds
inmodernfinanceavailabletoanybodywithacomputer,modem,andphoneline.Second,andevenmoreimportant,istheproliferationofinexpensiveindexedinvestmentvehicles.Noweventhesmallestinvestorscanbuildportfoliosasefficientlyandalmostascheaplyasthebiggestplayers.Particularthanksgoto
JonathanClements,RobertBarker,FrankArmstrong,JohnRekenthaler,DavidWilkinson,SteveDunn,ScottBurns,andthemanyotherswhohaveprovidedmewithadviceandcountenanceoverthepastfewyears.I’mdeeplygratefultoSusanSharin,whoseuniquecombinationofmoney-managementskillsandfinancialknowledgeprovedinvaluable.Finally,the
greatestthanksgotomywife,Jane,withoutwhoseencouragementandeditingsupportthisbookwouldnothavebeenpossible.
WilliamJ.BernsteinNorthBend,OR
Introduction
Imaginethatyouaresuddenlytransportedtoacountryyouhaveneverbeforevisited.Tryingtofindyourwayhome,youaretoldthatthereisanew,well-equipped,comfortable,andreliablecarparkednearby.Youarehandedthekeysand
toldtodrivetoanairportseveralhundredmilesawaywhereaflighthomeawaitsyou.Whatdoyoudo?Doyou
stridetothecarwithoutfurtherado,driveaway,andhopethatbyluckyoucanpickyourwaytoyourintendeddestination?Youhesitate.Itdoesnotgounnoticedbythelocalsthatyouarearube,andfurther
theprouddriverofanexpensiveautomobile.Severalsleazycharacterscrowdaroundyoutooffertheirexpertassistance.Doyoutrustyourselftooneofthem?Hopefullyyoudoneither
andinsteadfindthenearestbookshop,purchaseadetailedroadmap,andplotthemostefficientroutetotheairport.Onlythendoyou
startonyourway.Mostinvestorsfind
themselvesinaverysimilarsituation.Manychoosethefirstcourseandbegintheirinvestingcareerswithboldaction(usuallycommittingalargeamountoftheircapitaltoaveryriskymarketsectoratornearitstop).Theyrarelyhaveaclearideaofexactlywheretheyareheadedorhowtogetthere.Manymore
knowthattheyarelostanddependonthekindnessandexpertiseofstrangers(otherwiseknownas“accountexecutives”or“financialplanners”)tofindtheirway.Alltoooften,theinterestsofthese“experts”areverydifferentfromtheirclients.Learninghowtoinvest
successfullyonyourownismuchlikegettingfromone
citytoanotherinthemannerofourfictionaltraveler.Theroadmapisasimpleoneandwillbebrieflydescribedbelow.Theroutewillpassparticularlandmarksinapreciseorder;eachonewillbedescribedinitsownchapter.Thejourneywillbeslowandpainstakingattimes,andtherewillbenoshortcuts.Thisbookcannotbereadquickly;itmustbemethodicallyconsumed,one
pageandchapteratatime.
TheRoadMap1.Takeadeepbreath,anddonothingforseveralweeksormonths,oraslongasittakestocompletethefollowingsteps.Youareinnorushtoimmediatelyandradicallyalteryourfinances.Youhavetherestofyourlifetoget
youraffairsinorder;thetimeyoutakelearningandplanningwillbetimewell-spent.
2.Acquireanappreciationofthenatureofandfundamentalrelationshipbetweenriskandrewardinthefinancialmarkets.
3.Learnabouttherisk/rewardcharacteristicsofvariousspecificinvestmenttypes.
4.Appreciatethatdiversifiedportfoliosbehaveverydifferentlythantheindividualassetsinthem,inmuchthesamewaythatacaketastesdifferentfromshortening,flour,butter,andsugar.Thisiscalledportfoliotheoryandiscriticaltoyourfuturesuccess.
5.Estimatehowmuchriskyoucantolerate;then
learnhowtouseportfoliotheorytoconstructaportfoliotailoredtoproducethemostreturnforthatamountofrisk.
6.Atthispointyouarefinallyreadytopurchaseindividualstocks,bonds,andmutualfunds.Ifyouhavesucceededintheabovetasks,thisisbyfartheeasieststep.TheIntelligentAsset
Allocatorwilltakeyouthroughtheabovestepschapterbychapteronyourjourneytoacoherentandeffectivelifetimeinvestmentstrategy.Canyouinvest
successfullywithoutacquiringasolidunderstandingofriskandrewardinthecapitalmarkets,andofportfoliotheory?Certainly—manypeoplehave
doneso.Itisalsopossibletolearntoswimortoflyanairplanewithoutlessons.Idon’trecommendit.
HowtoReadThisBook
ThisisnotaGrishamnovel;thematerialtobemasteredrequiressomeeffort.Eachchapterformsthefoundationforthenext,sothebookmustbereadpagebypage,chapterbychapter;noskipping
aroundallowed.Ideally,thebookshouldbetakenwithyouonvacationandtackledfirstthinginthemorningwhileyouarestillfresh.Putitdownafteranhourorso,anddonotpickitupagainuntilthenextday.Afacilitywithnumbers
willhelpbutisnotessential.Someofthekeymathematicalconceptsandtechniquesaredescribedin
greaterdetailinafewseparate“mathdetails”sections.Thesecanbeskippedifyouhavelimitedtimeorabsenceofmathematicalinterest.Themostimportantpartof
thisbookisChapter9,“InvestmentResources.”Investingisajourneyoflifelonglearning,andmyfondesthopeisthatthisbookwillinstillathirstforfurther
explorationofthesubject.
1General
Considerations
ImaginethatyouworkforyourrichbuteccentricUncleFred.Heisaconscientiousandkindemployer,andafteryouhavespentsomeyearsinhisservicehedecidestoletyouinonthecompany
pensionplan.Youare30yearsoldandwillworkforyouruncleuntilyouretirein35yearsatage65.Eachyearhewillcontribute$5000toyourretirementaccount.Further,youmustpickaheadoftimeoneoftwoinvestmentchoicesforthedurationofyouremployment:
Option1.Certificatesofdepositwitha3%annualized
rateofreturn.Option2.Amostpeculiar
option:AttheendofeachyearUncleFredflipsacoin.Headsyoureceivea30%investmentreturnforthatyear,tailsaminus10%(loss)fortheyear.Thisoptionwillbe
referredtoas“UncleFred’scointoss,”orsimply,the“cointoss.”
Thefirstchoicegivesyouafixedrateofreturnand,infact,anabsolutelycertainlumpsumattheendofyour35years.Youareadeptwithafinancialcalculator,andinafewsecondsyoudeterminethatthisoptionwillyielda
sumof$302,310withwhichtosupportyourgoldenyears.Yourealizethatinflationwilldiminishthefuturevalueofthisprincelysum.Infact,ifinflationisalso3%,youwillbeleftwithonly$107,436ofcurrentspendingpower.Thesecondchoice
confusesyouatfirst.Thethoughtoflosing10%ofyourhard-earnedretirementmoneywiththetossofacoin
istoomuchtobear.Whatifyouhaveastringoflosingyears?Ifyougettailsall35years,youcouldbeleftwithonlyapittanceforyourretirement.Ontheotherhand,ifyougetheadsall35yearsyouknowthatyouwillbankruptpoorUncleFredwithyourgains—hewilloweyou$162,000,000!Let’slookabitmore
closelyatthesecondchoice.
Overalongenoughperiod,youwillgetexactlyhalfheadsandhalftails.Ifyourepresentthiswithanalternatingseriesofheadsandtails,thenyourreturnineachtwo-yearperiodisrepresentedby:
1.3×.9=1.17
Thefirstyearreturnof30%resultsinyouraccount
beingmultipliedby1.3,whilea10%lossmultipliesyoursumby0.9.Foreachdollaryouhadatthebeginningofthetwo-yearperiod,younowhave$1.17.Youagaingetoutyour
calculatorandfindthata17%returnattheendoftwoyearsisthesameasanannualreturnof8.17%.Thisisclearlysuperiortothe3%returnofthefirstoption.Of
course,youcouldhaveastringofbadluckandgettailsmorethanhalfofthetime.However,withsometrialanderroronyourcalculator,youdiscoverthatyouwouldhavetoget12headsand23tailsbeforeyoucomeoutworsethanthefirstoption,andyoudecidethattheoddsofthisarequitelow.Youvisityourformercollegestatisticsprofessor,whochidesyouforforgettingthat
youcouldhaveeasilycalculatedtheoddsofanycombinationofcoinflipswiththeso-calledbinomialdistributionfunction.Yourblanklookelicitsasighfromhim,heheadsovertohiscomputer,pullsupaspreadsheetprogram,andafterafewkeystrokeshandsyouthegraphinFigure1-1.Whataretheoddsthatyouwillfliplessthan13headsandcomeoutbehind?Less
than5%.Actually,thisisabitofanoversimplification.Theorderofthecointossesmattersagreatdeal.Ifyoutoss16straightheadsthen19straighttailsyouwillstillcomeoutbehind,butifyoutoss27straighttailsfollowedby8straightheadsyouwillactuallycomeoutahead.However,theseareextremelyunlikelyevents,andtheprecedingformulationandthegraphinFigure1-1arean
accuraterepresentationoftheoddsinyourfavor.
Figure1-1.UncleFred’scointossprobability.
Thecointossalsointroducesthedifferencebetweentheaverageandtheannualizedreturnofanasset.Someofyoumaywonderwhythereturnofthecointossisnot10%insteadof8.17%,sincetheaverageof+30%and−10%is+10%(30
minus10,dividedby2).Theaveragereturnissimplytheaverageofeachoftheindividualannualreturns.Theannualizedreturnisamoresubtleconcept.Itisthereturnthatyoumustearneachandeveryyeartoequaltheresultofyourseriesofdifferingannualreturns.Ifyouownastockwhichdoubles(hasa100%return)thefirstyearandthenloses50%thenextyearyouhavea
zeroannualizedreturn.Ifthestockwasworth$10pershareatthestart,itwasworth$20attheendofthefirstyear,and$10againattheendofthesecondyear.Youhavemadenomoney,andyettheaveragereturnisaso-called25%(theaverageof+100%and−50%).Yourannualizedreturniszero.Theannualizedandaveragereturnclearlyarenotthesame.Thecointosshasanaveragereturnof10%
andanannualizedreturnof8.17%.Theannualizedreturnisalwayslessthantheaveragereturn.Ifinthecointossyoucomeupwithhalf−10%andhalf+30%returns,thisisthesameashavingan8.17%returneachandeveryyear.Youpayyourbillswithannualizedreturn,notaveragereturn.Thisiswhyannualizedreturnsaresoimportant.
UncleFred’scointossmayseemamostbizarrescenario,andyetitisnearlyidenticaltothechoicefacedbymostinvestorsbetweenthe“safety”ofmoneymarketaccountsorTreasurybillsandthe“gamble”ofcommonstocks.Thesecondoptionoffersanearcertaintyofasuperiorresult,yetcomesataprice:thesmallpossibilityofaninferiorresultand,moreimportantly,thatgut-
wrenchingcointosssessionwithUncleFredeachyear.Yet,itisthe3%certificateofdepositoptionwhichisthemosttrulyfrightening—youwillalmostcertainlyliveyourgoldenyearsinpoverty.IconstructedUncleFred’s
cointosswithsomedeliberation—it’seasytograspandquitecloselyapproximatesthereturnsandrisksofcommonstocks.The
returnofcommonstocksoverthepast73years(1926–1998)was11.22%,inthesameleagueasthecointoss.Moreimportantly,the“riskiness”ofthecointossandofcommonstocksarenearlyidentical.Ishallexplainshortlyhowtomeasurepreciselythisriskiness.Thecointossisahandysymbolicrepresentationoftherisksandreturnsofcommon
stocks.Itwillalsoprovideapowerfulwayinwhichtounderstandthebehaviorofportfolioswithmultipleassettypes.Youhavejustbeen
introducedtooneofthefundamentallawsofinvesting:inthelongrunyouarecompensatedforbearingrisk.Conversely,ifyouseeksafety,yourreturnswillbelow.Experiencedinvestors
understandthatrewardandriskareinextricablyintertwined;oneofthemostreliablewaystospotinvestmentfraudisthepromiseofexcessivereturnswithlowrisk.Let’sconsideranexample
ofinvestmentreturnslightlymorecomplexthanthecointoss.SaythatyouhaveinvestedinassetA(itdoesn’tmatterwhatitis).Thereturns
foreightconsecutiveyearsareasfollows:
WhatisyourreturnonassetA?Inyear1yourreturnwas20%,soyoumultiplyyourassetvalueby1.2.Inyear2youmultiplyby1.0.Inyear3youmultiplyby1.1,andinyear4,whenyoulose10%,youmultiplyby0.9.Thus,overthefulleightyearsyourfinalvalueiscalculatedas:
1.2×1.0×1.1×0.9×1.3×1.15×1.1×1.05=2.051
Inthisexample,ifassetAwasworth$10atthebeginningoftheperiod,itisnowworth2.051timestheoriginalvalue,$20.51.Thetotalreturnovereightyearsis105.1%.(Don’tbeconfusedbythis;rememberthatagainof50%meansmultiplyingyourinitialamountby1.5,andthatagainof100%meansmultiplyingby2.)Theaveragereturnissimplytheaverageoftheeight
individualreturns,or10%.However,weknowthatwhatreallycountsistheannualizedreturn(thatis,thereturnwhichwouldberequiredeachyeartoyieldthesameresult).Howdowecalculatethis?Ifyouarefamiliarwithspreadsheetsthisisasnap—allspreadsheetpackageshaveextensivefinancialcalculationcapability.Ifyouareunfamiliarwith
spreadsheets,thentheeasiestwaytodothisiswithafinancialcalculator.Ifyoudonotownone,youshould.TheTexasInstrumentBA-35,oritsequivalent,canbefoundinalmostanylargedrugorgeneralmerchandisestore.Itshouldcostabout$20.Iurgeyoutolearnhowtousetheannuityfeaturesonthisorasimilardevice—youwillfinditindispensableforplanningyourretirement,calculating
loanpayments,etc.Thiscalculatoralsohasastatisticalfunctionthatwillenableyoutorapidlycalculateinvestmentriskfromaseriesofreturns.Pluggingthenumbersintotheannuityfunction,wefindthattheannualizedreturnfortheaboveexampleis9.397%.Itshouldnotsurpriseyouthatthisisslightlylessthanthe10%averagereturn,sinceannualizedreturnisalways
lessthanaveragereturn.
TheStandardDeviation
WearenowreadytocalculatetheriskofassetA.Thisisdonebycalculatingastandarddeviation,orSD,whichisameasureofthe“scatter”ofasetofnumbers.Itscalculationcanbedonebyhand,butthisisquitetedious.Again,thisistypicallydonewithaspreadsheetor
financialcalculator.Inthecaseoftheaboveeightreturns,theSDwas11.46%.Whatdoyoudowitha
standarddeviation?Firstandforemost,youshouldbecomefamiliarwiththisasameasureofrisk.Typically,thestandarddeviationoftheannualreturnsforvariousassetclassesareasfollows:
Moneymarket(cash):2%–3%
Short-termbond:3%–5%Long-termbond:6%–8%Domesticstocks
(conservative):10%–14%Domesticstocks
(aggressive):15%–25%Foreignstocks:15%–25%Emergingmarketsstocks:
25%–35%
AlmostallofthemutualfundratingserviceslisttheSDintheirreports.
MorningstarInc.,acompanythatcompilesinformationaboutandanalyzesmutualfunds,listsstandarddeviationsofannualreturnsforthepreceding3,5,and10years.Insomecasesyoumayhavereturnsforonlyayearortwo.HerethestandarddeviationofannualreturnsmaybeestimatedbymultiplyingthequarterlyreturnSDby2orthemonthlyreturnSDby3.46.
Anytimeasalespersonorbrokerattemptstosellyouasecurityofanytype,askhimorherwhatitsstandarddeviationofannualreturnsis(orisexpectedtobeifitisanewoffering).Ifheorshedoesn’tknow,don’teventhinkaboutbuyingit.Ifyourbrokerisnotfamiliarwiththeconceptofthestandarddeviationofreturns,getanewone.
Whatdoesthestandarddeviationnumberactuallymean?Itmeansthattwo-thirdsofthetimetheannualreturnoftheassetwillliebetween1standarddeviationaboveand1standarddeviationbelowthemeanvalue.InthecaseofassetAthismeansthattwo-thirdsofthetimeitwillbebetween−1.46%(10minus11.46)and21.46%(10plus11.46).I’vegraphedthe“downside”for
assetAinFigure1-2.Thisshowsthatthereisa1-in-6chanceofalossworsethan1.46%.Thereisa1-in-44chanceofalossworsethan12.92%(2standarddeviationslessthanthemean)anda1-in-740chanceofalossworsethan24.38%(3standarddeviationsbelowthemean).Touseasimplerexample,let’sassumethatyouareconsideringaLatinAmericanstockfundwithan
expectedreturnof15andaveryhighSDof35%.Thistellsyoutoexpectalossof20%orworseevery6years,alossofworsethan55%every44years,andalossof90%every740years.Iverymuchdoubtthatmanyofthefundsalespeopleorbrokerstoutingthesefundsinrecentyearsconveyedsuchinformationtotheirclients.Infact,onesignofadangerouslyoverbought
marketisageneralizedunderappreciationoftherisksinherentinit.
Figure1-2.AssetAreturnsdistribution.
MathDetails:OtherMeasuresofRisk
Thoseofyouwithsophisticatedmathbackgroundswillrecognizethelimitationsofthe
SDasameasureofrisk.Forexample,intherealworldofinvesting,returnsdonotfollowaclassic“normaldistribution,”butinsteadmorecloselyapproximatealognormaldistribution.Further,thereisa
degreeofasymmetryaboutthemean(skew)aswellasasomewhathigherfrequencyofeventsattheextremesofrange(kurtosis).Themostimportantcriticismofstandarddeviationasameasureofriskisthatit
assignsequalimportancetoreturnsbothaboveandbelowthemean,whereasclearlyonlyeventsoccurringbelowthemeanareofimportancetoanymeasurementofinvestmentrisk.Thishaspromptedsomeacademicsandpractitioners
tosuggest“semivariance,”orthemeanvarianceofeventsoccurringbelowthemean,asamorerealisticmeasurementofrisk.Inpractice,however,bothvarianceandsemivarianceyieldverysimilarresults,and
variance/standarddeviationisstillanexcellentmeasureofrisk.Infact,simplevariance/SDhastheadditionaladvantageofgivingyoutwochancesofcatchingexcessivevolatility.IntherecentnotoriouscaseofLongTerm
CapitalManagement,thefirmdidnotdevelopasignificantlynegativesemivarianceuntilshortlybeforebankruptcy.Simplecalculationoftheplain-vanillaSD/varianceofmonthlyreturnswouldhave
warnedoftroubleyearsbeforetheottomanhitthefan.
Therearenearlyasmanydefinitionsofriskastherearefinanceacademics.Otherpossiblemeasuresincludetheprobabilityofanominalloss,oraninflation-adjusted
loss,a“lossstandarddeviation,”ortheprobabilityofunderperformingagivenindex,suchastheS&P500orT-billyield.Ameasurefavoredbymanyistheprobabilitythatyourinvestmentwillunderperformarisk-freeasset,
usuallyT-bills.Thisiseasilycalculatedfromaformulausinga“standardnormalcumulativedistributionfunction,”similartothebinomialdistributionfunctionusedbyourhypotheticalstatisticsprofessor.
Youcaneasilymakeupyourownriskmeasure.Suchindividualmeasuresofriskandreturnarereferredtoas“utilityfunctions.”
Ifyouhavedigestedallofthematerialinthischapterthusfar,youhaveeitherworkedveryhardoryouare
goodwithnumbers(oryouhavehadacourseinstatistics).Taketherestofthedayoff,sitbythepool,haveamargarita.You’veearnedit.Whenyoureturn,weshallbeginourconsiderationofrealassets.
2RiskandReturn
IndividualAssetClasses:1926–1998
Youshouldnowhaveagraspofthestatisticalmeaningofreturnandrisk.Youarereadytotacklethelong-termhistoricalrecordofawide
rangeofassets.Presumably,youwouldnotpurchaseacarorrefrigeratorwithoutcheckingitsperformanceandrepairrecordinasuitablepublicationlikeConsumerReports.Inasimilarfashion,youshouldnotcommitasizableportionofyourdisposableincometoaninvestmentwithoutagoodideaofitsexpectedreturn(performance)andrisk(repairrecord).Fortunately,thereis
alargeamountofusefuldataouttherewaitingforyou,anditiseasilyaccessibleandcheap.Howlongdoesittaketogetagoodideaofthelong-termreturnandriskofanassetclass?Opinionsvary,butatleast20or30yearsofdataarenecessarytogetagoodideaofexpectedreturn.Youcangetagoodideaofassetriskbylookingatmonthlydatafornotmuchmorethan5or10years.
WhenitcomestoU.S.securities,wearesittinginclover;thereisusabledatagoingbacktothebirthoftheRepublicregardingcommonstocksandgovernmentbonds,andextremelydetaileddatagoingbackto1926.OneofthegreatbargainsintheinvestingworldistheIbbotsonmonograph,Stocks,Bonds,Bills,andInflation(knownintheinvestingworldas“theSBBI”).This
containseverypossiblebreakdownforreturns,risks,andcorrelationsofalargenumberofU.S.assetsforperiodsrangingfromamonthtodecades.Weshallconsiderfiveassets:largeandsmallU.S.stocks,and30-day,5-year,and20-yearTreasurysecurities.Table2-1summarizeswhatyoureallyneedtoknowaboutU.S.stocksandbondsintheaggregate—itwouldnotbea
badideatocommittheapproximatereturnandSDfiguresforthesefiveassetstomemory.
Table2-1.AssetClassesfrom1926to1998
Let’srevieweachassetindividually.Youshould
refertotheaccompanyingseriesofgraphsforeachasset.Theterminologyforgovernmentsecuritiesisconfusing.Asecurityoflessthan1yeariscalledaTreasurybill,ormoresimply,aT-bill.Anobligationof1to10yearsiscalledanote,andofgreaterthan10yearsabond.
TreasuryBills.ATreasurybill(seeFigure2-1)
isthesafestinvestmentonearth.Shortofnationaldestruction,thereisnopossibilityofdefault,althoughUncleSamoccasionallyprintsmoneytomakegood.Thepricepaidforthissafetyissteep;thereturnisonly3.77%,whichisbarelyabovetheinflationrateof3.08%forthe1926–1998period.Further,althoughmanyacademiciansconsiderT-billstobe
“riskless,”aquickperusaloftheT-billgraphshowsconsiderablevariationofreturn,meaningthatyoucannotdependonaconstantincomestream.ThisriskisproperlyreflectedintheSDof3.22%.ThebestthatcanbesaidfortheperformanceofT-billsisthattheykeeppacewithinflationinthelongrun,althoughtherewereprolongedperiodswheneventhiswasnottrue,particularly
inthe1970s.
Figure2-1.Treasurybills,1926–1998.
Intermediate-Term(5-Year)TreasuryNotes.LikeT-bills,intermediate-term(5-year)Treasurynotes(seeFigure2-2)offernearabsoluteprotectionfromdefaultonprincipalandinterest,butdocarryonerisk—thatofrisinginterestrates.
Anoteorbondyieldingafixedcouponwilldeclineinmarketvaluewheninterestratesrise,andthelongerthematurityofthenoteorbondtheworsethedamage.Atamaturityoffiveyears,thelossinprincipalmarketvaluecanexceedthecouponofthenoteorbond,resultinginanegativetotalreturnfortheyear.Thishashappenedseventimesinthepast73years,and,infact,theworst
lossforthisperiod(2.65%)occurredin1994.Forbearingthisrisk,youarerewardedwithanother1.5%oflong-termreturn.Inthelongrun,thereal(inflation-adjusted)returnwasabout2%.
Figure2-2.Five-yearTreasurynote,1926–1998.
Long-Term(20-Year)TreasuryBonds.Long-termTreasuriesbehaveinmuchthesamewayastheintermediatenotes,exceptthattheirinterestrateriskismuchworse,producinglossesin20ofthepast73years,withonelossofnearly
10%,andmanylossesinexcessof5%(seeFigure2-3).Surprisingly,youdonotseemtoberewardedatallforbearingthisrisk;thereturnisalmostidenticaltothatoffive-yearnotes.
Figure2-3.Twenty-yearTreasurybond,1926–1998.
Whydomanysophisticatedinvestorsinvestinlongbondswhentheycanhavethesamereturnwithlessriskwithintermediatebonds?Theanswer,whichweshallexploreinlaterchapters,isthatmuchofthe“excessrisk”oflong
Treasuriesdisappearsinaproperlyconstructedportfolio.Thatpartoftheriskthatdisappearswithdiversificationiscallednonsystematicrisk,andthatpartwhichremainsandcannotbediversifiedawayiscalledsystematicrisk.ThereisanotherreasonwhythereturnsonlongTreasuries(andotherlongbonds)aresolow:Theyareafavoriteinvestmentofinsurance
companies,whichhavelong-livedfixedliabilitycommitmentsthatcanbepreciselyoffsetwithlongbonds.Infact,therearemany
assetswhoseapparentrisksseemoutofproportiontotheirmeagerreturns.Thebestexampleofthisistheclassofpreciousmetalsstocks,withreallong-termreturnsofafewpercentandanannual
SDofabout30%.
LargeCompanyCommonStocks.Forthepast73years,thisassetclasshasconsistedofvariousgroupsoflargecompanies,or“indexes.”ThelatestincarnationisthefamiliarS&P500.Thereadermayfindtheterminologyofthisgroupconfusing.Theyarereferredtovariouslyas“largestocks,”“theS&P,”or“the
S&P500.”Forthepurposesofthisbook,allofthesetermsareinterchangeable.Therewardsofthisasset
areconsiderable:arealreturnofgreaterthan8%(seeFigure2-4).Thelureofcommonstocksisundeniable—yourinflation-adjustedwealthwilldoubleeverynineyears.Putaway$10,000foryournewbornchild,andin50yearsheorshewillhave
$470,000ofcurrentspendingpowerforyourgrandkids’collegeeducations.Thisreturndoesnotcomefree,ofcourse.Theriskscanbestomach-turning.TheSDforlargecompanycommonstocksis20.26%.(ThisisthenumberbehindUncleFred’scointoss—itsSDisalso20%.)Youcanlosemorethan40%inabadyear,andduringthefourcalendaryears1929–1932theinflation-
adjusted(“real”)valueofthisinvestmentclassdecreasedbyalmosttwo-thirds!
Figure2-4.Commonstockreturns,1926–1998.
SmallCompanyStocks.Companieswhosetotaloutstandingstockvalue,or“marketcap,”placestheminthebottom20%oftheNewYorkStockExchangebysizeareconsideredsmallcompanystocks.(Inthecurrenteramostofthese
stocksareactuallytradedoverthecounter.)Here,thereturnsandrisksareindustrialgrade(seeFigure2-5).Yourrealreturnisnowgreaterthan9%,meaningthatyouwilldoubleyourmoneyininflation-adjustedtermsinjusteightyears.Putaway$10,000foryourgrandkidsandyouwillhave$785,000in50yearsincurrentspendingpower.Butoh,therisks:for1929–1932
thisinvestmentclasslostover85%!
Figure2-5.Smallstockreturns,1926–1998.
Figures2-6and2-7showtheeffectsoflongerholdingperiodsforlargecompanyU.S.stocks.Figure2-6showsrollingfive-yearreturnsforlargestocks;exceptfortheGreatDepression,thingsdonotlooksoscary,withonlyafewlosingperiods.The
pictureshowninFigure2-7for30-yearholdingperiodsispositivelytranquil;thereisnotasingle30-yearperiodwithareturnoflessthan8%!Themessageisclear:stocksaretobeheldforthelongterm.Don’tworrytoomuchabouttheshort-termvolatilityofthemarkets;inthelongrun,stockswillalmostalwayshavehigherreturnsthanbonds.
Figure2-6.Commonstock5-yearreturns,1926–1998.
Figure2-7.Commonstock30-yearreturns,1926–1998.
Thissubjectcanalsobeanalyzedfromatheoreticalviewpoint.Usingsomerelativelysimplestatisticalmethods,youcancalculatetheriskofunderperformingthe“risk-free”T-billinvestment.Thismethodassumesareturnoncommon
stockof10%,anSDof20%,andaT-billrateof3%.Inanygivenyear,theriskofstocksunderperformingT-billsis36%.Fora5-yearperiod,thisriskis22%;for10years,13%;for20years,6%;for30years,3%;andfor40years,itisonly1%.Themessageisthesame:thelongerone’stimehorizon,thelesslikelytheriskofloss.Awordofcautionhere.
Somehaveinterpretedtheabovedataasdemonstratingthatstocksgrowlessriskywithtime.Thisisnotquitetrue.TakealookatFigure2-7.Thedifferencebetweenthehighestandlowest30-yearreturnisalmost5%.Compoundinga5%returndifferenceover30yearsproducesanalmostfourfolddifferenceinendwealth.Figure2-8demonstratesthevastlydifferentendwealthof
$1investedoverthevarious30-yearperiodssince1926.Thisgraphshowsthatwhenyoumeasureriskasthestandarddeviationofendwealth,stocksactuallybecomeriskierwithtime.Thisisnotatrivialortheoreticaldistinction.Probablythemostrelevantdefinitionofriskisthelikelihoodofrunningoutofmoney.Itisvitallyimportantthatyouthinkaboutwhat
measureofriskbestdescribesyourownpersonalneedsandperceptions.
Figure2-8.Commonstock30-yeargrowthof$1.
Everybody’sGrandchildrenOughttoBeRich
Inthehalcyonearlysummerof1929,JohnJ.Raskob,aseniorfinancieratGeneralMotors,grantedaninterviewtoTheLadiesHomeJournal.Thefinancialzeitgeistofthelate1920sisengagingly
reflectedinaquotefromthispiece:
Supposeamanmarriesattheageoftwenty-threeandbeginsaregularsavingsoffifteendollarsamonth—andalmostanyonewhoisemployedcandothatifhetries.Ifheinvests
ingoodcommonstocksandallowsthedividendsandrightstoaccumulate,hewillattheendoftwentyyearshaveatleasteightythousanddollarsandanincomefrominvestmentsofaroundfourhundreddollarsamonth.Hewillbe
rich.AndbecauseanyonecandothatIamfirminmybeliefthananyonenotonlycanberichbutoughttoberich.
Mr.Raskob’shypotheticalyoungmanwasaninvestmentgeniusindeed—turning$15permonthinto$80,000in20yearsrequiresanannualizedrateofreturn
ofover25%.Thisinterviewandtheinvestmentschemehewaspromotingarerememberedtothisdayasanabsurdexampleoftheinfectiousmoodunderlyingthepre-1929stockbubble.Andyet,inthelongrun,
Mr.Raskobwasnotfaroffthemark.Let’simaginethatMr.Raskob’shypotheticalyoungmanbeganinvesting$15permonthincommon
stocksonJanuary1,1926andcontinueddoingsountilhediedatage91onDecember31,1994.Bythatdatehewouldhaveaccumulated$2,462,295.Hadheinvestedinsmallstocks,hewouldhave$11,730,165.Obviously,thiscalculationcontainsanumberofunrealisticassumptions:thattheprincipalanddividendswereneverspent,taxeswerenotpaid,andstockswere
boughtfreeofcommissions.Perhapsourestimatesareoffbyafactorof2or3;still,thelong-termresultsareimpressive.Anoptimistmightcitethisasanexampleofthe“magicofcompoundinterest.”Toomuchismadeofthisphenomenon.Apessimistwouldnotethatourindustrioussaverdiedanoldmanwithoutenjoyinghisfortune.Hadheconsumedevenasmallpercentageof
hissavingseachyear,hisestatewouldhavebeenvastlysmaller.Personally,I’dratherbea26-year-oldroamingtheboulevardsofPariswithafewfrancsinmypocketthanaricholdman.Everyonecannotberich,butperhapstheirgrandchildrencan.Iurgeyoutospendafew
minutesperusingFigures2-1to2-8sothatyouaresuitablyimpressedwiththe
magnitudeoftherisksinvolvedinbondsandcommonstocks.Thenext73yearswilllikelybejustasbumpyasthelast.Individualinvestorsare
inevitablydrawnintostocksduringpowerfulbullmarkets;thespectacleofone’sfriendsandneighborsachievingquickandeffortlessprofitawakensthepowerfulforcesofhumannature.Those
suckedintothemarketforthefirsttimeduringsuchenthusiasmsinvariablylackaproperappreciationoftherisksassociatedwithhighreturns;theydrawcomfortfromtheblandishmentsofexpertsthattheycan“keepclosetotheexits”andselltheirstocksthemomentthebeargrowls.Aftertheyhavesufferedtheinevitablelosses,theyareovercomebyanevenmorepowerfulelementof
humanfinancialnature:theurgetopsychologicallydistancethemselvesfromtheir“failure,”andthussellatagreatloss,usuallywhenpricesarethelowest.Theplainfactofthematteristhatnoinvestor,nomatterhowskilled,everavoidsbone-crushinglossesattimes,evenwhenundertakingthemostprudentmarketrisks.Allinvestors,noviceorexperienced,arewellserved
bythewordsofJohnMaynardKeynes:
Idonotfeelthatsellingatverylowpricesisaremedyforhavingfailedtosellathighones.…Ifeelnoshameatbeingfoundowningasharewhenthebottomofthemarketcomes.Idonot
thinkitisthebusiness,farlesstheduty,ofaninstitutionaloranyotherseriousinvestortobeconstantlyconsideringwhetherheshouldcutandrunonafailingmarket,orfeelhimselftoblameifsharesdepreciateonhis
hands.Iwouldgomuchfurtherthanthat.Iwouldsaythatitisfromtimetotimethedutyoftheseriousinvestortoacceptthedepreciationofhisholdingswithequanimityandwithoutreproachinghimself[italicsadded].An
investorisaiming,orshouldbeaiming,primarilyatlongperiodresults,andshouldbesolelyjudgedbythese.Thefactofholdingshareswhichhavefalleninageneraldeclineofthemarketprovesnothingandshouldnotbeasubjectof
reproach.
Fortunately,therearewaystolessentherawrisksofsingleassets,andthereareeventimeswhentheadditionofasmallamountofaveryriskyassettoyourportfoliowillactuallylessenitsvolatility.
AssetClassesinthe1970–1998Period
Thepreviouslydiscussed1926–1998databaseforU.S.assetsprovidesareliableestimateoftheexpectedlong-termreturnandriskinU.S.stocksandbonds.Infact,therearedataonthelong-termreturnsandrisksoftheseassetsgoingback200years,albeitconsiderablylessdetailedandaccurate;theinflation-adjustedreturnsandSDdataareverysimilartothe1926–1998data.(Foran
excellentdiscussionofstockreturnsthroughouttheentire200yearsofU.S.history,seeJeremySiegel’sStocksfortheLongRun.)Unfortunately,the1926–
1998databaseisconfinedtoU.S.equitiesandhigh-qualitybondsandisthusmuchtoolimitedtobeofrealusetothemoderninvestor,whohasavailableamuchwidervarietyofcapitalmarketsto
choosefrom.Thereisgreatadvantagetobegainedfromwidediversificationamongasmanypotentialinvestmentcategoriesaspossible.Allinvestors,smallandlarge,requireaccurateestimatesofthereturnsandrisksofeachoftheseinvestments.Ihavechosen1970asthestartingpointforthisexpandeddatabasebecausehigh-qualitydataareavailablefromthisdateforawidevarietyof
assetsandbecause1970formsanimportantwatershedininvestmenthistory.Thebearmarketof1973–1974wastheworstdownmarketexperiencedbythecapitalmarketsgloballysincetheGreatDepression.Itisinstructivetoincludetheperformanceforthesetwoyearsforeachassetasaguidetotheirrisk.Includingsuchaferociousbearmarketprovidesahealthydoseof
“realitytesting.”Thisdatabasealsohasonefurtheradvantage—itisalmostcompletelyaccessiblefromawidevarietyofsources,suchasMorningstar,foranominalfee(seeChapter9forfurtherdetails).ThereturnsandSDsfortheseassetsaresummarizedinTable2-2.
Table2-2.AssetPerformancefrom1970
to1998
YouhavealreadyencounteredT-bills,5-yearTreasurynotes,20-yearTreasurybonds,theS&Pstocks,andsmallU.S.stocksinthe1926–1998database.Realestateinvestmenttrusts(REITs)arecompaniesthatderivetheirrevenuefromthemanagementofcommercialproperty.IexcludethoseREITsthatderivetheirincomeprimarilyfrom
mortgageactivity,andincludeonlyso-calledequityREITs.TheEuropean,PacificRim,andJapanesestockindexesderivefromtheMorganStanleyCapitalIndexesandrepresentthelargeststocksinthosemarkets.Preciousmetalsstocksrepresentthegoldandsilverminingindustry.Finally,internationalsmallstocksareforeignequivalentofU.S.smallstocks.This
indexiskeptbyDimensionalFundAdvisors,andcareisurgedinitsusebecausebefore1988itconsistedofonlytwocountries:theUnitedKingdomandJapan.Casualperusalsuggests
thatreturnsforthe1970–1998periodarehigherthanforthe1926–1998period(about4%higherforthethreebondcategories,1.5%forsmallstocks,and2.5%
forlargestocks).However,inflationfortherecentperiodwas5.23%annualizedversus3.1%forthe1926–1998period,sorealreturnswereaboutthesameforlargestocks,smallerforsmallstocks,andhigherforallthebondcategories.Comparingthetablesforthetwoperiodsalsosuggeststhatthe1929–1932bearmarketwasmuchworsethanthe1973–1974market.Again,thisislargely
illusion,asthe1929–1932bearmarketwascharacterizedbyseveredeflation,andthe1973–1974marketbysevereinflation.Inrealterms,the1929–1932marketwasonlyslightlyworsethanthemorerecentoneforlargestocks.Aswiththe1926–1998
database,thereisagoodcorrelationbetweenriskandreturnwithtwonotable
exceptions—preciousmetalsstocksandPacificRimstocks,whosereturnswerenotcommensuratewiththeirrisks.NotethatdataforthereturnsofbothREITandpreciousmetalsstocksarenoteasilyavailable.Toestimatethelong-termreturnsforpreciousmetalsstocks,IusedtheMorningstarmutualfundobjectivedata,whichgobackto1976.Fortheyears1970–1975,Iusedthereturnsofa
“proxy”mutualfund—theVanEckGoldFund.ForREITs,IuseddatafromtheNationalAssociationofRealEstateInvestmentTrusts(NAREIT),whichextendsbackonlyto1971.ThemakeupoftheREITsectorhasundergonedramaticchangesinthepastfiveyears,andthehistoricalNAREITreturnsmaynolongerberepresentative.Thelong-termreturnsdataforREITsand
preciousmetalsarehighlysuspect,andshouldnotbeusedforplanningpurposes.However,evenifthereturnsofthesetwoassetswereverylow,manyinvestorsmaystillwantexposuretothem.Themainreasonforthisisthattheyareperceivedtobeinflationhedges,andlikelytodowellinaninflationaryenvironmentinwhichotherstocksandbondswouldbeadverselyaffected.Thisisthe
sameassayingthatmuchoftheriskofpreciousmetalsandREITscanbe“diversifiedaway.”MoreaboutthislaterinChapters3and4.Figures2-9and2-10plotreturnandriskforthe1926–1998and1970–1998assetbases.Theriskforeachasset,quantifiedastheSD,isplottedalongthehorizontalaxis(orxaxis).Safeassetsareclusteredontheleftsideofthegraph;aswemoveoff
totheright,risk(SD)increases.Annualizedreturnisplottedalongtheverticalaxis(oryaxis).Aswemovefrombottomtotop,returnincreases.Notehowforalmostallassets,asreturnincreases,sodoesrisk.Ifweweretodrawanimaginarylinethroughthepoints,itwouldslopeuptotheright.Mostassetslieonafairlystraightline,showingclearlythedirectrelationship
betweenriskandreturn.ThetwomajorexceptionstothisarepreciousmetalsandPacificRimstocks,asnotedabove.
Figure2-9.Riskandreturn,1926–1998.
Figure2-10.Riskandreturn,1970–1998.
TheProblemwithHistoricalReturns
Oneareawhichgivesevenfinanceprofessionalsrealproblemsistheestimationoffutureassetreturns.Oneexpedientissimplytousehistoricalreturns;thequality
anddetailoftheavailabledata,particularlyfromIbbotson,makethisparticularlyattractive.Mostanalystslearnfromhardexperience,however,thatitcanbehazardoustoblindlyextrapolatepastreturnsintothefuture.Itisextremelyhelpfultohaveanintuitiveideaofhowtoestimatethefuturereturnsofstocksandbonds.
Longbondsarerelativelyeasy.Agoodapproximationoftheirreturnissimplythecoupon.Sayyouhavea6%30-yearTreasurybond.Ifinterestratesdonotchange,youwillinfactreceivea6%long-termreturn.Ifratesfall,thenyouwillobtainaslightlylowerreturn,asthecouponswillbeinvestedatalowerrate(so-calledreinvestmentrisk).Ifratesrise,theoppositewilloccur.Still,
evenwithsignificantlong-termbondmarketvolatilitythelong-termreturnwillnotbemorethanafewpercentoffthecouponrate.Atthebeginningof1926,thecoupononlong-termAAAcorporatebondswas4.9%—nottoofarofftheactualreturnfor1926–1998of5.77%.Longbondsalsonicely
illustratethedangersof
relyingonhistoricalreturnstooheavily.From1958through1983,bondsunderwentabrutal,grindingbearmarket,aslong-termTreasuryratesrosefromlessthan3%toover14%.(Bondpricesmoveinthedirectionoppositeinterestratechanges.)Becauseofthis,theannualizedreturnof20-yearTreasurybondsforthe50-yearperiodfrom1934to1983wasonly3.5%,which
wasactuallyslightlylessthaninflation.Hadyoureliedonthishistoricalreturn,youwouldhavecomeupwitharidiculouslypessimisticestimateoffuturebondreturnsin1984.Asitturnsout,in1984the14%couponforthe20-yearTreasurybondmoreaccuratelyforecastedthe12.85%returnoverthesubsequent15years.(Thelowerannualizedreturnresultingfromthefactthat
thecouponshadtobereinvestedatanever-fallingrate.)Asthisbookisbeingwritten,longTreasuriesareagainyieldingareasonable6%,sotheirexpectedreturnshouldbeclosetothehistorical5%norm.Stockreturnsarelesseasy.
Probablythemosttime-honoredmethodofestimatingfuturestockreturnsinvolvestheso-called
discounteddividendmethod.Itgoessomethinglikethis:overalongenoughtimeperiod,allcompaniesgobankrupt.Ifyoudon’tbelievethisgotoalargereferencelibraryandexamineastockpagefromtheCivilWar;you’llfindthatalmostnoneofthenamesarerecognizable.Thevalueofastockthuscomprisesthe“discountedvalue”ofallofitsfuturedividends.(We’ll
discussinChapter7justhowtogoaboutdoingthissortofcalculationandpreciselywhatwemeanby“discountedvalue.”)IfyouwereaRipVanWinkleinvestorwhoplaced$10,000inthestockmarketandthenwenttosleepfor200years,allyouwouldbeleftwithwhenyouawokewouldbegenerationsofreinvesteddividendsfromalonglistofmostlydefunctcompanies.
(Mindyou,thiswouldbeaverylargeamountofmoney.)Estimatingthevalueofastockorstockmarketbythismethodisaverycomplicatedcalculation,butcanbesimplifiedasfollows:
Return=dividendyield+dividendgrowthrate+multiplechange
Since1926,stocksactuallyyieldedanaverageofabout
4.5%.Earningsanddividendshavegrownatabouta5%rate.Thetermmultiplechangereferstotheincreaseordecreaseintheoveralldividendrate.Inthiscase,itreferstothefactthatstockswhichsoldfor22timesdividends(a4.5%rate)in1926nowsellfor77timesdividends(a1.3%rate).Thiscalculatesouttoanannualizedmultiplechangesincethenofabout1.7%.
Addthesethreenumberstogetherandyouget11.2%comparedtotheactualhistoricalreturnof11.22%.Nottooshabby.(Therewere,ofcourse,afewbumpsontheroadtothatreturn.)Unfortunately,aswestart
themillennium,thingslookalittledifferent.ThecurrentdividendyieldoftheS&P500isabout1.3%.Dividendgrowthisstillabout5%.And
theprudentinvestorshouldnotexpectanyfurtherexpansionofearningsanddividendmultiples.Addingthetwonumbersgivesanexpectedreturnoncommonstockofonlyabout6.3%versusthe6.0%percentcoupononlongbonds.Thus,overthenextfewdecades,stockreturnsshouldbeonlyslightlyhigherthanbondreturns.
Simplyput,thecurrentoptimismsurroundingstockinvestingdoesnotappeartobewell-founded.(Infact,in1998theexpectedreturnofcorporatebondscalculatedinthismannerbrieflyexceededthatofstocks.)Thefamousfinancial
analystBenjaminGrahamoncesaidthatintheshortrunthestockmarketisavotingmachine,butthatinthelong
runitisaweighingmachine.Whatitweighsareearnings.Intheseebullienttimes,thetorpidandoccasionallystutteringgrowthofcommonstockearningscannotbestressedstronglyenough.Forthisreason,I’veplottedtheearningsoftheDowJonesIndustrialAveragefrom1920.Figure2-11showsearningsinnominaldollars,withnoadjustmentforinflation.Thegraphslopes
upwardatabout5%peryear.Figure2-12showsthesamedataininflation-adjusteddollars,relativetothevalueofadollarin1920.(Toconvertto2000dollars,multiplyby9.)Itslopesupwardatonlyabout2%peryear.ItisillogicaltoexpectthevalueofabroadindexofU.S.stockstosignificantlyexceedthis“natural”realgrowthrateof2%.Tothisreturncanbeaddedyour
dividends.Toexpectmoreisfolly.
Figure2-11.DowJonesnominalearnings.
Figure2-12.DowJonesrealearnings.
Itismoredifficulttoperformasimilaranalysisforotherassetclasses.ItappearsthattheexpectedreturnsofEuropeanandJapanesestocksshouldbeaboutthesameasforU.S.stocks.U.S.smallstocksshouldhavesomewhathigherreturns.
PacificRimandemergingmarketsstockscurrentlyyieldabout3%to4%.TheymayalsohavegrowthrateshigherthanintheUnitedStatesandthusmayhavehigherreturns—butofcoursewithmuchhigherrisk.Thegreatestanomalyofall,however,iswithREITs,whicharecurrentlyyieldinganalmostunbelievable8.8%.Eveniftheyexperiencenoearningsgrowth,theirreturns
shouldbehigherthantheS&P500.And,toroundthingsoff,
theT-billreturnisalmostimpossibletoforecast,sinceits“coupon”(strictlyspeaking,ithasnone,asT-billsaresoldatadiscountandmatureatpar)changesfrommonthtomonth.So,asthefamoustestpilot
ChuckYeagerwouldsay,we’vegotalittleproblem
here;futurestockreturnsestimatedbythediscounteddividendmodelareconsiderablylowerthanhistoricalreturns.Whatistheintelligentinvestortodo?Thereisnorightanswerto
thisdilemma,butIwoulderrontheconservativesideandgowiththediscounteddividendmodel.Usingthismethod,itshouldbepossibleforyoutocalculateyour
long-termexpectedinvestmentreturnbasedonyourinvestmentchoices,or“assetallocationpolicy.”Youshouldalsobeabletoestimatetheriskthatyouaretakingtoachievethisreturn.Asalreadyalludedto,the
mostusefulwaytoestimateyourexpectedreturnisasinflation-adjusted,or“real,”return.Thiswillinturnsimplifyyourretirement
calculations,astheeffectsofinflationhavealreadybeendiscounted.Projectinga4%stockreturninrealdollarsiseasierthanprojectinga7%nominalreturnandadjustingfora3%inflationrate,particularlywhenyourwithdrawalsmaybespreadover15to30years.Table2-3providesahandy“back-of-the-envelope”summarytohelpyouplanyourfinances.Yousayyoucantoleratea
25%bearmarkethitaslongasitoccursonlyonceinyourlife?Fine.UsingthepercentagesinTable2-3,let’sconstructaportfolioconsistingof50%stock,splitbetweenlargeandsmallcompanies,and50%bondsofshortduration.Thiswillloseabout25%inaonce-in-a-lifetimebearmarket.Yourinflation-adjustedportfolioexpectedreturncanbecalculatedasfollows:
Table2-3.ExpectedAssetClassCharacteristics
1.25%ofyourportfolioinsmallstocks:.25×6%=1.5%
2.25%ofyourportfolioinlargestocks:.25×4%=1.0%
3.50%ofyourportfolioinbonds:.5×3%=1.5%Thus,thereallong-term
expectedreturnofyourportfoliois:
1.5%+1%+1.5%=4%
Thismeansthatyouwillaboutdoubletherealvalueofyourportfolioevery18years.(Thisiseasilycalculatedfrom“theruleof72,”whichsaysthatthereturnratemultipliedbythetimeittakestodoubleyourassetswillequal72.Inotherwords,at6%returnyourcapitalwilldoubleevery12years.)Takeanotherbreak.Don’t
lookatthisbookforatleasta
fewmoredays.Inthenextchapterweshallexplorethestrangeandwondrousbehaviorofportfolios.
Summary1.Riskandrewardareinextricablybintertwined.Donotexpecthighreturnswithouthighrisk.Donotexpectsafetywithoutcorrespondinglylowreturns.
2.Thelongerariskyassetisheld,thelessthechanceofapoorresult.
3.Theriskofanassetoraportfoliocanbemeasured.Theeasiestwaytodothisisbycalculatingthestandarddeviationofreturnsformanytimeperiods.
4.Thosewhoareignorantofinvestmenthistoryareboundtorepeatits
mistakes.Historicalinvestmentreturnsandrisksofvariousassetclassesshouldbestudied.Investmentresultsforanassetoveralongenoughperiod(greaterthan20years)areagoodguidetothefuturereturnsandrisksofthatasset.Further,itshouldbepossibletoapproximatethefuturelong-termreturnandriskofa
portfolioconsistingofsuchassets.
3TheBehaviorofMultiple-AssetPortfolios
UncleFredMakesYouAnotherOffer
Timepasses.YouhavespentseveralmoreyearsintheemployofyourUncleFred,
andyouhavetrulygrowntodreadtheannualcoin-tosssessions.Thelawsofprobabilityhaveservedyouwellbyprovidingyouwithanequalnumberofheadsandtails.Unfortunately,yoursuccessandsenioritymeanthatthestakesoneachcointossgrowprogressivelyhigher.Remember,attheendofeachyearUncleFredadds$5000toyourretirementfundanddetermineswithacoin
tosswhetheryourreturnonthewholeaccountisagainof30%(heads)oralossof10%(tails).Anever-growingamountofmoneyridesoneachtoss,andyourunclesensesyourincreasingdiscomfort.Hemakesyouanother
offer.Attheendofeachyear,hewilldivideyourpensionaccountintotwoequalpartsandconductaseparatecoin
tossforeachhalf.Justwhatisyourwily
uncleupto?Yourfirstinstinctistorecoilinhorror—ifonecointossunnervesyou,surelytwomustbeworse.However,youhaveananalyticalframeofmind,andyoubegintodissecthisproposition.Yourealizethattherearefourpossibleoutcomesfortwocointosses,eachwithanequal
probability:
Outcomes1and4arethesameastheywouldbeinasinglecointoss,withtheoriginalreturnsof+30%and−10%,respectively.
However,therearetwoadditionalpossibleoutcomes,inwhichthetwotossesresultinoneheadandonetail.Thetotalreturninthesecasesis10%(one-halfof+30%plusone-halfof−10%).Sinceeachofthefour
possibleoutcomesisequallylikely,andinarepresentativefour-yearperiodyouwillhaveoneofeachoutcome,youfindthatyouraccount
willincreasebyafactorof:
1.3×1.1×1.1×.9=1.4157
Beinghandywithnumbers,youcalculatethatyourannualizedreturnforthistwo-coin-tosssequenceis9.08%,whichisnearlyafullpercentagepointhigherthanyourpreviousexpectedreturnof8.17%withonlyonecointoss.Evenmoreamazingly,
yourealizethatyourriskhasbeenreduced—withtheadditionoftworeturnsatthemeanof10%,yourcalculatedstandarddeviationisnowonly14.14%,asopposedto20%forthesinglecointoss.WiseoldUncleFredhas
introducedyoutothemostimportantconceptinportfoliotheory:
Dividingyourportfoliobetween
assetswithuncorrelatedresultsincreasesreturnwhiledecreasingrisk.
Thisseemstoogoodtobetrue.Thekeywordhereisuncorrelated;theresultofthefirstcointossinnowayinfluencestheresultofthesecondtoss.Thinkaboutit—ifthetwocointosseswere
perfectlycorrelatedandthesecondcointossalwaysgavethesameresultasthefirst,thenwewouldgetonlytheoriginal+30%and−10%returns.
MathDetails
Thoseofyouwithsophisticatedinvestmentbackgroundsknowthataputoption
onasecurityorafuturescontractsoldshortwillhaveahighlynegativecorrelationwiththereturnofitsunderlyingasset.However,inthatinstancethetwopositionswillhavenearlyoppositereturns,withanearzerototal
portfolioreturn.Amoreprecisestatementwouldbethattwoassetswithpositivereturnsshouldnothavepersistenthighlynegativecorrelations.
Wewouldbebacktotheoriginalsinglecointoss,withitslowerreturnandhigher
risk.Ifthesecondcointosswereperfectlyinverselycorrelatedwiththefirstandalwaysgavetheoppositeresult,thenourreturnwouldalwaysbe10%.Inthiscase,wewouldhavea10%annualizedlong-termreturnwithzerorisk!Thepointcannotbestatedstronglyenough:mixingassetswithunncorrelatedreturnsreducesrisk,becausewhenoneoftheassetsiszigging,it
islikelythattheotheriszagging.Intherealworldof
investing,itisoccasionallypossibletofindtwostockorbondclasseswhichhavezerocorrelation,producingapercentorsoincreaseinreturnandamoderatereductioninrisk.Restassured,however,thatinthelongrun,meaningfulnegative(inverse)
correlationsareneverseen—thiswouldsimplybetoogoodtobetrue.
ModelingtheBehaviorofSimplePortfolios
Thecoin-tossexampleshouldconvinceyouofthevalueofdiversifyingyourassets.Intherealworldofinvesting,youarefacedwithaseeminglylimitlesschoiceof
assetswhichcanbecombinedintoaliterallyinfinitenumberofportfolios.Yet,foreachlevelofriskyouchoosetobear,thereisonlyasingle“right”mixofassetsthatwillresultinthemaximuminvestmentreturn.Evenworse,theright,oroptimal,assetmixbecomesapparentonlyinretrospect;theoptimalmixforthenext20yearsisunlikelytolookanythingliketheoptimalmixforthepast
20years.HowonGod’sgreenearthdoyoufindthebestfutureassetmix?Inordertofindtheanswer,
webeginbysettingupa“laboratory”whichwillsimulatetheperformanceofcomplexportfolios.Tobetterunderstandthis,weshallstartwithsomeverysimpleexamples.
Example1.Themodelconsistsofonlytwoassets:
Thefirstasset,UncleFred’scointoss,withequallylikelyreturnsof+30%and−10%,whichweshallcallstockinthisexample;andasecondasset,withequallylikelyreturnsof0%and+10%,whichweshallcallbond.Stockhaslong-termreturnandriskcharacteristicssimilartothoseofcommonstocks,andbondhaslong-termreturnandriskcharacteristicssimilarto
thoseoffive-yearTreasurynotes.Therearefourpossibleoutcomes:
Youareallowedtochooselong-terminvestmentinanycombinationofthesetwoassets,from100%stockto
100%bond,withanycombinationinbetween.Attheendofeachyearyoumustrebalanceyourportfoliobacktothiscombination.Let’sassumethatyoupicka50/50mixofstockandbond.Inotherwords,attheendofeachyear,50%ofyourportfolioissubjecttothe0or+10(bond)cointoss,andtheother50%issubjecttothe+30or−10(stock)cointoss.Ifthebondreturns+10%and
thestockreturns−10%foragivenyear,attheendofthatyearyounowhavemorebondthanstock,andyoumustsellsomebondandusetheproceedstobuymorestock.Inthoseyearswhenstockreturns30%,youmustsimilarlyexchangeenoughstockforbondtoresetthemixbackto50/50.Thereasonsforthisareseveral.Firstandforemost,rebalancingincreaseslong-
termportfolioreturnwhilereducingrisk.Second,failuretorebalanceaportfolioofstocksandbondseventuallyleadstoanalmostall-stockportfolio,becauseofthehigherlong-termreturnsofstock,resettingyourreturn-riskcombinationtoahigherlevel.Last,andmostimportant,thehabitofrebalancinginstillsintheinvestorthedisciplinenecessarytobuylowandsell
high.Inthissameexample,now
assumethatyouhavechosenaportfolioofone-quarter(25%)bondandthree-quarters(75%)stock.WhereRbandRsarethereturnsofbondandstock,respectively,thereturnforthisportfolioinanygivenperiodis:
(.25×Rb)+(.75×Rs)
Thus,ifinagivenperiodthestockreturnis+30%andthebondreturnis+10%,thentheportfolioreturnis:
(.25×10)+(.75×30)=25%
Thereturnsforeachofthefourpossibleoutcomesare:
Theannualizedreturnforthisportfoliois7.70%,anditsSDis15.05%.First,notethatthereturnofthisportfolioisonly0.47%lowerthan100%stock,andyetitsrisk(SD)isdecreasedby
almost5%.(Putanotherway,one-quarteroftheriskhasbeeneliminatedatacostofonlyone-seventeenthofthereturn.)Thisissimplyanotherdemonstrationofthebenefitsofdiversification.Thisparadigmprovidesyouwithasimpleyetpowerfulwaytostudytherisk-versus-returncharacteristicsofthemostcommondiversificationtool:thestockandbondcombination.Thoseofyou
whoarefamiliarwithspreadsheetswillrecognizethatasimplefileanalyzingtheriskandreturnfromtheaboveparadigmcanbewritteninafewminutes.InFigure3-1,thesevaluesareplottedinamanneridenticaltoFigures2-9and2-10.Remember,asyoumoveupthegraph,returnincreases.Aswemovefromlefttoright,riskincreases.
Figure3-1.Riskversusreward.
Therightsideofthegraphisnotterriblysurprising;asyouaddinsmallamountsofbondtothestock,thereisadramaticreductionofrisk(SD)witharelativelysmalllossofreturn.However,thebehavioroftheleftsideofthegraphistrulyremarkable.
Ifyoustartwithanall-bondportfolio,addingsmallamountsofstockincreasesreturn,asexpected.However,addingasmallamountofstockalsodecreasestheportfolioriskslightly,withthe“minimumrisk”portfolioconsistingofabout7%stock.Astockpositionof12%producesthesameriskastheall-bondportfolio.Thus,theinvestorwhosesoleaimistominimizeriskmustof
necessityownsomestock.Thisisaphenomenonweshallencounterrepeatedlyinourstudyofportfoliobehavior.
Example2.Let’sperformasimilarexerciseforUncleFred’stwo-coin-tossportfolioatthebeginningofthechapter,wheretwodifferentassetsreturneither+30%or−10%,andwhereeachasset’sreturnisindependentofthe
other.Tosummarize:
Figure3-2graphsthereturnandriskofaportfolioofdifferentmixesofAandB,inthesamefashionaswasdoneforExample1.SincebothassetshavethesamereturnandSD,youneedto
plotonlyhalfofthepoints,sincea75/25mixofA/Bwillbehavethesameasa25/75mix.Theresultsareclear-cut.Therisklessens(youmovetowardtheleft)andreturnincreases(youmoveup)asyoumovetowarda50/50mix.Eachpointonthegraphrepresentsa5%changeincomposition,andyoucanseethatmostofthegaininreturnversusriskoccursasyoumovefrom100%ofeither
assettoa75/25composition.Thetripfrom75/25to50/50producesmuchlessadditionalbenefit.Theriskandbenefitofa65/35mixdoesnotdiffersignificantlyfromthe50/50mix—lessthan0.1%ofreturnand0.5%ofSD.Thisexamplemakesthesekeypoints:
Figure3-2.Riskversusreward.
1.Iftwoassetshavesimilarlong-termreturnsandrisksandarenotperfectlycorrelated,theninvestinginafixed,rebalancedmixofthetwonotonlyreducesriskbutalsoactuallyincreasesreturn.Youalreadyknowthatthereducedriskistheresultof
theimperfectcorrelationbetweenthetwoassets;abadresultforoneassetisquitelikelytobeassociatedwithagoodresultfortheother,mitigatingyourloss.Theincreasedreturnisanotherfacetofthesamephenomenon:Ifagoodresultforoneassetisassociatedwithabadresultfortheother,thentherebalancingrequirementforcesyoutosellsomeofthesuccessfulasset
(sellhigh)inordertobuymoreoftheunsuccessfulasset(buylow).Thisexcessreturnisnotobtainedwithoutrebalancing.2.Iftwopoorlycorrelated
assetshavesimilarreturnsandrisks,thentheoptimalmixofthetwowillbecloseto50/50.3.Thereisplentyof
marginforerroravailableinassetallocationpolicy.Ifyou
areoff10%or20%fromwhatinretrospectturnedouttobethebestallocation,youhavenotlostthatmuch.Asweshallsee,stickingbyyourassetallocationpolicythroughthickandthinismuchmoreimportantthanpickingthe“best”allocation.
DealingwithMoreThanTwoImperfectlyCorrelatedAssets
Theabovemodelshavebeenquiteusefulfordemonstratingtheeffectofdiversificationonriskandreturnoftwosimilarassets(Example2)andtwodifferentassets(Example1)withzerocorrelation.Unfortunately,theaboveexamplesarenomorethanusefulillustrationsofthetheoreticalbenefitsofdiversifiedportfolios.Intherealworldofinvesting,wemustdealwithmixesof
dozensofassettypes,eachwithadifferentreturnandrisk.Evenworse,thereturnsoftheseassetsareonlyrarelycompletelyuncorrelated.Worsestill,therisks,returns,andcorrelationsoftheseassetsfluctuateconsiderablyovertime.Inordertounderstandrealportfolios,weshallrequiremuchmorecomplextechniques.Thusfarwehavedealt
withportfolioswithonlytwouncorrelatedcomponents.TwouncorrelatedassetsmayberepresentedwithfourtimeperiodsasinUncleFred’scointoss,threeassetswitheightperiods,fourassetswith16periods,etc.Intherealworldofinvesting,however,itisdifficulttofindtwoassetsthatareuncorrelated,anditispracticallyimpossibletofindthree.Itisabsolutelyimpossibletofind
morethanthreemutuallyuncorrelatedassets.Thereasonforthisissimple.Aportfoliooftwoassetshasonlyonecorrelation.Threeassetshavethreecorrelations,andfourassetshavesixcorrelations.(Thisisthesamereasonwhybigofficeshavemessierpoliticsthansmallones.Athree-personofficehasthreeinterpersonalrelationships;a10-personofficehas45relationships.)
Realassetsarealmostalwaysimperfectlycorrelated.Inotherwords,anabove-averagereturninoneissomewhatmorelikelytobeassociatedwithanabove-averagereturnintheother.Thedegreeofcorrelationisexpressedbyacorrelationcoefficient.Thisvaluerangesfrom−1to+1.Perfectlycorrelatedassetshaveacorrelationcoefficientof+1,anduncorrelatedassetshave
acoefficientof0.Perfectlyinversely(ornegatively)correlatedassetshaveacoefficientof−1.Theeasiestwaytounderstandthisistoplotthereturnsoftwoassetsagainsteachotherformanyperiods,asisdoneinFigures3-3,3-4,and3-5.
Figure3-3.S&P500/U.S.smallstock,correlationof.777.
Figure3-4.S&P500/EAFE,correlationof.483.
Figure3-5.Japansmallstock/REITcorrelationof.068.
Eachfigureplotsthe288monthlyreturnsforeachassetpairforthe24-yearperiodfromJanuary1975toDecember1998.Eachpointonthegraphrepresentsthereturnforoneofthosemonths;thereturnforthe
firstassetisreadonthex(horizontal)axis,andforthesecondassetonthey(vertical)axis.Iftheassetsareperfectlycorrelated,theywillallfitonastraightline.(Ifthecorrelationispositive,thelinewillrunfromlower-lefttoupper-right;ifnegative,thelinewillrunfromupper-lefttolower-right.)Iftheyareuncorrelated,theywillbewidelyscattered.
Figure3-3plotsthemonthlyreturnsfor1975–1998oftheS&P500versusU.S.smallstocks.Mostofthepointslieonnearlyastraightline;apoorreturnforonewasinvariablyassociatedwithapoorreturnfortheother.Thecorrelationcoefficientof.777forthesetwoassetsisquitehigh.ThisgraphdemonstratesthataddingU.S.smallstockstoaportfolioofU.S.largestocks
doesnotdiminishriskverymuch,asapoorreturnforonewillbeverylikelyassociatedwithapoorreturnfortheother.Figure3-4plotstwo
looselycorrelatedassets—U.S.largestocks(S&P500)andforeignlargestocks(EAFEIndex).Althoughtheredoesappeartobealooserelationbetweenthetwo,itisfarfromperfect.
Thecorrelationcoefficientofthispairis.483.Lastly,Figure3-5plots
twoverypoorlycorrelatedassets(correlationcoefficientof.068):JapanesesmallstocksandREITs.Thisplotisa“scattergram”withnodiscernablepattern.Agoodorbadresultforoneoftheseassetstellsusnothingabouttheresultfortheother.
MathDetails:
HowtoCalculateaCorrelationCoefficient
Inthisbook’spreviousversions,Iincludedasectiononthemanualcalculationofthecorrelationcoefficient.Inthepersonalcomputerage,thisisanexercisein
masochism.Theeasiestwaytodothisiswithaspreadsheet.Let’sassumethatyouhave36monthlyreturnsfortwoassets,AandB.EnterthereturnsincolumnsAandB,nexttoeachother,spanningrows1to36foreachpairofvalues.
InExcel,enterinaseparatecelltheformula=CORREL(A1:A36,B1:B36)
InQuattroPro,theformulawouldbe@CORREL(A1..A36,B1..B36)
Bothofthesepackagesalsocontainatoolthat
willcalculatea“correlationgrid”ofallofthecorrelationsofanarrayofdataformorethantwoassets.Thoseofyouwhowouldlikeanexplanationofthestepsinvolvedincalculatingacorrelationcoefficientare
referredtoastandardstatisticstext.
Whyisthissoimportant?Asalreadydiscussedthemostdiversificationbenefitisobtainedfromuncorrelatedassets.Theaboveanalysissuggeststhatthereisnotmuchbenefitfrommixingdomesticsmallandlargestocksandthatthereisgreat
benefitfrommixingREITsandJapanesesmallstocks.Intherealworldofinvesting,thisturnsouttobethecase.
Summary1.Theconceptofcorrelationofassetsiscentraltoportfoliotheory—thelowerthecorrelation,thebetter.
2.Diversifyingyourportfolioamong
uncorrelatedassetsreducesriskandincreasesreturn.Itisnecessarytorebalanceyourportfolioperiodicallytocapturethisincreasedreturn.
4TheBehaviorofReal-WorldPortfolios
Sofarwe’veexploredtwoofthecriticalbuildingblocksofinvestmenttheory:thebehaviorofsingleclassesofstocksandbondsandthe
behaviorofverysimplemodelportfolios.Itistimetoexaminethebehaviorofportfoliosofactualstocksandbonds.Weshallthenbegintoapproachthecentralquestionofportfolioanalysis:Whatportfoliosproducethemostreturnfortheleastamountofrisk?
ExaminingtheBehaviorofComplexPortfolios:The
Return-RiskPlot
Thusfar,wehavedealtonlywithsimpleportfolioshavingtwocomponentswithzerocorrelation.A“complex”portfolioisonewithmanycomponentswhosecorrelationsvarywidely.And,unfortunately,correlationsarerarelyzero;youcanexpecttoseevaluesanywherebetween0and1,withmostvaluesclustering
between.3and.8.Thesearethesortsofportfoliosyouencounterintherealworld.Itisnothardtostudy,or“model,”thebehaviorofcomplexportfoliosifyouapproachtheproblemmethodically.Let’stakethetwomostcommonlyusedriskyassets:largecompanystocksandlong-termduration(20-year)U.S.Treasurybonds.Theannualreturnsoftheseassetsareavailable
fromtheIbbotsonSBBI,discussedinChapter2.Assumethatwewishtostudythebehaviorofa50/50mixofthesetwoassets.Foranygivenyear,thereturnforthisportfolioisthesumofeachindividualreturntimesitsportfoliocomposition,inthiscase.5.Ifthereturnofstocksforagivenyearis24%andthereturnofbondsis2%,a50/50mixhasareturnof:
(.5×24%)+(.5×2%)=12%+1%=13%
Fora60/40mixthereturnis:
(.6×24%)+(.4×2%)=14.4%+.8%=15.2%
Wecancalculatetheportfolioreturnforanygivenassetmixforeachofthe73
yearsbetween1926and1998.AnannualizedreturnandSDforeachportfoliocanbecomputedfromthese73annualportfolioreturns.Soundtedious?Itisifyouaredoingitbyhand.Thoseofyoufamiliarwithcomputersandspreadsheetswillrecognizethatafilethatperformsthistaskcanbewritteninamatterofminutes.Youcaneasilywriteaspreadsheetfileinsucha
waythatyouhavetoenteronlytheportfoliocomposition,andthereturnandSDdatainstantlyappearforthatmix.(Forthosewhoareinterested,asamplespreadsheetfileisavailableathttp://www.efficientfrontier.com/files/sample.exeWestartwith100%stock,
thena95/5mixofstock/bond,then90/10,then85/15,andsoon,allthewayto100%bond.The
spreadsheetwillcomputetheannualizedreturnsandSDsasfastastheportfoliocompositionsarekeyedin.Youcanusethesamespreadsheetsoftwaretoploteachofthe21portfoliocompositionsonanx–ygraph,usingSDforthexvalueandannualizedreturnfortheyvalue.TheresultisdisplayedinFigure4-1.
Figure4-1.Stock/20-yearTreasurymixes,1926–1998.
Suchgraphsareessentialtoyourunderstandingofinvestmentstrategy.Youhaveseensimilargraphsinthepreviouschapters.Remember,aswetravelupthegraph,returnincreases,andaswetraveltotheright,
riskincreases.Thetriangles(plotted
points)areconnected,andwecantravelalongthedescribedpath.Letusstartatthebottomleft,atthepointlabeled“100%Bond.”Wetravelfromthispointtowardthe“stock”pointintheupperrightofthegraph.Thepathinitiallyheadsnearlystraightup.Thismeansthataddingthefirst15%(threeticks)or
soofstockaddsnoriskatall,whilethereturnisincreased.Asweaddanother10%(twoticks)orsoofstock,thepathstartstocurveslightlytotheright,meaningthatfurtherincreasesinreturnareaccompaniedbyaslightincreaseinrisk.Bythetimewearepastthe50/50mark,theadditionofmorestocktothemixaddsonlyslightlytothereturn,whileincreasingtheriskconsiderably.Looked
atfromanotherperspective,onecanstartfromtheotherend,at“100%Stock.”Fromthispoints,thepathheadsalmoststraighttotheleft.Addingasmallamountofbondstostockdramaticallyreducesriskatalmostnocostinreturn.Notethattheplotofthereturn-versus-riskdataforthevariousstockandbondmixesinFigure4-1describesacurvewithaslightupwardbulge,whichtellsusthatwe
aregettingextrareturnfromourdiversification.Also,attheextremeleftofthecurvethereisamoreprominentbulgetotheleft,whichtellsusthatthereisasignificantreductioninrisktobehadbyaddingasmallamountofstocktoanall-bondportfolio.Youwillseemoresuchcurvesinthecomingpages.Youcangaugethediversificationbenefitofanyassetpairbytheamountof
bulgethecurveexhibits.Themorebulge,thebetter.Youmayrecognizethat
Figure4-1looksalmostlikeFigure3-1inthepreviouschapter.RecallthatthisisderivedfromExample1,thestock-bondparadigm.Itisremarkablethatsuchasimplemodelsoaccuratelydescribesthebehaviorofstocksandbondsintherealworld.Recollectthatthe1926–
1998Ibbotsondatabasecontainsotherassetsaswell,includingU.S.Treasuryobligationsofshortermaturity,aswellasthosewildandwoolysmallstocks.Itisasimplemattertoaddthemtoourspreadsheetandproducereturn-versus-riskplotsforthem.Figure4-2containsthe
samekindofstockand20-yearbondplotasFigure4-1,
exceptthatwehavetwomorebondchoices:30-dayT-billsand5-yearTreasurynotes.Thethreedifferentcurvesrepresentthemixtureofstocksand20-yearbonds,stocksand5-yearnotes,andstocksand30-dayT-bills.Whatdoesthistellus?First,lookattherighthalfofthegraph.Thethreecurvesarereallyquiteclosetogetheratthispoint.Assumeyoucantoleratehighportfoliorisk,
sayatthelevelofa15%SD.Toobtainaportfoliowiththislevelofriskyouwillbedilutingyourstockwithonlyasmallamountofbond,anditreallydoesn’tmatterwhichofthethreedifferentbondsyouuse.Yourreturnandriskwillbethesame.Nextassumethatyoucantolerateonly10%SDofrisk.Clearly,atthisleveltheuseof5-yearnotesissuperiortotheothertwobondchoices;overmost
ofitsextentitliesabovetheothertwocurves,indicatingthatforeachdegreeofriskthe5-yearnotesandstockmixyieldsmorereturn.OnlyatlowrisklevelsistheuseofT-billsdesirable.Portfoliosimulationswithotherdatabasesusingbothbacktestingandanothertechniquecalledmean-varianceanalysisalsosuggestthesuperiorityofshort-termbonds.On
occasionitmaybeadvantageoustouselong-termbondsorT-billsinsmallamounts.Ingeneral,however,youwillnotgofarwrongbystickingtobondmaturitiesofsixmonthstofiveyearsfortherisk-dilutingportionofyourportfolio.
Figure4-2.Stock/bondmixes,1926–1998.
TheIbbotsondatabasecontainstwootherassets:smallstocksandlong-termcorporatebonds.Thesmallcompanystocksbehavesimilarlytolargestocks,andlong-termcorporatebondsbehavenearlyidenticallyto20-yearTreasurybonds.
RiskDilution
Ifyouareunhappywiththedegreeofriskinyourportfolio,youhavetwowaystoreduceit.Thefirstwayistoemploylessriskyindividualassets.Anexampleofthiswouldbetosubstitutelargestocksforsmallstocks,domesticstocksforforeignstocks,orutilitystocksforindustrialstocks.Thesecondwayistostickwithyour
basicallocationamongstockgroupsandsimplyreplaceasmallamountofyourentirestockallocationwithalikeamountofshort-termbonds.Indoingsoyouaretravelingfromrighttoleftonthereturn-riskcurve,loweringyourriskandreturnatthesametime.Riskdilutionreferstothisprocessoftravelingfromrighttoleftonareturn-versus-riskcurve.
Ifyoubelievethatyouhavefoundaneffectivestockallocation,itisgenerallyabetterideatoemployriskdilution,asthisleavesyourchosenstockstrategyundisturbed.Reshufflingyouroverallstockstrategyislikelytoresultinalesseffectiveportfolio.Aswehavealreadyseen,aconservative,risk-averseinvestmentstrategywillalmostalwaysinvolveatleast
asmallamountofexposuretoveryriskyindividualassets.Thisisseenintheleft-handportionsofFigures4-1and4-2;theadditionofasmallamountoflarge(orsmall)stockstoa100%bondportfolioactuallyreducesriskslightly.Startwiththefirstdatapointontheleftofthesegraphs,indicatingtheall-bondportfolio.Proceedingupthenextfewpoints,asoneaddsinasmallamountof
stocksallofthecurvesinitiallytravelbothup,indicatinghigherreturn,andtotheleft,indicatingslightlylowerrisk.Onlyasoneaddsinstillmorestockdoesthecurvemoveofftotheright,indicatinghigherrisk.Thestockcompositionofahigh-riskportfoliousuallydoesnotdiffermuchfromthatofalow-riskportfolio.Themaindifferenceisinthebroadallocationbetweenstocksand
bonds.
ForeignAssets
Recallthetwo-coin-tossmodeldiscussedinChapter3.Theextrareturnobtainedfromhavingthereturnsforeachhalfofyourportfoliodeterminedbydifferentcointossesdependsupontheresultsofthetwocointossesbeingindependentofeachother,i.e.,uncorrelated.Ifthe
twocointosseswerealwaysthesame(highlycorrelated),therewouldbenoadvantagetothetwo-coin-tossmodel.Theessenceofeffectiveportfolioconstructionistheuseofalargenumberofpoorlycorrelatedassets.Unfortunately,theall-U.S.1926–1998databasecontainsonlytwobroadcategoriesthatdonotcorrelatewell:stocksandbonds.Thecorrelationoflargeandsmall
stockswitheachotherisquitehigh,asisthecorrelationofintermediateandlongbonds.Itisnecessarytouseforeignsecuritiesifwewishtoconstructaportfoliocontainingmanyimperfectlycorrelatedcomponents.Good-qualitydataforforeignstockandbondreturnsareavailableafter1969.Thisisfortunate,astheworstbearmarketofmoderntimesoccurredin1973–1974.
Examinationofportfoliobehaviorintheseyearsyieldsagoodmeasurementofbear-marketrisk.Adecadeagooneoften
heardaboutthehighreturnsavailablefromforeigninvesting.By1985youcouldn’tlookatthe“MoneyandInvesting”sectionofTheWallStreetJournalwithoutreadingabouthowthemanagersoflargepension
funds,endowments,andprivatepoolswereincreasingtheirforeignexposuretocapturethishighreturn.Financialgurusofallstripesdiscoursedlearnedlyontheamountofexposureallottedtoforeignassets.Themostwidelyavailable
foreignstockindexistheMorganStanleyEurope,Australasia,andFarEastIndex,commonlyknownas
theEAFE(pronounced“eef’ah”).Forthe20-yearperiodending1988,EAFEreturnswereabout2%higherthancomparableU.S.equityreturnsforbothlargeandsmallstocks.(Atthattime,foreignbondsalsohadhigherreturnsthantheirdomesticcounterpartsbyaboutthesamemargin.)The1969–198820-yearreturn-versus-riskplotforS&P500andEAFEmixesisshownin
Figure4-3.Talkaboutafreelunch!Startatthebottomofthecurve.EachincrementofaddedEAFEexposureincreasedreturn,andthefirstfewnotchesactuallydecreasedrisk.Add30%EAFEtoyourfuddy-duddydomesticstocksandyouget2%moreannualizedreturnwithalmostnoextrarisk.
Figure4-3.S&P500/EAFEmixes,1969–1988.
Doesthissoundtoogoodtobetrue?Well,itis.Let’sseewhatthelast20yearslookedlike,from1979to1998,inFigure4-4.Goodbyefreelunch.AlthoughthefirsttwonotchesofEAFEdecreaserisk,theyalso
decreasereturn.Andafterthat,it’ssteeplydownhillforbothriskandreturn.In2000,asthisbookisbeingwritten,whatarethegurustellingus?“Stayathomeforhigherreturns.Buythecompaniesyouknow.Diversifyabroadonlyatyourperil.And,ifyoumustinvestabroad,dosoonlywhereyoucandrinkthewater.”
Figure4-4.S&P500/EAFEmixes,1979–1998.
Asmalldigression.I’lltalkaboutthefieldofbehavioralfinancelaterinthebook,butthisisaperfectexampleofso-calledrecency,thesinglebiggestmistakethateventhemostexperiencedinvestorsmake.Thisreferstoour
tendencytoextrapolaterecenttrendsindefinitelyintothefuture.Inmoreformalterms,itreferstooveremphasisonrecent,butincompletedataandthedismissalofolder,butmorecompletedata.Itishumannaturetoweighmostheavilyrecentdramaticevents.Readersofacertainagewillvividlyrememberthegreatinflationaryperiodofthe1970sandearly1980s.Atthe
time,itwasdifficulttoimaginethiseconomicscourgeeverending.Theonlyassetstoownwererealestateandgold.Andifyouwereunfortunateenoughtobeholdingwhatwerederisivelyknownas“paperassets,”(stocksandbonds),youhadyourheadhandedtoyou.MorereaderswillrememberthemixedfeelingofdreadandaweofJapaneseeconomicprowessadecade
ago.TheUnitedStates’realestatecrownjewelswerebeingpurchasedlikesomanydetergentboxesata“blue-lightspecial,”andourgreatmanufacturingconcernsseemedunabletocompetewithTokyo’scorporatejuggernaut.Inbothcases,investment
decisionsbasedontheseperceptionswouldhavebeendisastrous.BothJapanese
stocksandpreciousmetalshavesincebeenhorridinvestments.Arecurringthemeinthesepagesisthatyoutryashardasyoucantoidentifythediversestrainsofcurrentfinancialwisdominorderthatyoumayignorethem.Nowthatwe’ve
ascertainedthatthepopularviewofinternationaldiversificationhasbeen
poisonedbytherecentpoorperformanceofforeignstocks,whatdoesthe“complete”datashow?Figure4-5istherisk-returnplotforthefull30-yearperiodfrom1969to1998.ForthisperiodthereturnsfortheS&P(12.67%)andEAFE(12.39%)werenearlyidentical.Notealsohownarrowlyspacedthereturnvaluesontheyaxisare,withlessthan1%separatingallof
theportfolioreturns.Notehow“bulgy”thisplotis.Portfoliosofupto80%EAFEhavehigherreturnsthaneitherassetalone.Portfoliosofupto40%EAFEalsohavelessriskthaneitherassetalone.Therecanbenoquestionthatforthepast30yearsinternationaldiversificationhasworkedsuperbly.
Figure4-5.S&P500/EAFEmixes,1969–1998.
Howcompleteiseventhe30-yeardata?Goodquestion.Rememberthattheyearsfrom1914to1945werenotterriblykindtomanyequitymarkets.TheboursesofJapanandGermanywereessentiallyobliteratedbywar,
andalmosttheentireprivatesectorsofnumerousothernationsinLatinAmericaandEasternEuropewereexpropriatedbycolonelsandapparatchikswhodidn’tpayenoughattentioninEconomics101.Twoacademics,WillGoetzmannofYaleandPhillipeJorionoftheUniversityofCalifornia,Irvine,havelookedatreturnsafter1920outsideoftheUnitedStatesandhavetried
tomeasurethedamagewroughtbythese“marketextinctions”onaglobalinvestmentstrategy.TheyfoundthattheUnitedStateshadtheworld’shighestequityreturns,about8%overinflation,withCanada,theUnitedKingdom,Switzerland,Sweden,andAustraliafairlyclosebehind.However,manyothernations,particularlycountriesthatwewouldnowterm
“emergingmarkets,”hadmuchlowerreturns,somenegativeinrealterms.Ifyoudoreadthispaper,listedintheBibliography,beawarethatthereturnspresentationisveryconfusing.Returnsarereportedininflation-adjustedterms,withdividendsnotincluded.Thus,theU.S.returnisreportedatabout4%.Tothismustbeaddedanaverage4%dividend(foratotalrealreturnof8%)plus
another3%forinflation,foratotalnominalreturnof11%.Themainpointofthe
Jorion-Goetzmannworkisthatthecarefulinvestormustbeawareofso-calledsurvivorshipbias.Thatis,itiseasytolookjustatU.S.returnsandconcludethatlong-termrealreturnswillcontinuetobehigh.However,theUnitedStateshasbeenthewinnerinthe
globalequitysweepstakes;thereturnsinmostothermarketshavenotbeennearlyashigh.Ofcourse,thereisnoguaranteethattheUnitedStateswillcontinuewinning.Moreover,itiseasytolookattheS&PandEAFEandbeencouragedbytheirhighreturns.Butthesetwoindexesconstitutethe“survivors.”Hadyoustartedbylookingatallofthemarketsextantin1920,you
wouldfindthatmanyofthemdisappeared,andyourtotalglobalreturnwouldhavebeenmuchlower.Thesameisnodoubttruetodayaswell.Itisbynomeanscertainthateventoday’slargestmarketswillbeinbusiness30yearsfromnow.Rememberthatin1930someoftheworld’sbiggestbourseswerelocatedinBerlin,Cairo,andBuenosAires.
JorionandGoetzmann’sconclusionsaboutglobalinvestingarereasonablyupbeat,however.Theyfoundthataglobalportfolioweightedaccordingtonationalgrossdomesticproductreturnedabout1%lessthanadomesticportfolio,butalsohadamuchlowerstandarddeviation.Theyconcludedthatthemainadvantageofinternationaldiversificationwasnot
increasedreturnbutdecreasedrisk.Thisisborneoutbylookingatthe1930sand1970s,whichwerebrutalbearmarketsintheUnitedStates.Duringbothperiods,losseswerelesselsewhere,benefitingtheglobalinvestor.Justasinvestorsadecade
agowereoverlyoptimisticaboutforeigndiversification,investorstodayareoverlypessimisticaboutit.Foreign
stocksbelongineveryone’sportfolio.
AnotherVisitwithUncleFred
Yourbenevolentunclehastakenaninterestinyourexplorationofportfoliotheoryandsensesyourdiscomfortconcerningforeignstockexposure.ThetwoofyoudiscussFigures4-
3through4-5andwrestlewiththeirmeaning.BynowyouknowthatUncleFredneverprovidesadirectanswertoyourproblems.Youdon’tknowwhatto
makeofsuchdisparatedata.Figure4-3showsthatheavilyweightingforeignoverdomesticstocksisclearlyadvantageous,Figure4-4showstheexactopposite,andFigure4-5indicatesthat
healthyamountsofbothareneeded.“Well,”saysyourwiseold
uncle,“sinceyoucan’tpredictequityreturns,whydon’tyoutrysplittingthedifference?Alsoremember,youngman,youaren’tgoingtoinvestallofyoursavingsinstocks.”So,yougobacktoyour
spreadsheetandcomeupwithFigure4-6.This
displaystheproblemaswellasthesolution.Itshowstherisk-returnplotforthetwooverlapping20-yeartimeperiods.Thethin-lined“sail”istheearlierperiod,andthethick-linedsailisthelaterperiod.Theplotforeachperiodcontainsthreebasicstockmixes:S&Ponly,EAFEonly,anda50/50mixofboth.Foreachperiod,allthreeofthesearethenmixedwithfive-yearTreasury
notes,whicharethetwopointsinthelowerleftofthegraphonwhichallthreelinesforeachperiodconverge.
Figure4-6.S&P500/EAFE,1979–1988.
First,noticethatreturnsingeneralweremuchhigherinthelaterperiod.Infact,fortheearlierperiodthereturnoftheS&Pwasnotmuchgreaterthanthatofthefive-yearnote.Andthisplotdoesnotshowthemostdiscouragingthingaboutthe
1969–1988period;inflationwasalmost7%,sotherealreturnsofbothdomesticstocksandbondswerenearlyzero.Inflationinthelaterperiodwasnearly2%lower,withrealreturnsbeingcorrespondinglyhigher.Thisgraphisagoodstudy
in“recency.”In1988,everybodyandtheirdogswereenthusiasticaboutforeignequity,asithadmuch
higherreturnsthandomesticequity.Moreimportantly,enthusiasmforstocksingeneralwasnotparticularlyhigh,so1988wasagreatyeartosellyourforeignstocksandbuydomesticequity.Now,lookatthemore
recent(upper,heavier-lined)period.U.S.equityreturnshavebeenquitehigh,and“everybodyknows”that
stockshavethehighestinvestmentreturns,particularlyU.S.stocks.Recency,again.RememberBernardBaruch’sfamousdictum:
Somethingthateveryoneknowsisn’tworthknowing.
Itcannotberepeatedoften
enough.Identifytheera’sconventionalwisdomandthenignoreit.Nowlookattheindividual
plotsinFigure4-6.Pickingtheworstofthestockandbondlinesineachera(S&Pandbondintheearlierperiod,EAFEandbondinthelaterperiod)wouldhaveproducedpoorreturns,andthebeststockandbondlineexcellentreturns.The
trouble,asYogiBerraoncesaid,isthatit’sverydifficulttomakepredictions,particularlyaboutthefuture.Ifyoutakeyouruncle’sadviceandsplitthedifference,youfindthatyoudoreasonablywellinbotheras.Inbothcasesthereturnofthe50/50lineismuchclosertothebest-performingassetlinethantheworst-performingassetline.Andfortheentire30-yearperiod,
wealreadyknowthatthe50/50mixisinitselfthe“best”equityasset.Almostalloftheforeign
stockadvantageoftheearlier1969–1988periodcamefromcurrencygain,asrisesintheyenandEuropeancurrenciesprovidedU.S.investorswithabout2%ofextrareturn.And,thereversalinfortunesintheforeign-versus-domesticponyraceofthe
past20yearsmayturnouttobeequallyanomalous.Whoknowswhetherforeignordomesticstockswillhavethehigherreturnoverthenext20,30,oreven50years?However,itseemshighlylikelythata50/50mixwillnotbetoofarfromthebestforeign-versus-domesticallocation.Therealpurposeofportfoliobacktesting,mean-varianceanalysis,oranyotherkindofportfolio
analysisisnottofindthe“best”assetmix.Rather,itistofindaportfoliomixthatwillnotbetoofaroffthemarkunderawidevarietyofcircumstances.
SmallStocksversusLargeStocks
It’simportanttorealizehowlargeandsmallstocksbehaverelativetoeachother.Until
recentlyitwasgenerallyacceptedthatsmallstockshadhigherreturnsthanlargestocks.WiththerecentremarkableperformanceoftheS&P500,theso-calledsmall-cappremiumhasbeenquestioned,althoughoverthepast73yearsthispremiumstillseemstobeabout1%.Wearelookingatrecencyagain—ourtendencytooveremphasizerecentevents.However,noonequestions
thatsmallstocksaremoreriskythanlargestocks.InFigure4-7,I’veplottedvariousmixesofsmallandlargestockswiththeubiquitousfive-yearTreasurynotes.First,notethatthetwoplotsnearlyoverlap.Inotherwords,therisk-returncurvesareverysimilar,exceptthatthesmall-stockcurveextendsoutalotfarthertotherightthantheS&Pcurve.Inthepresentgraph,largestockand
bondmixesappeartobeslightlymoreefficientthansmallstockandbondmixes.Ontheotherhand,whenthesamegraph,wasdrawnfouryearsago,thesmall-stockcurvewasslightlymoreefficientthanthelarge-stockcurve.ThemostimportantrevelationinFigure4-7,however,isthatalittlesmallstockgoesalongway.Noticehowinthe1926–1998period,a50/50mixofsmallstocks
andbondshasalmostthesameriskandreturnas100%largestocks.Morerecentdatasuggeststhatthis“potency”hasdecreasedsomewhat,perhapstoonly1.5timesthatoftheS&P.Butthebasicprincipleremainsthatyougetmorebangforthebuckintermsofbothriskandreturnfromsmallstocks.
Figure4-7.Largeandsmallstocks/bonds,1926–1998.
Finally,tocompletethepicture,smallforeignstocksneedtobeconsidered.There’saproblemhere:themostcommonlyusedinternationalsmall-capindexisanextremelypeculiarone.ConstructedbyDimensional
FundAdvisors,thisindexgoesbackto1970,almostasfarastheEAFEitself.Unfortunately,until1988itconsistedofjusttwomarkets—JapanandtheUnitedKingdom.After1988,itscompositionisquitesimilartotheEAFE.Withthatcaveatinmind,I’veplottedthebehaviorofmixturesofU.S.smallstocksandinternationalsmallstocksforthe1970–1998periodin
Figure4-8.Notehow“bulgy”thiscurveis.Attheextremerightpartofthecurve,notehowtheadditionofU.S.smallstocksreducesriskwithalmostnolossofreturn.Attheoppositeendofthecurve,theadditionoflargeamountsofinternationalsmallstocksdramaticallyincreasesreturnwithoutincreasingrisk.Figure4-8paintsarelativelyrosypictureofglobalsmall-
stockinvesting,butithasadarkside.I’vetabulatedthereturnsforU.S.andforeignstocks,bothsmallandlarge,forthefirst20years(1970–1989)andthelastnineyears(1990–1998)ofthe1970–1998period:
Figure4-8.U.S./internationalsmall-stockmixes,1970–1998.
Noticewhatawildrideinternationalsmallstockshavebeen,withstaggeringreturnsduringthefirstperiodfollowedbytrulyawfulreturnsduringthesecond.Itseemsthatwhenforeignstocksdowell,foreignsmall
stocksdoespeciallywell,andviceversa.Dotheybelonginyourportfolio?Itdependsuponhowmuch“trackingerror”youcantolerate.Ifitbothersyougreatlytotemporarilydopoorlywhileothersaredoingwell,inspiteofyourgoodlong-termreturns,thenthey’reprobablynotforyou.
TheEfficientFrontier
Noticehowcomplicatedthingsbecomewiththethree-assetportfolioswe’vediscussedabove.Intherealworld,ofcourse,wehavetodealwithdozensofassetclasses.Thereareaninfinitenumberofwaystocombinesuchacomplexpaletteofingredients.Howcanyoupossiblyarriveatareasonablyefficientmixtureofthem?
Forillustrativepurposes,I’vechosensixbasicequityassetswhicharepartofmostglobalinvestors’portfolios(whethertheyknowitornot):theS&P500,U.S.smallstocks,Europeanstocks,Japanesestocks,PacificRimstocks,andpreciousmetalsstocks.Andonceagain,I’vechosenfive-yearTreasurynotesforriskdilution.I(ormoreaccurately,mycolleagueDavidWilkinson)
generated800randomportfoliosconsistingofthesesevenassets.Ithencalculatedtheannualreturnsandstandarddeviationsfortheseportfoliosforthefive-yearperiod1992–1996.Theresult,whichisplottedinFigure4-9,displaysacloudofportfoliosofdifferingreturnsandrisks(standarddeviations).
Figure4-9.Randomportfolios,1992–1996.
Aresomeoftheseportfoliosbetterthanothers?Absolutely.Noticethatthisgraphisdividedbyahorizontallineandbyaverticalline.Theverticallinerepresentsallportfolioswithastandarddeviationof15%,whichisaboutthesame
degreeofriskasaportfoliooflargeU.S.stocks.Noticehowsomeoftheportfoliosalongthislinehavereturnsaslowas6%,whereasothershavereturnsashighas14%.Obviously,then,it’sbettertobeonthetopofthecloudthanthebottomofthecloud.Ifyou’regoingtoexposeyourselftoriskatthe15%SDlevel,youmightaswellgetthebestpossiblereturn.
Thehorizontallinedefinesallportfolioswitha10%return.Noticethatsomeoftheseportfolioshaveaslittleas8%ofSD,whereasothersalongthislinehaveover20%ofSD.Obviously,then,it’sbettertobeontheleftsideofthecloud.Nowstepbackandlookat
theentirecloud.Noticehowreasonablywelldefinedtheupperleftedgeis.Thisis
wherewewanttobe—gettingeitherthemostreturnforagivendegreeofriskorbeingexposedtotheleastriskforagivenreturn.Thisedgeofthecloudiscalledtheefficientfrontier.Theconceptoftheefficientfrontieriscentraltoportfoliotheory.Unfortunately,itisalsothesourceofmorethanalittlemischief.
SantaClaus
Manyinvestorsandfinancialanalystsspendalotoftimethinkingabouttheefficientfrontier.TheyremindmeofchildrendreamingofSantaClaus.Afterall,thisistheultimatefreelunch:highreturnsatlowrisk,ordecentreturnswithalmostnoriskatall.There’sonlyoneproblem.ThereisnoSantaClaus.It’salittleliketryingtogenerateelectricalpowerbyplacingabatteryanda
lightningrodatthelastplaceyousawlightningstrike.Itisn’tlikelytostrikethereagain.Inotherwords,nextyear’sefficientfrontierwillbenowherenearlastyear’s.Anybodywhotellsyouthattheirportfoliorecommendationsare“ontheefficientfrontier”alsotalkstoElvisandfrolicswiththeEasterBunny.Toillustratethispoint,I
hadmycolleagueDavidWilkinsongenerate800moreportfoliosforthesamesevenassets,butthistimeforthe27-yearperiodfrom1970to1996.TheresultsareplottedinFigure4-10.Firstnotethattheportfoliocloudisshapedquitedifferentlyfromthefirstone—it’squiteabitflatter.Thisisbecauseovershorttimeperiodsannualizedreturnsforassetstendtobequitedifferent,butthese
differencestendtodisappearoverlongerperiods.Inotherwords,oververyshortperiodsyourprecisestockallocationmattersagreatdeal,butthisbecomeslessimportantoververylongtimeperiods.
Figure4-10.RandomPortfolios,1970–1996.
Muchmoreimportantiswhatthegraphsdon’tshow.Theefficientfrontierportfoliosforthe1992–1996periodwereheavywithS&P500andEuropeanstocks,whiletheefficientfrontierportfoliosforthelongerperiodareheavywith
Japanese,U.S.small,andpreciousmetalsstocks.Infact,hadyoucalculatedtheefficientfrontierforthefirsthalfofthewholeperiod(1970–1983)andusedittodetermineyourportfolioforthesecondhalfoftheperiod(1984–1996),you’dhavegottenyourheadhandedtoyou.Theefficient-frontierportfolioofJapanese,preciousmetals,andU.S.smallstocksforthefirsthalf
wouldhavetankedinthesecondhalf.Anotherthingtheclouds
don’tshowiswhathappenswhenyouradicallyalteryourallocationovertime.RememberthatalloftheaboveportfoliosimulationsI’veshownyouassumeaconstantallocationoverthetimeperiodstudied.Couldyouearnhigherreturnsbypickingthebestperforming
assetforeachone-yearorfive-yearperiodinyouranalysis?Ofcourse.It’sjustthatthisisnothumanlypossible.Aswe’vealreadydiscussed,nobodyconsistentlytimesthemarket;shiftingyourallocationovertimeisarecipefordisaster.Infact,mostglobalinvestorswoundupdoingmuchworsethanshowninthecloudsinFigures4-9and4-10forpreciselythisreason.
Institutionalmoneymanagersarefondof,andsmallinvestorsareentrancedby,so-calledstrategicassetallocation.Whatthisentailsisspendinglargesumsofclientmoneyonsophisticatedmacroeconomic,political,andmarketanalysesinanattempttoguesswhichassetswillperformthebest.Andit’safool’serrand.Why?Becausethemarketshavealreadyimpoundedthis
informationintothecurrentprice.YousaythattheU.S.economyistheworld’sstrongestandwillcontinuetobefortheforeseeablefuture?Thatmaybetrue,butthewholeworldknowsit,andthatiswhy$100buysyouonly$3earningsonWallStreet,versus$8to$15ofearningsinSeoul,HongKong,orSa~oPaulo.Again,thinkrecency.Andthenexttimeyouseesomeimpressive
guyina$2000suitspinningaveryplausiblepatteronthefuturedirectionoftheeconomiesormarkets,rememberthathisfatherwasprobablypushingKrugerrandsin1979,andhisolderbrotherurgingJapanesestocksin1989.Thekeypointaboutthe
efficientfrontieristhis:it’sachimera,theimageofyourAuntTillieinacloud
scuddingoverheadafewminutesago.Andagain,ifsomebodytellsyouheorsheknowswhereitis,turnandruntheotherway,asfastasyoucan.Still,ifyou’retryingto
capturelightninginajar,youarebetteroffinTexasthaninAlaska.Therearecertainassetcombinationsandportfolioswhicharelikely(butnotcertain)todo
reasonablywell.
TheImportanceofRebalancing
Animportantassumptionunderliesalloftheportfoliodiscussionsthusfar:thatattheendofeachyeartheinvestorrebalancestheportfoliobacktothetargetcompositions.Ifaparticularassethasdoneextraordinarilywell,itsportfolioweighting
willincrease;consequently,enoughofitmustbesoldandreinvestedinthepoorlyperformingassets,toreturntothetargetcomposition.Thistargetcompositionisoftenreferredtoasthe“policyallocation.”Youcannotunderestimatetheamountofdisciplineandpatiencerequiredforthisprocess,becauseitmeansdoingexactlytheoppositeofwhatmostoftheinvestmentworld,
almostallofwhomareprofessionalsandexperts,isdoing.Apsychologistfriendpointsoutthatthisisaneffectivewayofbecominga“contrarian,”alwaysmovingintheoppositedirectionofthecrowd.Youwillofnecessitybesellingwhateverybodylovesandbuyingwhattheyhate.YouhaveonlytorememberthatthegreatbuyingopportunitiesinU.S.stocksin1974and
Japanesestocksin1970,tonameafew,followedseveralyearsofgrindingbearmarkets.Butbeforewarned:investingduringmarketbottomshasthedistinctfeelofthrowingmoneydownarathole.
TheExperts
Smallinvestorsoftenconsiderthemselvesatadisadvantagewith
professionalswhomanagelargesumsandhaveaccesstosophisticatedandtimelyanalysis.Nothingcouldbefurtherfromthetruth.Thesmallinvestorhasthreeoverwhelmingadvantagesoverthelargeinstitutionalinvestor:
1.Sheorhecanaggressivelyrebalanceaportfoliowithouthavingtodealwithclientsannoyed
withthepurchaseofpoorlyperformingassets.Anoft-quotedanalogylikenssuccessfulinvestingtodrivingthewrongwayupaone-waystreet.Thisisdifficultenoughwithyourownvehicle.ItisnearlyimpossiblewhenyouareachauffeurpilotingaRollsRoycewhoseownerisinthebackseat,squawkingateverypotholeandpotentialcollision.
2.Thesmallinvestorcaninvestinsmallstocks.Largeinstitutionsareeffectivelybarredfromthisareabythehugesumstheymustinvest.Youcanbuyonlysomuchofasmall,thinlytradedcompanybeforethepriceisbidtoohightoprovideareasonablereturn.3.Youwillnotbefired
afterabadquarter.Eventhemostsuccessfulinvestorhas
dryspells,occasionallylastingyears.JoeDiMaggiohadslumps,andWarrenBuffettoccasionallygetsburned.Moreimportantly,eventhemostexpertlycraftedassetallocationwilloftenunderperform“themarket,”usuallydefinedastheDowJonesIndustrialAverageortheS&P500.Infact,mostsuccessfulassetallocationstrategieswillunderperformtheDJIAand
S&P500aboutfouryearsoutof10.
ToillustratethispointIcalculatedtheefficientfrontierportfoliosforthesevenassetsinFigures4-9and4-10fortheentire1970–1996period.ThebestreturnwasobtainedwithamixofapproximatelyequalpartsU.S.small,Japanese,andpreciousmetalsstocks.Ofcourse,theoddsthatthis
allocationwillbethatsuccessfulinthefuturearesmall—thisallocationfailscommonsenseandthe“prudentmantest”ineveryrespect.Nonetheless,thisparticularmixoutperformedtheS&Pbywellover3%onanannualizedbasisforthe1970–1996period.Andyet,thisextremelysuccessfulallocationunderperformedtheS&Pin12outofthe27yearsstudied—i.e.,44%of
thetime.IwouldgoonestepfurtherandstatethatifyourassetallocationneversignificantlyunderperformstheS&P500thenyouareprobablydoingsomethingwrong.Theprofessionalinvestorwithlaggingperformancefeelsenormouspressuretobuyeverybodyelse’sfavoritestocks.Doingsoisusuallyapreludetodisaster.
It’seasytobeimpressedwithglibmarketanalysesofferedinthenewspaperortelevision.Often,whileIamlisteningtoananalystonTV,I’llfireupMorningstar’sPrincipiaonmyPCandseeifheorshemanagesapubliclytradedclosed-endoropen-endmutualfund.Theresultsareinstructive.Afamousmarketanalyst,creditedwith“callingthecrash”in1987,actuallyranamutualfundfor
amajorinvestmentfirmthatsogrosslyunderperformedthemarketthatitwasfinallyfolded.Anotheranalyst,whoappearsregularlyonanextremelywell-knownpublictelevisioninvestmentprogram,alsocreditedwith“callingthecrash”infrontof20millionviewers,runsseveralclosed-endandopen-endfundswhoseperformancecancharitablybecalledmediocre.Anoted
newsletterwriterwhoappearsregularlyonaprime-timepublictelevisionmarketprogramhashadhisrecommendationsanalyzedbyahighlyrespectedpairofacademics.Theyfoundthatifyouactuallyhadtakenhisadvice,youwouldhavelost5.4%peryearannualizedover13years.Andsoitgoes.Justasacompulsiveand
unskilledgambler
occasionallybeatsthehouse,sotoowillthese“professionals”occasionallybestthepatientindividualinvestor.Inactualfact,itisthesmallinvestorwithafixedassetallocationpolicywhohasanunfairadvantageovertheprofessional.Theobjectistodevelopalong-termstrategy,sothatyoubecomethecasinoowner,notthemark.
Summary
Itispossibletostudythebehaviorofvariousassetmixesviatheuseofhistoricaldata.Thesetechniquestellus:1.Theadditionofasmallamountofstocktoabondportfolioincreasesreturnwhileactuallyreducingriskslightly;eventhemostrisk-averseinvestorshouldownsomestocks.
2.Theadditionofasmallamountofbondstoastockportfoliosignificantlyreducesriskwhilereducingreturnonlyslightly.
3.Favorshort-termbonds(ofsixmonthstofiveyears)asyour“riskdiluting”asset,ratherthanlong-termbonds.
4.Smallstockshavetobedilutedwithmorebonds
thanlargestocksinordertoobtainthesamedegreeofrisk(i.e.,a50/50small-stockandbondmixwillhaveaboutthesamedegreeofriskasa75/25large-stockandbondmix).
5.Bewareofrecency,anddonotbeoverlyimpressedwithasset-classreturnsoverperiodsoflessthantwoorthree
decades.Inspiteoftheirrecentpoorshowing,foreignstocksandsmallstockshaveaplaceinyourportfolio.
6.Periodicallyrebalanceyourportfoliobacktoyourpolicyallocation.Thiswillincreaseyourlong-termreturnandenhanceinvestmentdiscipline.
5OptimalAssetAllocations
Let’srecapwhatwe’velearnedsofar:
1.Thelong-term(expected)returnsandrisksofmanykindsofstocksandbondsarewellknown.
Unfortunately,overperiodsofupto10or20years,actualreturnsmaybesignificantlyhigherorlowerthantheexpectedreturn.Theamountof“scatter”fromtheaveragevalueisknownasthestandarddeviation(SD)andisvirtuallysynonymouswithrisk.2.Effectiveportfolio
diversificationcanincreasereturnwhilereducingrisk.
Achievingmaximalbenefitfromeffectivediversificationrequiresperiodicrebalancingofportfoliocompositionbacktothetarget,or“policy”composition.Thisisoftenemotionallydifficulttodo,asitalmostalwaysinvolvesmovingagainstmarketsentiment.3.Whetheryoulikeitor
not,youareamoneymanager.Assetallocation
accountsformostofthedifferenceinperformanceamongmoneymanagers.Arrivingataneffectiveassetallocationisbothcriticallyimportantandnotthathardtodo.Long-termsuccessinindividualsecurityselectionandmarkettimingisdifficulttoimpossible;fortunately,theyarenearlyirrelevant.ThefailureofmarkettimingandactivesecurityselectionwillbediscussedinChapter
6.4.Sincethefuturecannot
bepredicted,itisimpossibletospecifyinadvancewhatthebestassetallocationwillbe.Rather,ourjobistofindanallocationthatwilldoreasonablywellunderawiderangeofcircumstances.5.Stickingbyyourtarget
assetallocationthroughthickandthinismuchmoreimportantthanpickingthe
rightassetallocation.
TheCalculationofOptimalAllocations
Firstofall,let’sbeclearaboutwhatwemeanwhenwesay“optimalallocations.”Wecanactuallybetalkingaboutoneofthreeallocations:future,hypothetical,orhistorical.Youcannotknowfutureoptimalportfolio
compositionanymorethanyoucansproutwingsandfly,playpointguardfortheLakers,orwintheMissAmericapageant.AnybodywhotellsyouthattheyknowtheoptimalfutureallocationbelongsinSing-SingorBellevue.(Andwereyouactuallyabletodothis,yousure-as-shootin’wouldn’tneedthisbook.Youwouldknowthefuturereturnsofallassetclasses,andyou
wouldn’tneedassetallocation.WhatyouwouldinfactneedisacompetentpilotforyourGulfstreamVtogetyoubackandforthbetweenyourvillasinDavos,PalmSprings,JacksonHole,andMartha’sVineyard.)Hypotheticaloptimal
allocationreferstotheprocessofpostulatingasetofreturns,SDs,andcorrelationsandthencalculatingthe
optimalallocationsfortheseinputs.Historicaloptimal
allocation,whatwasoptimalinthepast,canbecalculated.Thisisaninterestingexercise,andonethatweshallshortlyengagein,butitisaverypoorwaytodeterminefutureallocations.We’vealreadyhintedat
onemethodforcalculatinghistoricaloptimalallocations.
Recalltheportfolio“clouds”inFigures4-9and4-10.Theportfoliosattheupperleftedgeofthecloudlayclosetotheefficientfrontierandareveryclosetobeingoptimal.Itisnotthatdifficulttospreadsheetthehistoricalreturnsandfiddlewithyourallocationsuntilyouarenolongerabletoimproveportfolioreturnversusrisk.Infact,mostspreadsheetscontainanoptimizertoolthat
willallowyoutodeterminetheportfolioswhichwillgiveyouthemost(orevenleast!)returnatagivenSDlevel,ortheleastSDatagivenlevelofreturn.Thisisasortof“poorman’soptimizer.”However,bothofthesemethodsarequiteslowandcumbersomeandarenotappropriatefortheseriousstudentofportfoliotheory.Foronething,itisanenormousamountofworkto
do“whatif”analysesofwhathappenswithvariationsofanasset’sreturnorSD,andalmostimpossibletochangeitscorrelationwithotherassets.Thereisamuchfasterand
easierwaytooptimizeportfolios—mean-varianceanalysis,devisedseveraldecadesagobyHarryMarkowitz(andforwhichheearnedaNobelPrize).A
softwareapplicationwhichusesthismethodiscalledamean-varianceoptimizer(MVO).AnMVOwillrapidlycomputeoptimalportfoliocompositionsfromthreesetsofdata.Theseare:
1.Thereturnforeachasset2.Thestandarddeviationofeachasset3.Thecorrelationsamongalltheassets
Untilveryrecently,MVOswerequiteexpensiveandtheinputdataevenmoreso.Becauseofthis,Ispentafairamountofeffortdescribingspreadsheettechniquesinthisbook’spreviousversions.Fortunately,thisisnolongernecessary.MVOsarenowavailableforunder$100,andthedatahasbecomemucheasiertoobtainaswell.SeeAppendixAforproductandvendorinformation.
MVO’sonedisadvantageisthatitdoesnottakerebalancingintoaccount,asitisaso-calledsingle-periodtechnique,andrebalancingisamultiple-periodphenomenon.However,optimalportfoliosarethesamewhetherornottheyarerebalanced.Further,itisrelativelyeasytoadjustforrebalancingoncetheefficientfrontierhasbeencalculated.
Asanexample,let’sconsiderthesevenassetsforthe1970–1996periodusedinFigure4-10,pluslongbondsandT-bills.ThecompleteMVOinputsforthistimeperiodarelistedinTable5-1.
Table5-1.OptimizerInputsfor1970–1996
Thefirsttwocolumnsaretheannualizedreturnsandstandarddeviations.Theadjacentcolumnsshowthe
correlationsbetweentheannualreturnsofeachassetforthe27annual-returnperiods.Theseinputsarefedinto
theoptimizer,inthiscaseMVOPlus,producedbyEfficientSolutions.LikeallMarkowitzoptimizers,thisprogramutilizestheso-calledcritical-linetechniquetoproduceaseriesof“cornerportfolios,”whichdefinethe
compositionoftheefficientfrontierforthissetofinputdata.Let’stakealookattheoutput,showninTable5-2.Figure5-1showstheactualgraphicaloutputfromMVOPlus.
Table5-2.CornerPortfolios1970–1996
Figure5-1.Optimizeroutput,MVOPlus.
Corner1istheminimum-varianceportfolio;itistheonewiththeleastrisk.Noticethatitconsistsof92.5%T-bills,withtheother7.5%consistingofassetsthatwewouldgenerallyconsiderquiterisky.Mostoftheportfoliosintheriskrange
whichmostofuswouldconsiderreasonable,livebetweencorners7and8.Portfolios1through6consistalmostentirelyofshortbonds,andaboveportfolio8,theportfoliosbecomeveryrisky.Portfolio10isthemaximum-returnportfolio.
MathDetails:
MVOPlushastheuniqueabilityto
identifytheportfoliowiththemaximumannualized(geometric)return,whereasallothercommerciallyavailableoptimizerswillidentifytheassetwiththehighestarithmeticreturnasthelastportfolio,whichis
nottheonewiththehighestgeometricreturn.Thisisbecausethedifferencebetweenthearithmeticandgeometricreturnsisapproximatelyhalfitsvariance,or(SD)2/2,andiscalledvariancedrag.Aswemovetowardtherighton
thereturn-versus-riskplot,variancedragincreasestothepointwheregeometricreturnbeginstofall.Remember,you“eat”geometricannualizedreturn,notarithmeticreturn.
Youarenotlimitedtothe
cornerportfolios,ofcourse.Ifyoudecidethathalfwaybetweenportfolios7and8iswhereyouwanttobe,thenyousimplyaveragethecompositionsofthetwoportfoliosforeachasset.Lookatportfolio7fora
moment.Itisaboutone-thirdstockandtwo-thirdsfive-yearTreasuries.Sofar,sogood.Butlookattheequitycomposition—almostentirely
U.S.small,Japanese,andpreciousmetalsstocks.Thisisnotaportfoliothatanyrationalpersonwouldown.Itisnoaccidentthatthesearethethreeassetswiththehighestreturnsforthe1970–1996period.We’vejustrunintooptimization’sfatalweakness:itisoverlyfondofassetswitharecenthistoryofhighreturns.Infact,withabitofpractice,itispossibletogettheoptimizertospit
outalmostanyportfolioyouwant.Changethereturninputsofmostassetsbyafewpercentineitherdirectionandthatassetwilleitherdominatetheportfolioorcompletelydisappearfromit.Doyouthinkthatyoucanpredictthefuturereturnsofallthemajorassetclassesinyourportfolio?Ifyoucan,thenyouareverytalentedindeed.Hence,thetwofundamentallawsofoptimizers:
Anoptimizerwillheavilyfavorthoseassetswithhighhistoricalorassumedreturns.Ifyoucanpredicttheoptimizerinputswellenoughtocomeclosetothefutureefficientfrontier,thenyoudon’tneedanoptimizerinthefirstplace.
Thedangersofblindlyfeedinghistoricalreturns,SDs,andcorrelationsintoanoptimizershouldalreadybeapparentfromtheaboveexample.Assetreturnshaveatendencyto“meanrevert”overlongtimeperiods;anassetwithstellarreturnsoverthepast10yearsismorelikelythannottohavebelow-averagereturnsinthe
subsequent10years.Somewagshavereferredtooptimizersas“errormaximizers”forjustthisreason.Inordertobetter
understandthepitfallsofoptimization,let’stakealookatwhatactuallyhappenswhenoneuncriticallyfeedshistoricaldataintoanoptimizer.Let’sdivide1970–1998intofive-yearperiods
withafinalfour-yearperiod.Next,we’lloptimizeeachfive-yearperiod,andseehowtheoptimalall-stockallocationdoesinthesubsequentfive-yearperiodcomparedtoa“coward’sportfolio”consistingofequalpartsofallsixstockassets(U.S.largecap,U.S.smallcap,European,PacificRim,Japanese,andpreciousmetals).
Westartin1970–1974.Forthisperiod,theoptimalreturnisproducedbyanallocationof99.8%preciousmetalsand0.2%Japan,producing29.97%annualized.Carryingthatallocationforwardto1975–1979producedareturnof14.71%versus25.38%forthecoward’sportfolio.For1975–1979,the
optimalallocationwas100%
U.S.smallstocks,withareturnof39.81%annualized.Thisallocationactuallydidprettywellgoingforwardto1980–1984,withareturnof21.59%versus14.75%forthecoward’sportfolio.For1980–1984,the
optimalallocationwas73%U.S.smalland27%preciousmetalswithareturnof21.94%.Goingforwardto1985–1989thisallocation
returned11.83%versus24.14%forthecowards.For1985–1989,thebest
allocationwas100%Japanesestocks,producinganastonishingreturnof40.24%annualized.Thenextfiveyears?Negative3.5%annualizedversustoplus7.54%forthecoward’sportfolio.Again,it’susefultotakea
shortjauntinthe“wayback
machine”tothelate1980s.AfewsquaremilesofTokyorealestatewereworthmorethanallofCalifornia,andshortlywewereallgoingtobespeakingJapanese.“TheNikkeitooexpensiveat100timesearnings?Westernersjustdon’tunderstandhowtovalueequityontheTokyomarkets.”Andfinally,for1990–1994
thebeststrategywas100%
PacificRim,returning15.27%annualized.Forthenextfouryears(1995–1998)thisstrategyreturnednegative3.22%versusplus6.61%forthecoward’s.Andonceagain,in1994“everybodyknew”thattheAsianTigerswouldattainanAmericanstandardoflivingwithinthedecade.Overthewhole1975–1998
periodtheabovefive-year
optimizationstrategywouldhavereturned8.40%annualized,whichisworsethananyoftheindividualstockassets,andmuchworsethanthe15.79%returnedannuallyforthecoward’sportfolio.Whatyouareineffect
doingbyoptimizinghistoricalreturnsisacceptingcurrentconventionalwisdom.Thisisnotacoincidence.
Marketsthathaveexperiencedabnormallyhighreturnshaveusuallyundergoneasubstantialincreaseinpriceasamultipleofearnings,andthisisalmostalwaystheresultofincreasingoptimismsurroundingthatasset.Wheredowestandwith
ouroptimizer?Inthewordsofaformerpresident,wearein“deepdoo-doo.”Wecan’t
predictreturns,SDs,andcorrelationsaccuratelyenough.Ifwecould,wewouldn’tneedtheoptimizerinthefirstplace.Andoptimizingrawhistoricalreturnsisaone-waytickettothepoorhouse.So,forgetaboutgettingthe
answerfromamagicblackbox.We’llhavetolookelsewhereforacoherentallocationstrategy.
MoreBadNews
Awell-diversifiedportfolioisnotafreelunch.Itdoesnotcomeanywhereneareliminatingrisk;economiccatastrophesdonotrespectnationalborders.Theeventsof1929–1932and1973–1974involvedallmarkets,andthedamagevariedonlyindegreeamongnationalmarkets.Markowitzmean-varianceanalysistellsusthatifone
assethasanSDof20%,thentwocompletelyuncorrelatedassets(zerocorrelation)willhaveanSDof14.1%,andfourmutuallyuncorrelatedassets,anSDof10%.Inpracticaltermsitisnearlyimpossibletofindthreemutuallyuncorrelatedassets.Consequently,wecannothopeforariskreductionofmorethanaboutone-quartertoone-thirdfromdiversification.
Worse,thecorrelationcoefficientscalculatedbetweenassetssomewhatoverstatethediversificationbenefitbecausethecorrelationofbelow-averagereturnsturnsouttobehigherthanforabove-averagereturns.Inotherwords,the“negativesemicorrelations”aregreaterthanthe“positivesemicorrelations.”TranslatedintoplainEnglishthismeansthattheactualcorrelationof
assetreturnsinseverebearmarketsishigherthanthe“raw”correlationcoefficientwouldsuggest.ThereductioninSDaffordedbydiversificationoftenislostinseverebearmarkets.AcademicianBrunoSolnikstatessimply,“Diversificationfailsusjustwhenweneeditmost.”ThiswaswellseenonOctober19,1987andinthefallof1990whenalloftheworld’sstock
indexessufferedsignificantlosses,inspiteoftheirlowcorrelationsinmorenormaltimes.ThisiswhysimpleportfoliobacktestingisavaluablesupplementtoMVO;onecanactuallyseehowwellaproposedportfoliorespondedinanactualbearmarket.Amajorargumentagainst
internationaldiversificationisthatofsovereignrisk—the
possibilitythatone’sassetswillbeexpropriatedbyaforeigngovernmentorbelostinawar.ConsiderthatbeforetheSecondWorldWartwooftheworld’smajorcapitalmarketswereGermanyandEgypt;onewasdestroyedinthewarandtheothernationalizedafterit.LatinAmericannationshavebeendefaultingontheirdebtwithnearclocklikeregularityforthepastcentury.Theperilsof
long-terminternationalinvestingshouldnotbeunderstated,butitisimportanttounderstandthemathematicalnatureoflong-termrisk.Letusassumethatatsomepointduringa70-yearinvestmenthorizonone-halfofourcapitalsuddenlyandirretrievablydisappears.Thislowersourlong-termreturnbyonly1.0%.Further,considerthatwhileJapaneseandGermancapital
disappearedatthebeginningoftheSecondWorldWar,spectacularreturnswereearnedinthesemarketsinthefourdecadesfollowing1945.Othersarguethatbecause
oftheglobalizationofoureconomy,internationaldiversificationhaslostitsvalue.Noonecandoubtthatoureconomiclifeisbecomingincreasinglyglobalized.Theeventsin
foreigncapitalmarketsseemtoexertaninstantaneouseffectonourown,leadingmanytopredictthatthemarketreturnsofnationswillbecomeincreasinglycorrelatedandthatthebenefitsofinternationaldiversificationwilldisappear.Thisargumentissoprevalentthatithasacquiredanauraoffact.Fortunatelyfortheinvestor,thedataindicateotherwise.Forexample,there
isgooddataforthereturnsofU.K.andU.S.marketsdatingfrom1919.The1919–1994periodcanbebrokendownintofourperiodsof19yearseach,andcorrelationsforannualreturnscanbealsocalculatedforeachperiod:
Whilethecorrelation
betweentheU.S.andU.K.marketscanbeseentovarywidely,thereisnopatternofincreasingcorrelation;thelowestcorrelationisforthelastperiod.Similarly,itispossibleto
followcorrelationsformanyindividualnationalmarketreturnsforthe1969–1998period.Ingeneral,thereisnopatternofincreasingcorrelation.Theone
exceptionistheincreasingcorrelationsamongEuropeanmarketsoverthepasttwodecades.Figure5-2isaplotofthe
correlationcoefficientfortheS&P500/EAFEpairformonthlyreturns(three-yearrollingperiods)for1969to1998.Thecorrelationisseentovarywidelyduringthisperiod,butthereiscertainlynoclear-cutincreaseinthis
valueovertime.(Theredoesseemtohavebeenariseinthecorrelationoverthepasttwoyearsorso.ThiswasprobablycausedbytheAsian-flu-relatedvolatilityof1997–1998.)Thereislittleevidencetosupportthenotionofanincreasinginternationalmarketcorrelationresultingfromaglobalizingeconomy.
Figure5-2.S&P500/EAFEcorrelations,1969–1998.
Probablyofgreaterimportancethantheriskreductionderivedfromdiversificationisthe“rebalancingbonus,”theextrareturnproducedbyrigorousrebalancing.Thebenefitderivedfrom
rebalancingisnotonlypecuniary,butalsopsychological.Bygettingintothehabitofprofitingbymovinginthedirectionoppositethemarket’s,theinvestorgainsbothahealthyself-relianceandascornformarketsentiment.Thisdistrustofsentimentand“expertopinion”isoneofaninvestor’smostusefultools.Yetanotherpsychological
benefitofadiversifiedportfolioresultsfromitslimitedexposuretoanyonemarketsegment:youarenever“bettingthefarm”ononeasset.Ifonly5%or10%ofyourportfolioisinvestedinemergingmarketsstocks,thentheinevitable30%or50%lossoccasionallyseeninthisareawillnothurttoomuch;itishighlylikelythatgainsinotherareaswillmakeupforpartoralloftheloss.
Moreimportantly,yourlowexposuremaymakeyoueagertorebalance,thus“buyingcheap.”
InternationalDiversificationwithSmallStocks
Furtherdiversificationbenefitcanbeobtainedthroughtheuseofinternationalsmallstocks.Considerthe
correlationgridsforlargeandsmallstockreturnsfor1990–1998,showninTable5-3.Thefirstnumberisthecorrelationforlargestocksintheassetclasspair,thesecondforsmallstocks.
Table5-3.CorrelationsofGlobalLargeandSmallStocks,1990–1998(MonthlyReturns)
Forexample,fortheJapanandU.S.pairthecorrelationofmonthlyreturnsforlargestocksis.310and.195for
smallstocks.Infact,ineachcasethecorrelationforsmallstocksislessthanforlargestocks.ThiseffectisparticularlydramaticforU.S.-U.K.andU.S.-ContinentalEuropeancorrelations,thethreeclassesthatmakeupthebulkofmostglobalportfolios.Inspiteofthefactthatsmallstockindexesofindividualnationsareconsiderablymorevolatilethantheirlarger
cousins,aportfolioofglobalsmallstocksisonlymarginallymorevolatilethanasimilarportfolioofforeignanddomesticlargestocks.Forexample,theSDoftheDimensionalFundAdvisors’globallargecompanyindexfor1990–1998was13.46%,versus14.37%fortheglobalsmallcompanyindex.Therealriskofsmall
stocksistheirtrackingerror
—thepropensitytohavereturnswhichcanbeconsiderablylower,aswellasconsiderablyhigher,thanlargestocks.Inotherwords,diversificationintothisareaworkswhetherwewantittoornot.Thishasbeenparticularlypainfuloverthepastdecade,aslarge-companystockshaveoutperformedsmall-companystocksaroundtheglobe,inspiteofsmallstocks’higher
long-termreturns.Rationalinvestorsdeal
withthelarge-versus-smalldilemmainthesamewayastheydealwiththeforeign-versus-domesticproblem.Firstandforemost,guardagainstrecency—donotbeoverlyimpressedwiththelastdecade’striumphofdomesticoverforeign,andoflargeoversmall.Ifanything,thesephenomenamakeitmore
likelythattheoppositewilloccurinthenextdecade.Second,hedgeyourbetswithlargeandsmallstocksinthesamewaythatUncleFredshowedyouforforeignanddomesticstocks.Inotherwords,ownall“fourcorners”oftheglobalequitymarket:largedomestic,largeforeign,smalldomestic,andsmallforeign.
AllocatingAssets:TheThree-StepApproach
Wearefinallyreadytoallocateyourassets.Youmustaskthreequestionsinsequence:
1.HowmanydifferentassetclassesdoIwanttoown?2.How“conventional”aportfoliodoIwant?3.HowmuchriskdoIwanttotake?
AssetClasses
Howmanydifferentassetclassesshouldyouown?Youmightaswellaskthemeaningoflife.Aboutallonecansayis“morethanthree.”Portfolioscomeinmanydegreesofcomplexity,andthenumberofassetsyouemploywilldependlargelyuponhowmuchyoutoleratedealingwiththiscomplexity.I’llmakeasmallconfession
atthispoint;I’manasset-classjunkie—Ijustcan’townenoughofthethings.Ienjoydealingwiththem,andifIhavetomanageaportfoliowith20or30,that’sallright.Butthelawofdiminishing
returnsappliestoassetclasses.Yougetthemostdiversificationfromthefirstseveral.Thenextseveral,maybeabitmore.Beyondthatyou’reprobablyjust
amusingyourself.Sohereisthehierarchy.
I’llstartwithlevel-oneportfoliocomplexity:
TheLevel-OneAssetPaletteU.S.largestocks(S&P
500)U.S.smallstocks(CRSP
9-10,Russell2000,orBarra600)Foreignstocks(EAFE)U.S.short-termbonds
TheCRSP9-10isanindexofsmallstocks,producedbytheCenterforResearchinSecurityPrices,andconsistsofalmostallstockswithmarketcapitalizationvaluesinthebottomfifthoftheNewYorkStockExchange.Infact,mostofitscompaniestradeontheNasdaq.TheRussell2000consistsofthe2000smalleststocksintheRussell3000Index.Finally,theS&P600are600small
companiesselectedbyStandard&Poor’sasrepresentativeofthesmall-capuniverse.Ifyoudon’tlikeinvesting
allthatmuch,andifreadingthisbookistheequivalentofrootcanalwork,thenthesearetheonlyfourassetsyoureallyneed.Youcangetmostofthediversificationoffarmorecomplexportfoliosfromthisshortlist.Allfour
oftheseassetclassesareavailableasinexpensiveindexfunds.And,asI’vealreadysaid,ifhistoryisanyguideaportfoliodividedequallyamongthesefourassetswillmostlikelyoutperformtheoverwhelmingmajorityofinvestmentprofessionalsoverthenextfewdecades.We’lldiscusslaterinthischapterwhatproportionstoassigneachasset.
TheLevel-TwoAssetPaletteU.S.largestocks(S&P
500)U.S.smallstocks(CRSP
9-10,Russell2000,orBarra600)ForeignlargestocksEmergingmarketsstocksForeignsmallstocksREITsU.S.short-termbonds
Thispaletteisfortheindividualwhoisseriousaboutdiversificationandwantsitsfullbenefit.Youmaywishtoaddotherassetclassesaswell,suchaspreciousmetalsstocksandinternationalbonds.I’mnotgoingtolistallof
thepossibilitiesthatthelevel-threeassetpalette“truebeliever”mightwanttoown,sinceit’saverylongand
boringone,butIwillinsteadprovideadescription.Equityassetscannotonlybedividedaccordingtothesizeofcompany(large-versus-small)butalsobyvalueversusgrowthorientation.We’lltalkmoreaboutvalueinvestinginChapter7,butsufficeittosaythatcompaniescomeintwovalueflavors—growthandvalue.Forgrowth,thinkMicrosoft,Wal-Mart,andAmazon.com.Theseare
rapidlygrowingcompaniessellingforupwardsof35timesearnings(iftheyhaveanyearningsatall!),becausetheseearningsareexpectedtogrowrapidly.Forvalue,thinkGeneralMotors,Kmart,orJ.P.Morgan.Thesearecompanieswithpoorgrowthprospects,whichconsequentlysellmorecheaplythangrowthstocks.So,wenowhavethree
dimensionsofstockcharacterization—nationality,size,andvalueversus-growth-orientation.Youcaneasilydividetheworldupinto10differentregions,andforeachyouhavelargeversussmallandvalueversusgrowth.That’s40possibilitiesrightthere.Andthat’snotincludingsectors(REITs,preciousmetals,naturalresources,utilities)orbondsforeachnation.Notall
ofthesecategoriesareeasilyavailableinthemarketplace,butasurprisingnumberare.Itisrelativelyeasytobuyanemergingmarketssmall-companyfund,forexample,ifyoureallywantone.Onecangoevenfurtherandbuysingle-countryvehicles,orevenindividualforeigncompaniesavailableontheU.S.exchangesasAmericanDepositaryReceipts(ADRs).
Idon’trecommendthelevel-threepaletteforanyonewhodoesn’ttrulyenjoyinvestingandwhodoesn’thavethetimeandpatiencetodealwithitscomplexity.
HowUnorthodoxAreYou?
Let’sstartwiththelevel-onepaletteandassumethatyouareoneofthoserareindividualswhocantoleratea100%equityportfolio.
Insteadofthefourassetslisted,youonlyhavetoconsiderthefirstthree.JusthowdoyouallocateyourassetsbetweenU.S.largestocks,U.S.smallstocks,andforeignstocks?Historytellsusthatsmallstockshavehigherreturnsthanlargestocksandforeignstocks,butwithgreaterrisk.Whynotsimplytakethe“coward’sway”anddivideourassetsequallybetweenthesethree
classes?Thisisinfactnotan
unreasonablewaytogoandshoulddoquitewellinthelongterm.However,rememberthatwhetherwelikeitornot,U.S.largestocksare“themarket.”Allofus,consciouslyorsubconsciously,compareourownreturnstothisbenchmark,usuallytheS&P500.
Attimes,this“equalmix”alsowillbehaveverydifferentlyfromthebenchmark.Therefore,let’slookataportfoliowhichisverysimilartothatusedbymanyinstitutionalinvestors—60%U.S.largestocks,with20%eachU.S.smallandforeignstocks(a“conventionalportfolio”)forthesix5-yearperiodsstarting1969.Theportfoliocompositionsandreturnsare
showninTable5-4.
TABLE5-4.TrackingErrorofVariousEquityMixes,1969–1998
First,notethatthelong-
termreturns(lastrow)ofallthreeportfoliosareverysimilar.Alsonoticethatthecoward’sportfoliounderperformedtheS&P500by4%peryearin1969–1973and1989–1993,andbyover8%inthelast5-yearperiod.(Thesearetheboldfacednumbersinthetable.)TheconventionalportfoliolaggedtheS&Pbyconsiderablyless.Whileitmaybetruethat
thelong-termreturnsofahighlydiversifiedportfolioarethesameasamoreconventionalportfolio,fromtimetotimeitwillseriouslyunderperformit.Howmuchwouldsuchtemporaryunderperformancebotheryou?Presumablymanyofyoualreadyownsomesmallstocksandforeignstocks.Howdisturbedhaveyoubeenbytheirrecentlaggardperformance?Iftheansweris
“very,”thenyoushouldchooseaportfoliomoreheavilyweightedtowardU.S.largestocks.Ontheotherhand,ifyoucantoleratethissortof“trackingerror,”thenamoreunconventionalportfolioheavilyweightedtowardforeignandsmallstocksmaybeappropriate.Aswemovetoward
portfoliosofgreatercomplexity,thistracking
errorbecomesmorepronounced,andyourtolerancetoitbecomesever-moreimportant.RecallfromChapter4thatinternationalsmallstockshavelaggedtheS&P500by19%peryearsince1990,eventhoughtheirperformanceoverthepast30yearshasbeenoutstanding.Infact,themoreexoticassetclassesyouaddtoyourmix,thehigheryourtrackingerrorwillbe.Remember,that
trackingerrordoesnotmeanlowerreturns,itjustmeansthatyourportfoliowillbehaveverydifferentlyfromeveryoneelse’s,andthatitwilloftentemporarilyunderperformeverybodyelse’s.
RiskTolerance
Thethirdstepintheassetallocationprocessisbyfartheeasiest.Youhavealready
donetheheavylifting—decidingwhatstockassetclassestouse,andinapproximatelywhatproportiontousethem.Nowallyouhavetodetermineistheoverallmixofstocksandbonds.Inthefirstversionsofthisbook,Irecommendedthatthemostaggressiveinvestorsmightconsidera100%equityportfolio.Thisisbecausehistoricallystockshavereturnedseveralpercent
moreonanannualbasisthanbonds,albeitatconsiderablymorerisk.Andyet,aswebeginthenewmillennium,itseemshighlylikelythatoverthecomingdecadesstockreturnswillbeatbestonlyslightlyhigherthanbondreturns.AsalreadyalludedtoinChapter2,theS&P500currentlyyieldsabout1.3%,andhistoricallyearningshaveonlygrownatareal(inflation-adjusted)rateof
2%peryear(discussedinChapter2andshowninFigure2-12).Somemayfinditdifficulttobelievethatrealcorporateearningshavegrownatalong-termrateofonly2%peryear,butthisisinfactthecase.In1920theDowJonesIndustrialAverageearned$9.12pershare,andin1998itearned$378.06.Thiscompoundsouttojust4.89%peryear.Duringthesameperiod,the
inflationratewas2.87%.Thus,therealreturn—thedifferencebetweenthesetworates—wasalmostexactly2%.(Dividendshavegrownevenmoreslowlyat1.5%peryearininflation-adjustedterms.)Thisaddsuptoanexpectedrealstockreturnoflessthan3.5%.NowconsiderthatTreasurybondscurrentlyyieldabout6%.Withtheinflationratecurrentlyat1.6%,thisresultsinareal
yieldof4.4%.Andifyouareafraidthatanuptickininflationmaywipeoutsomeofthoserealreturns,youcanpurchaseaTreasuryInflationProtectedSecurity(TIPS)atagovernment-guaranteed4.1%realyield.Inotherwords,itisquitepossiblethatoverthenextfewdecadesstockreturnsmayactuallybelessthanbondreturns.Forthisreason,eventhe
mostaggressiveinvestorsmaywishtoholdperhaps25%bonds,withmoderatelyaggressiveinvestorsholdinga50/50mixofstocksandbonds,andconservativeinvestorsintherangeof30%stocksand70%bonds.Toreiterate,the
aggressivenessofyourportfolioisreflectedinyouroverallstockandbondmix,notinthekindsofequityyou
hold,whichshouldbesimilaratalllevelsofrisk.
TheMadonnaPortfolio
Let’slookatafewmoreexamplesofhowthisprocessworks.Assumethatyouareaboldinvestorandhaveansweredthethreequestionsposedearlierinthechapterasfollows:
1.Complexity:moderate
(level-twopalette,pluspreciousmetals)
2.Conventionality:low.YouhavedeterminedthatyoucantoleratealargeamountoftrackingerroranddonotmindatallifyourallocationunderperformstheS&P500foruptoadecade,aslongasyourlong-termreturnsarereasonable.
3.Risktolerance:high.You
haveshownanabilitytowithstandlargelossesinyourportfoliowithoutflinching.
Here’swhatsuchaportfoliomightlooklike:
10%S&P50010%U.S.smallstocks10%REITs10%internationallarge-
capstocks10%internationalsmall-capstocks10%emergingmarketsstocks10%preciousmetalsstocks30%U.S.short-termbonds
Thisportfolioismoreorlessequallydividedbetweendomesticandforeign,and
smallandlargecap.Itisextremelyunconventionalinthisregard,anditwillhavereturnsthatwillberadicallydifferentfromtheS&P500inmanyyears,ineitherdirection.Ontheotherhand,itslong-termreturnsshouldbequitehigh.Weholdafairamountofbondsbecausethediscounteddividendmodeltellsusthatstockreturnsgoingforwardmaynotbemuchgreaterthanbond
returns.Thisportfolioisnotrecommendedforallbutthehardiestofsoulsandmostindependentofthinkers.
TheGapPortfolio
Let’sanswerthebasicportfolioquestionsabitdifferently:
1.Complexity:high.Wedon’tmindholdingmorethanadozenassetclasses.
2.Conventionality:high.Wewantadequatediversificationandreturns,butwishtokeeptrackingerrortoaminimum.
3.Risktolerance:low.Wereallydon’twanttolosemorethanabout6%ofournetworthinagivenyear.
ThefollowingportfolioistakenfromtheDimensional
FundAdvisors’(DFAs)“moderatebalanced”strategy,withlow-to-midrisk.This40/60stock/bondportfolioisavailablefromDFA,aboutwhichmorewillbesaidinChapter8:
8%U.S.large-capgrowth8%U.S.large-capvalue4%U.S.small-capgrowth4%U.S.small-capvalue4%REIT
4%internationallarge-capvalue2%internationalsmall-capgrowth2%internationalsmall-capvalue1.2%emergingmarketslarge-capgrowth1.2%emergingmarketslarge-capvalue1.6%emergingmarketssmall-capgrowth
15%one-yearcorporatebonds15%two-yearglobalbonds15%five-yearU.S.governmentbonds15%five-yearglobalbonds
First,thecomplexityofthisportfolioshouldsatisfyallbutthemostexactingportfoliobuff,withnoless
than15assetclasses.Secondly,itisquiteconventional,witha28/12domestic/foreignsplit,anditismuchheavierinlarge-capthansmall-capstocks.Thisportfolioprovidesadequatesafetyanddiversification,andyetitsreturnonlyrarelyvariesmorethanahalf-dozenpercentfromadomestic40/60S&P500/T-billmix.Younowhaveanideaof
howtheallocationprocessworks.First,decidehowmanydifferentstockandbondassetclassesyouarewillingtoown.Increasingthenumberofassetclassesyouemploywillimprovediversificationbutwillalsoincreaseyourworkloadandtrackingerror.TheGapPortfoliogetsaroundthisproblemwithaheavyweightingoflargeanddomesticstocksinitsequity
portion.Second,decidejusthow
muchtrackingerroryoucantolerate.Ifyouareunabletotoleratemuchtrackingerror,keepyourproportionofforeignandsmall-capstockslow.Andlast,adjustyour
stock-versus-bondmixaccordingtohowmuchriskyoucantolerate,rangingfromamaximumof75%
stockforthemostaggressiveinvestorsdownto25%fortheleastaggressive.Uptothispointour
journeythroughportfolioanalysishasbeenfairlyacademic—wehavenotyet“gottenourfingersdirty”withrealinvestments.InChapters6and7weshallexaminethenuancesofhowrealmarketsactuallywork,andinChapter8weshall
explorethenutsandboltsofimplementingourassetallocationplan.
Summary1.Itisimpossibletoforecastfutureoptimalportfoliosbyanytechnique.
2.Overthelongterm,awidelydiversifiedglobalportfolioofsmall-andlarge-companystocksshouldhavefavorable
return-versusrisk-characteristics.
3.Yourpreciseassetallocationwilldependonthreefactors:yourtolerancetoS&P500trackingerror,thenumberofassetsyouwishtoown,andyourtolerancetorisk.
6MarketEfficiency
Therearetwokindsofinvestors,betheylargeorsmall:thosewhodon’tknowwherethemarketisheaded,andthosewhodon’tknowthattheydon’tknow.Thispertainstoanymarket,beitstocks,bonds,LouisXIV
chairs,orporkbellies.Thenagain,thereisactuallyathirdtypeofinvestor—theinvestmentprofessional,whoindeedknowsthatheorshedoesn’tknow,butwhoselivelihooddependsuponappearingtoknow.Itseemsintuitively
obviousthatstockselectionshouldbeaskilllikeanyother.Withenoughintelligence,training,
experience,andeffort,oneshouldbeabletobeatthemarket.However,theprimary
strengthofWesterncultureisitsrelianceonthescientificmethod.Theshortversionofwhichisthatanyrationalbeliefshouldbefalsifiable—thatistosay,testable.Considerbaseballhitters.Yousaythatthereissuchathingas“hittingskill”?A
trivialthingtoask,ofcourse,butstilleasytotest.Thebattinganalogyis
usefulbecauseitforcesustothinkaboutthestatisticalnatureofskill.Probablythebestwaytodefineitisintermsofpersistenceofperformance.Let’ssaythatthemeanbattingaverageamongbaseballplayersis.260.Nowlet’slookatlastyear’s.300hitters.Were
therenosuchthingasbattingskill,thentheirperformancethisyearwouldbemerelyaverage—inotherwords,.260.Ofcourse,oneyear’s.300hittersasagroupalwaysdowellaboveaveragethefollowingyearbysuchawidemarginastoremovealldoubtthattheirperformanceisduetoskill,andnotchance.Interestingly,whenexposedtotheharshlightofstatisticalanalysis,morethan
afewsportsbeliefsdofailtopassmuster.Oneoftheseisthe“hothand”phenomenoninbasketball.Feedingtheballtotheshooterona“hotstreak”isatime-honoredcourtstrategy.Andyet,aplayerwhohasrecentlyhitahigherpercentageofgoalsthanhisusualisnomorelikelythanusualtodosogoingforward.Thatis,suchperformancedoesnotpersist.Thishighlightsahuman
foiblethathasgreatimportinfinance—ourtendencytoseepatternswherethereareinfactnone.Andyet,itwasnotuntil30
yearsagothatresearchersbegantoapplythesametechniquestomoneymanagers.Itturnsoutthatforallpracticalpurposesthereisnosuchthingasstock-pickingskill.ThefirsttodocumentthiswasMichael
Jensen,who,inalandmarkpaperpublishedin1968intheJournalofFinance,lookedatmutualfundperformanceforthe20yearsfrom1945to1964andfoundnoevidenceofpersistenceoffundperformance.Lastyear’shotmanager,ontheaverage,willbesimplymediocrenextyear.Sincethen,dozensofcarefulanalysesofmoneymanagerperformancehavebeendone,
andtheresultsareeye-opening.Manystudiesshowasmallamountofpersistence,buttheeffectisalwayssotinythatafteryoupayfundexpenses,youstillcomeoutbehindthemarketperformance,onaverage.Furthermore,thepersistenceisusuallyoverrelativelybriefperiods(ayearorless)andnotoverthelongerterm.Let’stakealookatsome
ofthedata.AstudydonebyDimensionalFundAdvisors,aninstitutionalinvestmentfirminSantaMonica,CA,lookedatfundperformancefortheperiodJanuary1970toJune1998.Theyexaminedthetop30diversifiedmutualfundsforsequentialfive-yearperiodsandthensubsequentperformance.TheresultsaretabulatedinTable6-1.Ineachexample,thetopfundsforthefirstperiod
underperformedtheS&P500inthesubsequentperiodandintwoofthefiveexamplesactuallyunderperformedtheirpeersaswell.
Table6-1.SubsequentPerformanceofTopPerformingFunds,1970–1998
Doesthislookliketheperformanceofhighlyskilledmoneymanagers?No.Wearelookingattheproverbialbunchofchimpanzeesthrowingdartsatthestockpage.Their“success”or“failure”isapurelyrandomaffair.ThemostsuccessfulmanagerswindupbeinginterviewedinMoney,TheNewYorkTimes,andbyUncleLou.Theirassets
undermanagementballoon,andtheirshareholders’admirationisvindicatedbythemediaattention.However,timepasses,and
thelawsofchanceeventuallycatchupwiththesefolks.Hundredsofthousandsofinvestorsfindthatthehandsomeprincemanagingtheirfundsturnedouttobejustanotherhairysimian.Infact,withtheparticularly
perverselogicoffundflows,veryfewinvestorsactuallyobtainthespectacularearlyreturnsofthe“top”funds.Worstofall,largeassetinflowstendtodepressfuturereturnsbecauseofso-calledmarketimpactcosts,whichwillbedescribedlaterinthischapter.Theseearlyhighreturnsinevitablyattractlargenumbersofinvestors,whowindupwithmerelyaverageperformance,ifthey
arelucky.
MathDetails:HowtoStatisticallyTestforSkill
Adetailedexplanationofhowtostatisticallydemonstrateskilliswellbeyondthescopeofthisbook.However,asimple
illustrationisuseful.Let’susetheexampleofa.260meanbattingaverage,withanSDamonghittersinanygivenyearof.020.Inotherwords,a.300averageplacesthehitter2SDs[(.300−.260)/.020]abovethemeanforthatsingleyear.If
ahitteraverages.280over10seasons,isheskilled?The“standarderror”(SE)ofrandomlyperformingbatterswithanannualSD.020overa10-yearperiodis
.Inotherwords,inarandomworldan
annualSDof20pointstranslatesintoanSDof6.3pointsover10years.Thedifferencebetweenthebatter’sperformanceandthemeanis.020,anddividingthatbytheSEof.0063givesa“zvalue”of3.17.Sinceweareconsidering10
years,performance,thereare9“degreesoffreedom.”Thezvalueanddegreesoffreedomarefedintoa“tdistributionfunction”onourspreadsheet,andoutpopsapvalueof.011.Inotherwords,ina“randombatting”
world,thereisa1.1%chanceofagivenbatteraveraging.280over10seasons.
Whetherornotweconsidersuchabatterskilledalsodependsonwhetherweareobservinghim“insample”or“outofsample.”Insample
meansthatwepickedhimoutofalargenumberofbatters—say,allofhisteammates—afterthefact.Inwhichcaseheisprobablynotskilled,sinceitwouldnotbeunusualfor1of30individualstoexperiencea1.1%randomevent.On
theotherhand,ifhisperformancemeasuredisoutofsample—thatis,wehadpickedhimaloneamonghisteammates—thenheprobablyisskilled,sincewewouldhaveonlyonechanceata1.1%occurrenceinarandombattingworld.Anonly
slightlymorecomplexformulationisusedtoevaluatemoneymanagers.Onehastobeextremelycarefultodistinguishout-of-samplefromin-sampleperformance.Oneshouldnotbesurprisedifonepicksoutthebest-
performingmanageroutof500andfindsthathispvalueis.001.However,ifoneidentifieshimaheadoftime,andthenhisperformancepvalueis.001afterthefact,thenheprobablyisskilled.
FromAlphaMantoApeman
OneofthebestillustrationsofhowthisreversalcanoccurisprovidedbyRobertSanborn,whoranOakmarkFund.Mr.Sanbornisanundisputedsuperstarmanager.Frominceptionin1991toyear-end1998Oakmark’sannualizedreturnwas24.91%versus19.56%fortheS&P500.In1992it
beatthebenchmarkbyanastonishing41.28%.ByanystatisticalcriteriaMr.Sanborn’sperformancecouldnothavebeenduetochance.However,adifferentstory
emergeswhenweexaminethefund’sperformanceandassetsbyindividualyear.ThefirstrowtrackstheperformanceofOakmarkFundrelativetotheS&P500,thesecondrowtracksthe
fund’sassets:
Whatweseeistheall-too-familiarpatternoffundinvestorschasingperformance,withmoreandmoreinvestorsgettinglower
andlowerreturns.Infact,ifwe“dollar-weight”thefund’sreturns,wefindthatbecausemostinvestorshoppedonthebandwagonafterthebestreturnshadoccurred,theaverageinvestorinthisfundunderper-formedtheS&P500by7.55%annually.IndefenseofMr.Sanborn,
itisfairtopointoutthatS&P500trackingerrorisnotareasonablemeasureoverthe
pastfewyearsforavaluemanager’sperformance.Onecangetaroundthisbycalculatingthefund’salpha,whichreferstotheexcessreturnaddedbyamanageraftertakingintoaccountsuchfactorsasmarketexposure,mediancompanysize,andvalueorientation.Thisisdonewithatechnique(availableinmostspreadsheetpackages)knownasregressionanalysis,in
whichthemonthlyorquarterlyreturnsforthemanagerinquestionarelaidalongsidethereturnsofbenchmarksforvariousmarketfactorsorsectors.Themanager’sreturnsare“fitted”tothereturnsoftheotherfactors,resultinginacustom-madebenchmarkforthatmanager.Thealphaisthedifferencebetweenthefund’sperformanceandthatoftheregression-determined
benchmarkandameasureofhowwellthemanagerhasperformed.Itisexpressedthesamewayasreturn,inpercentperyear,andcanbepositiveornegative.Forexample,ifamanagerhasanalphaof–4%peryearthismeansthatthemanagerhasunderperformedtheregression-determinedbenchmarkby4%annually.Oakmark’salphaforthefirst29monthsistruly
spectacular,andquitestatisticallysignificant,withapvalueof.0004.Thismeansthattherewaslessthana1-in-2000possibilitythatthefund’ssuperbperformanceinthefirst29monthscouldhavebeenduetochance.Unfortunately,itsperformanceinthelast29-monthperiodwasequallyimpressive,butinthewrongdirection.
MyinterpretationoftheabovedataisthatMr.Sanbornismodestlyskilled.“Modestlyskilled”isnotatallderogatoryinthiscontext,since99%offundmanagersdemonstratenoevidenceofskillwhatsoever.However,unfortunatelyeventheseskillswereoverwhelmedbythe“impact-costdrag”(tobediscussedinthenextsection)ofmanagingbillionsofdollarsofnewassets,chasing
upstockpricesandloweringultimatereturns.Thetake-homemessage
hereisclear.It’shumannaturetofindpatternswheretherearenoneandtofindskillwhereluckisamorelikelyexplanation(particularlyifyou’retheluckymanager).Butsuccessfulorluckyactivelymanagedfundssowtheseedsoftheirowndestruction.
Avoidthem.
WhyFundManagersDoSoPoorly
Mutualfundmanagerperformancedoesnotpersistandthereturnofstockpickingiszero.Thisisasitshouldbe,ofcourse.Thesefolksarethemarket,andthereisnowaythattheycanallperformabovethemean.
WallStreet,unfortunately,isnotLakeWobegon,whereallthechildrenareaboveaverage.Sothebadnewsisthatthe
processofmutualfundselectiongivesessentiallyrandomresults.However,thereallybadnewsisthatactivelymanagedfundsaresoexpensive.Funds,ofcourse,incurcosts.Sadly,eventhebest-informedfund
investorsareusuallyunawareofjusthowhighthesecostsreallyare.Mostinvestorsthinkthat
thefund’sexpenseratio(ER),listedintheprospectusandannualreports,istheirtruecostoffundownership.Wrong.ThereareactuallythreemorelayersofexpensesbeyondtheER,whichmerelycomprisesthefund’sadvisoryfees(whatthe
managersgetpaid)andadministrativeexpenses.Thenextlayeroffeesarethecommissionspaidontransactions.ThesearenotincludedintheER,butsince1996theSEChasrequiredthattheybereportedtoshareholders.However,theyarepresentedinsuchanobscuremannerthat,unlessyouhaveanaccountingdegree,itisalmostimpossibletocalculatehow
muchreturnislostasaproportionoffundassets.Thesecondextralayeris
thebid-askspreadofstocksboughtandsold.Astockisalwaysboughtataslightlyhigherpricethanitissold,toprovidethemarketmakerwithaprofit.This“spread”isabout0.4%forthelargest,mostliquid,companiesandincreaseswithdecreasingcompanysize.Forthe
smalleststocksitmaybeaslargeas10%.Itisintherangeof1%to4%forforeignstocks.Forexample,atthemarketcloseofbusinessonApril12,2000,Microsoftwasquotedatabid(thepriceatwhichaninvestorcouldsellthestock)of$80.125andanask(thepriceatwhichaninvestorcouldbuythestock)of$80.25.Thedifference—one-eighthofadollar—isthe
spread.BecauseMicrosoftisoneofthemostactivelytradedstocksintheworld,thisrepresentsjust0.15%oftheprice.Attheotherendofthespectrum,onthesamedayOfficeland,atinycompanydealinginusedcopyingmachines,tradedat$0.65/$0.70ofbidtoask,aspreadof7.7%.Thelastlayerofextra
expense—so-calledmarket-
impactcosts—isthemostdifficulttoestimate.Impactcostsarisewhenlargeblocksofstockareboughtandsold.Imaginethatyouownhalfthesharesofasmallpubliclytradedcompanyworth$20million.Let’sfurtherimaginethatyouhavegottenyourselfintoajam,needcash,andmustquicklysellallofthoseshares.Thesellingpressurecausedbyyouractionswilldrasticallyreducethestock’s
price,andthelastsharessoldwillfetchconsiderablylessthanthefirstsharessold.Thereversewouldoccurifaninvestordecidedthatheorshewantedtoquicklyacquirealargeblockofyourcompany.Impactcostsarenota
problemforsmallinvestorsbuyingsharesofindividualcompanies,buttheyarearealheadacheforlargemutual
funds.Obviously,themagnitudeofimpactcostsdependsonthesizeofthefund,thesizeofthecompany,andthetotalamounttransacted.Asafirstapproximation,assumethatitisequaltothespread.
TheFourLayersofMutualFundCostsExpenseratioCommissions
Bid-askspreadMarket-impactcostsTakentogether,thesefour
layersofexpensesaresmallestforlarge-capfunds,intermediateforsmall-capandforeignfunds,andgreatestforemerging-marketsfunds.TheyaretabulatedinTable6-2.
Table6-2.ActiveFundExpenses
Recallthatthereturnoflargestocksfor1926–1998was11.22%peryear.Itshouldbepainfullyobviousthatthisisnotthereturnthatyou,themutualfund
investor,wouldactuallyreceive.Youmustsubtractoutofthatreturnthefund’stotalinvestmentexpense.Nowthefullmagnitudeof
theproblembecomesclear.ThebottomrowofTable6-2showstherealcostsofowninganactivelymanagedfund.Infairness,thisdoesoverstatethingsabit.Moneyspentonresearchandanalysisisnotatotalloss.
Suchresearchdoesseemtoincreasereturns,butalmostalwaysbyanamountlessthanthatspent.Howmuchofthefirst“expenseratio”lineisspentonresearch?Figureaboutahalf,ifyou’relucky.Soifthelong-termreturnofequityingeneralisabout11%,thenactivemanagementwillloseyouabout1.5%inalarge-capfund,3.3%inaforeignorsmall-capfund,and8%inan
emerging-marketsfund,leavingyouwith9.5%,7.7%,and3%,respectively.Notanappetizingprospect.Themutualfundbusinesshasbenefitedgreatlybythehighreturnsofrecentyears,whichhaveservedtomaskthestaggeringcostsinmostareas.Oneexceptiontothishasbeenintheemergingmarkets,wherethecombinationoflowasset-classreturnsandhigh
expenseshasresultedinamassexodusofinvestors.
ACaseStudy:TheJanuaryEffect
Oneofthegreatironiesofinvestingisthattheuniversalavailabilityoffinancialinformationisinfactthereasonbehindthefailureofsecurityanalysis.BeforetheSecuritiesActof1933
mandatedperiodicpublicdisclosureofcorporateperformance,eventhemostbasicfinancialinformationaboutacompanywasusuallyacloselyguardedsecret.WhenBenjaminGrahamwrotethefirsteditionofSecurityAnalysis,thesimpleactofascertainingacompany’searningsorrevenueswasoftenamatterofspendingadayortwoonatrain,thensweet-talkingthe
informationoutofasecretarywhilebeingcarefultoavoidherboss’swatchfuleye.Sucheffortswereoftenwell-rewarded.Intheinformationage,
everyaspectofacompany’sfinancesisimmediatelyavailabletoanyonewithacomputerandmodem.Andsinceeveryonehasaccesstothisdata,itisimmediatelydiscountedintothesecurity’s
price,sothereisnofurtherprofitfromactingonit.Anexcellentexampleof
howtheprocessworksisprovidedbythe“Januaryeffect”(JE).TheJEisexplainedasfollows:
Small-companystocks,becauseoftheirhigherrisks,haveahigherreturnthanlarge-companystocks.Formanydecadesalmost
allofthisexcessreturnoccurredinJanuary.
Table6-3showsthattheJanuaryexcessreturnisactuallylargerthantheexcessreturnfortheentireyearforthesmalleststocks,asmeasuredbyIbbotsonAssociates.IbbotsondividesdomesticstocksintodecilesbyNewYorkStockExchangesizesandthenmeasuresthe1926–1994
excessreturnoverthelargest(first)decile.
Table6-3.ReturninExcessofFirstDecile
Theprecisereasonfortheconcentrationofsmall-stock
excessreturninJanuaryisunknown,butthereisnoshortageofcandidates.
End-of-yeartax-losssellingismyfavorite,buttherearenoeasyanswers.Entirehow-tobookshavebeendevotedtothe“incredibleJanuaryeffect,”andit’salsoaperenniallate-yeartopicformaterial-starvedfinancialwriters.Unfortunately,thereare
twofundamentalproblemswiththeJE.First,itsmagnitudeisroughlyequivalenttothebid-askspreadforeachdecile.Forexample,lookattheJanuaryexcessreturnof10.28%forthesmallest(decile10)stocks.Inordertorealizethatexcessreturn,youwouldhavehadtobuyeachstockonDecember31andhavesolditonJanuary31.Butsincetheask(buying)price
forthesesmalleststocksisalsoabout10%abovethebid(selling)price,youwouldnothavemadeanactualprofit.Inotherwords,thesimpleactofbuyingandsellingsmallstockseliminatesthebenefit.SoifyouwanttorealizetheJanuaryeffect,youhavetoholdsmallstocksformanyyears.Thesecondproblemisthat
theJEnolongerexists.
Figure6-1showsthe10-yearrollingaverageofthesmall-cappremium,calculatedasthedifferencebetweentheJanuaryreturnoftheCRSP9-10IndexandtheS&P500.Ascanbeseen,theeffecthasfadedintoinsignificance.Thisisoneofthereasonswhyprofitablestrategies,iftheyexistatall,donotlastforverylong.Assoonastheyarediscovered,theyareacteduponbytheinvestment
community,biddingupthepriceoftherelevantassets,thuseliminatingtheirexcessreturn.
Figure6-1.Ten-yearJanuaryCRSP9–10decileminusS&P.
TheIndexingSolution
Moneymanager,writer,andfinancialelderstatesmanCharlesEllisobservedthreedecadesagowithgrowingalarmthefirstdatademonstratingalackof
moneymanagerskill.Hethoughttohimself,“I’veseenthissomewhereelse.”Anavidtennisplayer,herealizedthatformostamateurparticipantswinningorlosingwaslessamatterofskillthansimplyplayingconservativelyandavoidingmistakes.Hewroteafamousarticle,appearinginthe1972FinancialAnalystsJournalcalled“TheLoser’sGame,”inwhichhecompared
professionalinvestingtoamateurtennis.Justastheamateurtennisplayerwhosimplytriestoreturntheballwithaminimumoffancymovesistheonewhousuallywins,sotoodoestheinvestorwhosimplybuysandholdsawidelydiversifiedstockportfolio.Thisinvestoristheonewhousuallycomesoutontop.Thetitleofthepiecereferstotheconceptthatinbothamateurtennisand
professionalinvesting,successislessamatterofwinningthanavoidinglosing.Andtheeasiestwaytoloseininvestingistoincurhighcostsbytradingexcessively.Theultimateloss-
avoidancestrategy,then,istosimplybuyandholdtheentiremarket,i.e.,toindex.Thereasonshouldbeapparentfromtheprecedingdiscussionoffundcosts.
Sinceconstantlyanalyzingandadjustingyourportfolioresultsinhighexpensesandalmostnoexcessreturn,whynotjustworkatminimizingallfourlayersofexpensesbybuyingandholdingthemarket?Table6-4liststhefourexpenselayersforanindexedapproachtoinvesting.Thelastrowshowsthetheoreticaldifferenceinreturnsbetweentheactiveandindexedapproach.
Table6-4.IndexFundExpenses
Again,ithastobepointed
outthatthisisatheoreticaladvantage,sinceatleastsomeoftheactive-fundexpensesarespentonresearch,whichhasbeenshowntobeofbenefit.Butrememberthatresearchexpensesalmostnevercompletelypayforthemselves,andonlyasmallportionofanactivefund’stotalfour-layerexpensestructureisspentonanalysis.Thebasicthingtoremember
aboutresearchexpenseisthatitresultsinturnover,whichinturnincreasestotalexpensethroughcommissions,spreads,andimpactcosts.
MathDetails
Theaveragerandomscatterofactivemanagerreturnsinanygivenyearhas
about8%ofSD,butoverannyearperiod(wherenisthenumberofyears)thatscatterwillbereducedbythesquarerootofn.Inotherwords,overafour-yearperiodthereturnsscatterofactivemanagersisreducedbyhalf,andover25years
by80%.So,overa25-yearperiod,therandomscatter(SD)offundperformancewillbe8%/5=1.6%.
So,weseethattheaverageactivemanagerisflyingintoanannualheadwindofanywherebetween1%and8%.SincetheSD,or“scatter”ofannualreturnsfor
activefundsisabout8%inanygivenyear,adifferenceofafewpercentmaynotbenoticed.Butovermanyyears,ittakesatoll,astheSDof25-yearreturnsisonly1.6%(seeMathDetails).Forlarge-capfunds,this
meansthattheindex-fundadvantage,whichhasaboutthesame1.6%value,willresultina+1SDperformance.Meaningthat
theindexfundshouldbeat84%ofactivelymanagedfunds.Asmallorforeignindexfundwitha3.2%advantageshouldperform2SDsabovethenorm,meaningthatitshouldbeat97%ofactivefundsovera25-yearperiod.Andanemerging-marketsindexfundwithaseveral-percentage-pointadvantageshouldbestallofitsactivelymanagedpeers.
Unfortunately,therealworldisnotnearlythisneat,anditisworthlookingattheactualdata.Weshallcompareindex-fundandactive-fundperformancewiththeMorningstarPrincipiadatabase.Thisniftytoolisworthsomediscussion.Morningstaristhepremierpurveyorofmutualfunddataforbothsmallandinstitutionalinvestors.Itisbestknownforitsprint
publications,availableinmostlargepubliclibraries,butIhighlyrecommendthePrincipiasoftwarepackage.Thegutsoftheprogramaremonthlyreturnsfor11,000orsomutualfunds,andmoreimportantly,benchmarkindexes.Thisallowsyoutocalculate,display,andgraphfundrankingsandperformanceinanalmostinfinitevarietyofways,andeventocalculatecorrelations
amongfundsandassetclassesviatheirindexes.Awidevarietyofotherinformationregardingvaluationandfundoperationaldataisalsoincluded.Muchofmyresearchdependsonthispackage.Forstarters,itisimportant
torealizethatwehavetobecarefuljusthowwebenchmarkandcompareour
activelymanagedfunds.Theearliestpersistencystudiessimplylookedatallequityfunds.Thisissuboptimal.Itisimportanttocomparelikewithlike.Forexample,overthepastseveralyearslarge-capgrowthstocks(thinkMcDonald’s,Microsoft,Wal-Mart)havebeenthestrongestperformers.Itwouldbeunfairtocompareasmall-caporforeignfundtogeneral-equityfunds,whichasa
grouptendtohaveaheavyconcentrationofthesestocks,ortotheS&P500forthesamereason.Principiaemploysaparticularlyeffectiveapproachtothisproblem.Theydividedomesticstockfundsintoa3-by-3gridofsizeversusvalueorientation.Theycategorizefundsbycompanysizeintosmall,medium,andlarge.Theyalsopigeonholefundsasvalue,growth,or
“blend”(halfwaybetweengrowthandvalue).Thisproducesninecategoriesandisagoodwaytocompareperformancebetweenfundsfairly.Let’sstartwiththe
granddaddyofallindexmutualfunds,theVanguard500IndexFund.Itisnoaccidentthatsometimewithinthenextyearthisshouldbecomethebiggest
mutualfundintheworld.Overthe15-yearperiodendingDecember1998itrankedinthe8thpercentileoftheMorningstar“large-capblend”category,meaningthatitbeatover92%ofitspeers.Thisisactuallybetterthanwe’dexpectfromafundwitha1.5%expenseadvantageinacategorywith8%SDofannualactive-managerscatter
SDabovethemean,whichisabout23rdpercentile).We’llcometothereasonwhyinaminute.
MathDetails:TheUltimateBenchmark
Ifyou’rereallyseriousaboutbenchmarkingafund,aswellas
lookingforskill,youperformathree-factorregressiononfundreturns.Here’showitworks.DevelopedbyKenFrenchofMITandEugeneFamaofUniversityofChicago,theregressionstartswithmonthlyreturnsforthe
broadstockmarket,aswellasmonthlyreturncontributionsforsmall-stockandvalue-stockexposure.Youthenlaythemonthlyreturnsforthefundormanagerinquestionsidebysidewiththesethreebenchmark
seriesandperformamultipleregression.Thisstatisticaltechnique,availableonmostspreadsheetpackages,producesthe“bestfit”ofthethreefactorstothemanagerreturnsseriesandspitsoutablizzardof
outputnumbers.Themost-importantoftheseistheresidualreturn(theinterceptoftheregression),oralpha.Thealphaistheexcessreturnleftafterexposuretothemarket,size,andvaluehavebeentakenintoaccount.Formost
managers,itisanegativenumber.Theoutputalsoincludesthestatisticalsignificanceofthealpha,tellingushowlikelyitistheresultsareduetochance(alowpvaluesuggestingskillorlackthereof,dependingonwhetheritis
positiveornegative).Italsocalculatestheactualbehavioroftheportfolioalongthesmall-largeandvalue-growthaxes.Thismethodologyisnowthepreferredtechniqueformeasuringperformanceofpensionfund
managersandisalsoheavilyfavoredintheacademiccommunity.
Vanguardalsorunstwootherlarge-capindexfunds,oneforgrowthandoneforvalue.Overthefive-yearperiodendingDecember1998,theGrowthIndexFundrankedinthe2ndpercentile
oftheMorningstarlarge-capgrowthcategory.TheValueIndexFundrankedinthe21stpercentileofitslarge-capvaluecategory.Again,bothofthesearebetterthanwe’dcalculatefromtheaboveformulation,whichwouldpredictonlyabout34thpercentilefive-yearperformance.Finally,tocompletethe
picture,let’slookatsmall-
capindexing.Theoldestsmall-capindexfundistheDimensionalFundAdvisors(DFA)9-10SmallCompanyFund.Overthepast15years,ithasrankedinthe57thpercentile,actuallyworsethanaverage.Asuperficialanalysisof
theabovedatasuggeststhatindexingworksforlarge-capstocks,butnotforsmall-capstocks.Butifwedigalittle
deeper,wefindthatthisisnotthecase.Thereisadirectrelationshipbetweenhowwellindexingworksinaparticularassetcategoryandhowwellthatassetcategoryisdoingcomparedtootherassetclasses.Let’sconsiderthe
extraordinaryperformanceoftheVanguardGrowthIndexFund,withit’s2ndpercentilefive-yearrecord.Itisno
accidentthattheBarraLargeCapGrowthIndex,whichittracks,hadthehighestfive-yearreturnofanyassetclass—27.94%annualized—forthefive-yearperiodfrom1994to1998.TheValueIndexFunddidreasonablywellalso,at21stpercentilefortheperiod.Again,itstrackingindex,theBarraLargeCapValueIndex,didreasonablywell,returning19.88%fortheperiod.
Now,comparethe15-year8thpercentilerankingoftheVanguard500totheDFA9-10SmallCompanyIndexFund’s57thpercentileranking.Itisnocoincidencethatthe15-yearreturnsoftheirtrackingindexeswere17.91%and9.17%,respectively.Ifonelooksalittlecloserattheperformanceofthesetwoindexfunds,onefindsthatthereisadirectrelationship
betweenhowwellsmallstocksdidvig-à-vislargestocksandtheirrelativerankings.Forexample,forthethree-yearperiodfrom1992to1994,smallstocksoutperformedlargestocksby7.59%annually,andtheVanguard500IndexFundrankedinonlythe46thpercentileofitscategory,whiletheDFA9-10SmallCompanyrankedinthe13thpercentileofitscategory.
Dunn’sLaw
Thereisinfactarelationshipbetweenasset-classperformanceandindex-fundperformance,knownasDunn’slaw(afterSteveDunn,afriendwithanastuteeyeforassetclasses):
“Whenanassetclassdoesrelativelywell,anindexfundinthat
classdoesevenbetter.”
Themechanismbehindthisisrelativelystraightforward.Let’sagaintaketheperformanceoftheDFA9–10SmallCompanyIndexFundandtheVanguard500IndexFundasexamples.Anindexfundtakesthefullbruntofanassetclass’sexcellentorpoor
performancerelativetootherassetclasses.Duringthepast15years,mostactivelymanagedsmall-capfundshaveownedsomemidsizeandlargestocks,andthishashelpedtheirperformancerelativetothesmall-capindex.Thereverseisalsotrueofalmostallactivelymanagedlarge-capfunds,whichfrequentlyownstockssmallerthanthoseintheS&P500.Thishashurttheir
performancerelativetotheS&P500.So,tosummarize,because
ofthedominanceoflarge-companystockreturnsoverthepast15years,large-capindexinglooksbetterthanitactuallyis,andsmall-capindexinglooksworsethanitactuallyis.Thesamephenomenonis
observedinotherareas.DFA’sindexfundsforREITs
andinternationalsmallcompanieshavepoorpercentilerankings.Thisisnotduetoanylackofefficacyofindexingintheseareasbutrathertoanartifactofthepoorperformanceoftheassetclassesthemselves.Thesituationwith
internationalindexingisextremelyinteresting.CharlesSchwabhastheoldestdiversified
internationalindexfund,anditsfive-yearrankingfor1994–1998isarespectable21stpercentile.IfoneusestheEAFEindexasaproxyindexfund,onecomesupwithanawful10-year90thpercentileranking,butanamazing1stpercentile15-yearranking.Theproblemhereiscalled“Japan.”TheEAFEuntilrecentlywasoverweightedinJapan,whichcomprised65%oftheindex
attheheightoftheNikkeibubbleinthelate1980s.DuringperiodswhenJapaneseequitydidparticularlypoorly,sodidforeignindexing,andviceversa.However,itishearteningtonotethatinspiteofthefactthatJapanunderperformedtheEAFEasawholebymorethan5%annuallyoverthepast15years,thereisnotonediversifiedinternationalfund
withahigherreturnoverthesameperiod,becauseoftheexpenseadvantage.Aswediscussedearlier,
thebiggesttheoreticaladvantageofindexingshouldbeintheemerging-marketsarea.Andinfact,overthepastfiveyearstheDFAandVanguardEmergingMarketsFundshaverankedinthe10thand15thpercentileoftheirpeers,respectively,in
spiteoftheterriblereturnsofthisassetclassfortheperiod.
APossibleException
Oneplacewhereindexingseemstofail,evenafteralloftheabovefactorsaretakenintoconsideration,istheareaofsmall-capgrowthstocks.Thesecompaniesarehighlyentrepreneurial,rapidlygrowingaffairs,andtherearedatatosupportthenotionthat
resourcesspentonresearchingthesecompaniesmaymorethanpayforitself.Anotherreasonmaybethatthesestocksoftenexhibitconsiderableprice“momentum.”Asmall-capindexingstrategywouldofnecessitysellthemostrapidlyappreciatingstocksastheygrewbeyondtheindex’ssizeborders,wheninfactthesearethecompanieswiththehighestreturnsgoing
forward.Aswe’lldiscussfurther
alonginthischapter,small-capgrowthstockshavepoorlong-termreturns,anditisprobablywisetoavoidinvestinginthisarea,activeorindexed.
SurvivorshipBias
Thedeeperonedelves,theworsethingslookforactively
managedfunds.ConsiderforamomentwhathappenswhenyouopenupthequarterlyNewYorkTimessupplementandstartsamplingfundperformanceoverthepast10years.Youmightthinkthatyou’regettingafairlyaccuratepictureofhistoricalfundperformance.Andyou’dbewrong.Thatisbecausewhatyou’relookingatisnottheperformanceofallofthe
fundsinexistenceoverthepastdecade,butonlytheonesthatsurvived.Inotherwords,theveryworstfundsinthegroupgotkilledoff(ormorelikely,mergedwithotherfunds),soyouarelookingatanoverlyoptimisticpictureofoverallfundperformance.BurtonMalkiel,authorof
ARandomWalkDownWallStreet,haslookedatthisprobleminsomedetail,and
heestimatesthattheeffectisontheorderof1.5%.Inotherwords,thereportedperformanceoftheaveragefundcategoryisabout1.5%higherthanthatofthetruecategoryperformance.Andit’salmostcertainlyhigherforsomefundcategories,particularlysmallstocks,whereitmaybeasmuchas3%.Thisisnotasmallpoint.IscreenedtheMorningstarPrincipiadatabase
(November1999)fordomesticsmall-capfunds.Ifound213withafive-yeartrackrecord,withanaverageannualizedfive-yearreturnof12.19%.Theindexfundsinthecategoryhadonlyslightlyhigherreturns(VanguardSmallCapFund,13.64%;DFA9-10SmallCompanyFund13.10%).Soyoumightormightnotbeimpressedwiththeirperformance.ButMorningstar’sdatabase
containsonlysurvivingfunds,soit’slikelythatthetrueaverageannualizedreturnforthegroupisactuallyinthe9%–10%range.Inwhichcasetheindexfundshavedoneverywellindeed.
DoYouPayTaxes?
IfthecaseI’vepresentedforindexingisnotpowerfulenough,thenconsiderthe
effectoftaxes.Whilemanyofusholdfundsinourretirementaccounts,wheretaxabilityofdistributionsisnotanissue,mostinvestorsalsoownfundsintaxableaccounts.Whileitisprobablynota
goodideatoownactivelymanagedfundsingeneral,itisatrulyterribleideaintaxableaccounts,fortworeasons.First,becauseof
theirhigherturnover,activelymanagedfundshavehigherdistributionsofcapitalgains,whicharetaxedatyourcapitalgainsrateatboththefederalandstatelevel.Anindexfundallowsyourcapitalgainstogrowlargelyundisturbeduntilyousell.Thereisanotherfactorto
consideraswell.Mostactivelymanagedfundsareboughtbecauseoftheir
superiorperformance.Butaswe’vedemonstratedabove,thisoutperformancedoesnotpersist,andmostsmallinvestorsusingactivefundmanagerstendtoturnovertheirmutualfundsforthisreasononceeveryseveralyears,generatingmoreunnecessarycapitalgainsandresultanttaxes.Forthetaxableinvestor,indexingmeansneverhavingtosayyou’resorry.
Acaveataboutsmall-capindexingandtaxes.Small-capindexfunds(bothforeignanddomestic)tendtohavehigherturnoversthanlargeforeignanddomesticindexfunds.Evenworse,theygeneratehighcapitalgainsdistributionsproportionatetotheirturnover,sincetheprimaryreasonforsellingastockisalargepriceincrease,resultinginthatstock’s“graduating”outoftheindex.
Forthisreason,theymaynotbesuitablefortaxableinvestors.Fortunately,“taxmanaged”small-capandlarge-capindexfundsarenowavailable.Thesestrivetominimizedistributions,andmorewillbesaidabouttheminChapter8.Asmutualfundshave
becometheprimaryinvestmentvehicleofsmallinvestors,theyhavecometo
manageevermoremassiveamountsofcapital—about$5trillionatthetimeofthiswriting.Buttherealmoneyismanagedbypensionfunds—abouttwiceasmuch.TheInvestmentCompanyInstituteestimatesthatin1998only7%ofmutualfundassetswereindexed,versus34%ofthepensionassetsofthe200largestU.S.corporations.
Itshouldcomeasnosurprisethattheworld’sbiggestmoneymanagershaveembracedindexing.Theworldofpensionmanagementiscomplex.Therearefourbasicplayershere,andit’susefultosurveythescene.Thefirsttwoarethepensionfundsponsors(thecorporationsthemselves)andtheiremployeesandbeneficiaries.Nextarethepensionfundmanagers.The
competitionforpensionfundinvestmentmanagementslotsisunbelievable.Althoughthesemanagersarepaidonlyafewbasispointsofmoneymanaged,0.02%of$10billionannuallyain’tchumpchange.Underperformthebenchmarkformorethanafewquartersand“you’retoast.”Lastarethepensionconsultants.Theirprimaryfunctionistogooutandfindthe“best”ofthesemoney
managersforthepensionsponsors.Bynow,youknowhow
thismovieends.Almostnoneofthesemanagersinrealityhasevenadropofskill.Likeourmutualfundmanagers,theyarejustonemoretribeofhairyapesthrowingprojectilesatastocklist.Somewillgetluckyandattracttheattentionofthepensionconsultants,whowill
sellthemtothesponsors.Followingwhichthelawsofprobabilitytakeoverandtheyunderperform,getsacked(perhapsalongwiththepensionconsultantthatfoundthem),andthecyclestartsagain.Thisisoneexpensivemerry-go-round—approximately1%of$10trillionoftotalpensionexpensesannually,or$100billion.
Ontheaverage,thesepensionfundsholdabouta60/40stock/bondmix.ConsultingfirmPiscataquaResearchfoundthatfortheperiod1987–1996only8%ofthenation’slargestpensionplansactuallybeatanindexed60/40mix.So,onebyonethelight
bulbsgoonoveratthepensionfundsponsors,outgothestockpickers,andin
manycaseseventhepensionconsultantsthemselves.Itseemshighlylikelythatinthenextdecademostpensionmoneywillbeindexed.Andsoshouldyours.
InvestmentNewsletters
OK,sohumanbeingscannotpickstocks.Perhapsamorefruitfulapproachwouldbetotimethemarketandavoidlossesbypullingoutofstocks
duringthebearmarkets.Maybeinvestmentnewsletterwriters,whosespecialtythisis,mighthelpusdobetter.JohnGrahamandCampbellHarvey,twofinanceacademics,recentlyperformedanexhaustivereviewof237newsletters.Theymeasuredtheabilityofthesenewsletterstotimethemarketandfoundthatlessthanone-quarteroftherecommendationswere
correct,muchworsethanthemonkeyscoreof50%.Evenworse,therewerenoadvisorswhosecallswereconsistentlycorrect,althoughthereweremanywhowerewrongwithamazingregularity.Theycitedoneverywellknownadvisorwhosepredictionsproducedanastoundingannualized5.4%lossduringa13-yearperiodwhentheS&P500produceda15.9%gain.Astonishingly,thereisevena
newsletterwhichrankstheperformanceofothernewsletters;itspublisherbelievesthathecanidentifypersistentlyexcellingadvisors.TheworkofGrahamandHarveysuggeststhatinrealityheisactuallythejudgeatacoin-flippingcontest.Whenitcomestonewsletterwriters,rememberMalcolmForbes’famousdictum:theonlymoneymadeinnewslettersisthrough
subscriptions,notfromtakingtheadvice.Notedauthor,analyst,and
moneymanagerDavidDreman,inContrarianMarketStrategy:ThePsychologyofStockMarketSuccess,painstakinglytrackedexpertopinionbackto1929andfoundthatitunderperformedthemarketwith77%frequency.Itisarecurringthemeofalmostall
studiesof“consensus”or“expert”opinionthatitunderperformsthemarketaboutthree-fourthsofthetime.Mr.Dremanarguesthatthisisapowerfulargumentagainsttheefficientmarkethypothesis:howcanthemarketsbeefficientwhentheexpertslosewithsuchdepressingregularity?Allofthisevidencefalls
undertherubricofwhatis
knownasmarketefficiency.Adetaileddiscussionoftheefficientmarkethypothesisisbeyondthescopeofthisbook,butwhatitmeansisthis:it’sfutiletoanalyzetheprospectsforanindividualstock(ortheentiremarket)onthebasisofpubliclyavailableinformation,sincethatinformationhasalreadybeenaccountedforinthepriceofthestock(ormarket).Cognoscentifrequently
respondtonewsaboutacompanywithaweary,“It’salreadybeendiscountedintothestockprice.”Infact,averygoodargumentcanbemadethatthemarketmoreoftenthannotoverreactstoevents,fallingtoomuchonbadnewsandrisingtoomuchongoodnews.Thecorollaryoftheefficientmarkethypothesisisthatyouarebetteroffbuyingandholdingarandomselection,oraswe
haveshownabove,anindexofstocksratherthanattemptingtoanalyzethemarket.Iamcontinuallyamazedat
theamountoftimethefinancialandmassmediadevotetowell-regardedanalystsattemptingtodivinethemovementsofthemarketfrompoliticalandeconomicevents.Thisisafool’serrand.Almostalwaysthese
analystsaretheemployeesoflargebrokeragehouses;onewouldthinkthattheseorganizationswouldtireoflookingfoolishonsoregularabasis.(Ifyouarenotconvincedofthefutilityoftryingtopredictmarketdirectionfromeconomicconditions,thenconsiderthatthebiggestmoneyismadebybuyingwhenthingslookthebleakest:1932,1937,1975,and1982wereallgreattimes
tobuystocks.Thenconsiderthatthemostdangeroustimestobuyorownstocksiswhenthereisplentyofeconomicbluesky;thosewhoboughtin1928,1936,or1966weresoonsorry.)Intheend,itiseasyto
understandwhytheaggregateeffortsofallofthenation’sprofessionalmoneymanagersfailtobestthemarket:Theyarethemarket.
DealingwithMr.Market
ThereisasmalltownnotfarfromwhereIlivewhichhasonlyonestore.Anownerofthestore,whodiedmanyyearsago,hadamanic-depressivedisorder.Oneweekhewouldbeinthemanicphase,cheerfulandexpansive,andduringtheseperiodswouldmarkupthepricesofhisgoods.Thenextweekhemightbecome
depressedandwouldmarkdownprices.Thetownspeoplelearnedtostockupduringhisdepressedperiodsandbuyonlywhatwasnecessarywhenhewasmanic.Thefinancialmarketsareaboutasrationalasthisstoreowner,andtheintelligentinvestorstocksupwhenpricesarelowandlightensupwhentheyarehigh.Itwouldbeverysillyindeedtomimicthemoodsof
ourstoreowner,andbuytomatoessimplybecausetheirpricewasrising.Yetthisseemstobewhatmostinvestors,especiallyprofessionals,do.Thissortofbehaviorisdeeplyingrainedinhumannature;nobodylikesbeingleftoutoftheparty.SomereaderswillnotethesimilarityofourstoreownertoMr.MarketfromBenGraham’sTheIntelligentInvestor.Ifyoureadonlyone
bookaboutstocks,thisshouldbeit;mybookisnamedinitshonor.Mr.Graham,infact,wrote
afamousarticleinawomen’smagazinemanydecadesagoinwhichhemadethesexistbutwiserecommendationthatstocksshouldbeboughtinthesamemannerasgroceries,andnotperfume.Hadheinsteadadvisedmentobuystocks
liketheybuygasoline,andnotliketheybuyautomobiles,hewouldhaveoffendedourtendermodernsensibilitiesless.Thetrickforthesmall
investor,then,istoknowjusthowmuchheorsheispayingforthosetomatoes.Youknowthattheyareabargainat25centsperpound;youknowyouarebeingrobbedat$3perpound.Buyingastock
oramarketsectorwithoutknowinghowcheaporexpensiveitisconstitutesthepinnacleoffoolishness.AsweshallseeinChapter7,determiningthecheapness(or“valuation”)ofamarketsectorisquiteeasy.
NotQuiteaRandomWalk
BynowIhopethatI’veconvincedyouthatmarketmovementsareessentiallya
“randomwalk”—unpredictableineveryregard,makingstockselectionandmarkettiminganimpossibility.Itturnsoutthatmarketmovementsarenottotallyrandom,andalthoughitisnearlyimpossibletoprofitfromthisbehavior,itstillbehoovestheinvestortobeawareofmarketpatterns.Inordertodothis,wehavetobeclearaboutwhatwemeanbythetermrandomwalk.
Thismeansthatyesterday’s,lastmonth’s,orlastyear’smarketreturnconveysnoinformationaboutfuturereturns.Isthisstrictlytrue?Toanswerthisquestionwe
firsthavetoaskhowonegoesaboutlookingfornonrandombehavior.Therearedozensofwaystodoso,butthesimplestistolookfor“autocorrelations”inpricechanges.Whatwearein
effectaskingis,“Doesthepricechangefromthepreviousday,week,month,year,ordecadecorrelatewiththepricechangeofthesucceedingday,week,month,year,ordecade?”Let’stakethemonthly
returnsfortheS&P500fromJanuary1926toSeptember1998.That’s873months.Thencreatetwoseparateseries,thefirstwiththefirst
returneliminated,thesecondwiththelastreturneliminated.Whatwenowhavearetwoseriesof872monthlyreturns,offsetbyonemonth.Thankstothemagicofmodernspreadsheets,itisasimplemattertocalculateacorrelationcoefficientofthesetwoseries.Theoutputofthiscorrelationofareturnsserieswithalaggedversionofitselfiscalledan
autocorrelation.Apositiveautocorrelationmeansthataboveorbelowaveragereturnstendtorepeat,ortrend.The“momentum”ofagivenassetclassorsecurityisdefinedbyapositiveautocorrelation.Anegativeautocorrelationdefinesso-calledmeanreversion,meaningthatanabove-averagereturntendstobefollowedbyabelow-averagereturnandviceversa.And
finally,azeroautocorrelationdefinesarandomwalk.Itturnsoutthatthe
autocorrelationoflargestocks’monthlyreturnsfor1926through1998is.081.Notterriblyimpressive,butpositivenonetheless,meaningthatagoodreturnthismonthmeansaslightlybetterthanaveragechanceofagoodreturnnextmonth.Whataretheoddsthatthis
couldhavehappenedbychance?Inordertodeterminethis,wehavetocalculatethestandarddeviationofautocorrelationsforadataseriesof873randomdatapoints.Theformulaforthisis
,whichfor873is.034.Thus,theautocorrelationof.081ismorethantwicetherandom-walkstandarddeviationof.034.Thisinturnmeansthat
theoddsofthisoccurringwith873randomnumbersislessthan1in100.So,yes,U.S.security
pricesappeartoexhibitsomemomentumoverperiodsofonemonth.Anicesummationofthe
autocorrelationdataforU.S.stocksisfoundinCampbell,Lo,andMacKinlay’s(CLM)TheEconometricsofFinancialMarkets.The
followingtablesummarizestheirautocorrelationdatafor1962through1984.Thevalue-weighted(alsoknownastheCRSP1–10Index)andequallyweightedindexescanbeveryroughlythoughtofaslarge-stockandsmall-stockproxies,respectively.
Thisdataprettyconclusivelydemonstratesmomentumeffectsofhighstatisticalsignificanceforanindexoflargestocksfromdaytoday,butnotforlongerperiods.Anindexofsmall
stocksdoesdemonstratemomentumoverdays,weeks,andmonths.(Iwouldn’tgettooexcitedoverthe.350autocorrelationforsmallstocksfordailyperiods.Rememberthatmanyofthesesecuritiesdonottradeeveryday,sothatabigmarketmoveupordownonedaywillbefollowedbyappropriatemovesinensuingdaysinthestocksthatdidnottrade.)
ItisratheramazingthatwhenCLMlookedformomentuminindividualstocks,nonewasfound.Inotherwords,thegenerationsofinvestorswhohavebeengazingatstockpricechartslikelyhavebeenwastingtheirtime,buttherecentphenomenonofchartingmutualfundpricesmayhavesomevalidity.CLMexplainthisapparentparadoxbynotingthattherearehighly
significant“crossautocorrelations”betweenlargeandsmallstocks,meaningariseorfallinlargestocksisusuallyfollowedbyariseorfallinsmallstocks.
WhatItAllMeans
OK,somovementsarenotcompletelyrandom.Howdoesthisdataaffecttheaverageinvestor?Onlyatthemargins.Lestwegettoo
carriedaway,themostimpressiveautocorrelationswe’veencounteredareinthe.2range.Thatmeansthatnomorethan4%(.2squared,orR-squared)oftomorrow’spricechangecanbeexplainedbytoday’s.Thatdoesn’tbuyalotofyachts.Forthetaxableinvestor,thisstuffistotallyirrelevant—whateveradvantagethereistothistechniqueisobliteratedbythecapitalgainscapturefrom
buyingandsellingwiththehighfrequencynecessitatedbymomentumtechniques.Certainly,however,these
effectscannotbeignored.Forthetax-shelteredassetallocator,themessageisloudandclear:Donotrebalancetoofrequently.Ifasset-classpriceshavea
tendencytotrendoverrelativelylongperiods(saymonths,orevenonetotwo
years)thenrebalancingoverrelativelyshortperiodswillnotbefavorable.Thisisasomewhattrickyconcept.Assetvariance(whichisthesquareofthestandarddeviation)isoneofthemainenginesofrebalancingbenefit.Ifanassethasmomentum,thentheannualizedvarianceswillbegreateroverlongperiodsthanovershortperiods—thisisinfactagoodwaytotestfor
momentum.ThinkabouttheJapanese
andU.S.markets.Bothhaveexhibitedprettyimpressivemomentum(inoppositedirections)since1989.Obviously,rebalancingaslittleaspossiblefromtheU.S.toJapanwouldhavebeenmoreadvantageousthandoingitfrequently.Yetanotherwayof
thinkingaboutthisisthe
followingparadigm—rebalanceonlyovertimeperiodswheretheaverageautocorrelationofyourassetsiszeroorless.Inpracticalterms,thismeansrebalancingnomorethanonceperyear.
Yin,Yang
Ratherthanbeingpolaropposites,momentuminvestingandfixed-assetallocationwithcontrarian
rebalancingaresimplytwosidesofthesamecoin.Momentuminforeignanddomesticequityassetclassesexists,resultinginperiodicassetovervaluationandundervaluation.Eventuallylong-termmeanreversionoccurstocorrecttheseexcesses.Over2decadesago,
EugeneFamamadeapowerfulcasethatsecurity
pricechangescouldnotbepredicted,andBurtonMalkielintroducedthewords“randomwalk”intothepopularinvestinglexicon.Unfortunately,inatrulyrandom-walkworld,thereisnoadvantagetoportfoliorebalancing.Ifyourebalance,youprofitonlywhenthefrogsinyourportfolioturnintoprinces,andviceversa.Intherealworld,
fortunately,therearesubtledeparturesinrandom-walkbehaviorthattheassetallocator-investorcanexploit.WriterandmoneymanagerKenFishercallsthischangeinassetdesirability,andtheresultantshort-termmomentumandlong-termmeanreversion,the“WallStreetWaltz.”Asmuchasitpainsmeto
admitit,momentumexists.
Understandingwhatitmeansforrebalancingandassetbehaviorwillmakeyouabetterassetallocator.
Summary1.Moneymanagersdonotexhibitconsistentstock-pickingskill.
2.Nobodycantimethemarket.
3.Becauseof1and2,itis
futiletoselectmoneymanagersonthebasisofpastperformance.
4.Becauseof1,2,and3,themostrationalwaytoinvestinstocksistouselow-costpassivelymanagedvehicles,i.e.,indexfunds.
7OddsandEnds
Noinvestmentguideiscompletewithoutadiscussionofcertainancillarytopics.Nowthatyou’vemasteredthebasicsofasset-classbehaviorandportfolioconstruction,we’lltiethingstogetherwithatreatmentofthefollowing
areas:valueinvestingandthethree-factormodel,“newera”investing,hedging,dynamicassetallocation,andbehavioralfinance.
ValueInvesting
Isitpossibletobeatthemarketinthelongrun?IhopebynowthatIhaveconvincedyouotherwise.Abetterquestioncanbeasked:Aretheremarketsegments
andsubsegmentsthatoutperformorunderperformrelativetotheirrisk?Examplesofthishavealreadybeenpresented;thelong-termreturnofpreciousmetalsandother“hardassets”(collectibles,preciousstones)istriflingcomparedtotheirveryhighrisk.Moresubtly,theriskofowninglong-termbondsismuchhigherthanthatofshort-termbonds,yettheirreturnsarethesame.
Arethereanycharacteristicsofstocksthatpredicthigherorlowerexpectedreturn?Wearealreadyawareofone:companysize.Aswehaveseen,smallstocksoutperformlargestocksinthelongrun.Unfortunatelythiscomesatthecostofhigherrisk.Stocksoutperformalmost
allotherassetsinthelongrunbecauseyouarebuyingapieceofouralmost
constantlygrowingeconomy.Thinkofallthetechnologicaladvancesofthetwentiethcenturyandthewealththeyhavecreated:airtransport,radio,television,automobiles,consumerelectronics,andcomputers.Youbenefitfinanciallyfromthesewondersbyowningstock,notT-billsorcorporatebonds.Sofar,sogood.Unfortunately,investorsthenmakeafatalextrapolation:
thatthemostprofitablestockstoownmustbethoseofthemostrapidlygrowingcompanieswiththehottestproducts.Theseareknownas“growthcompanies.”Akeyinvestmentconcept
isthatof“valuation,”i.e.,howtotellwhenanindividualstockorstockmarketisexpensiveorcheap.(Itisamuchsimplermattertotalkaboutthevaluationof
thestockmarketasawholeorofanindividualmarketsector.)Therearethreecommonly
usedmeasuresofindividualstockorofaggregatestockmarketvalue:price/earnings(P/E)ratio,price/book(P/B)ratio,anddividendyield.Ultimately,youarebuyingastockinordertoownapieceofitsearnings.P/Edescribeshowmuchyouarepayingfor
thoseearnings.SayXYZMultimedia,Inc.earns$5pershareandsellsfor$100pershare.IthasaP/Eratio(alsocalledthemultiple)of20;youarepaying$20foreach$1ofearnings.AcompanysellingataP/Eof30issaidtobeexpensive,andonesellingataP/Eof10issaidtobecheap.Unfortunately,companyearningsarenotparticularlystable.Quitefrequentlytheearningsof
eventhelargestandmoststablecompaniesdisappearentirely,andonrareoccasionsnetcorporateprofitsdisappearfortheentireU.S.stockmarket.(ThishappenedforaprolongedperiodduringtheGreatDepressionandforabriefperiodduringtheearly1980s;thelossessustainedbymanylargeU.S.corporationsexceededtheprofitsoftherest,resultinginanetlossfor
U.S.industryasawhole.)Further,itiseasyforcorporateaccountantsto“fiddle”withreportedearningstothepointwheretheyaremeaningless.Forthisreason,P/Ehasonlylimitedvalue.BenGrahammadetheastuteobservationthatcorporateearningsprovideusefulinformationonlywhenaveragedoverseveralyears.Allcompanieshaveabook
value;thiscanbethoughtofasthenetvalueofacompany’stotalassets,althoughtheaccountingrealityofthisnumberismuchmorecomplex.Itisaroughnumber.Thebookvalueofanairlineiseasilyunderstood;itisprimarilythevalueofitsplanes,buildings,andofficeequipment,minusitsliabilities.Let’sassumeABCAirlinesownsassetsvaluedat$2billionand
liabilitiesof$1billion,resultinginnetassetsof$1billion;let’sfurtherassumethatthevalueofallofitsoutstandingstockis$2billion.ItsP/Bratiois2;itissellingfortwiceitsbookvalue.AstockwithaP/Boflessthan1issaidtobecheap;onewithaP/Bofmorethan5issaidtobeexpensive,atleastrelativetoitsbookvalue.Thebookvalueofastockisvery
stable;corporateaccountantsusuallyhavenoneedtofudgethisnumber.Finally,thereisdividend
yield.Thisiseasytounderstand—itissimplytheamountofdividendremittedtotheshareholdersdividedbythepriceofthestock.IfXYZMultimedia,Inc.sellsfor$100pershare,earns$5pershareandremits$3ofthistotheshareholders,then
thedividendyieldis3%.Itispossibleforacompanytopaymoreindividendsthanitsearnings,butitobviouslycannotdothisindefinitely.Smallorrapidlygrowingcompaniesfrequentlypaynodividendsatall;theyneedtoretainalloftheirprofitsinordertogrow.Untilveryrecently,large,slowlygrowingcompaniesoftenpaiddividendsinexcessof5%.
Wearenowcapableoftellinghowexpensivethetomatoesare.First,itisusefultoexaminetheP/E,P/B,anddividendyieldoftheentireU.S.stockmarket.Figure7-1plotstheP/Eofthemarketoverthepast73years.Weseethatthisnumberusuallyvariesbetweenabout7and20andaveragesabout14;infact,thenumbercanbemuchlargerthanthisifearningsarenear
zerobecausethedenominatorissosmall.WhenthemarketP/Eisabout7,itisdefinitelycheap;whenitisgreaterthan20,itisexpensive.
Figure7-1.Price/earningsratio,1926–1998.
Figure7-2plotstheP/Bofthemarket.Untilrecentlyithadvariedbetweenabout1(cheap)and3(expensive);itaveragesabout1.6.Recentlyithasballoonedtoabout8.Becauseoftherecentdata,somehavequestionedthevalidityofthismeasureof
expensiveness.
Figure7-2.Price/bookratio,1926–1998.
Figure7-3plotsdividendyield.Historicallyithasvariedbetween2.5%(expensive)and7%(cheap);itaveragesabout4.5%.Thehighertheyield,thecheapertheprice;thelowertheyield,thehighertheprice.Again,currentlystocksyieldahistoricallylow1.3%,and
manyquestionitsusefulnessaswell.
Figure7-3.Stockdividendyield,1926–1998.
SoliddataontherangesofP/E,P/B,anddividendyieldareavailableonlyforthelargestU.S.stocks.ForsmallerU.S.stocks,thedataaremorefragmentary,buttherangesofP/EandP/Baresimilar;dividendyieldsareconsiderablysmaller.
Valuationofforeignstocksishighlyproblematicbecauseofthedifferencesinaccountingstandardsamongnations;nonetheless,therangesofP/BofmostoftheEAFEnationsseemsimilartothatoftheUnitedStates.Weshallseethatlong-term
returnsareusuallyhigherwhenvaluationsarecheapandlowerwhentheyareexpensive.Whetherthisisof
anypracticaluseisopentoquestion.Atanyonetime,some
individualstocksarecheaperthanothers.Isitusefultopurchasecheapstocksinpreferencetoexpensiveones?Thereisaverylargevolumeofdatathatanswersthisquestionresoundinglyintheaffirmative.
StudiesonValueInvesting
Thefirststudyofbuyingcheapstockuseda“DowP/Estrategy,”similartotherecent,morepopularDowdividendstrategydescribednext.In1964PaulMiller,headofresearchatDrexel&Co.,examinedbuyingthe10lowestP/EstocksoftheDow30.Hepublishedamemoranduminwhichhesummarizedtheresultsofthistechniqueforthe28yearsfromJuly1936toJune1964
(Table7-1).
TABLE7-1.Value-StockPerformance,1936–1964
Mr.Miller’sdatawascollectedinaslightlyunusual
manner.First,heusedJulytoJunefiscalyears.Second,thereturnstatisticusedwaspricechangeonly;thisdoesnottakereinvesteddividendsintoaccount.Addinginreinvesteddividendswouldresultinactualreturnsofabout5%higher.Thesedataareclear-cut:ThelowestP/Estocks(theonesthateverybodyhates)greatlyoutperformedthemarket,andthehighestP/Estocks(theonesthat
everybodyloves)greatlyunderperformedthemarket.Doesthisextrareturncomeathigherrisk?Thishypothesisissupportedbythestandarddeviationand“worstannualloss”data,whicharegreaterforthelowP/EstocksthanforthehighP/EstocksandthewholeDowJones30.ThehigherSDofthelow-P/Estocksismostlyduetotheverylargegainsregisteredbythemin
severalyears.Thelow-P/Estocksareactuallytheleastriskywhenlookedatfromtheperspectiveofthetotalnumberoflosingyearsoroflossesgreaterthan10%.Investorsareincreasingly
seekinghigherreturnswithvaluestocks,butlet’stakeastepbackandseewhatthismeansinactualpractice.Perhapsthemostcurrentlypopularmethodistheso-
calledDowdividendstrategy,whichbuysthefivehighest-yieldingDowstocks.I’velistedthefivehighest-yieldingandlowest-yieldingstocksatthetimeofthiswriting:
Mostreaderswillrecognizethehigh-yielding(cheap)groupas“terrible”companies,andthelow-yielding(expensive)as“good”companies.Probablythemost
impressiveworkinthisareawasdonebyProfessorsFamaandFrench,publishedintheJournalofFinanceinJune1992.TheyexhaustivelystudiedstockreturnsfromJuly1963throughDecember1990andfoundthatallofthevariationinreturnamongstockscouldbeexplainedbyjusttwofactors:companysize(nosurprisehere)andP/B.Theydividedtheirstockdatabaseinto10groups
rangingfromthelowestP/B(cheapest)tothehighestP/B(mostexpensive).Thecheapestone-tenthofthemarketreturned19.6%annually,andthemostexpensivetenth,7.7%annually.Thesmallestcheapeststocksreturned23%annually.TheyalsofoundP/Euseful,butnotnearlyasusefulasP/B.AftertakingP/Bintoconsideration,P/Ehadnopredictivevalue.
AreBenGraham,Fama,French,andalegionofothersalltellingusthatweshallprofitbybuyingbadcompanies?Yes.Badcompaniesarecheap;itisquitepossiblethatmanagementwillturnthecompanyaroundandmakethembackinto“good”companies.Further,evenifabadcompany’sperformanceworsens,itwillnotsurprisetheinvestmentworld;the
pricewillprobablynotdropallthatmuch.Ontheotherhand,goodcompaniesareexpensive;theyareexpectedtogrowtothesky.When,asinevitablyhappens,theystopgrowingtothesky,theyaretakenoutandshotbythemarket.DavidDremanhasbeautifullydocumentedthisphenomenon.Thelargestmovementsinacompany’spriceusuallyoccurwhenitsearningseithergreatlyexceed
orfallshortofanalysts’expectations.(Notethatintheshorttermitmatterslittletothepriceofastockwhetheritsearningsarehigh,low,ornegative.Whatreallymattersiswhethertheyarehigherorlowerthanthe“Street”anticipates;bettertohavealossforthequarterwhichislessthantheStreetexpectsthantohavegreatearningswhicharelessthantheStreetexpects.)Dreman
hasobservedthat“value”stockstendtofallmuchlessinpricethan“growth”stockswhenearningsdisappoint.Conversely,“value”stockstendtorisemoreinpricethan“growth”stockswhenearningsexceedexpectations.Torepeat:
Goodcompaniesaregenerallybadstocks,andbadcompaniesare
generallygoodstocks.
Thisconceptisveryhardforbothsmallinvestorsandprofessionalstograsp,andprobablyunderliesthepoorperformanceofmostprofessionalmoneymanagers.Nomatterhowmanyfinancejournalstheyread,theycannotbringthemselvestobuybad
companies.Probablythemostvivid
exampleofthegoodcompany–badstockparadigmwasprovidedbythepopular1982bookInSearchofExcellence,bymanagementguruTomPeters.Heidentifiednumerous“excellent”companiesusingseveralobjectivecriteria.Severalyearslater,MichelleClayman,afinanceacademic
fromOklahomaStateUniversity,examinedthestockmarketperformanceofthesecompaniesandcompareditwithamatchedgroupof“unexcellent”companiesusingthesamecriteria.Forthefive-yearperiodfollowingthebook’spublication,theunexcellentcompaniesoutperformedtheexcellentcompaniesbyanamazing11%peryear.Asyoumightexpect,the
unexcellentcompanieswereconsiderablycheaperthantheexcellentcompaniesbyP/E,P/B,anddividendcriteria.Peoplenaturallyassumethatgoodcompaniesaregoodstocks,whentheoppositeistruemostofthetime.Psychologistsrefertothissortofsyllogisticerroras“representativeness.”Ithaslongpuzzled
academicefficient-market
theoriststhatthesepopularstrategies(lowP/E,lowP/B,highdividend)haveworkedsowellforsolong.Theyaresowell-knownthatenoughpeopleshouldusethemsothattheiradvantageshouldvanish.Thereasonwhythesestrategiesstillwork,decadesaftertheyweredescribedissimple:Cheapcompaniesaredogs,andmostpeoplecannotbringthemselvestobuythem.BenGrahamwrote
SecurityAnalysis50yearsago,whichisbasicallyaprimeronhowtoidentifycheap,safestocks.BenGraham’sdisciplesareamongthemostsuccessfulmoneymanagersintheUnitedStates.Oneofthem,WarrenBuffett,isoneofthewealthiestmenintheworld.Byallrights,Graham’smethodshouldhavelongsincestoppedworking,butitcontinuestowork.
EverybodywantstoownAmazon.com,Microsoft,Intel,andAOL.NoonewantstobuyWoolworth’s.
ValueversusGrowth
Lookingforcheapstocksiscalledvalueinvesting.Theoppositeofthisisgrowthinvesting,lookingforcompanieswithrapidlygrowingearnings.Althoughtherecertainlyaresomevery
successfulgrowth-stockinvestors,theyhavebeenswimmingupstream.Youaremorelikelytoswimfasterifyouheaddownstream.Efficient-markettheorists
arefondofpointingoutthatthereisnopatterntostockormarketprices.(Aswehavealreadyseen,thisisnotstrictlytrue.)Growth-stockinvestorsbelievethattheycanpickthosecompanies
whichwillhavepersistentearningsgrowthandthusreapthebenefitsoftheirever-increasingearningsstream.Unfortunately,establishedgrowthcompaniesareveryexpensive,oftensellingatP/Estwoorthreetimesthatofthemarketasawhole.Acompanygrowing5%fasterthantherestofthemarketandsellingataP/Etwicethemarket’swillhaveto
continuegrowingforanother14yearsatthatratebeforetheshareholderisfairlycompensated.Aswe’vealreadyseen,stockpricemovementsareessentiallyanunpredictable“randomwalk.”Interestingly,itturnsoutthatearningsgrowthalsoexhibitsrandom-walkbehavior;acompanywithgoodearningsgrowththisyearisquitelikelytohavepoorearningsgrowthnext
year(andviceversa).Inotherwords,thisyear’sgrowthstockisquitelikelytobecomenextyear’svaluestock,atgreatcosttoitsshareholders.Contrariwise,avaluestockwithpoorearningsgrowthwillfrequentlysurprisethemarketwithstrongearningsgrowth,withanagreeablechangeinP/Eandprice.Thistypicallyhappenstoonlyafewstocksinavalue
portfolioinagivenyear,buttheeffectsontotalportfolioperformancearestilldramatic.Perhapsthemostlucid
explanationofthevalueeffectcanbefoundinRobertA.Haugen’sTheNewFinance:TheCaseAgainstEfficientMarkets.ProfessorHaugenpointsoutthatinmid-1993the20%ofstockswiththehighestP/E(growth
stocks)hadanaverageP/Eof42.4.Thisresultedinanearningsyieldof2.36%.(TheearningsyieldissimplytheinverseoftheP/E—it’stheamountofearningsyou’rebuyingforeachdollarofstock.)Thelowest20%(valuestocks)hadaP/Eof11.93,oranearningsyieldof8.38%.Inotherwords,whenyouboughttheglamorousgrowthstocksinmid-1993,youweregetting$2.36in
earningsforeach$100invested;whenyouboughtthedoggyvaluestocks,youweregetting$8.38.Ifyouaretocomeoutaheadwithgrowthstocksinthelongterm,theirearningswillobviouslyhavetogrowoverthreetimeslargerthanthevaluestocks.Haugenthenfollowedtheearningsgrowthofthegrowthandvaluecohorts.Whilethegrowthstocks,asexpected,
experiencedhigherearningsgrowth,thisadvantagedecayedovertime,andtheirdollarearningsneversurpassedthoseofthevaluegroup.Infact,theyneverevengotclose;Haugenestimatesthateachdollarinvestedingrowthstocksleavesyouwithlessthanhalfofthelong-termearningsobtainablefromvaluestocks.Again,asBenGrahamsaid,intheshorttermthemarkets
areavotingmachine,butinthelongruntheyareaweighingmachine.Andwhattheyareweighingisearnings.Inapaperpublishedinthe
JournalofFinanceinDecember1994,JosefLakonishokandcolleaguesconfirmedearlierworkdemonstratingthesuperiorityoflowP/BandlowP/Estocks.Theyalsofoundthatsalesgrowthaffectedfuture
returns;themostrapidlygrowingcompanieshadthelowestreturns.AlthoughFamaandFrenchandLakonishokandcolleaguesallagreethatlowP/BandP/Estocksoutperformgrowthstocks,theydisagreeastowhy.FamaandFrencharedevout“efficientmarketeers,”andbelievethatthehigherreturnofvaluestocksmustbeduetosomesortofassociatedincreased
risk.They’vehadadifficulttimeexplainingtotheinvestmentcommunitytheprecisenatureofthisrisk,butitgoessomethinglikethis:Valuestocksaresickcompanies.Theyhaveweakprofitability,earningsgrowth,andbalancesheets.Aneconomicdownturnorevenaslightbreezemaybankruptthem.Becauseofthisincreasedrisk,theymustofferhigherreturns.Afterall,
ifbothKmartandWal-Martofferedthesamefuturereturn,whowouldwanttoownKmart?Ergo,valuestocksarebydefinitionnotafreelunch.Ontheotherhand,
Lakonishokandcolleaguesmaintainthatthehigherreturnsofvaluestockscomewithouthigherrisk,andthenpresentconvincingevidencethattheriskofvaluestocksis
lowerthanthatofgrowthstocks.Inotherwords,thereisafreelunch.WilshireAssociatespublishesdataofthereturnsofgrowthandvaluestockgroupingsofvariouscompanysizesfrom1978(oneofthemanygoodiesavailableintheMorningstardatabase).Foreachcompanysize,thevalueportfolioreturnsseveralpointsmoreannualizedperformancethanthesame
company-sizegrowthportfolio,withaconsiderablylowerstandarddeviation.Infact,itappearsthatvaluestocksseemtooutpacegrowthstockspreciselybecausetheyarelessrisky.Duringbullmarketsgrowthbeatsvalue,butduringbearmarketsvaluestockslosemuchlessthangrowthstocks.Attheendoftheday,thereturnsonvaluestocksmaybesuperiortogrowth
stockssimplybecauseoftheirmorebenignbear-marketperformance.
TheThree-FactorModel
Thealternativehypothesis,aswe’vealreadymentioned,isthatthereisnoexcessreturnwithoutincreasedriskexposure.ThistheoryisadvancedbyFamaandFrenchintheformoftheirthree-factormodel.This
simple,yetpowerfulconstructisextraordinarilyusefulinunderstandinglong-termreturnsinmarketsaroundtheglobe.Simplyput,anystockassetclassearnsfourdifferentreturns:
Therisk-freerate,thatis,thetimevalueofmoney.Usuallysetattheshort-termT-billrate.Themarket-riskpremium.Thatadditionalreturn
earnedbyexposingyourselftothestockmarket.Thesizepremium.Theadditionalreturnearnedbyowningsmall-companystocks.Thevaluepremium.Theadditionalreturnearnedbyowningvaluestocks.
Everyoneearnstherisk-freerate.SointheFama-
Frenchuniverse,theonlyimportantdecisionyouhavetomakeishowmuchexposureyouwanttotheotherthreefactors.Ifyou’reacompletecoward,youhavezeroexposuretoallthreeandownonlyT-bills.Andifyou’reahighlyrisk-tolerantindividual,youhavemaximalexposuretoallthreeandownonlysmallvaluestocks.Let’slookateachrisk
factorindividually.InFigure7-4,I’veplottedthetrailingfive-yearannualized“marketpremium”(thereturnoftheCRSP1-10Index—roughlytheWilshire5000—minustheT-billreturn)forthepast36years.Noticethatwhileithasbeenpersistentlypositiveforthepasttwodecades,thingswereagooddealrockierinthe1960sand1970s.Overtheentireperiod,thepremiumwas5.65%
annualized.Itcertainlywasn’tasurething,beingpositiveinonly78%oftherollingfive-yearperiods.
Figure7-4.Five-yearannualizedmarketpremium.
Isitpossibletobearmoreriskandthusearnstillhigherpremiums?Yes.Youcandecidetoinvestinsmallercompanies,whicharemorelikelytosuddenlydisappearthanlargeones.Forthepast36years,the“sizepremium”
(definedasthereturnofthesmallesthalfofcompaniesontheNYSEminusthelargesthalf)hasbeen1.71%.I’veplotteditinFigure7-5.Itsrollingfive-yearreturnhasbeenpositiveonly53%ofthetime.
Figure7-5.Five-yearannualizedsizepremium.
Last,thereisthethird,andmuchmorecontroversial,premium,whichI’veplottedinFigure7-6.AccordingtoFamaandFrench,ifyouarearealriskjunkieandwanttoincreaseyourpremiumpaymentsevenfurther,you
caninvestinvaluecompanies.Thesearethesickestpuppiesinthelitter.ThinkHarvester,Kmart,Nissan.Theyareidentifiedbytheirlowvaluations,suchasprice/bookratio.The36-yearpremiumforinvestinghere(definedasthereturnofthestockswiththelowestP/BratiosminusthereturnofthestockswiththehighestP/Bs)hasbeen3.77%annualized.Somewhat
surprisingly,asyoucanseeintheplot,thispremiumhasbeenfairlyconsistent,beingpositive87%ofthetime.Infact,thereliabilityofthevaluepremiumhascausedsometoquestionwhetherthisisnotreallyafreelunch,asopposedtoareal“riskstory.”
Figure7-6.Five-yearannualizedvaluepremium.
Thesethreeriskpremiums—market,size,andvalue—havebeenresearchedextensivelybyFamaandFrench.They,andothers,haveshowntheexistenceofallthreeintheU.S.marketoveraverylongtimeperiod,
aswellasinmanyothercountries.Arethereotherpremiums?Probably.Thereislikelyapremiumforinvestinginmomentumstocks.Thenatureoftheriskassociatedwithmomentum—ifany—hasyettobedetermined.Thethree-factormodelhas
anotheruse,whichwe’vepreviouslyencountered,andthatistheevaluationof
moneymanagers.Throughtheuseofsophisticatedstatisticaltechniques,itispossibletoattributejusthowmuchofamanager’sreturnscanbeaccountedforbyeachoftheriskfactors,andhowmuch,ifany,isduetoskill.Forexample,ifamanagerdoesparticularlywellinagivenperiod,itmaybebecauseheorshewasskillful(orlucky).However,itmayalsobebecausethemanager
wasexposedtoamarketfactorthathadhighreturns.Asyoumightalreadysuspect,itturnsoutthatmostoftheperformanceoftop-rankedmanagersisduetotheirfactorexposureandthatfew,ifany,ofthesetop-rankedmanagersactuallydemonstrateanythingwhichlookslikeskillinastatisticalsense.Ultimately,therewardsof
thecapitalmarketplacegotothosewhocanmostintelligentlybalancethethreeriskfactors,aswellastherisksoftheiremployment.Asmallexample:Employeesofcyclical,“value”companiesshouldbeparticularlywaryofvalueportfolios,asintheeventofasevererecessionboththeirjobprospectsandportfolioswillsufferdisproportionately.Workerswhotendtokeeptheirjobsin
hardtimes,likelettercarriersandrepomen,areinabetterpositiontoownvaluestocks.
InvestingintheNewEra
Theinvestmentclimateofthepastfiveyearshasbeensovastlydifferentfromthatofthepriordecadesthatadiscussionofourso-calledneweraiswarranted.Asthisbookisbeingwritten,stocksaresellingatvaluationsfar
higherthaneverbeforeseen.Dividendyieldsoflargestocks,whichtypicallyrangebetween3%and7%,arenow1.3%.P/Bratios,whichtypicallyrunbetween1and3,arenow8.Andstocksnowsellatabout30timesearnings,comparedtothehistoricalnormofbetween10and20.Argumentsastohowtheoldstandardsdon’tmatteranymore,andthatweareina“newera”attemptto
rationalizecurrentprices.So,hastheinvestment
paradigmpermanentlychanged?Aretheoldroadmarkersnowuseless?Investmentparadigmsdosometimesshift:In1958,forthefirsttimeinhistory,stockyieldsfellbelowbondyields,anddisasterwaspredicted.Noneoccurred(exceptforbonds!),andstockyieldsneveragainroseabovebond
yields.Andyet,itisdifficultto
argueagainstmathematicsandthelawsofgravity.In1958itcouldstillbepointedoutthatstockdividendsgrewovertime,whereasbonddividends,beingfixed,didnot.Soitisnotunreasonablethatbondyieldsshouldbehigherthanstockyields.Butthereisnogetting
aroundthefactthatinthe
longrunequityreturnsarecloselyapproximatedbythesumofthedividendrate,now1.3%,andtheearningsgrowthrate,historicallyabout5%.Addthesetogethertodayandyougetanexpectedstockreturnof6.3%.So,inordertojustifycurrentvaluationsonehastopostulatethatearningsanddividendswillbegintorisefasterthantheyhaveinthepast.
Nosuchthingseemstobehappening.GobacktoFigure2-11,whichplotsDowearningsoverthepast80years.Thetopsurfaceoftheplotistheplacetofocus.Fromtimetotime,recessionsanddepressionsproducesharpdownwarddeviationsinearnings,buttheuppersurfaceoftheplotrepresentsthe“fullcapacity”ofcorporateearnings.Doyouseeanacceleratingtrendthe
pastdecadeortwo?Ifyoudo,MulderandScullyarerightoutside,andtheyhavesomelittlegreenmenthey’dlikeyoutomeet.Oneoftenhearsthe
argumentthatwiththeacceleratingpaceoftechnologicalchange,U.S.companiesareonthevergeofdramaticallyincreasedprofitability.Abitofhistoricalperspectiveis
useful.Theperiodfrom1830to1860sawthearrivalofthetwomostdramaticallytransformativeinventionsinthehistoryofmankind—thesteamengineandthetelegraph.Withinafewshortdecades,thespeedofcross-countrytransportationincreasedbyalmostanorderofmagnitude.Cheapandreliablepowerbecameavailabletomanufacturersforthefirsttimeinhistory.
Long-distancecommunicationbecamealmostinstantaneous.Ofcourse,thepast30yearshavealsoseenwondroustechnologicalinnovation.However,considerthattodayreallyimportantnewsgetsfromNewYorktoSanFranciscoonlyslightlyfasterthaninGroverCleveland’stimeand,morelikelythannot,ittakesyouandmelongertotravelcrosstownor
crosscountrytodaythanitdid30yearsago.Ohyes,thereturnofU.S.equityfrom1830to1860was4.2%.Infact,we’veheardthe
new-eraargumentbefore—firstin1926–1929,theninthelate1960s.Onbothoccasions,theconventionalwisdomwasthattheoldmethodsofstockvaluationhadbecomeobsoleteandthatitwasacceptabletopay50or
100timesearningsforcompaniespoisedonthecuttingedgeoftechnologicalprogress.IcannotrecommendhighlyenoughBenGraham’sdescriptionofthenew-erastockmarketofthe1920sintherecentlyreprinted1934editionofSecurityAnalysis.Onedoesnothavetochangeverymanywordstogetavividdescriptionoftoday’smarketfrenzysurrounding
technologyandInternet-relatedearnings.Justchange“100timesearnings”to“100timessales”andyou’rethere.Finally,it’sworth
reflectingontherecentreturnsofsomeselectedassetclasses.Forthe10-yearperiodfrom1989to1998,thereturnoftheBarraLargeCapGrowthIndexwasanastonishing21.35%annualized;thelarge-cap
valueindex16.67%;for9–10decilesmall-capstocks,13.2%;andtheEAFEindex,offoreignstocks5.54%.Theexperienceofthepastdecadehasconvincedmanythatlarge-capstockshavehigherreturnsthansmall-capstocks,thatgrowthoutperformsvalue,andthatdomesticoutperformsforeign.Aswe’veseenfrommorecompletehistoricaldata,itislikelythatnoneofthese
assumptionsistrue.Forthosetemptedtoinvest
alltheirmoneyinMcDonald’s,Coke,Microsoft,andIntel,I’vecalculatedthegrowthof$1investedfromJuly1927toMarch1998forthemostextremequintilesofsmallvalue,smallgrowth,largevalue,andlargegrowthinFigure7-7.Theannualizedreturnswere17.47%for
smallvalue,2.18%forsmallgrowth,13.99%forlargevalue,and10.04%forlargegrowth.Onealwayshastobecautiousinterpretinghistoricaldata.First,theydonotincludethetradingexpensesdetailedearlierinChapter6.Second,thepre-1960sdataisextremelysketchyinplaces.
Figure7-7.Valueof$1investedJuly1927.(Source:KennethFrench)
Thatsaid,themessageisclear:Overthelongtermvaluebeatsgrowth,andsmallvaluemayverywellbeateverythingelse.Themiserablereturnsforsmallgrowthstockswillhopefully
comeasawake-upcalltothoseofyouconsideringinvestinginsmalltechnologycompanies.Recentreturnsinthisareahavenotbeenquitethatbad,withtherealdamagebeingsustainedinthepre-1960era.Butclearly,thisisanareatobewaryof.Infact,thepoorreturnsof
smallgrowthstocksaresomethingofamystery,astheyareevenlowerthan
academictheorywouldpredict.Myowntheoryisthatthereisa“lotteryticket”premiumbeingchargedtheseinvestors.Justaspeoplepurchaselotterytickets,whichhaveareturnofabout−50%,ontheoffchancethattheymaywinthegrandprize,sotoodoinvestorsinvestinsmall,rapidlygrowingcompaniesontheslimchancethattheyaregettinginonthegroundfloorofthenext
Microsoft.Inotherwords,thisassetclassmakesupinentertainmentvaluewhatitlacksinreturn.
TheNewParadigm:Dow36,000
Thenewerahasrecentlygottenapersuasiveboostfromthebestsellerlist.Writingintheop-edsectionofTheWallStreetJournal,
theAtlanticMonthly,andmorerecentlytheirbook,Dow36,000,journalistJamesGlassmanandeconomistKevinHassett(hereafterreferredtoasGH)contendthatthemarket,farfrombeinghistoricallyovervalued,isactuallyridiculouslyundervalued.NervousatDow11,000?Getoverit.Thisfearlessduoseesfairvalueatabout36,000.
Theirchosenvehicleisthevenerablediscounteddividendmodel(DDM),whichwehavealreadyencounteredinChapter2.Formulatedin1938byJohnBurrWilliams,itrestsonadeceptivelysimplepremise:Sinceallcompanieseventuallygobankrupt,thevalueofastock,abond,oranentiremarketissimplythevalueofallitsfuturedividendsdiscountedtothe
present.(InGH-speak,thisisreferredtoasthe“perfectlyreasonableprice,”orPRP.)Sinceadollaroffuturedividendsisworthlessthanadollartoday,itsvaluemustbereduced,ordiscounted,toreflectthefactthatyouwillnotreceiveitimmediately.Thisamountofreductioniscalledthediscountrate(DR).Andasweshallsoonsee,fiddlingevenalittlebitwiththeDRopensthedoortoall
kindsofmischief.Ifthismodellooks
complicated,itis.Foreachfutureyearyoutakethepresentdividend,multiplyitby(1+g)n,wheregistherateofdividendincreaseandnisthenumberofyearsinthefuture,andthendivideby(1+DR)n.Plus,youhavetocomputethisforaninfinitenumberofyears.Itcangetworse,withtwo-andthree-
stagemodelswithvaryinggrowthratesovertime.Butdon’tsweatthemath,becausewithaconstantgrowthratethewholeinfinitesequencesimplifiesto:
PRP=(div)/(DR−g)
where
IftheDowthrowsoffabout$150peryearindividends,andifyouoptimisticallyassume(asGHdo)thatdividendsaregrowingat6%peryear,thentheonlyothernumberlefttotossintotheaboveequationisthatpeskyDR.And
amazingly,throughoutmuchofthebookGHmaintainthattheappropriateDRistheTreasurybondrate,whichatthetimewas5.5%.BecausethegrowthrateisgreaterthantheDR,aninfinitevalueforthemarketresults(becauseinthiscasethediscounteddividendriseseachandeveryyear,adinfinitum),whicheventheyfindhardtoswallow.(Whattheauthorsmissedisthattheir6%
dividendgrowthratecoveredaperiodwheninflationwasaround4%–5%,whiletherecent5.5%rateforTreasurybondspresumablyreflectsaconsiderablylowerfutureinflationrate.)Solowerthedividendgrowthto5.1%,keeptheDRat5.5%,andabracadabra,theaboveequationyieldsDow37,500:
PRP=150/(.055−.051)=150/.004=37,500
Perfinanceconvention,thenumbersinthedenominatorareexpressedasdecimals,where.055referstotheDRof5.5%,and.051tothedividendgrowthrateof5.1%.Noticehowtinythedenominatorof.004isrelativetotheinputnumbers.Movebothofthenumbersinthedenominatorthewrongwaybyjust1%(.01)andyouhaveaDowPRPof6250.Andifthatdispleasesyou,
makeyourestimatesjustahairmoreoptimistic,andyougetaDowPRPofinfinity.Inotherwords,usingtheGHmodel,youcanmakethePRPoftheDowwhateveryouwantittobebymovingthediscountrateandgrowthrateasmidgenineitherdirection.TheGlassman-Hassett
modelisakintobalancinganelephantonafencepost:One
smallwobbleinthepostandseveralthousandpoundswilllurchinanunexpecteddirection.ThisisevidencedbyFigure7-8,whichshowstheDow’svalueusingtheGlassman-Hassettgrowthassumptionsoverarangeofdiscountrates.
Figure7-8.1999dividends=$150,growth=5.1%.
Toreiterate,thevalueoftheDRiscritical.Forexample,iftheactualDRis8%insteadof5.5%,thenfairvaluefortheDowfallsto5172.Oops.Thesamethinghappensifthedividendgrowthestimateisoff.As
alreadymentioned,the6%dividendgrowthofthepasttwodecadesincludedover4%ofinflation.Inotherwords,realgrowthwaslessthan2%.Sothedividendgrowthrategoingforwardmaybequiteabitlowerthanithasbeeninthepast.Decreasingdividendgrowthby2.5%hasthesameeffectasincreasingtheDRbythesameamount—Dow5172.
SowhatdeterminestheappropriateDR?Itisverysimplytwothings:thecostofmoney(ortherisk-freerate)plusanadditionalamounttocompensateforrisk.ThinkoftheDRasthe
interestrateareasonablelenderwouldchargeagivenloanapplicant.Theworld’ssafestborroweristheU.S.Treasury.IfUncleSamcomesmywayandwantsa
long-termloan,I’llchargehimjust6%.AtthatDRtheDDMpredictsthataperpetual$1annualloanrepayment,orcoupon,iswortha$16.67loan.Nextthroughthedooris
GeneralMotors.Stillprettysafe,butnotasrisklessasUncleSam.I’llchargethem7.5%.AtthatDRaperpetual$1repayment/couponiswortha$13.33loan.
Finally,instrutsTrumpCasinos.Phew!FortheriskoflendingtheseclownsmymoneyI’llhavetocharge12.5%,whichmeansthatTheDonald’sperpetual$1repayment/couponisworthonlyan$8loan.SotheDRweapplytothe
market’sdividendstreamhingesonjusthowriskywethinkthemarketis.Andherethingsgetreallysticky.
Relyingonlong-termdata,GHobservethatthestockmarketisactuallylessriskythanthelongTreasurybond.Forexample,since1926theworst30-yearannualizedreturnforcommonstockswas8.47%versusonly1.53%forTreasuries.Ofcourse,averydifferent
pictureemergeswhenonelooksatshorterperiods.Forexample,theworstone-year
returnsare−43.35%forstocksand−7.78%forbonds.Andatagutlevel,nomatterhowmuchofalong-terminvestoryouthinkyouare,themarketstillprobablygotyourattentiononOctober19,1987.SotheGH-Dow
controversydependsonwhetheryouthinkthatinvestorsexperienceriskasashort-termoralong-term
phenomenon.WhattheauthorsaresayingisthatU.S.investorshaveabruptlylengthenedtheirrisktimehorizon:
Seventyyearsagofewinvestorsunderstoodthatexcessivetradingunderminesprofits,thatstock-pricefluctuationstendtocancel
themselvesoutovertime,makingstockslessriskythantheymightappearatfirstglance,andthatitisextremelydifficulttooutperformthemarketaverages.Americanshavelearnedtobuyandhold.
OnewonderswhatplanetGHinhabit.Aretheyunawarethattradingvolumehasbeensteadilyincreasingfordecades,notdecreasing?Thataveragedomesticmutualfundturnoverhasincreasedfrom30%toover90%inthepast25years?Thatarecentsurveyofover66,000accountsatalargeWestCoastdiscountbrokerageshowedanaverageannualportfolioturnoverof
75%?Thatonly7%ofmutualfundinvestmentsareindexed?Thatthehistoricallymodestmarketdeclinesof1987,1990,and1997,farfromresultingininflowsfromlegionsoflong-termersbuyingcheap,produceddramaticmutualfundoutflows?Mostauthoritativelyofall,inanelegantstudypublishedintheQuarterlyJournalofEconomicsin1993Shlomo
BenzartiandRichardThalercalculatedthattheriskhorizonoftheaverageinvestorwasjustoneyear.Theeasiestwayof
thinkingabouttheinterplayofshort-andlong-termriskistoimagineanewkindof30-yearTreasurybond,similartotheconventionalbond,exceptthatthegovernmentstandsreadyatalltimestoredeemitatpar(facevalue).
Clearly,theredeemablebondwouldcarryaconsiderablyhigherpriceandloweryieldbecauseitisimmunizedagainsttheshockofashort-termincreaseinrates.AndyetontheGHplanet,whereinvestorsonlycareaboutlong-termreturn,itwouldbepricedidenticallytotheconventional30-yearbond,sincebothhavethesamereturntomaturity.
EvenconcedingGH’spointthatinvestorsareincreasinglyfocusedonstocksforthelongrunandwillmanagetopushtheDowuppast36,000,onehastoaskjusthowfreeofriskstockswouldbeatthatpoint.Theauthorsignorearatherinconvenientfact:thatrecentmarkethistoryhasdramaticeffectsonDR.In1928,justastoday,everybodywasa“long-terminvestor,”andthe
DRforstockswasquitelow(althoughprobablynotaslowasitistoday).Fiveyearslater,withtheattritionrateofbuy-and-holdersapproaching100%,theDRwasdramaticallyhigher.AndatDow36,000,itwouldn’ttakemuchofachangeintheDRinorderfortherisk-freeworldofstockstocometoanabruptend.Ifinvestorsdecidedthattheydemandedevenameasly1%risk
premium,theDowwoulddeclinebyabouttwo-thirds.TheironybeingthattotheextentGHarerightaboutanear-term“correction”ofstockpricespast36,000,therisksofsubsequentstockownershipincreasedramatically.Ignoringthecrashscenario
stilldoesnotmaketheGHplanetlookveryappetizing.FortheDRhasanother,even
moreprofoundsignificance.Namely,thattheDRofanassetisthesameasitsexpectedreturn.Ifthetruediscountrateis5.5%andtheDowiscorrectlypricedat36,000,thenthefuturereturnofstocksisalso5.5%.Assuminginflationaverages2.5%overthenext30years,that’sarealreturnofjust3%.Whywouldanyrationalinvestorinvestinstockspricedtoa3%realreturn
withTreasuryInflationProtectedSecurities(TIPS)pricedtoproduceaguaranteed4%realreturn?Thereareother,more
fundamentalproblemswithDow36,000.Forstarters,considerthesignificanceofa5.5%long-termstockreturn.The“costofcapital”forcorporationsisnecessarilythesameasthislong-termreturn.Atadirt-cheapcapital
costof5.5%,corporationsarenotgoingtobeparticularlycarefulabouthowtheyspendit.Thefree-spendingbehaviorofthedot-coms,whosecapitalcomesevencheaper,isnotencouraging.(Or,onagranderscale,justhowcarefulisUncleSamwithhis5.5%capital?)Thatsaid,onrare
occasionsinvestmentparadigmsdodramatically
andpermanentlyshift.We’vealreadymentionedwhathappenedin1958,whenforthefirsttimestockyieldsfellbelowbondyields.Atthetimetherewasanalmostuniversaloutcryfromfinancialpunditsthatthiswasanunnaturalstateofaffairsandthatstockpricesweredestinedtofall,onceagainraisingtheiryields,soastorestoretheoldorder.Andyetthestockmarketnever
lookedback;pricescontinuedtorise,andstockyieldsfellevenfartherbelowbondyields.(Newparadigmscanalsobepainful.Theyear1958alsobroughtthestartofabearmarketinbondsmuchworsethananythingseensincethetimeofAlexanderHamilton.)Today,stocksyieldafull4%–5%lessthanbonds.SoIwouldnotdismissDow36,000outofhand.Butsomeskepticismis
inorder.(Eventheauthorsthemselvesadmitthattheycouldbewrong,andthusholdabout20%oftheirassetsinbonds.)
Hedging:CurrencyEffectsonForeignHoldings
Theholderofaforeignstockorbondissubjectnotonlytotheintrinsicrisksofthatsecuritybutalsotothe
additionalriskofcurrencyfluctuation.Forexample,abonddenominatedinU.K.poundswillriseorfallinvaluealongwiththevalueofthatcurrencyrelativetothedollar.Thiscurrencyriskcanbeeliminated(hedged)bysellingforwardapoundcontractinthefuturesmarketatnominalcost.Intherealworld,youmustfirstbuysomethingbeforeyousellit.Butinfinance,youcanoften
sellsomethingfirstbeforebuyingitbacklater;thisiscalledsellingforward(andissimilarto“shorting”astock).Acurrencycontractthatissoldforwardincreasesinvalueasthatcurrencyfalls,andviceversa.Theresultanthedgedbondgenerallyhasconsiderablylowerriskthantheunhedgedbond,sincethecurrencyvaluechangeinthebondisexactlycounterbalancedbythe
oppositechangeinvalueofthefuturescontract.However,thesituation
withforeignstocksismuchmorecomplicated.Considerthe20yearsendingOctober1999.TheannualizedstandarddeviationforhedgedEuropeanstocks(MorganStanleyCapitalIndex-Europe)was14.92%fortheperiod.(ThehedgedindexisthereturnthataEuropean
investorwouldseeinthenativecurrency.Itisalsocalledthelocalreturn.)Thepastdecadeshavebeenanextremelyturbulenttimeintheforeignexchangemarkets,withthemonthlyreturnsoftheEuropeancurrenciesthemselvesexperiencinganannualizedSDof10.44%.However,becausethiscurrencyreturnisuncorrelatedwiththestockreturn,theSDofthedollar-
denominatedEuropeanmarketwasjust16.25%—onlyslightlyhigherthanthatofthehedged(localcurrency)index.ItisinfactnotdifficulttofindshortperiodswherehedgingactuallyincreasedtheriskofaEuropeanstockportfolio.Bynow,ofcourse,youare
sophisticatedenoughtoknowthatjustbecauseunhedgedforeignstocksareslightly
moreriskythanthehedgedvariety,thisdoesnotimplyadverseportfoliobehavior.Inordertoexaminethisproblem,IlookedatthebehaviorofthreeassetsfortheNovember1979toOctober1999period:thebroadU.S.market(representedbytheCRSP1-10Index)andthehedgedandunhedgedMSCI-Europe.Oneproblembecomesimmediatelyapparent—the
returnsforthethreeassetsaresomewhatdifferent.ThehedgedEuropeanindexyieldeda13.43%return,withthecurrencyreturnboostingtheunhedgedportfolio’sreturnto15.18%.And,aswesawinChapter4,duringthe1980sand1990sthedomesticU.S.returnwasmuchhigher—inthiscase17.21%.Duringthisperiod,then,hedgingandforeignexposurewerebothhighly
detrimental,andthebestportfoliowasalmostexclusivelydomestic.TocorrectthesebiasesI
adjustedtheunhedgedEuropeananddomesticportfolioreturnsdowntothe13.43%levelofthehedgedEuropeanportfolio,andlookedatthereturn-versus-riskcharacteristicsofthevariousU.S.andEuropeanmixesinFigure7-9.Ascan
beseen,thehedgedportfolios(theloopontheleft)havebothlowerreturnandlowerriskthantheunhedgedportfolios(theloopontheright).Inanycase,notetheverynarrowverticalreturnsscale—wearetalkingaboutlessthanadozenbasispointsdifference.Soallthingsbeingequal,hedgingEuropeanstocksisawash.But,ofcourse,intherealworldthingsareneverequal.
Itisquitelikelythatcurrencyexposuremayturnouttobeeitherhighlybeneficialordetrimentalinthecomingyears.Andwecan’tpredictwhichinadvance.
Figure7-9.Hedgingeffect,U.S.andEurope,November1979toOctober1999.
Fortunately,theadvantagesofhedging(lowerindividualassetrisk,positivehedgingreturn)anddisadvantages(highercorrelationwiththerestoftheportfolio)largelyoffset
eachother;intheverylongrunthereisnotthatmuchdifferenceinriskandreturncharacteristicsofhedged-versus-unhedgedportfolios.Overshorterperiods,however,thedifferencescanbeconsiderable.Forexample,duringtherapiddepreciationofthedollarthatoccurredin1984–1986and1994–1995,unhedgedportfoliosgreatlyoutperformedhedged
portfolios.Theoppositeoccurredwhenthecurrencycycleunwoundin1998–1999.Forthosefewpeoplewho
areplanningtospendtheirretirementinEuropeorJapan,theireventualriskmaybelessenedbynothedging.Inotherwords,sincetheirliabilitieswillbeinforeigncurrency,thechanceofhavingsufficientfundsto
meettheirneedsisincreasedbynothedging.
MathDetails:TheHedgingHallofMirrors
Tocomplicatethingsevenmore,thecostofhedgingneedstobeconsideredaswell.Attheinstitutionallevelofmutual
funds,thefees,commissions,andopportunitycostsassociatedwithhedgingareminimal,perhapsnomorethanafewdozenbasispoints.Therealcostofhedginghastodowiththenatureofforwardcurrencycontracts.Asthisisbeing
written,thespotandsix-monthforwardcontractsforthepound,yen,anddeutschemarkareasfollows:
Whenyoupurchaseahedge,
you“sellshort”theforwardrateandbuyitbackatalaterdate.Ifyousellshortthesix-monthforwardcontractandwaituntiljustbeforeitexpiressixmonthslatertobuyitback,youwillbebuyingthecurrency(or“coveringtheshortposition”)atthe
spotrate.Ifthespotandforwardratesdonotchangeintheinterim,youwillearnaprofitequaltotheforwardpremium,whichisthedifferencebetweenthespotandforwardrates.Thisisnegligibleinthecaseofthepound,3.01%fortheyen,
and1.32%forthedeutschemark.Ineffect,youarebeingpaidtohedgethesecurrencies.(Thisisbecauseatthepresenttimeinterestratesarelowerineachofthesecountriesbyanamountequaltotheforwardpremiumrate.Ifyouwishedto
hedgeanunstablecurrencywithhighinterestrates,suchastheruble,theforwardpremiumwouldbehighlynegative,withaveryhighhedgingexpense.)
And,ifyouownstocksorbondsexactlyequaltoyourhedging
amount,youwillearntheforwardpremiumnomatterwhathappenstotheexchangerate,aslongastheforwardpremiumstaysintact.Youwouldthinkthattheforwardratewouldbepredictiveofthefutureexchange
rate.Itisn’t.Forexample,thereasonthattheyenforwardpremiumissohigh(3%oversixmonths,or6%peryear)isthatJapaneseinterestratesaresolow.WhattheforwardpremiumseemstobesayingtotheU.S.holderofaJapanesefive-
yearbond(currentlyyieldingonly1%)is:“Don’tworryaboutthelowyield,you’llmakeupthedifferencewitha6%annualcurrencyappreciation.”Infact,however,exchangeratehistorysuggeststhatonaverage
thisdoesn’thappen.Overthepastseveraldecades,globalbondmanagershavemadeexcessreturnspurchasingunhedgedhigh-yieldingbondsofdevelopednationswithnegativeforwardspreads,reapingadvantagewhenthe
underlyingcurrencyfailstodepreciateasmuchasforecastbytheforwardspread.Thismarketinefficiencyisprobablytheresultofthefactthatgovernmentsaremajorplayersinthecurrencygame;governmentsaredifferentfrom
individualandinstitutionalinvestorsinthattheirprimarygoalisnotprofit,butrathercurrencydefense.
Lastly,hedgingcostneedstobeconsideredwhenevaluatinghistoricaldata.Aspointedoutby
JeremySiegelinStocksfortheLongRun,in1910thepoundwasworth$4.80.Ithassincefallentoone-thirdthatvalue.Onemightthinkthathedgingthecurrencywouldhaveincreasedone’sreturnfromBritishstocks.Wrong.Sincefor
almostallofthatperiodBritishinterestrateswerehigherthanthoseintheUnitedStates,thehedgingcostswereconsiderable;you’dhavebeenmuchbetteroffnothedging.
Thequestionofhowmuch
currencyhedgingisbestisoneofthethorniestquestionsfacedbyinvestors;neithermean-varianceanalysisnorspreadsheetanalysisprovidesanyclear-cutanswers.Asapracticalmatterthisdecisionhasalreadybeenmadeforyou.AlloftheforeignstockindexfundsrecommendedinChapter8areunhedged,andtheonlylow-costforeignbondfundsarehedged.And,aswe’vealreadyseen,thisis
notabadstateofaffairs.Moreimportantly,be
awarethatthedegreeofhedgingstronglyaffectstheshort-termperformanceofforeignstockandbondmutualfunds;donotbetooupsetifoneormoreofyourfundshasabadyearsimplybecausetheywerecompletelyhedgedwithafallingdollar,orviceversa.Aslongasyourfundsstickto
theirhedgingpolicies,youwillberewardedwhenthecurrencypendulumswingstheotherway,whichitalmostalwaysdoes.
DynamicAssetAllocation
Dynamicassetallocationreferstothepossibilityofvaryingyourpolicyallocationbecauseofchangingmarketconditions.Afterspendingmuchofthisbookconvincing
youofthevirtueoffixedallocations,whyamIrelaxingthisvaluabledisciplinesolateinthegame?Isn’tchangingthepolicyallocationtantamounttomarkettiming,ademonstrablyprofitlessactivity?Beforeproceedingfurther,
letmebeclear:Adherencetoafixedpolicyallocationwithitsrequiredperiodic
rebalancingishardenough.Ittakesyearstobecomecomfortablewiththisstrategy;manylosetheirnerveandneverseethethingthrough.Youcannotpilotamodernjetfighterbeforemasteringthetrainer;likewise,youshouldnotattemptdynamicassetallocationbeforemasteringfixedassetallocation.Inthe1995versionofthis
book,IprovidedanexampleofhowchangingthestockandbondallocationintheoppositedirectionofP/Bproducedaslightimprovementinrisk-adjustedreturn.Alas,thisisnolongertrue,asaP/Bsensitiveinvestorwouldhavecompletelyexitedthestockmarketbylastyear.However,forwhatit’sworth,Figure7-10isagraphofP/Bversusfive-yearforward
averagereturn.Althoughthereissomescatter,thereisobviouslyastrongtendencyforreturnstobehighwithlowstartingP/Bs,andlowwithhighP/Bs.Themostremarkableaspectofthisplotisthatthelowerboundaryofthedatapointsformsquiteastraightline;thisrepresentstheminimumreturnwhichcanbeexpectedforagivenP/B.AtaP/Bof1.5,anaveragefive-yearreturnof
about2%seemsguaranteed;ataP/Bof1.25,7.5%;andat1.0,areturnof13%seemsassured.Isthisausefulrelationship?That’sanybody’sguess.However,Figure7-10isagoodreminderthatwhenstocksgetmoreexpensive,theirfuturereturnsarelikelytodecline,andthatwhenstocksareverycheap,futurereturnsarelikelytobemoregenerous.
Figure7-10.Five-yearforwardstockreturnsversusP/B1926–1993.
However,itisstillnotabadideatooccasionallychangeyourallocationslightlyintheoppositedirectionfromvaluation.Iftwoyearsagoyouthoughtthata6%exposuretoemergingmarketswas
appropriate,perhapswiththerecentcarnageinthisarea7%or8%mightnotbeinappropriate.Ifthreeyearsagoyouwereholding40%S&P500,perhaps35%mightnotbeabadideainthecurrentbubblyenvironment.Thinkofitthisway—whenyourebalanceyourportfolioinordertomaintainyourtargetallocation,youpurchasemoreofanassetthathasdeclinedinprice,and
thusgottencheaper.Whenyouactuallyincreasethetargetportfolioweightingofanassetwhenitspricedeclinesanditgetscheaper,youaresimplyrebalancinginamorevigorousform—youare“overbalancing.”Asimplerwayofoverbalancingistoincreaseyourtargetallocationeversoslightly—perhapsby0.1%foreverypercentthattheassetfallsinvalue,andviceversa.
Dynamicassetallocationgetsabadrapbecausemostinvestorschangetheirallocationsaroundinresponsetochangesineconomicorpoliticalconditions.Aswehavediscussed,thisisapoorapproach.Intheauthor’sopinion,changesinallocationthatarepurelymarket-valuationdrivenarequitelikelytoincreasereturn.Rebalancingrequiresnerve
anddiscipline;overbalancingrequiresevenmoreofbothofthesescarcecommodities.Veryfewinvestors,smallorinstitutional,cancarryitoff.
BehavioralFinance
Theoverarchingpremiseofthisbookisthatrationalinvestors,facedwiththefactsofmoderninvesting,willmakecertainlogicaldecisionsandchoices.There’sonlyone
problem.Humanbeingsarenotrational.Thepastfewdecadeshaveseenanexplosioninthefieldofbehavioralfinance—thestudyofthelogicalinconsistenciesandfoiblesthatplagueinvestors.Threehumanbehavioralphenomenaareworthdiscussing:overconfidence,recency(whichwehavealreadymentioned),andriskaversionmyopia.
Overconfidence
Forthoseofyouwithacongenitaldislikeofpublicradio,fornearlytwodecadesshowhost,writer,and(dareIsayit)singerGarrisonKeillorhasproducedAPrairieHomeCompanion,setinthemythicaltownofLakeWobegon,Minnesota.(Asmallconfession:Ilistenedtotheshowforovertwoyearsbeforenaggingdoubtssent
metomyRandMcNally.)Mr.KeillorisheardtointoneatthebeginningandendofeachshowthatinLakeWobegon,“allthewomenarestrong,allthemenaregood-looking,andallthechildrenareaboveaverage.”Well,onWallStreet
everyone’saboveaveragetoo.InapieceoninvestorpreconceptionsintheSeptember14,1998,
“AbreastoftheMarket”seriesinTheWallStreetJournal,writerGregIpexaminedtherevisionininvestorattitudeswiththemarketdeclineinthesummerof1998.Hetabulatedthechangeininvestors’returnexpectationsasfollows:
Thefirstthingthatleapsoutofthistableisthattheaverageinvestorthinksthatheorshewillbestthemarketbyabouttwopercent.Whileitispossiblethatmanyinvestorsmayinfactbeatthemarketbyafewpercent,itisofcoursemathematicallyimpossiblefortheaverageinvestortodoso.Infact,aswe’vealreadydiscussed,theaverageinvestormustofnecessityobtainthemarket
return,minusexpensesandtransactioncosts.Eventhemostcasualobserverofhumannatureshouldnotbesurprisedbythisparadox—folkstendtobeoverconfidentOverconfidencelikelyhas
somesurvivaladvantageinastateofnature,butnotintheworldoffinance.Considerthefollowing:
Inonestudy,82%ofU.S.driversconsidered
themselvesinthetop30%oftheirgroupintermsofsafety.(InSweden,notunsurprisingly,thepercentageismuchlower.)Inanotherstudy81%ofnewbusinessownersthoughttheyhadagoodchanceofsucceeding,butthatonly39%oftheirpeersdid.Severalhousewivesfrom
Beardstownformaninvestmentclub,incorrectlycalculatetheirportfolioreturns,andthenwriteabestsellerdescribingthereasonsfortheir“success.”
Thefactorsassociatedwithoverconfidenceareintriguing.Themorecomplexthetask,themoreinappropriatelyoverconfidentweare.Calibration(receipt
ofresults)ofone’seffortsisalsoafactor.Thelongerthefeedbackloopbetweenouractionsandtheircalibration,thegreaterouroverconfidence.Forexample,meteorologists,bridgeplayers,andemergencyroomphysiciansaregenerallyquitewellcalibrated.Mostinvestorsarenot.
Recency
ThesecondsurprisingpieceofdatafromtheabovetableofreturnexpectationswasthatinSeptember1998,afterpriceshadfallenbyaconsiderableamount,investors’estimatesofstockreturnswerelowerthantheywereinJune.Thisishighlyirrational.Considerthefollowingquestion:OnJanuary1,youbuyagoldcoinfor$300.Intheensuingmonththepriceofgoldfalls,
andyourfriendthenbuysanidenticalcoinfor$250.Tenyearslater,youbothsellyourcoinsatthesametime.Whohasearnedthehigherreturn?Veryfewinvestorswould
notchosethecorrectanswer—yourfriend,havingboughthiscoinfor$50less,willmake$50more(oratworst,lose$50less)thanyou.Viewedinthiscontext,itisastonishingthatanyrational
investorwouldimputelowerexpectedreturnsfromfallingstockprices.Thereasonforthisiswhatbehavioralscientistscallrecency—wetendtooverweightmorerecentdataandunderweightolderdata,evenifitismorecomprehensive.Hadanyconversationslatelywithsomeonewithlessthanfiveyears’investingexperienceandtriedtoconvincehimthathecannotexpect20%equity
returnsoverthelongterm?Blamerecency.Maketherecentdataspectacularand/orunpleasant,anditwillcompletelyblotoutthemoreimportant,ifabstract,longer-termdata.Allveryinteresting,you
say,butofwhatusearesuchmetaphysics?Firstandforemost,itexplainswhymostinvestorsare“convex”traders.Thisisatermcoined
byacademiciansWilliamSharpeandAndrePeroldtodescribe“portfolioinsurance”strategiesinwhichequitiesareboughtaspricesriseandsoldastheyfall.A“concave”strategyrepresentstheopposite—buyingaspricesfallandsellingastheyrise.Althoughsomemayfindoneortheotherstrategymoreappealing,SharpeandPeroldmakeamoreprofoundpoint:
Inaworldpopulatedbyconcavetraders,itisadvantageoustobeaconvextrader,andviceversa.Financialhistoryinfactsuggeststhatbecauseofrecencytheoverwhelmingmajorityofequityinvestorsareconvex—whenpricesrise,investors’estimatesofreturnsirrationallyrise,andtheybuymore.Ifindeedmostinvestorsexhibitsuchconvexbehavior,thenthe
rationalinvestorisconcave.(Bondinvestors,ontheotherhand,appeartobelesssubjecttorecency,andthusabitlessconvex,probablybecausefallingbondpricesmakethemostovertfeatureofabond,itscurrentyield,moreimmediatelyattractivetotheinvestingpublic.)
RiskAversionMyopia
Humanbeingsexperience
riskintheshort-term.Thisisasitshouldbe,ofcourse.Inthestateofnature,ourancestors’abilitytofocusontherisksofthemomenthadmuchgreatersurvivalvaluethanalong-termstrategicanalyticability.Unfortunately,avisceralobsessionwiththehereandnowisofratherlessvalueinmodernsociety,particularlyintheworldofinvesting.
Overemphasisonthepossibilityofshort-termlossisreferredtoasriskaversionmyopia.InChapter2,afterlookingatthelong-termsuperiorityofstocksoverbonds,youmighthavefoundyourselfaskingthequestion,“Whydoesn’teverybodybuystocks?”Clearly,inthelongterm,bondsareactuallymoreriskythanstocks;thereisnoperiodofmorethan30yearsinwhichstocksdidnot
outperformbonds.Infact,manyacademiciansrefertothisas“theequityrisk-premiumpuzzle”—whystockshavebeenallowedtoremainsocheapthattheirreturnssogreatlyandconsistentlyexceedthatofotherassets.Theansweristhatourprimordialinstincts,auselessrelicofmillionsofyearsofevolutionaryhistory,causeustofeelmorepainwhenwesuddenlylose30%
ofourliquidnetworththanthemoredamagingpossibilityoffailingtomeetourlong-termfinancialgoals.Howbadistheproblem?I’vealreadymentionedtheimmenselycleverarticlebyShlomoBenzartiandRichardThaler(oneofbehavioralfinance’sbrighteststars)whichexaminedtheinteractionoftheriskpremiumandinvestorpreference.Theyestimated
thattheriskhorizonoftheaverageinvestor,wasaboutoneyear.Myopicindeed.Socratestoldusthatthe
unexaminedlifeisnotworthliving.Forthemoderninvestor,failureofself-examinationcanbeasdamagingtothepocketbookastothesoul.
Summary1.Badcompaniesare
usuallygoodstocks,goodcompaniesareusuallybadstocks.Valueinvestingprobablyhasthehighestlong-termreturns.
2.Currencyhedginghasimportanteffectsonshort-termportfoliobehavior,butlittleinthewayoflong-termimpact.
3.Itispermissibletochangeyourallocationslightlyfromtimetotime,aslong
asyoudosoinadirectionoppositefromvaluationchanges.
8ImplementingYourAssetAllocation
Strategy
ThereisamemorablepassagefromthemovieFullMetalJacket,abouttheexperiencesofaMarineunitinVietNam.Thestorycentersonacallow
youngjournalistwhofallsinwithagroupofgrizzledveterans.TheMarineCorpshasadialectallitsown;afterafewminutesofbanteratopsergeantturnstothejournalistandchallengeshimwith,“Iseeyoucantalkthetalk,butcanyouwalkthewalk?”Understandingthetheoryofassetallocationiseasy;pullingitoffisanothermatter.
ChoosingYourAllocation
Bynowyoushouldhaveafairlygoodideaofwhatyourbasicallocationshouldlooklike.Ifyoudon’t,Ishallwalkyouthroughtheprocess.ThisisessentiallyarecapitulationoftheChapter5discussion,exceptthatI’vechangedtheorderofthesteps:
1.Determineyourbasicallocationbetweenstocks
andbonds.First,answerthequestion,“WhatisthebiggestannualportfoliolossIamwillingtotolerateinordertogetthehighestreturns?”Table8-1summarizestheprocessofdeterminingyourrisktolerance.
Table8-1.AllocatingStocksversusBonds
Inpreviousversionsofthebook,Iallowedthemostrisk-tolerantinvestors100%equityexposure.Atthe
presenttime,however,itappearsthatexpectedstockandbondreturnsgoingforwardmaynotbeallthatdifferent,andadollopofbondsisrecommendedforallinvestors.Thepercentagestock
recommendationsinTable8-1willneedtobereviseddownwarddependingonyourtimehorizon.Yourmaximumstockallocationshouldbe10
timesthenumberofyearsuntilyouwillhavetospendthemoney.Forexample,ifyouneedthemoneyintwoyears,yourstockallocationshouldnotexceed20%;ifyouwillneedthemoneyinsevenyears,itshouldnotexceed70%.2.Determinehowmuch
complexityyoucantolerate.Iskeepingtrackofsixdifferentassetclassesmore
thanyoucanhandle?Orareyouan“asset-classjunkie”whocravesaportfolioofexoticbirdssuchasPacificRimsmallcompaniesoremergingmarketsvalueexposure?
Forstarters,you’llneedatleastfourassetclasses:
U.S.largestocks(S&P500)U.S.smallstocks(CRSP
9-10,Russell2000,orBarra600)Foreignstocks(EAFE)U.S.short-termbonds
Ifthisisallyoucanhandle,fine.Theabovefourclasseswillprovideyouwithmostofthediversificationyou’llneed.However,ifyoucantoleratetheaddedcomplexity,I’drecommendbreakingthingsdownabit
further:
U.S.largestocks—marketandvalueU.S.smallstocks—market,value,andREITsForeignstocks—Europe,Japan,PacificRim,emergingmarkets,andsmallcapU.S.short-termbonds
3.Determinehowmuchtrackingerroryoucan
tolerate.AreyouthekindofinvestorwhomentallycompareshisreturnsonafrequentbasiswiththatoftheDoworS&P500?Doyougetdepressedwhenyourstockallocationdoesn’tdoaswell?Thenperhapsyoushouldconsideranallocationheavyinlarge-capU.S.stocks,whoseperformancewillnotvarygreatlyfromthatofthedomesticbenchmarks.
PlanningforTaxes
Somewhereinthelastfewparagraphs,withoutrealizingit,weranintoanenormousobstaclecalled“taxes.”Ifallofyourassetsareintax-shelteredvehiclessuchasanIRA,Keogh,401(k),403(b),privatepensionplan,orannuity,thenthisisnotaproblem.Butifasignificantpartofyourassetsistaxable,extremecareiscalledfor.For
example,theS&P500isarelativelytax-efficientindex,butthesmall-capindexesareanotherstory.Thesebenchmarks,andthefundsthattrackthem,haverelativelyhighturnover.Worse,stocksusuallymoveoutofasmall-capindex,andthusneedtobesold,afteralargepriceappreciationplacesthemintothemid-orlarge-capcategory,generatingdisproportionately
largeamountsofcapitalgains.Thesameistrueofforeignsmall-capstocks.Thisalsooccurswithvalue
indexfunds—bothlargeandsmallcap.Themajorreasonforastock’smovingoutofthevaluecategoryisthatapriceriseoftenplacesthestockinthegrowthcategory.Again,unwantedcapitalgainsdistributionsaretheresult.
REITspresentanevenworseproblem.Becausemostoftheirreturnistheresultofdividends,theyaretaxableatyourfullmarginalrate,andthusareverylikelynotappropriatefortaxableaccounts.Finally,bondspresent
similartaxproblems.Dependingonyourstateofresidence,amunicipalbondfundorTreasuryladdermay
beadvantageous.
Indexing:VanguardandDFA
Atthispoint,wearefinallyabletoconsiderindividualinvestmentvehicles.Inthepreviousversionsofthebook,Itookamoreeclecticattitudetowardindividualfundselection,butrecenteventshavemadethingsagooddeal
simplerbecauseawidevarietyofindexedinvestmentproductshavebecomeavailablefromtheleadersinthefield:VanguardandDimensionalFundAdvisors(DFA).Thestructureofthe
VanguardGroupisuniqueinthemutualfundindustry;itisownedentirelybyitsindividualfunds,andthusbyitsshareholders.Inother
words,theprofitsoftheentiremutualfundgrouparedistributedbacktothefundsthemselves,andthustoyou,theinvestor.Almostallothermutualfundprovidersareownedbytheircompanystockholders,orelseareprivatelyowned:profitsfromthefunds’managementmostdefintelydonotflowtothefunds’shareholders.Thisisacriticaldistinction;mostmutualfundcompaniesare
rewardedbycharging(somewouldsaymilking)theirfund’sshareholdershighmanagementfees.Theconceptofthe“expenseratio”iscentraltomutualfundinvesting.Afund’sexpensesincurredbyaccounting,shareholderservicing,andinvestmentmanagementfeesaresubtractedfromthereturnthatthefundactuallyearnedonitsinvestments.The
averageexpenseratioofaU.S.stockfundis1.32%,andforforeignfundsitisnear2%.Moreover,aswesawinChapter6,theexpenseratioisjustthebeginning,withcommissions,spreads,andimpactcostsfurtherloweringyourreturns.Ofcourse,Vanguardalsoincursthesecosts,butbecauseoflowindexfundturnover,theseexpensesaremuchlessthanthatofconventionalactively
managedfunds.HerearetheVanguard
stockfundsI’drecommend:
1.Vanguard500IndexFund.Thegranddaddyofallindexfunds,whichtrackstheS&P500.Sometimeinthenextyear,itwillalmostcertainlybecometheplanet’slargestmutualfund.Afinechoiceforthelonghaul,particularlyintax-shelteredaccounts,itdoeshavesome
modestdrawbacksforthetaxableinvestor.Standard&Poor’speriodicallyaddsanddeletesstocksfromtheindex,incurringdistributionsasthefundrearrangesitsportfolioaccordingly.Becauseofthis,I’drecommendtwoalternativesforthetaxableinvestor—theVanguardTotalStockMarketIndexFundandtheVanguardTax-ManagedGrowthandIncomeFunds.
2.VanguardTax-ManagedGrowthandIncomeFund.Thistax-managedversionofthe500IndexFundseekstominimizedistributionsbysellinghigh-basis-costsharesfirstandsellingotherpositionsatalosstooffsetgainsales.Noteshouldbemadeofthefund’shigherminimum($10,000versustheusual$3000)aswellasa2%redemptionfeeforsharesheldlessthanoneyearanda
1%feeforsharesheldlessthanfiveyears.3.VanguardTotalStock
MarketIndexFund.ThisfundtrackstheWilshire5000Index(whichnowincludesmorethat7000stocks)andisparticularlysuitablefortaxableinvestors.Asitowns“thewholemarket,”itsellsastockonlyifthecompanyisboughtoutforcash.Itcanbethoughtofasconstituting
75%largecap,15%midcap,and10%smallcap.4.VanguardValueIndex
Fund.Thisfundtracksthebottom50%ofmarketcapitalizationoftheS&P500whensortedbyprice/bookratio.ThispeculiardivisionoftheS&P500resultsinabout380valuestocksand120growthstocks,becausethelatterhavemuchhighermarketcapitalizationsthan
theformer.Becausethisstrategyresultsinhighturnover,itisnotsuitablefortaxableaccounts.IsuspectthatVanguardwillbecomingoutwithatax-managedlarge-capvaluestrategysoonerorlater,butthey’renotthereyet.5.VanguardSmall-Cap
IndexFund.ThisfundtrackstheRussell2000Index.Itissuitableonlyfortax-sheltered
accounts.6.VanguardTax-Managed
Small-CapFund.Fortaxableaccounts,thisfundusesthetax-managedstrategydescribedabove.Thisfundhasa$10,000minimumandthesame1%or2%redemptionfeeastheTax-ManagedGrowthandIncomeFund.Italsocarriesa.5%purchasefee,payabletothefunditselftomitigatethe
spreadandimpactcostsinthisarea.7.VanguardSmall-Cap
ValueIndexFund.Thisfundissuitablefortax-shelteredaccountsonlybecauseitislikelytohavehighturnoveranddistributions.Ithasa.5%purchasefee.Vanguarddoesnotyethaveatax-managedsmall-capvaluefund.8.VanguardEuropeanand
PacificStockIndexFunds.
Thesefundshavealowturnoverandaresuitablefortaxableaccounts.ThePacificStockIndexFundisessentiallyaJapanesefund,withJapancomprisingalmost80%offundassets.9.VanguardEmerging
MarketsStockIndexFund.Becauseoftheveryhighspreadsandtransactionalcosts,thereisa.5%purchasefeeanda.5%redemptionfee.
Itisuncertainhowmuchindistributionsthefundwillyieldinthelongterm,andthushowsuitableitwillbefortaxableaccounts.However,Vanguardhasahistoryofkeepingfundtransactionsataminimum,anditissensitivetothehightradingcostsinthisarea.10.VanguardTotal
InternationalStockIndexFund.Thisistheonefor
thoseofyouwhoprizeportfoliosimplicity.Itissuitablefortaxableaccounts.ThereisalsoaTax-ManagedInternationalFundwiththesame$10,000minimumandredemptionfeescheduleastheothertax-managedfunds,plusa.25%purchasefee.11.VanguardREITIndex
Fund.Becausealmostallofthelong-termreturnofREITscomesfromdividends,this
assetclassshouldbeusedonlyinthetax-shelteredsetting.Thereisa1%redemptionfeeforsharesheldlessthanoneyear.
Althoughit’stoughtobeatVanguardforindexedasset-classcoverage,thereareafewholes,particularlyinthetax-managedvaluedepartment.Inaddition,Vanguardlacksinternationalsmall-capandinternational
valuevehicles.Ifyoumusthaveexposuretotheseareas,thenyouwillneedDimensionalFundAdvisors.BasedinSantaMonica,DFA’sstrategiesaredesignedbysomeofthebrighteststarsinacademicfinancialeconomics,includingGeneFama,KenFrench,andRexSinquefield.DFAoffersalmostanyindexfundyoucanthinkof:U.S.largestocks;U.S.large-value
stocks;internationallargestocks;internationallarge-valuestocks;U.S.smallstocks;U.S.smallvalue-stocks;internationalsmall-valuestocks;U.K.,Japanese,Continental,andPacificRimsmallstocks;aswellasemergingmarketssmall-capandvaluestocks.Inaddition,DFAoffersforeignanddomestictax-managedvaluefunds.DFA’sexpensesarealmostaslowasVanguard’s.
DFAfundsareavailablethroughanapprovedfinancialadvisor,whowillofcoursechargeyouafee.Further,youwillhavetobuyitsfundsthroughoneofthe“supermarkets”(Schwab,Vanguard,orWaterhouse),wheretransactionswillrun$24–$50apop.Still,ifyoumusthavetheseassetclasses,youmayfinditworthwhiletocanvasfinancialadvisorsforonewhowillchargea
reasonablefeefortheservice.Small-capinternational
exposureisaparticularproblem.Inpreviousversionsofthisbook,IrecommendedAcornInternationalandTweedyBrowneGlobalValuefundsforthispurpose,andinfactthesechoiceshavedonequitewelloverthepastfewyears.Theonlyproblemisthatthey’rereallynotsmall-capfunds.Inspiteof
theirrelativelysmallmedian-market-caps($035Mand$2543MperMorningstar,April1999),theycorrelatemuchmorehighlywiththevarious(large-cap)MorganStanleyCapitalIndexes,andeventheS&P500,thanasmallforeignfundshould.Thus,therealreasonwhythosetwofundshaveperformedsowellisthattheyare,infact,mediumtolarge—andnotsmall—foreign
funds.Ifyouwantauthenticexposuretointernationalsmallcaps,youhavethechoiceofdealingwithDFAthroughafinancialadvisororwaitingforVanguardtocomeoutwithaninternationalsmall-capfund.Table8-2summarizesthe
VanguardandDFAindexfundsappropriateforbothtaxableandtax-shelteredinvesting,fortax-sheltered
onlyinvesting,andtaxableonly(tax-managed)investing.Someofyouwillnoticetheabsenceofgrowthindexfundsintheabovelist.Inspiteoftherecentsuperbresultsoflarge-capgrowthinvesting,Ibelievethat,inthelongrun,growthinvestingisabadidea,particularlyinthesmall-caparena.Inanycase,theS&P500andsmall-capindexes,beingcapitalization
weighted,areforallpracticalpurposesgrowthproxies.
Table8-2.StockIndexFundSummary
Anewdevelopmentintheworldofindexingareso-calledexchange-tradedfunds(ETFs).Thesecomeinmanysizesandshapes.Themostpopulararespiders(SPDRS),basedontheS&P500.Unlikemutualfunds,thesesecuritiestradelikestocksontheAmericanStockExchange.Theyhavebothadvantagesanddisadvantagesrelativetoaconventional
indexfund.Ontheplusside,theycanbetradedthroughouttheday,asopposedtoaconventionalfund,whichispricedonlyattheendofthetradingday.SPDRSdonotgenerateappreciablecapitalgainsandarethusslightlymoretax-efficientthanconventionalS&Pindexfundsaswell.Ontheotherhand,thepurchaseandsaleofanETFincursbothcommissionsandspreads,
andsoisslightlymoreexpensivetoown.Also,ETFsreinvestdividendsonlyquarterly,andthuswillsufferaslightperformancedragrelativetoaconventionalfund,whichcontinuouslyreinvestsitsdividends.Onthewhole,unlessyouareanactivetrader,ETFsholdnorealadvantageoveraconventionalindexfund.Thereisalsoanexchange-tradedfund,QQQ,aimedat
theNasdaq100index,andseveralnewSPDRSthattrackS&Psectorindexes.AlsoavailableareETFsthatindexvariousforeignmarkets,knownasWorldEquityBenchmarkSecurities,orWEBS.Hereamuchclearerrecommendationcanbemade—stayaway.Overthepastseveralyears,WEBShaveunderperformedtheirnationalmarketindexesbyanaverageof2%peryear
becauseofexcessiveexpensesandturnover.AlthoughWEBSoffercertaintheoreticaladvantagesovertheVanguardandDFAforeignindexfundsrelatingtoportfoliorebalancing,inpracticethesepotentialadvantagesareoutweighedbytheirexpensedisadvantage.Thecomingyearswillsee
anexplosionintheasset-
classvarietiesofferedbyETFsthatmayinthelongrunproveaboontothepassiveasset-class-basedinvestor.However,beforepurchasingoneofthesevehiclesI’dmakesurethatithasnottraileditsbenchmarkindexbymorethanitsexpensesforaperiodofatleastoneortwoyearsandthatitsexpensesarenotexcessive.
Bonds
Herethingsseparateoutmuchmorecleanlyintotaxableandnontaxablebonds.Asthisisbeingwritten,considertheyieldsonthefollowingVanguardshort-term(2-3yearmaturity)bondfunds:Short-TermCorporateFund,5.95%;Short-TermTreasuryFund,5.25%;andLimited-TermTax-ExemptFund,3.71%.
Forthetax-shelteredinvestor,thisisano-brainer—yougowiththehighest-yieldingShort-TermCorporateFund.Forthetaxableinvestor,thingsareabitmorecomplex.Assumethatyouareinthe36%marginalfederalbracketandyourstateimposesa5%incometax.TheTreasuryFundissubjecttothefederalbutnotthestatetax,andyields3.36%aftertax.The
Tax-ExemptFundissubjecttothestatebutnotthefederaltax,andyields3.52%aftertax.TheCorporateFundissubjecttoboth,andyields3.62%aftertax.Thus,atthepresenttime,short-termcorporatebondshaveaslightadvantage.However,thisrelationshipchangesfrommonthtomonthandovervaryingmaturities.Atthepresenttimethe
situationwithrespecttoforeignbondfundsishighlyunsatisfactory.Forstarters,becauseofChairmanEmeritusBogle’sdislikeofcurrencyexposure,Vanguardoffersnolow-expenseinternationalbondfunds.ProbablythebestisStandish,InternationalFixed-IncomeFund,butthishasaminimumof$100,000,or$10,000whenboughtthroughcertainsupermarkets.Itisfully
hedgedandhasareasonableexpenseratioof0.53%.AmericanCenturyandT.RowePriceofferlargelyunhedgedfundswithlowerminimumsbuthigherexpenses(about0.8%).DimensionalFundAdvisorshastwofineshort-termglobalbondfunds(hedged)withreasonableexpenses,ifyoudecidetogothatway.Presently,EuropeanandJapanesegovernmentbond
yieldsareactuallylowerthanavailablefromtheU.S.Treasury,andithardlyseemswisetopay12%–20%oftheaveragecouponinexpensesforthesefunds.Myoveralladvicewith
respecttofederal,corporate,andmunicipalbondfundsistouseVanguard’sshort-termandintermediate-termofferings.ConsideraTreasuryladder,whichI’ll
shortlydiscuss,ifyouhaveatleast$50,000tocommittothisarea.StayawayfromforeignbondfundsunlessyouarealreadyaDFAclientoruntilsuchtimeasVanguardentersthisarea.
TreasuryLadders
Finally,thoseofyouwithmorethan$50,000inbondassetsshouldconsideraTreasuryladder.Treasury
bondscanbeboughtatauctionwithnospreadthroughmostbrokeragehouses.Considerthata$25commissiononthepurchaseofafive-yearnotefor$20,000amountstojust0.125%ofthepurchaseprice,ortoatotalexpenseof0.025%peryearforyourownpersonalTreasury“mutualfund.”Purchasingfive-year(andinitiallysometwo-yearandone-year)notesatregular
intervalswillresultinasteadystreamofmaturingsecurities.Further,itispossibletopurchaseTreasuriesatauctionwithoutanycommissionundercertaincircumstances.FidelityBrokerage,forexample,doesnotchargeacommissionforauctionpurchasesover$20,000,andVanguarddoesnotchargeanauction-purchasecommissionfortheir“Flagship”accounts
($750,000totalfamilyassets).Finally,itisalsopossibletobuyTreasuriesatauctiondirectlyfromUncleSam(TreasuryDirect),butthebondsboughtinthismannerarenoteasilyavailableforsalebeforematurity,ifnecessary.Treasuriesareconsidered
toberiskless,andthegapbetweenTreasuryandcorporateyieldscanbe
consideredthe“priceofsafety.”Whenthisgapissmall,safetyischeap,andTreasuriesshouldbepurchased.
DeterminingYourPreciseAllocation
InChapter5,westudiedseveraldifferentportfoliosarrangedaccordingtorisk,complexity,and
conventionality.Bynowyoushouldhavesomeideaofwhereyoufitalongthesethreedimensionsofportfolioconstruction.However,wedidnotconsiderthevaluedimension,nordidweconsidertheeffectsoftaxation.Ofcriticalimportanceto
yourallocationistherelativeamountoftax-shelteredversustaxableassets.Onthe
oneextreme,ifallofyourassetsareinanIRAorpensionplan,thetaxconsequencesofyourinvestmentstrategymattersnotatall.Youmayusewhateverassetclassesyoulike,andrebalancehoweveroftenyoulike.Ontheotherhand,ifallof
yourassetsaretaxable,youareoperatingunderextremeasset-classconstraints,but
thisalsomakesthingsverysimple.YouarelimitedtotheassetclassesinthefirstandlastcolumnsofTable8-2,whichincludejusteightVanguardindexfunds.BasicallyyouarebacktoU.S.large,U.S.small,andforeign.Themostcomplex
situationsarewhereyouhavesubstantialamountsofbothtax-shelteredandtaxable
assets.Thestrategyhereistoputthemosttax-efficientassetclasses(thefirstandlastcolumnsofTable8-2)inyourtaxableaccountsandtheleasttax-efficientassetclasses(middlecolumn,basicallysmallandlargevalue,andREITs)inyourtax-shelteredaccounts.Togiveyouanideaofhow
thisisdone,let’sconsiderthecaseofaninvestorwith
$200,000—$100,000eachintaxableandtax-sheltered(IRA)accounts.Usingtheaboveprinciples,theinvestorhasdecidedonthefollowingpolicyallocation:
15%U.S.largemarket10%U.S.largevalue5%U.S.smallmarket10%U.S.smallvalue5%European5%Pacific
5%Emergingmarkets5%REITs20%Municipalbonds20%Short-termcorporate
bonds
UsingTable8-2forthestockfunds,hedecidestousethefollowingVanguardfundsandplacethemintheappropriatetaxableortax-shelteredaccount:
TaxableAccount
15%TotalStockMarketIndexFund5%Tax-ManagedSmall-
CapIndexFund5%EuropeanStockIndex
Fund5%PacificStockIndex
Fund20%Limited-TermTax-
ExemptFund
IRAAccount10%ValueIndexFund
10%Small-CapValueIndexFund5%EmergingMarkets
StockIndexFund5%REITIndexFund20%Short-TermCorporate
Fund
Noticehowtheinvestorhassegregatedthemosttax-efficientassetsintothetaxableaccount,andtheleasttax-efficientassetsintothe
IRA.
ExecutingthePlan
Fromapurelyfinancialpointofview,itisusuallybettertoputyourmoneytoworkrightaway.However,ifyouarenotusedtoowningriskyassets,thengettingstartedisalittleliketakingyourfirstswiminthelakeonMemorialDay.Itisnotagoodideatojumprightin—bettertowade
inveryslowlyinordertogetusedtotheicywater.Fromapracticalpointofview,ittakesquiteawhiletoaccommodateyourselftotheupsanddownsofthemarket.Italsotakessometimetoconvinceyourselfthatrebalancingisagoodidea,particularlyasyoufindyourselfpouringcashintoaprolongedbearmarketforone,several,orallofyourassets.
Thetraditionalwayofreachingafullyinvestedpositionisbydollarcostaveraging(DCA).Itinvolvesinvestingthesameamountregularlyinagivenfundorstock,illustratedasfollows.Assumethatamutualfundfluctuatesinvaluebetween$5and$15overagivenperiod,andthat$100isinvestedthreetimesatpricesof$10,$5,and$15.Now,theaveragepriceofthefund
overthepurchaseperiodis$10,butusingDCA,aloweraveragepriceisactuallyobtained.Here’show:Wepurchased10sharesat$10,20sharesat$5,and6.67sharesat$15,foratotalof36.67shares.Theaveragepricewasthus$8.18pershare($300/36.67),becausewepurchasedmoresharesatthelowerpricethanatthehigherprice.
DCAisawonderfultechnique,butitisnotafreelunch.Buyingthose20sharesat$5tookgreatfortitude,becauseyouwerebuyingatthe“pointofmaximumpessimism.”Securitypricesdonotgettobargainlevelswithoutagreatdealofnegativesentimentandpublicity.ThinkofwhatitfeltliketobebuyingstocksinOctober1987,junkbondsinJanuary1991,oremerging
marketsstocksinOctober1998,andyou’llknowwhatImean.DonotunderestimatethedisciplinethatissometimesnecessarytocarryoutasuccessfulDCAprogram.Ontheotherhand,therealriskofDCAisthatyourentirebuy-inperiodmayoccurduringapowerfulbullmarket,whichmaybeimmediatelyfollowedbyaprolongeddropinprices.Sucharetheuncertaintiesof
equityinvesting.Alwaysrememberthatyouarecompensatedforbearingrisk,andbuyingduringaprolongedbullmarketiscertainlyarisk.Thereisanevenbetter
methodofgraduallyinvesting,knownasvalueaveraging,(VA),describedbyMichaelEdleson.ProfessorEdlesonproducedtwoeditionsofabookbythat
title,andunfortunatelytheyarebothoutofprint.Asimplifiedversionofhistechniqueisasfollows.Insteadofblindlyadding,say,$100permonth,onedrawsa“value-averagingpath,”consistingofatargetamount,whichincreasesby$100permonth.Inotherwords,oneaimsathaving$100intheaccountinJanuary,$200inFebruary,andsoforth,outto$1,200by
Decemberofthefirstyear,and$2,400byDecemberofthesecondyear.Inthiscase,wearenotsimplyinvesting$100permonth;thiswillhappenonlyifthefunddoesnotchangevalue.Ifthefundvalue-declines,thenmorethan$100willberequired;ifthefundgoesup,thenlesswillberequired.Itisevenpossiblethatifthefundvaluegoesupagreatdeal,nomoneyatallwillhavetobe
addedinsomemonths.Further,assumethatwe
plananinvestmentof$3,600overthreeyears.UsingVA,wewillprobablynotcompleteour$3,600investmentinexactly36months.Ifingeneralthemarketsareup,itmayrequireanotherthreeorsixorninemonthstocompletetheprogram.If,ontheotherhand,thereisabearmarket,
thenwewillrunoutofmoneylongbefore36monthsisup.Let’snowreturntoour
investorwith$200,000toinvestintheaboveassets.Rightoffthebat,hehasaproblem.HisallocationtotheVanguardTax-ManagedSmall-CapFundis5%,or$10,000,whichistheminimuminvestmentamountforthisfund.Further,the
minimuminitialinvestmentfortheotherVanguardfundsisa$3000intaxableaccountsand$1000inIRAs.Table8-3displaysavalueaveragingpathfortheabovestrategy.
Table8-3.SampleValueAveragingPath
Atthebeginningoftheperiod,theamountsnotinvestedintheinitialfundminimumsareplacedintheLimited-TermTax-ExemptFundandShort-TermCorporateFundforthetaxableandIRAaccounts,respectively,fromwhichfurthercontributionstothestockfundsaredrawn.Thismethod,inmy
opinion,isaboutthebest
techniqueavailableforestablishingabalancedallocation,butitisnotperfect.Asalreadypointedout,ifthereisaglobalbearmarket,youwillrunoutofbondreserveslongbefore36monthsareup.Theoppositewillhappenifstockpricesrisedramatically.Itisalsopossible,infact,quitelikely,thatafteratimethetaxableandtax-shelteredhalvesofourallocationwillgetoutof
kilter.Whathappens,forexample,ifthereisadramaticbullmarketinemergingmarketsstocks,whileatthesametimeEuropeanandPacificstocksfallsignificantly?Inthatcase,thereisnoproblemwithsellingsomeofthetax-shelteredEmergingMarketsStockIndexFundandpurchasingadditionalEuropeanandPacificshares.Thismeansthatwewillwind
upwithmorethanour20%allotmentofbondsintheIRAandlessthan20%intheLimited-TermTax-ExemptFund,butthisisarelativelyminorimperfection.However,iftheopposite
happens,wehaveamoreseriousproblem.IfthePacificandEuropeansharesrisesignificantly,whatdowedo?IfwearestillintheVAphase,andbuildingupa
positionintheseassets,thenwewillsimplyhavetowaitafewmonthsbeforethe“valuepath”eventuallyrisesaboveourassetlevel,requiringfurtherpurchases.WhatifthishappensafterwehavecompletedourVAprogram?Inthatcase,sellingsharesofthesefundstogetbackto“policy”wouldhaveserioustaxconsequencesandshouldprobablybeavoided.Aboutthebestwecandoistoavoid
reinvestingdistributionsasaslow“safetyvalve”fortheseoverpricedassets.Valueaveraginghasmany
strengthsasaninvestmentstrategy.Firstandforemost,theinvestorisinvestingatbothmarketlowsandmarkethighs;onebuysmanymoresharesatthelowpointthanatthehighpoint,whichproducessignificantlyhigherreturns.Second,itgivesthe
investortheexperienceofinvestingregularlyduringtimesofmarketpessimismandfear—averyusefulskillindeed.VAisverysimilartoDCA,withoneimportantdifference:Itmandatesinvestinglargeramountsofmoneyatmarketbottomsthanatmarkettops,increasingreturnsevenfurther.YoucanthinkofitasacombinationofDCAandrebalancing.(Value
averagingworksjustaswellinreverse;ifyouareretiredandinthedistributionphaseofyourfinanciallifecycle,youwillbesellingmoreofyourassetsatmarkettopsthanatbottoms,stretchingyourassetsfurther.)Ofcourse,thereisno
reasonwhyyouhavetouseDCAorVA.Let’sassumethatyouhavehadahighstockexposureforyearsand
arewell-acclimatedtofinancialriskandloss.Thereisnoreasonnottoplungerightinandfullyreallocateyourassetsaccordingtoyournewplan.Pleasenotethatthereis
alsonothingsacredaboutmonthlyfundingoverthreeyears—thisismerelyanexample.Youcanusequarterly,weekly,orevendailyfundingifyouarea
whizwithspreadsheets.I’drecommendaminimumoftwotothreeyearsforfunding,however;ifmarkethistoryisanyguide,youshouldhaveanauthenticbearmarket(oratleastcorrection)duringthistime.Thiswillenableyoutotestyourresolvewiththerelativelysmallmandatedinfusionsandtoultimatelyconvinceyourselfofthevalueofrebalancing.
Onceyouhavetransferredallofyourcashandbondsintoyourdesiredallocation,itbecomesasimplemattertoperiodicallyrebalancetheaccountbacktothepolicy,or“target,”compositions.Howoftenshouldyoudothis?Again,thatdependsonwhetheryourassetsareinatax-shelteredorataxableaccount.
RebalancinginaTax-
ShelteredAccount
Howoftendoyourebalanceyourportfolio?Ifyouareinvestinginatax-shelteredaccount,youcandosoasoftenasyouwish,sincetherearenotaxconsequences.Inthisinstance,whatistheoptimalrebalancingfrequency?Recallthatthemajoreffectofrebalancingonreturnistherebalancingbonus,theexcessreturn
obtainedfrombuyinglowandsellinghighthatrebalancingforces.Rebalancingcanberegardedastheonlyconsistentlyeffectivemethodofmarkettiming.Whatwearereallyaskingis:Whatrebalancingperiodproducesthegreatestrebalancingbonus?Theansweriscomplexbutbasicallyhingesaroundfindingtheintervalforwhichtheaggregatecorrelation
amongportfolioassetsislowestandannualizedvariancesthehighest.Inotherwords,theassetvariancesandcorrelationcoefficientsduringagivenperiodaredifferentdependinguponwhatreturnintervalsarebeingused:e.g.,daily,weekly,monthly,quarterly,annually.Theintervalwiththelowestcorrelationsand/orthehighestvariancesistheoptimalrebalancingperiod.
I’veseenoptimalrebalancingperiodsrangingfrommonthlytoaslongasonceeveryseveralyearsforsimilarportfolios.Thereisprobablynowaytopredictinadvancewhichrebalancingperiodwillbeoptimalforagivenportfolio,butasageneralrule,longrebalancingintervalsarepreferred.ThisisbecauseofthemomentumphenomenondiscussedinChapter7;asset-classreturns
haveaslighttendencytotrend,anditisbesttotakeadvantageofthischaracteristic.Inotherwords,above-orbelow-averageasset-classperformancehasatendencytopersist,anditisbesttoletsuchbehaviorrunitscourseforawhilebeforerebalancing.Ifyou’rehavingtroublewiththerebalancingconcept,don’tfeelbad.It’saverycomplicatedareaandisoftenmisunderstoodbyeven
themostsophisticatedplayers.TheeasiestwaytothinkabouttherebalancingintervalproblemistoimagineaportfolioconsistingonlyofU.S.andJapanesestocks.Sincetheformerhasheadednearlystraightupandthelatternearlystraightdownoverthepastdecade,rebalancingasrarelyaspossible(perhapsevery10years!)wouldhavebeenpreferabletodoingso
frequently.Ifyourebalanceeveryyearortwo,youprobablywon’tgotoofarwrong.
RebalancingYourTaxableAccounts
Moredefiniterecommendationscanbemaderegardingrebalancingtaxableaccounts:Dosoassparinglyaspossible.Infact,agoodcasecanbemadefor
neverrebalancing,consideringthecapitalgainsjoltyouwillgeteachtimeyoudo.Firstandforemost,sellingyourtaxablestockandbondfundstriggerscapitalgainstaxesatthefederalandstatelevel.Second,frequentlybuyingandsellingtaxablemutualfundscanbeanaccountingnightmare,althoughVanguardandafewotherfundcompanieshavemadelifequiteabiteasier
withyear-endshare-trackingreports.Eventhemosttax-efficientindexfundshavesomeyear-enddistributions.Ifaparticulartaxablefundexceedsitspolicytarget,atleastavoidreinvestingthesedistributions.Instead,takethedistributionincash,soitcanberebalancedelsewhere.Itisfinetoaddfrequentlytoataxablemutualfund,butI’drecommendsellingatmostonceperyear.Rememberto
meticulouslyfileandsaveyourtransactionslipsandaccountstatements.Theopinionofyouraccountantshoulddefinitelybesoughtinthesematters.
DoesItHavetoBeThisComplex?
Thisbookisaimedattheinvestorwhowishestosqueezeeverybitofreturn
possibleoutofagivendegreeofrisk.Aswehaveseen,theessenceofthisinvolvessplittingyourportfoliointomanysmallimperfectlycorrelatedparts.Thismayseemdistastefullycomplextosomereaders.Thetraditionalall-U.S.half-stockandhalf-bondportfolioisextremelysimpleandeasytorebalance.VanguardevenofferssinglefundswhichwillprovidevariousmixesofU.S.stock
andbondindexes.Forthisconvenience,youareprobablysacrificing1%to2%oflong-termreturnforagivendegreeofrisk.Anothercompromise
wouldbetosplityourstockcomponentequallyintosixVanguardindexfunds(Value,500Index,Small-Cap,European,Pacific,andEmergingMarkets)foryourstockcomponentanduseone
oftheirshort-termbondfundsforthefixed-incomecomponent.Evensimpler,VanguardoffersaTotalInternationalIndexFund.Forthosewhovaluetheconvenienceofsimpleportfolios,thesecompromisesmaybeworthwhile.(OnecaveatabouttheVanguardTotalInternationalFund:Itisa“fundoffunds”andthusnoteligiblefortheforeigntax
credit.IrecommendthenewVanguardTax-ManagedInternationalFundforthispurpose.)
TheEverythingFund
Isitpossibletofindasinglefundwhichwillrelieveyouofallofthetroubleofassetallocation?Sure—themutualfundindustryisnothingifnotresponsivetoeverywhimoftheinvestingpublic.There
aremanyfundswhichwillprovideyouwithwhattheyconsidertobethe“optimal”assetallocation;thesearecalled,naturally,asset-allocationfunds.Thereareafewproblemswiththesefunds.First,theyhavenotbeenaroundforverylong,soitishardtoevaluatethem.Second,whatlittletrackrecordtheydohaveisnotparticularlyimpressive.Theaverage10-yearannualized
return(forApril1988–March1999)ofMorningstar’sasset-allocationandglobalfundswas10.79%,comparedwith17.70%forthebroadlybasedWilshire5000,and9.08%fortheLehmanLongBondIndex.Evenmoreamazingly,itwasalmostpreciselythesameasthe10.80%returnedbytheMSCIWorldIndex,inspiteofthefactthatthisbenchmarkstartedouttheperiodwithabout40%
Japaneseequity,whichsubsequentlyreturned−4.11%annually.Inotherwords,theaverageasset-allocationfundwilldoaboutaswellastheworstpossibleindexedglobalallocation.Itwouldbeniceif
Vanguardofferedareasonableglobalindexfund,buttheydonot.Theirasset-allocationfunds(Wellesley,Wellington,AssetAllocation,
LifeStrategies,STAR,andGlobalAssetAllocation)havethedisadvantageofbeinggrosslyunderweightedinforeignandsmallstocks.Idonotrecommendanyofthesefunds.Lastly,Vanguardmaygetitsacttogetherandcomeoutwithan“everythingindexfund”comprisingalloftheworld’sinvestableassets,nowthatMr.Bogle,whodislikesforeignassets,hasretired.Staytuned.
Forthosewishingtouseoneortwofunds,Imakethefollowingrecommendationwithsometrepidation.TheTweedy,Brownefirmhasalongrecordofconsistentvalueinvesting;onecouldeasilysplitone’sinvestmentsbetweentheirAmericanandGlobalValuefunds.Theyhaveadistinguishedrecordinprivatemoneymanagement,buthavebeeninthemutualfundbusinessforlessthan
sixyears.Theyhavedoneverywell,buttheirexpensesarefairlyhigh;I’dkeepaneyeonthem.Iwouldalsousethemonlyintax-shelteredaccounts.Thedangersofrecommendingactivelymanagedfundsarevividlyillustratedbythe“one-stop”choicesprovidedinapreviousversionofthisbook:SoGenInternationalandMutualDiscovery.Theformerhasfallenflatonits
face,andthelatterhaslostitsstarmanager(MikePrice)andhasbeengobbledupbythatfacelessconglomerateknownasFranklinResources.I’dliketobelievethatthesamewillnothappentoTweedy,Browne,butifhistoryisanyguide,itprobablywill.
KeepingAbreastofMarketValuation
InChapter7wediscusseddynamicassetallocation—changingyourpolicyallocationfromtimetotimeinlinewithassetvaluations.Don’ttrythisoneathome,unlessyouhaverebalancedsuccessfullythroughatleastafewmarketcycles.Ifyoudogettothatpoint,remember,increaseyourallocationofanassetonlyafterithasgottenmeasurablycheaperandonlyafterithasbeenhammeredin
price.Neverincreaseyourallocationtoanassetbecauseofeconomicorpoliticaleventsorbecauseyouhaveheardananalystmakeaconvincingcasefordoingso.Thesamegoesfordecreasingyourallocationinagivenarea:Dosoonlybecauseitsvaluationshavegottenmuchhigherafteramajorrun-up.Evenifyouhaveno
intentionofeverchanging
yourpolicyallocations,itisstillagoodideatobecomeinformedaboutmarketvaluations.ByfartheeasiestwaytodothisbypurchasingMorningstar’sPrincipiamutualfunddatabase.Then,lookuptheP/E,P/C(price/cashflow),P/B,anddividendyieldfortherelevantindexfunds:
Vanguard500Index(S&P500)
VanguardValueIndexVanguardGrowthIndexVanguardSmall-Cap
GrowthIndexVanguardSmall-Cap
ValueIndexVanguardSmall-CapIndex
(Russell2000)VanguardExtended
MarketIndex(Wilshire4500)VanguardTotalMarket
Index(Wilshire5000)
VanguardEuropeanStockIndex(EAFE-Europe)VanguardPacificStock
Index(EAFE-Pacific)VanguardEmerging
MarketsStockIndex(MSCI-EMindex)DFAU.S.9-10Small
Company(verysmallU.S.stocks)DFAU.K.SmallCompanyDFAEmergingMarkets
DFAJapaneseSmallCompanyDFAContinentalSmall
CompanyDFAPacificRimSmall
Company.(SoutheastAsia,Australia,andNewZealand)
Ifyou’renotwillingtopayforPrincipia,thenBarra’sWebsiteprovidesamultitudeofvaluationparametersforabroadrangeofdomestic(butnotforeign)assets.As
discussedabove,P/Banddividendyieldarethemoststablemeasurements,withP/EandP/Cbeingoflessuse.Dividendyieldistheonlymeasurethathasanymeaningacrossdifferentstockassetclasses.Itisalwaysagoodideato
knowhowexpensivethetomatoesare;keepingabreastoftheabovemeasuresisthebestwaytodothis.Each
timeIgetanewMorningstardisk,thefirstthingIdoisprintoutthevaluationparametersforalloftheabovefundsandfileitaway.ByfollowingP/Banddividendyieldovertime,itiseasytoseejusthowcheaporexpensiveanassetclasshasbecome.Howexpensivearethe
tomatoesrightnow?Asexpensiveastheyhaveever
been.TheP/BoftheS&Piscurrently10.5.Ithasneverbeenevenremotelythishighexceptoncebefore—in1929.Thedividendyieldisalsoatarecordlow1.3%.ThehistoricaldataonU.S.smallstocksandforeignlargestocksdonotgobackveryfar,buttheP/Boftheseareas(about3forsmallcap,and4forforeign)isalsoprobablyveryhighbyhistoricalstandards.ByP/Bcriteria,
smallforeignstocksseemcheaper(at2.4);whetherthisisausefulpieceofinformationisanybody’sguess,asthereisnotmuchinformationaboutthehistoricalrangeofP/Bforthisassetclass.ManynowassertthatP/Banddividendyieldhavebecomeirrelevant.However,atmarkethighs,onealwayshearsargumentsabouthowtheoldvaluationmeasuresdon’tmatterany
more.Infact,itisimpossibleformarketvaluationstogotoveryhighlevelswithoutawidespreadbeliefthattheoldyardsticksarebroken.Maybetheyare,butitisworthrememberingthelegendaryJohnTempleton’sadmonitionthatthefourmostexpensivewordsintheEnglishlanguageare“thistimeit’sdifferent.”(Theauthorwilladdthefivedumbestwords:“Thebullmarketremains
intact.”)
Retirement–TheBiggestRiskofAll
Thisbookisfocusedprimarilyontheinvestmentprocess,particularlytheestablishmentandmaintenanceofefficientallocations.Assetallocationinretirementisnodifferent,exceptthatyouwillprimarily
beusingyourwithdrawalstocontrolyourallocations,asopposedtodepositsandrebalancing.However,thereisarisk
peculiartoretirementcalled“durationrisk.”Inordertoexplorethis,let’sstartwiththesimplestandleastriskyofallinvestments,aone-yearTreasurybill.Abillisinrealityazero-couponbond,boughtatadiscount.For
example,a5%billwillsellatauctionfor$0.9524andberedeemedatpar($1).Ifafewsecondsafteritisissuedyieldssuddenlyriseto10%,thebillfallsinpriceto$0.9091,withanimmediatelossof4.55%invalue.Butifourinvestorholds
thebilltomaturity,heorshewillreceivethefull5%return,thesameasiftherehadbeennoyieldriseand
pricefall.Andbeyondoneyear,it’sallgravy—ourinvestorcannowreinvesttheentireproceedsatdoubletheyield.The“pointofindifference”isthustheone-yearmaturityofthebill;beforeoneyeartheinvestorisworseoffbecauseoftheyieldriseandpricefall;afteroneyear,theinvestorisbetteroff.Nowconsideraholderofa
30-year5%Treasurybond.Ifsoonafterpurchaseatparweseethesameriseinyieldto10%,ourhaplessinvestorhasreceivedafinancialkickinthesolarplexus—thebondisnowworthlessthan53centsonthedollar.(Thereasonisthatalmosttheentirevalueofthebondisrepresentedbythesubsequent5%couponpayments,worthonlyhalfofthecurrent10%marketyield.Thisispreciselywhat
happenedtobondholdersbetween1967and1979.)However,abondisaverydifferentbeastthanaT-bill:Itthrowsoffcouponsthatcanbereinvestedatthehigheryield.Becauseofthis,therecoveryfromdisastertakesconsiderablylessthan30years.Infact,itonlytakesourhaplessbondholder10.96yearstobreakeven.This10.96-yearperiodisknowninfinancialcirclesasthe
durationofthesecurity,andforacoupon-bearingbonditisalwayslessthanthematurity,sometimesconsiderablyso.(Forazero-couponbond,maturityanddurationarethesame.)Therearelotsofother
definitionsofduration,somedizzyinglycomplex,but“pointofindifference”isthesimplestandmostintuitive.(Theotherusefuldefinitionis
theratioofprice-to-yieldchange.Thatis,our30-yearbondwilldecrease10.96%inpricewitheach1%increaseinyield.)Durationisalsoanexcellentmeasureoftheriskofaninvestment.Thehighertheduration,thebiggertherisk.Toreiterate,after10.96years,ourunluckybondholderisbetteroffforthefallinpricebecauseoftheriseinyield.
Durationisalmostalwaysusedtodescribebonds,butthereisnoreasonwhyyoucan’tapplythesameconcepttostocksaswell.It’sasimplemattertomodelthedurationofthestockmarket.Forexample,stocksarecurrentlyyieldingabout1.3%.Iftheydecline75%,theabsoluteamountofthedividendremainsthesame,butyouarenowinvestingthosedividendsatayieldthat
isfourtimeshigher—5.2%.Eventuallythiswillredoundtoyourbenefit,andyouwillwindupbetteroffthanattheloweryieldandhigherprice.Howlongdoesittaketocatchup?Itdependsonthebeginningyieldandthemagnitudeofthedecline.Withtoday’s1.3%stockyield,a25%declinewouldhaveadurationof63years;a50%decline,51years;a75%decline,33years;anda90%
decline,only19years.Skepticswillpointoutthat
a90%stockdeclinewouldlikelybeassociatedwithadecreaseintheabsolutedividendamount,butevenduringtheGreatDepressiontherealdividendstreamoftheDowdecreasedbyonly25%.Infact,the1929–1933bearmarketprovidesasuperbrealitycheckoftheaboveparadigm.Onedollar
investedinstocksonLaborDay1929declinedinvalueto16.6centsbyIndependenceDay1932andincreasedbacktoparbytheendofJanuary1945—lessthan13yearsafterthebottom.Thedividendyieldwas
2.6%inSeptember1929,andforthe30yearsafterthat,earningsgrowthwasonly1.8%.Thus,hadthecrashnot
occurred,onlythenstockswouldhavereturned4.4%peryear,resultinginabreak-evenpointwithwhatactuallyoccurredinJanuary1952,or22yearslater,almostexactlythesameperiodpredictedbythedurationmodel.Viewedfromthisperspective,today’smarketisagooddealmorefrighteningthanthatof1929,sincea75%stockdeclineproducesadurationof19yearsatthe2.6%1929yield,
versus33yearsatthecurrent1.3%yield.Certainly,sucha
wrenchingmarketdeclinetodaywouldwreakhavoconthefinancialandsocialstructureoftherepublic,asitdid70yearsago.Butatthesametime,today’shighpricesandresultantlowyieldsarenogreatblessingeither.Thisisbecausethelowerthecouponordividend
yield,thelongertheduration.Thus,thelowertheyield,thehigherthemarketprice;thelongertheduration,thegreatertherisk.Isthereawaythat
individualscanshortenthedurationoftheirstockportfolio?Yes.Sincethesizeoftheyieldinfluencesduration(thegreatertheyield,theshortertheduration),youcaneffectively
increasetheyieldofaportfoliobyaddingtoiteverymonth.Let’sbeginwiththe1.3%yield,75%pricefall,and33-year-durationscenarioreferredtoabove.Ifyoustartwith$10,000andneitheraddnorwithdrawfromyouraccount,youwillbreakevenatthe33-yearduration.Butcontinuouslyaddin$200permonthandyoubreakevenatjustover11years.
Theexpedientofshorteningyourstockandbonddurationwithadditionalinvestmentisofcoursenotavailabletoyouinretirement;retireescanbedevastatedifthedurationoftheirstockandbondholdingsislongerthantheirretirementhorizon.Forthetrulylong-term
investor,theresultsofaprolongedbearorbullmarket
mayverywellproveoflittleconsequenceormayevenproducesurprisinglyparadoxicalresults.Butinreality,equanimitytomarketdeclinesdependsontimehorizon.Ifyou’reretiredandlivingoffsavings,youwillneitherhaveenoughtimetogetoverthedurationhumpnorbeabletomakethecontributionstoshortenit.Ifyou’reaboomerwhoisstilladdingtoadecent-sizednest
egg,thenyouwilllikelyhaveplentyoftime.Andifyou’reatwenty-somethingjustbeginningtosave,thengetdownonyourkneesandprayforamarketcrash.Therecanbenoquestion
thatinvestorsexperienceriskasashort-termphenomenon.Whenwethinkaboutinvestmentpain,thefirstthingthatcomestomindisabrutalbearmarketswhich
leavesourportfolioconsiderablylighterthantheywereafewmonthsoryearsbefore.But,aswe’veseen,timehealsalmostallasset-classwounds,andthebiggestriskthatwefaceissimplythatwewillrunoutofmoneybeforeweshuffleoffourmortalcoil.Afterall,mostofusaresavingandinvestingforapurpose,usuallyretirement,orsomeotherwell-definedfuturefinancial
need.Theivory-towertypesrefertothisasshortfallrisk,andit’sworthafewpagesofconsideration.(We’vealreadytalkedinChapter7abouthowinvestorstendtoobsessonshort-termrisksandrewards,whileignoringthemoreimportantlonger-termpicture.)Thereareeasilyavailable
retirementcalculatorswhichcanhelpyoudeterminethis
risk,butit’simportantforyoutodevelopanintuitivefeelfortheproblem.Let’sstartwithanestimateofyourbefore-taxneeds.Assumethatyou’vedeterminedthatyouneed,inadditiontoyourSocialSecurity,$40,000inannualincome.It’sbesttosimplifythecalculationbyfactoringoutinflationbyusingreal,orinflation-adjusted,investmentreturns.Thatwayyouarealways
dealingwithcurrent,constantpurchasing-powerdollars.Aswe’vealreadydiscussed,areasonableestimatefortherealreturnofamixedstockandbondportfolioissomewhereintheneighborhoodof4%.Thatmeansthatyoushouldbeabletospend4%ofyourportfolioeachyearwhilemaintainingitsrealvalueindefinitely.Andifyoucanmaintaintheportfolio’sreal
valueindefinitely,sotoocanyoumaintaintherealvalueofyourwithdrawals.Inthatcase,youwillneed$1,000,000inassets,since4%of$1,000,000is$40,000.Inotherwords:
Thiscalculationassumesthatyouwishtokeepyour
principalintact.Ifyouarewillingtoexpireonscheduleafter30yearswithzeroassets,youwillneedless.Usingtheannuity/mortgagefunctiononafinancialcalculator,suchasaTexasInstrumentsBA-35(about$20atmostdiscountstores),wecomeupwithrequiredsavingsofonly$691,681.Thesecalculationsvividly
demonstratetheextreme
importanceofkeepinginvestmentexpenseundercontrol.The4%returnassumptionreferstothemarketreturn,fromwhichinvestmentfeesandotherexpenseshavetobesubtracted.Ifyourretirementaccountor401(k)planusesthetypicalassortmentoffundchoicesbearing1%–2%totalexpenses,thenyoumayneeduptotwiceasmuch($40,000/0.02=$2,000,000)
inretirementsavingsthanifyouhadusedlow-costindexfunds.Thiskindofcalculationemphasizestheextremeimportanceofattentiontoexpense—inthissituation,2%ofadditionalcoststranslatesintoadoublingofyourretirementsavingsrequirement.Butthere’sanevenworse
problemembeddedintheretirementcalculation.
Retirementcalculatorsalmostallmakethesameerroneousassumption—thatourreturnisthesameeachandeveryyear.Forexample,inthecalculationaboveweassumedthatweshallreceivea4%returneveryyear.Wealreadyknowthatintherealworld,investmentreturnsarenotthesameeachyear.Itturnsoutthattheorderofthegoodandbadyearsmattersagreatdeal.
ToillustratethisphenomenonIwentbacktogoodoldUncleFred’scointoss,withitsreturnofeither−10%or+30%.Ifover30yearsyoutoss15headsand15tails,youearnacompoundedrateof8.17%.Ifyoustartwitha$1,000,000portfolioandrollalternatingheadsandtailsoverthe30-yearperiod,thenyouindeedcanwithdraw$81,700annually(8.17%oftheinitial
amount)overthenext30yearsandstillkeepthe$1,000,000principalintact.However,ifyouareunluckyenoughtoroll15straighttailsbeforerolling15straightheads,youcanwithdrawonly$18,600peryearbeforeallthemoneyrunsout.Reversetheprocessandrollthe15headsfollowedby15tails,andyoucanwithdraw$248,600peryear.Ifyouareinthesavingphaseofan
investmentprogram,youaremuchbetteroffhavingthebadyearsatthebeginningofyoursavingsprogramthanattheend.Inotherwords,aswe’vealreadydiscussed,youngerinvestorsshouldprayforabearmarket,andolderinvestorsforabullmarket.Thisphenomenonwasfirst
broughttotheattentionoftheinvestingpublicbyPhilipL.
Cooley,CarlM.Hubbard,andDanielT.WalzfromTrinityUniversity.Theylookedatthe“successrate”ofvariouswithdrawalstrategiesovernumeroushistoricalperiods,andtheycametotheconclusionthatonlyawithdrawalrateof4%to5%oftheinitialportfoliovalue(i.e.,$40,000−$50,000ofa$1,000,000portfolio)hadareasonableexpectationofsuccess(whichthey
definedasdyingwithoutdebt).Andremember,theywerelookingathistoricaldata,with7%realequityreturns.Onamorebasiclevel,
however,youcanapplyamuchsimpleracidtesttoyourwithdrawalstrategy:Whatwouldhappenifthedayyouretiredmarkedthebeginningofalong,brutalbearmarket,say,onJanuary
1,1966,andyoulivedforanother30years,untilDecember31,1995?Forthefirst17years(1966to1982),thereturnoftheS&P500wasapaltry6.81%.Bygruesomenumericalcoincidence,thiswasidenticaltotherateofinflationfortheperiod,makingtherealstockreturnforthewhole1966–1982periodzero.Thereturnforthenext13years(1983–
1995)wasspectacular,bringingtherealreturnforthewhole30-year1966–1995periodupto5.4%,nottoofarbelowthehistoricalnormof7%.Iconstructedanall-equity
allocationconsistingof80%S&P500and20%U.S.smallstocks,andmixedthiswithfive-yearTreasuries.Iassumedthatonebegantheperiodwith$1,000,000and
thencalculatedresultsofvariouswithdrawalratesfromthefollowingmixes:100%stock,100%bond,and75/25,50/50,and25/75mixesofboth.Theresultsof7%,6%,5%,and4%withdrawalrates(thatis,annuallywithdrawing$70,000,$60,000,$50,000,and$40,000)areplottedinFigures8-1through8-4.Theall-stockportfolioisthethickestline,andthethinner
theline,thelessstock.Again,itisimportanttorealizethattheamountsontheyaxesareininflation-adjusted1966dollars.Thisisthesimplestandclearestwayofperformingthissortofcalculation.
Figure8-1.$70,000annualreal(1966dollars)withdrawal.
Figure8-2.$60,000annualreal(1966dollars)withdrawal.
Figure8-3.$50,000annualreal(1966dollars)withdrawal.
Figure8-4.$40,000annualreal(1966dollars)withdrawal.
Theresultsareprofoundlydisturbing.Sincerealequityreturnswereover5.5%duringthisperiod,thismeansthata“penalty”ofabout1%–2%wasextractedby“theluckofthedraw.”Thismeansthatiffuturereal
portfolioreturnsaregoingtobeonly4%,theninaworstcasescenarioyoumayonlybeabletowithdraw2%ofthestartingamountofyournesteggeachyear.Andthisgetstotheheartofhowweperceiverisk.Theoddsarethatyouwillnotencountertheworstcaseofaprolongedandprofoundbearmarketatthebeginningofyourretirement.Infact,itisequallylikelythatthe
oppositemayoccur—aprolongedbullmarketatthebeginning—andthatyouwillbesittinginunexpectedclover,abletowithdraw6%ormoreofyourstartingamounteachyear.Butwecannotforecastthefuture.Ifyouplan“reasonable”withdrawals,thereisonlyasmallriskofdisaster,whichyoucanlessenbyloweringyourretirementlivingstandards.
Finally,UncleSamhasprovidedatemptingwayoutofthisdilemma—TreasuryInflation-ProtectedSecurities(TIPS)currentlyyielda4%inflation-adjustedreturn.Ifyoucanliveon4%ofbefore-taxsavings,andyoucanshelteralmostallofyourretirementmoneyinaRothIRA(whichwouldnotrequiremandatorydistributionsafterage70½),thenyouareguaranteed
successforupto30years.Fordevoutbelieversinthevalueofawell-diversifiedportfolio,thisoptionisprofoundlydisturbing—thefinancialequivalentofEden’ssnake.Ifindithardtorecommendthispath.However,ataminimumahealthycommitmenttoTIPSinyourtax-shelteredaccountisprobablynotabadidea.
CousinHarryAsksYourAdvice
Decadespass;youhaveallbuttakenoverthefamilybusinessfromUncleFred,whosedutieshavebecomeincreasinglyceremonial.Yourbeloveduncleretainsoneimportantareaofcontrol:theretirementfund.Youryoungercousin
Harryisafairlyrecenthire.Onedayhewalksintoyour
officewithaquizzicallookonhisface.Evenbeforeheopenshismouth,youknowwhyhehascome:UncleFredhasjustmadehimanoffer.Bynowyouhavegainedareputationaboutmattersfinancialequaltothatofyouruncle,butunlikehimyouarenotgiventoSocraticteaching.Youareverybusy,soyoutrytoanswerquestionsasdirectlyaspossible.Whatadvicecan
yougiveCousinHarry?
1.Riskandrewardareinextricablyentwined.Donotexpecthighreturnsfromsafeassets;investmentswithhistoricallyhighreturnsarecapableofinflictingferociouslosses.2.Thosewhodonotlearn
fromhistoryarecondemnedtorepeatit.Becomefamiliarwiththelong-termhistoryofthebehaviorofdifferent
classesofstocksandbonds;thesurprisedinvestorisafailedinvestor.3.Portfoliosbehave
differentlythantheirconstituentparts.Asafeportfoliodoesnotnecessarilyexcludeveryriskyassets;excessiverelianceonsafeassetsmayactuallyincreaseportfoliorisk.Eventheinvestorwhoseeksthesafestpossibleportfoliowillown
someriskyassets;aportfolioconsistingof“safe”largestockswilloftenhavelessreturnandhigherriskthanonepartitionedbetweenriskysmallerstocksandcash.4.Foragivendegreeof
risk,thereisaportfoliothatwilldeliverthemostreturn;thisportfoliooccupiestheefficientfrontierofportfoliocompositions.Theinvestorobviouslyseeksaportfolio
thatsitsontheefficientfrontier;unfortunately,itslocationbecomesknownonlyinretrospect.Theinvestor’sobjective,then,isnottofindtheefficientfrontier;thatisimpossible.Rather,thegoaloftheintelligentassetallocatoristofindaportfoliomixthatwillcomereasonablyclosetothemarkunderabroadrangeofcircumstances.Portfoliosconsistingofawidevariety
ofdomesticandforeignlargeandsmallstocks,andwhosebondsarebothforeignanddomestic,seemtodothisthebest.5.Focusonthebehaviorof
yourportfolio,notonitsconstituentparts.Smallportionsofyourportfoliowilloftensustainseriouslosses,butwillcauseonlyminordamagetothewholeportfolio.
6.Recognizethebenefitsofrebalancing.Thecorrectresponsetoafallinassetpriceistobuyabitmore;thecorrectresponsetoarisingpriceistolightenupabit.Rebalancingismerelyadisciplinedwayofaccomplishingthis.Prolongedmarketdeclineswillmakerebalancingseemafrustratingwasteofmoney;intheend,however,assetpricesalmostalwaysturn
around,andyouusuallywillberewardedhandsomelyforyourpatience.7.Themarketsaresmarter
thanyouare;theyarealsosmarterthantheexperts.Rememberthatastoppedclockisrighttwiceaday.Eventhemostineptanalystoccasionallymakesagoodcall,andhewillprobablybeinterviewedbyLouRukeysersoonafterhehasmadeit.
Nobodyconsistentlypredictsmarketdirection.Veryfewmoneymanagersbeatthemarketinthelongrun;thosethathavedonesointherecentpastareunlikelytodosointhefuture.Donotrunwiththecrowd;thosewhofollowtheelephantherdoftengetdirtyandsquashed.8.Knowhowexpensivethe
tomatoesare.Keepaneyeonmarketvaluation.Changesin
yourpolicyallocationshouldbemadeonlyinresponsetovaluationchanges,andtheyshouldbemadeinadirectionoppositetothepriceoftheasset.Rememberthatmarkethistoryteachesusthateconomicandpoliticalconsiderationsareworthlessasmarketpredictors;thebesttimestobuyarewhenthingsseemthebleakest.9.Goodcompaniesare
usuallybadstocks;badcompaniesareusuallygoodstocks.Favora“value”approachinyourstockandmutualfundchoices;theP/Bratioisthebestindicatorofthis.10.Inthelongrun,itis
veryhardtobeatalow-expenseindexmutualfund.Trytoindexasmanyofyourinvestmentsasyoucan;bondfundexpensesshouldbeless
than0.5%,domesticstockfundexpenseslessthan0.7%,andforeignfundexpenseslessthan1%.
9InvestmentResources
Ifyou’relikeme,youforgetmuchofwhatyouhavereadafterarelativelybriefperiodoftime.Ifyouaremanagingevenamodestassetpool,thematerialcoveredhereinissimplytooimportantto
forget.No,I’mnotsuggestingthatyouperiodicallyrereadthisbook.Rather,Isuggestthatyoumakefinancepartofyourregularreadingprogram.Ifyoureadjustoneusefulbookonfinanceperyear,youwillwindupbetterinformedthanmostprofessionals,andyourfiscalhealthwillimproveaswell.AllofthebooksIshallrecommendarequitewellwrittenandshouldnotserve
assubstitutesforsleepingmedicine.
AModestReadingList1.ARandomWalkDown
WallStreet,byBurtonMalkiel.Anexcellentinvestmentprimer,itexplainsthebasicsofstocks,bonds,andmutualfundsandwillreinforcetheefficient-marketconcept.
2.CommonSenseonMutualFunds.ReplacesBogleonMutualFunds,bywhoelse,JohnBogle.Thiswillprovidemoredetailthanyoueverwantedtoknowaboutthisimportantinvestmentvehicle.Mr.BogleisthechairmanandfounderoftheVanguardGroup,andhehasbeenanimportantvoiceintheindustryfordecades.Beautifullywritten,
opinionated,andhighlyrecommended.Thebookalsodemonstratesthedemocratizationwhichhasswepttheinvestmentindustryinrecentyears.Untiladecadeago,thesortofsophisticatedmutualfundanalysisdescribedinhisbookwasthebriefofjustahandfulofprofessionalswithaccesstoexpensiveproprietarydatabasesandmainframecomputers.Almostallof
Bogle’sworkwasdonewithasubscriptiontoMorningstarandastatisticallycompetentassistant;itcouldhavebeenperformedbyanysmallinvestorwithsimilarsoftwareandability.3.AssetAllocation,by
RogerGibson.Thiscoversmuchofthesamegroundasthisbook,withmoreemphasisonthequalitiesofindividualassets.Oriented
towardthefinancialadvisor.4.GlobalInvesting,by
RogerIbbotsonandGaryBrinson.Thisisabeautifullywrittenvolumeonthehistoryofinvestibleassets.Aninformedinvestorcannotknowenoughaboutmarkethistory,andthisisthebestsinglesourceinthisarea.WanttoknowwhatthereturnsforU.S.stockshavebeenineachofthepast200
years?Thepriceofgoldforthepast500years?Interestratesandinflationforthepast800years?It’sallhere.Asimpliedbythetitle,theauthorsalsoprovideanexcellentperspectiveontheplaceofforeignassetsinadiversifiedportfolio.Theyprovidesomeworthwhileinsightsonportfoliotheoryandtheefficiencyofthemarketplace.
5.WhatHasWorkedinInvestingisafreepamphletfromTweedy,Browne.Alow-keysalespitchfortheirfunds,itisalsothebestcompilationI’veseenofthedatasupportingthevaluemethod.Thephonenumberis1-800-873-8242.Itisalsoavailableonlineathttp://www.tweedy.com.6.TheNewFinance:The
CaseAgainstEfficient
Markets,byRobertHaugen.Ifyou’reintriguedbytheTweedypamphletandwonderwhyvalueinvestingstillworksafteralltheseyears,thisisyourbook.Theproseisbreezy,evenquirky—BenGrahammeetsHunterThompsononbadacid.7.ValueAveraging,by
MichaelEdleson.Anextremelyusefulhow-tobookondeployingalump
sumofmoneyamongmultipleassets.Unfortunatelyoutofprint,withluckitcanbefoundontheshelfofalargesecondhandbookstore.8.TheIntelligentInvestor,
byBenGraham.Apopularizedandmorereadableversionofhisearlierclassic,SecurityAnalysis,writtenwithDavidDodd.Althoughithasgreat
relevancetothemarketsingeneralandshouldbereadbyanyseriousinvestor,itisparticularlypertinenttoanybodywhofeelscompelledtobuyindividualstocks.Manyoftoday’smostsuccessfulmoneymanagersobtainedtheiroriginalfinancialinspirationfromthesetwobooks.Itisalwaysfuntolookatexcessesinthemarketplaceandask,“WhatwouldBensayaboutthis?”
(Bytheway,ifyougetbittenbytheGrahambuganddecidetoreadSecurityAnalysis,makesureyoureadtheoriginal1934edition,recentlyreprintedbyMcGraw-Hill.)9.TheWallStreetJournal.
TheWSJisactuallythreenewspapers.Thefirstsectionisasuperbnationalnewspaperwithincisivecommentaryonthemajor
issuesfacingmodernsociety,aswellasasurprisingdollopofwhimsy.First-timereaderswillalsobesurprisedattheliberalbentofmanyofthearticles.Thesecondsectionisamarketingperiodical,andmakesexcellentfishwrap.Thethirdsectioncontainsthemostcompletefinancialdataavailableinadailypaper,aswellasfinancialcommentary.Onceaweekasectiononpersonalfinance
appears,“GettingGoing,”coveringpersonalinvesting,individualassets,taxandretirementstrategy,andevensomeportfoliotheory.Thisseriesaloneisworththesubscriptionprice.Ihaveafileofthesearticlesathomethatisconstantlygrowing.10.JointheAmerican
AssociationofIndividualInvestors.Thefeeforthisisnominal,andwith
membershipyougettheAAIIJournal,whichcontainsmanyexcellentarticlesonpersonalfinance.11.IfyouhaveaPCat
homeoratwork,subscribetoMorningstar’smutualfunddatabase.Thiscostsfrom$95toover$600peryear,dependingonupdatefrequencyanddepthofdata;itissimplythebestbargainininvesting.Theserviceisan
effectivewaytodealwiththemorethan10,000mutualfundscurrentlyavailable.Themajoradvantageofthissoftwareisthatitallowsyoutocustomizeyourcriteriaforfundselection.Ifyouarenotcomputer-literate,MorningstarhasaprintlistingofmutualfundsusingtheValueLineformat;itcostsabout$300peryearandisavailableatmostlargepubliclibraries.
Forthosefewreaderswhowereintriguedbythemathematicalandtheoreticalaspectsofthisbook,Iwouldalsorecommendthefollowing:12.PortfolioSelection,by
HarryMarkowitz.Describesinfairlyunderstandabletermsmean-varianceanalysis.Themoreformaltext,Mean-VarianceAnalysisinPortfolioChoiceandCapital
Markets,isinaccessibletoallbutthosewithextensivemathematicalback-grounds.IfounditremarkablethatmostoftheanalystsIhavespokentohavenotreadeitherbook.13.Stocks,Bonds,Bills,
andInflation,fromIbbotsonAssociates.ContainsextremelydetailedfinancialdataonmanyimportantU.S.assetsgoingbackto1926,aswellasanexcellent
descriptionofthemathematicaloperationsinvolvedinassetandportfolioanalysis.
Finally,I’moftenaskedhowI“keepup”withfinance.Actually,amoreaccuratetermwouldbe“keepback.”Themosteffectivewayofcopingwithcurrentmarketconditionsistolearnasmuchaboutmarkethistoryasyoupossiblycan.Asuperb
placetostartisCharlesMackay’sMemoirsofExtraordinaryPopularDelusionsandtheMadnessofCrowds,originallypublishedin1841,andeasilyavailablefromreprintededitions.ThefirstchaptersdetailtheMississippiScheme,SouthSeaBubble,andTulipomaniaofcenturiesago.Changeafewofthenamesandyou’rereadingaboutInternetstocks.
Also,IsuggestalmostanythingbyJamesGrant,whoseentertainingproseandgraspoffinancialhistoryaresecondtonone.(MoneyoftheMind,MindingMr.Market,andTheTroublewithProsperityareallexcellentplacestostart.)Ifyoureallywanttokeep
up,subscribetotheJournalofFinance($80peryear,alongwithmembershipinthe
AmericanFinanceAssociation)andFinancialAnalystsJournal(about$150peryear).Thepiecestendtobeabstruse,jargonistic,andstrewnwithincomprehensibleformulae,butaboutonceperissuethereisatrulyimportantandcomprehensiblepiecewhichpaysforthesubscription.Forhard-corefinancetypesonly.
UsefulWebsitesfortheAssetAllocator
WhenIwrotethepreviousversionsofthisbook,Iwasnotimpressedwiththequalityofadviceanddataavailableon-line.Nolonger—thereisnowacornucopiaofusefulinformationoutthere.Belowisaveryincompletelist:Investingforthe21st
Century(http://www.fee-only-advisor.com/book/index.htmlFrankArmstrong’sgrandaddyofallon-lineinvestingbooks.Frank’sperspectiveissimilartomyown,exceptthathe’sfunnierandbetterlooking.Hisdog,Schatzke,isbetteratmarkettimingthananyoneelseonWallStreet.Chapter22in
particularisaclassicsend-upofWallStreetWeek.
InvestorHome(http://www.investorhome.comAcollectionofinvestmentdataandmedialinks.
FINWEB(http://www.finweb.com):Academicfinance’ssuperbwebresourcelocator.
ResearchJournalsinFinance(http://www.cob.ohio-state.edu/dept/fin/resources_research/rsjnl.htmLinkstoagrowinglistofon-lineacademicjournals.
TAMAssetManagement(http://www.tamasset.comJeffTroutner’sasset-class-basedwebsite.PublishesAssetClass,aperiodicreviewofasset
behavior.JeffalsopostsannualreturnsofmanyoftheDFA/MSCI/IbbotsondataseriesatthefollowingWebaddress:http://www.tamasset.com/allocation.html
Barra(http://www.barra.com)andWilshire(http://www.wilshire.comBothsitesoffersuperbasset-classdata
downloads.Barraisprobablythebestwayoffollowingmarketvaluation,withauniquehistoricalcompilationofU.S.valuationmeasures,whileWilshirehasmoreextensivemonthlyreturnsdata.
GlobalFinancialData(http://www.globalfindata.comBrianTaylor’sdataservice,providesa
panoramicviewofglobalassetreturnsovertimeandspace.
MorganStanleyCapitalIndexes(http://www.mscidata.comDownloadablereturnsforalloftheMSCInationalandregionalindexes.(Theseareavailableasmonthlyindexvalues.Toobtainthemonthlyindex
return,downloadthe“grossreturn”indexesandthendividethatmonth’sreturnindexbythepreviousmonth’sreturnindex.)
Bloomberg(http://www.bloomberg.comProbablythebestwaytokeepupwiththeglobalmarketplace,minutebyminute.
FinancialEngines
(http://www.financialengines.comNobelistBillSharpe’sassetallocationservice.Youcanseethefuture,butdoesitwork?Alsoseehisexcellenthomepage.
JournalofFinance(http://www.afajof.org):Ifit’simportant,it’slikelytobepublishedherefirst.Unfortunately,it’snotalwaysinplain
English.Mutualfundcompanies:Almosteveryfundfamilyhasanearlyworthlesspromotionalsite,andingeneralI’dstayaway.Therearethreedelightfulexceptions:Vanguard(http://www.vanguard.comhasafull-servicesitewithdownloadableprospectuses/applications/annual
reports,on-lineaccountservicing,andagreatdealofasset-class-basededucationalmaterials,DFA’ssite(http://www.dfafunds.comisalsoworthvisiting,evenifitisabitdifficulttonavigatearound.Finally,theTweedy’sBrownesite(http://www.tweedy.com)featurestheirpamphlets,especiallyWhatHas
WorkedinInvesting.Theirannualreportsarewellworthreading.
AppendixABecomingYourOwnPortfolioAnalyst
Thissectionisforthoseveryfewreaderswhoareinterestedinthedetailsofthespreadsheetanalysesandmean-varianceoptimizersreferredtointhisbook.Youwillneedsomefamiliarity
withspreadsheetwriting,particularlythe“copy”commandsthatenableyoutoseedagivenformulaintolargecellblocks.I’vepostedacompressed
templateExcelspreadsheetthatcalculatestheannualizedreturnsandSDsforthe1970–1998periodat:http://www.efficientfrontier.com/files/sample.exeThereturnsdataare
fictitious:Iwouldhaveliked
toplacetheactualdatainit,butunfortunatelythesearecopyrighted.Youwillhavetoobtainitonyourown.Fortunately,afairamountofmonthlyandannualreturnsseriesarenowavailableontheInternet.SeetheTAMAssetManagement,MSCI,Wilshire,andBarrasitesmentionedinChapter9formoreinformation.TheIbbotsondataisavailablerelativelyinexpensivelyfrom
itsannualyearbook,Stocks,Bonds,Bills,andInflation.Thebestsingle-pagelistingofasset-classreturnsisonJeffTroutner’sTAMAssetManagementsite(http://www.tamasset.com.allocation.htmlwherehepostsannualreturnsfrom1973forthemajorU.S.andforeignstyle-basedindexesandintermediateTreasuries.
Mean-VarianceOptimizers
Untilrecently,mean-varianceoptimizerswereoverpriced(moststillare)andsimplynotcost-effectiveifyouhadaspreadsheetoptimizersetup.Fortunately,Iwasabletoconvinceacolleague,DavidWilkinson,towriteandmarketapairofinexpensiveoptimizers(VisualMVOandMVOPlus),startingat$99,andavailablefromEfficient
Software(http://www.effisols.com).Hemayneverforgiveme.Beawarethatyouare
enteringasensitiveareaformostfinancialprofessionals.Most“retail”investmentprofessionalssuchasmutualfundsalespeopleandbrokerage“accountexecutives”areatbestonlydimlyawareofportfoliotheoryandMVO.Thosethat
arefamiliarwiththeseareasformtheeliteoftheinvestmentbusiness,andtendtobemanagersoflargeinvestmentpools.Thesefolkstreatportfoliotheoryalittlelikethetradesecretsofamedievalguild;don’texpectalotofhelpfromthem.Soyou’reonyourown.As
discussedinChapter5,mean-varianceanalysisisnotterriblyusefulforthedesign
ofyourportfolio.Rather,itisprimarilyateachingtoolthatyouwillfindhelpfulforlearningaboutportfoliobehavior.Atmostitissometimesusefulinansweringcertainhighlyspecificquestions.Forexample,supposeyouarewonderingabouttheroleof,say,preciousmetalsequity(PME)inyourallocation.YouwouldthensetupasimpleMVOanalysis
consistingofthreeassets:thestockandbondportionsofyourportfolioandPME.YoumightthenadjustthereturnofPMEupordowninordertodeterminethereturnsrequiredforitsinclusioninaportfolio.(Ofcourse,youwillneedtohaveagoodideaofitsSDandcorrelationwiththerestoftheportfolioinordertodothis.)Ifyouranalysisshowsthatpreciousmetalsequitystartsappearing
inyourportfolioatareturnof,say,5%,thenitmightbereasonabletouseit.Ontheotherhand,ifyouranalysisshowsthatareturnof10%isrequired,youmightbewary,asthelong-termreturnofpreciousmetalsequityislikelynotthathigh.
AppendixBCorrelation
CoefficientsAmongAssetClasses
Thefollowingarethecorrelationmatrixesforthreedifferenttimeperiods.Thevalueslistedbelowwillvarysomewhatwiththeperiod
sampledaswellaswiththeintervalmeasured;forexample,thecorrelationcoefficientforlargeandsmallU.S.stockreturnsfrom1926through1998isdifferentformonthly,quarterly,andannualperiods.Forthe1926–1998
Ibbotsondata,thecorrelationsforannualreturnsareaslistedinTableB-1,thecorrelationsforthe
1973–1998databasearelistedinTableB-2,andthecorrelationsforrecentquarterlyreturnsforasomewhatwiderrangeofassetsarelistedinTableB-3.Notethatsmallnegative
correlationsareoftenseenbetweenshort-termbondsandmanystockassetsbecauserisinginterestratesusuallyhaveadeleteriouseffectonstockpriceswhile
increasingtheshort-termbondreturn.Theoppositeoccurswithfallinginterestrates.Thisnegativecorrelationisnotseenwithlong-termbondsbecausetheeffectofchanginginterestratesonbondpriceoverwhelmsthechangeintheyield;thusrisingratesproducesafallinthetotalreturnofbothstocksandlongbonds.Thissmallbutfairlyconsistentnegative
correlationbetweenshort-termbondsandstocksisthereasonwhyshort-termbondsarefavoredoverlong-termbondsbymanyportfolioanalysts.Asnotedabove,
correlationcoefficientsvarysomewhatbysamplingintervalandperiod;thevaluesinthetablesbelowshouldbeusedonlyasstartingpoints.Forexample,
thecorrelationofquarterlyreturnsforthe1994–1998periodareingenerallowerthanformonthlyorannualreturnsduringthesameperiod.
TableB-1.CorrelationOfAnnualReturns1926–1998
TableB-2.CorrelationofAnnualReturns,1973–1998
TableB-3.CorrelationofQuarterlyReturns,1994–1998
Glossary
Activemanagement:Theprocessofusingsecurityanalysisinanattempttoobtainreturnshigherthanthoseofferedbythemarket.
Alpha:Thedegreetowhichamanager’sorfund’sreturndiffersfromthatofabenchmark.Thebenchmark
isusuallydefinedintermsofregressionanalysis.Forexample,analphaof+0.2%permonthmeansthatthemanagerorfundhasexceededtheregression-definedbenchmarkreturnbythatamountovertheperiodstudied.Bydefinition,themarkethasanalphaofzero.
Americandepositaryreceipts(ADRs):SharesissuedbyaU.S.depositary
bankofaforeigncompany.OneADRsharemayrepresentanyfixednumberofthecompany’ssharestradingonitsownexchange;i.e.,oneADRmayrepresent2,10,or4.5sharesofthestocktradingonitsdomesticbourse.TheADRpriceiskeptatalevelnearlyidenticaltothecurrency-adjustedforeignmarketpricebyarbitrage.
Annualizedreturn:The
constantreturnnecessarytoproduceagivenreturnorloss.Forexample,ifastockreturns0%,0%,and33.1%inthreesuccessiveyears,thentheannualizedreturnis10%(1.1×1.1×1.1=1.331).
Arbitrage:Thesimultaneousbuyingandsellingofagivensecurityindifferentmarketsatdifferentprices,yieldingarisklessprofit.(Themostprevalentvarietyisindex
arbitrage,whichtypicallyexploitssmalldifferencesinpricesbetweenfuturescontractsandtheunderlyingstocks.)
Askprice:Abroker’spricetosellastockorbond;alsocalledtheofferprice.
Assetallocation:Theprocessofdividingupone’ssecuritiesamongbroadassetclasses,i.e.,foreignanddomesticstocksandforeign
anddomesticbonds.
Assetclass:Categoriesofstocks,bonds,andotherfinancialassets.
Autocorrelation:Thedegreetowhichagivenreturninaseriespredictsthenext.Likeacorrelation,itsvaluerangesbetween+1(whereanaboveorbelowaveragereturnisalwaysfollowedbyanidenticalreturn)and−1(whereanaboveorbelow
averagereturnisalwaysfollowedbyasimilarbeloworaboveaveragereturn).Positiveautocorrelationsindicatemomentum,andnegativeautocorrelationsregressiontothemean.Azeroautocorrelationdefinesarandomwalk,whereanygivenreturncontainsnoinformationaboutthesucceedingreturn.
Averagereturn:Thesimple
arithmeticaverageofaseriesofreturns.Intheaboveexampleofastockwithreturnsof0%,0%,and33.1%inthreesuccessiveyears,theaveragereturnis11.033%.Theaveragereturnisoflittleusetothetypicalinvestor—itisalmostalwayslargerthantheannualizedreturnandoftengrosslyoverestimatestheactualreturnreceivedontheasset.
Beta:Theamountwhichastockorstockfundtendstomoveupordownwiththemarket.Forexample,abetaof1.3meansthata1%riseorfallinthemarketonaverageresultsina1.3%riseorfallinthesecurityorfundinquestion.High-betastocksandfundsarerisky.Alow-betastockorfundmaybelessrisky,butitmayalsobehighlyriskywithalowcorrelationwiththemarket.
Seecapitalassetpricingmodel.Bidprice:Abroker’spricetobuyastockorbond.
Bond:Debtissuedbyacorporationorgovernmentalentity.Carriesacoupon,ortheamountofinterestityields.Bondsareusuallyofgreaterthanone-yearmaturity.(Treasurysecuritiesof1–10years’maturityarecallednotes.)
Bookvalue:Acompany’sassetsminusintangibleassetsandliabilities;veryroughlyspeaking,acompany’snetassets.
Capitalassetpricingmodel(CAPM):Atheoryrelatingriskandexpectedreturn.Basically,itstatesthatthereturnofasecurityorportfolioisequaltotherisk-freerateplusariskpremiumdefinedbyitsbeta.This
theorycontainsalargenumberofunrealisticassumptionsandhasbeenshowntobeinconsistentwithempiricaldata(i.e.,intherealworlditturnsoutthathigh-betastocksdonothavehigherreturnsthanlow-betastocks).
Capitalgain:Theamountofprofitmadeonthesaleofasecurityorfund.Determinestheamountofapplicabletax
paid.
Cashflow:Earningsbeforedepreciationandothercharges.
Closed-endfund:Aninvestmentcompanythattradeslikeanyothercorporation,usuallydoesnotredeemitsshares,andonlyinfrequentlyissuesshares.Maytradeabove(premium)orbelow(discount)itsnetassetvalue(NAV),in
contradistinctiontothemorefamiliaropen-endfund,ormutualfund,whichtradeseachdayatitspreciseNAVandredeemsandissuessharesatwill.
Commission:Thefeepaidtoabrokertoexecuteatrade.
Contrarian:Onewhobuysorsellsunpopularorpopularassetclassesandsecurities,thusbehavinginamannercontrarytopopularsentiment
or“conventionalwisdom.”
Correlation:Thedegreetowhichtwoseriesofnumbers(infinance,usuallyreturns)relatetooneanother.Rangesbetween+1(anabove/belowaveragereturnforassetAisalwaysassociatedwithanabove/belowaveragereturnonassetB)and−1(anabove/belowaveragereturnforassetAisalwaysassociatedwitha
below/aboveaveragereturnonassetB).AcorrelationofzeroindicatesthatthereturnsofassetsAandBareunrelated.
Coupon:Theregularinterestpaymentmadetothebondholdersduringthelifeofthebond.Acouponof6%ona$1000bondmeansthat$60interestwillbepaid,usuallyastwosemiannual$30payments.
Currencyrisk/return:Theriskandreturnassociatedwithholdingaforeignsecuritycausedbyfluctuationsintheexchangerate.
Cyclicalstock:Asecuritythatisparticularlysensitivetoeconomicconditions,suchasanaircraftorpapercompany(asopposedtoafoodordrugmanufacturer,whoseprofitsandsalesarenotsensitiveto
economicconditions).
Discounteddividendmodel(DDM):Amethodofestimatingtheintrinsicvalueofacompanyormarketbycalculatingthediscountedvalueofitsexpectedfuturedividends.Theamountbywhichfuturedividendsarereducediscalledthediscountrate;ittypicallyapproximatestherisk-adjustedreturnoftheasset.
Diversification:Allocatingassetsamonginvestmentswithdifferentrisks,returns,andcorrelationsinordertominimizenonsystematicrisk.Efficientfrontier:Allofthepossibleportfoliocombinationswhichmaximizereturnforeverypossiblelevelofexpectedriskorwhichminimizeexpectedriskforevery
possiblelevelofexpectedreturn.Themathematicaltechniqueforcalculatingtheseportfolios,calledmean-varianceanalysis,wasinventedbyHarryMarkowitz.
Efficientmarkethypothesis:Theconceptthatmarketsimpoundinformationintopricessowellthattheanalysisofpubliclyavailableinformationwillnotproduce
excessreturns.
Expenseratio:Theportionoftheassetsspenttorunamutualfund,includingmanagementandadvisoryfees,overheadcosts,and12b-1(distributionandadvertising)fees.Theexpenseratiodoesnotincludebrokeragecommissions,spreads,ormarketimpactcosts.High-yield(“junk”)bond:
AdebtinstrumentwithaStandard&Poor’sratingofBBorless.Bydefinition,suchbondshaveyieldshigherthanlessriskyinvestmentgradebonds.Indexfund:Amutualfunddesignedtomimicthereturnsofagivenstockmarketindex,suchastheS&P500.
Indexing:Thestrategyofexactlymatchingtheperformanceofagivenstock
index,suchastheS&P500.Seealsopassiveinvestingstrategy.Initialpublicoffering(IPO):Theinitial,orprimary,publicsecuritysaleofacorporation.AftertheIPO,thesecuritythusissuedtradesinthesecondarymarket.Institutionalinvestors:Largeinvestmentorganizations,including
insurancecompanies,depositaryinstitutions,pensionfunds,andphilanthropies.
Ladder:Abondportfoliowithequalamountsinvestedinevenlyspacedmaturities.Forexample,afive-yearladderwouldhaveequalamountsinvestedinone,two,three,four,andfive-yearsecurities.MostcommonlyinvolvesTreasurysecurities.
Liquidity:Theleveloftradingactivity,whichdeterminestheeaseofbuyingandsellingandmarketimpact.Asecurityissaidtobeliquidwhentradingactivityishigh,withswifttradeexecutionatanarrowspread.Anilliquidsecurityhaslowtradingactivity,withahighspreadandsignificantmarketimpact.
Loadfund:Amutualfund
soldwithasaleschargeofupto8.5%,ano-loadfund.Marketcapitalization:Alsoknownasmarketcap;themarketvalueofallofacompany’sstock.Companiesarefrequentlydividedintolarge-,mid-,andsmall-capcategories.Moststockindexesarecap-weighted,meaningthattheyarerepresentedintheindexinproportiontotheirmarket
capitalization.Thismeansthatsuchindexesaredominatedbytheirlargestgrowthcompanies.
Marketimpact:Theincreaseordecreaseinpricecausedbybuyingorsellingalargeamountofasecurity.Thisadverselyaffectsthereturnsofinstitutionalportfolioswithhighturnover.Marketportfolio:A
portfolioorindexconsistingofallofthestocksavailabletoinvestors,heldinproportiontotheirmarketcapitalization.ItiscloselyapproximatedbytheWilshire5000,Russell3000,andCRSP-Allindexes.
Marketreturn:Thereturnofthemarketportfolio.Maturity:Thedateofabond’sprincipalrepayment.
Mean-varianceanalysis:Seeefficientfrontier.Modernportfoliotheory(MPT):Theunderlyingprinciplesoftheriskandreturntrade-off.
Mutualfund:Aportfolioofstocks,bonds,orotherassetsmanagedbyaninvestmentcompany,usuallyforsmallinvestors.Mutualfundsprovideinvestorswitheasyaccesstohighlydiversified
marketexposureandareregulatedbytheInvestmentCompanyActof1940.Seealsoloadfundandno-loadfund.Netassetvalue(NAV):Thevalueofafund’sinvestments.Ano-loadmutualfundisavailableforpurchaseorredemptionattheNAV,usuallyonadailybasis.Aclosed-endfundtradesinthesamemannerasastock,
sometimesatasubstantialdiscountorpremiumtotheNAV.
No-loadmutualfund:Amutualfundsoldwithoutasalesordistribution(12b-1)fee.
Nominalreturn:Actualreturn,notadjustedforinflation.
Nonsystematicrisk:Portfolioorsecurityriskthat
canbeeliminatedbydiversification.Alsoknownasdiversifiablerisk.Afternonsystematicriskhasbeeneliminated,systematicriskremainswhichcannotbeeliminated.(Theprefixesgetconfusing.Systematicriskisnondiversifiable,nonsystematicriskisdiversifiable.)
Open-endfund:Generallythesamemeaningasmutual
fund.Anopen-endfundcreatesandredeemsnewsharesondemandatthenetassetvalue.Seealsoclosed-endfund.Parvalue:Maturityorfacevalueofabond,usually100.
Passivemanagement,portfolio,orstrategy:Referstoasecurityselectionprocessnotinvolvingactivesecurityanalysis.Essentiallythesameasindexing,except
thatapassivelymanagedportfoliomayrejectsecuritiesbasedonmechanicaltrading,financial,orvaluationcriteria,anddoesnotneedtoconformtoanyparticularindex.
Portfolio:Anycollectionofsecurities.
Portfoliotheory:Thestudyoftherelationshipofoverallportfolioriskandreturnasafunctionoftherisk,return,
andcorrelationofitscomponentparts.
Price-book(P/B)ratio:Aratioobtainedbydividingacompany’smarketcapitalizationbyitsbookvalue.Mayalsobecalculatedonaper-sharebasis.Ameasureofcheapnessorvalue;lowP/Bstocksareusuallydefinedasbeingcheap,valuestocks.
Price-earnings(P/E)ratio:
Aratioobtainedbydividingacompany’smarketcapitalizationbyitsearnings.InterpretedinthesamemannerastheP/Bratio.Randomwalk:Aconditionofrandom,unpredictablesecurityprices,inwhichthereturn-seriesautocorrelationiszero.
Realinterestrate,realreturn:Theinterestrateor
returnofasecurityinexcessofinflation.Asecurityorportfoliowithzerorealinterestrateorreturnexactlymaintainsitsinflation-adjustedvalue.Asecurityorportfoliowithaconstantrealreturnofx%canmaintainanx%withdrawalrateindefinitelywithoutsufferinginflation-inducederosionofpayoutorprincipal.
Realestateinvestmenttrust
(REIT):Apropertyormortgagemanagementcompany.Requiredbystatutetoremit95%ofearningstoshareholders.
Rebalancing:Theprocessofbuyingandsellingportfoliocomponentssoastomaintainatarget,or“policy”assetallocation.Regressionanalysis:Amathematicaltechnique,availableinmostspreadsheet
packages,whichdeterminestherelationshipofmultipleseriesofnumbers.Infinance,itiscommonlyemployedtocalculatethecontributionofknownmarketfactorstoaportfolio’sreturns,andthealpha(returnaddedorsubtracted)ofanactivemanager.
Reinvestmentrisk:Theriskthatfuturebondinterestwillhavetobereinvestedata
lowerinterestrate.
Return:Thechangeinthevalueofaportfoliooveragivenperiod,includingdividendsandotherdistributions.
Risklessrate:Thereturnearnedonarisklessasset,usuallya30-or90-dayTreasurybill.Thisisthebasereturnthatallinvestorscanbeexpectedtoearn.Accordingtomodernportfoliotheory
andthecapitalassetpricingmodel,returninexcessoftherisklessrate(alsoknownastheriskpremium)canonlybeobtainedbybearingmarketrisk.Riskyasset:Anyassetexposedtomarketrisk.
Rsquared(R2):Thesquareofthecorrelationcoefficient.Itdefinestheamountofareturnsserieswhichcanbeexplainedbyanindexor
factor.Forexample,amutualfundwitha.80R2relativetotheS&P500has80%ofitsreturnsexplainedbythisindex.
Security:Almostanypieceofpaperthatcanbetradedforvalue,exceptforinsurancepolicies,fixedannuities,andfuturescontracts.Mostcommonlyreferstostocksandbonds.
Semivariance:Thevariance
ofthosereturnsfallingbelowthemean.Sincevariancemeasuresthescatterofreturnsbothaboveandbelowthemean,itisincreasedbyveryhighreturns.Sinceonlyreturnsbelowthemeanareasourceofrisk,semivarianceisfelttobeabettermeasureofrisk.
Spread:Thedifferencebetweenthebidandaskpriceofasecurity.Theamountof
spreadisameasureoftheliquidityofthesecurity.Standarddeviation(SD):Astatisticalmeasureofthescatterofaseriesofnumbers.TheSDofthereturnsofasecurityorportfolioisusuallyagoodestimateofitsrisk.
Survivorshipbias:Anupwardbiasintheestimationofaggregatesecurityorinvestmentcompanyreturnscausedbythedisappearance
oftheworstperformingmembersofthegroup.
Systematicrisk:Theriskofthemarketportfolio,whichcannotbediversifiedaway.
Totalreturn:Sameasthereturnofasecurityorportfolio—includespricechange,dividends,andotherdistributions.
Treasuryinflation-protectedsecurity(TIPS):
ATreasurybondornotewhosecouponandprincipalpaymentareindexedtoinflation.AtagivenmaturitythedifferencebetweenthestandardTreasuryyieldandTIPSyieldrepresentsthemarket’sestimateofinflationoverthatperiod.
Turnover:Theportionofaportfoliothatistradedinagivenperiodoftime,usuallyexpressedinpercentperyear.
Forexample,inaportfoliowithanannualturnoverof200%,theaveragesecuritypositionistradedtwiceperyear.
Utilityfunction:Amathematicalformulathatassignsaprecisevaluetoanyeconomicoutcome,usuallybasedonreturnandrisk.Usedtomodelordescribeinvestorbehavior.
Valuestock:Asecuritythat
sellsatadiscounttoitsintrinsicvalue.Valuestocksareoftenidentifiedbylowprice-bookandprice-earningsratios.Variance:Ameasureofthescatterofnumbersaroundtheiraveragevalue;thesquarerootofthevarianceisthestandarddeviation(SD).LikeSD,thevarianceofasecurity’sorportfolio’sreturnsisaproxyforitsrisk,
orvolatility.Yield:Thepercentageofasecurity’svaluepaidasdividends.
Zero-couponbond:Abondinwhichnoperiodiccouponispaid;principalandreinvestedinterestarepaidintotoatmaturity.
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Index
Activemanagement,95–99Alpha,89–90,98AmericanAssociationofIndividualInvestors,177
AmericanDepositaryReceipts(ADRs),78
Annualizedreturn,2–3,5AssetAllocation(Gibson),
176Asset-allocationfunds,162–164
Asset-allocationstrategy,26,143–174asset-allocationfundsin,162–164
bondsin,151–152determiningallocation,143–145,153–154
dynamic,137–139,163–164
executingplanfor,154–161
investmentresourcesfor,175–180
keypointsfor,173–174retirementaccountsand,153–154
stockindexingin,145–151taxesand,145Treasuryladdersin,152(SeealsoAssetclasses;Diversification;Optimal
assetallocation)Assetclasses:1926–1998,9–18,421970–1998,19–21inassetallocationprocess,76–83
correlationcoefficientsamong,183–186
lawofdiminishingreturnsand,76
standarddeviationofannualreturns,6
Assetvariance,109Autocorrelation,106–108Averagereturn,2–3
Backtesting,72Barraindexes,99,126Baruch,Bernard,52Behavioralfinance,139–142defined,139overconfidenceand,139–140
recencyand,47–48,52,53,
58–59,140–141riskaversionmyopiaand,141–142
Benchmarking:alphain,89–90,98withS&P500,60,78,79,86,88–90,145
Benzarti,Shlomo,131Bid-askspread,91,92,93,96Binomialdistributionfunction,2,7
Bogle,John,175–176Bondfunds,151–152Bonds:inassetallocationstrategy,151–152
commonstockversus,24historicalreturnsof,23,24standarddeviationofannualreturns,6
Bookvalue(P/Bratio):dataonrangesof,114
inneweraofinvesting,124
invalueinvesting,112–113,120
variationinreturnsand,116–117
Brinson,Gary,176Buffett,Warren,118
Calibration,140Capitalgainscapture,102,108
CenterforResearchinSecurityPrices,76
CharlesSchwab,100Clayman,Michelle,118Coin-tossoption,1–5,29–36,169
Commissions,90–91,92,96,152
CommonSenseonMutualFunds(Bogle),175–176
Commonstocks:1926–1998,4,13–16,17,
42–45discounteddividendmethodand,23–24,26,127–132
growth,97,112,117historicalreturnson,23–25large-company,(SeeLarge-companystocks)
longbondsversus,24risksandreturnsof,1–5small-company(SeeSmall-companystocks)
standarddeviationofannualreturns,5–8,63,65,96
Companysize:variationinreturnsand,116–117(SeealsoLarge-companystocks;Small-companystocks)
Complexportfolios,41–62defined,41efficientfrontier,55–59,64foreignassetsin,46–53
professionalversussmallinvestors,59–61
rebalancing,59returnandriskplot,41–45riskdilution,45–46smallversusbigstocksin,53–55,75
Compoundinterest,17Constantallocation,58Contrarianapproach,59,104ContrarianMarketStrategy
(Dreman),104Conventionality,inassetallocationprocess,78–79
Cooley,PhilipL.,169Cornerportfolios,65–71Correlation,36–40amongassetclasses,183–186
autocorrelation,106–108calculating,39defined,37
foreigninvestmentsand,46–53,72–73
imperfect,37negative,31,37overstatingofdiversificationbenefits,71-74
ofsmallstocksandlargestocks,53–55
zero,31Costofcapital,132Critical-linetechnique,65
Currencyrisk,132–137
DimensionalFundAdvisors(DFA),20,148,149,150,164analysisoffundperformance1970–1998,86
bondfunds,152globallargecompanyindex,74–75
moderatebalancedstrategy,82
small-capindex,54–55,98–99,100
Discountrate(DR),127–130Discounteddividendmethod:Glassman-Hassettmodeland,127–132
natureof,23–24,26Diversification,19,21,144benefitsof,33–36,41–45,71–74
impactonriskandreturn,31–36,63
international,46–53,72–75overstatementofbenefitsof,71–74(SeealsoOptimalassetallocation)
Dividendyield:dataonrangesof,114,115marketdeclinesand,166–167
inneweraofinvesting,124
invalueinvesting,113–115
Dividends:Dowdividendstrategy,116
growthof,80reinvesting,115REITsand,145
Dodd,David,176Dollarcostaveraging(DCA),154–155,159
Dow36,000(GlassmanandHassett),127–132
Dowdividendstrategy,116DowJonesIndustrialAverage,24–25,26,80
Dreman,David,104,117Dunn’slaw,99–100Durationrisk,165–167Dynamicassetallocation,137–139defined,137marketvaluationand,163–164
overbalancingin,138
EAFEIndex,38,39,46–53,100,126
Earningsyield,119EconometricsofFinancialMarkets,The(Campbell,Lo,andMacKinlay),107–108
Edleson,Michael,155–159,176
Efficientfrontier,55–59,64
Efficientmarkethypothesis,104–105,118–119,120
EfficientSolutions,65–71,181–182
Ellis,Charles,94Emergingmarkets,49–50,100,147–148
Europeanbonds,152Europeanstocks,19,20,25,156efficientfrontierand,55–59
hedgingwith,133mutualfunds,147
Excessrisk,12–13Exchangetradedfunds(ETFs),149,151
Expenseratio(ER),90,91,92,96,146
Expertopinion,74
Fama,Eugene,98,109,116–117,120–124,148
Financialcalculators,5,168
Fisher,Kenneth,109Fixedassetallocation,109Forbes,Malcolm,104Foreignassets:correlationand,47,72–73EAFEIndex,38,39,46–53,100,126
hedgingwith,132–137Foreigntaxcredit,161Forwardpremium,135Forwardrates,135–136
Fraud,investment,4French,Kenneth,98,116–117,120–124,126,148
Fundoffunds,161Futureoptimalportfoliocomposition,64
Gibson,Roger,176Glassman,James,127–132GlobalInvesting(IbbotsonandBrinson),176
Goetzmann,William,49–50
Goldstocks(SeePreciousmetalsequity)
Graham,Benjamin,24,93,106,112,117,118,119–120,125,176–177
Graham,John,104Grant,James,178GreatDepression,14,19,112,166
Growthinvesting:defined,112,118efficientmarkettheory
and,118–119valueinvestingversus,117,118–120
Growthstocks,97,112,117
Harvey,Campbell,104Hassett,Kevin,127–132Haugen,RobertA.,119,176Hedging,132–137costof,135–136defined,132extentof,136–137
Historicaloptimalallocation,64
Hubbard,CarlM.,169Hypotheticaloptimalallocation,64
Ibbotson,Roger,176IbbotsonAssociates,9–10,23,41–42,44,93,178
Imperfectcorrelation,37Insample,87InSearchofExcellence
(Peters),118Indexing,94–103advantagesoveractivemanagement,95–99
defined,95international,100mutualfundsin,145–151,174
ofsmall-companystocks,101,102,148–149
theoreticaladvantageof,95–96
Inflation,andrealreturn,80,168
Institutionalinvestors:evaluationof,123–124market-impactcostsand,86–90,91–92,96
pensionfunds,103persistenceofinvestmentperformance,90
smallinvestorsversus,59–61(SeealsoBenchmarking;Mutual
funds)IntelligentInvestor,The(Graham),106,176–177
Internationaldiversification:caseagainst,72correlationand,46–53,72–73
withsmallstocks,74–75sovereignriskand,72
Inversecorrelation,31,37Investmentclimate,124–127
InvestmentCompanyInstitute,103
Investmentfraud,4Investmentnewsletters,104–105
Januaryeffect,92–94Japanesebonds,152Japanesestocks,19,20,25,38,39,40,48,55,56,57,59,160
Jensen,Michael,86
Jorion,Phillipe,49–50
Keynes,JohnMaynard,18
Lakonishok,Josef,120Large-companystocks,13indexingadvantagewith,96,97–98
small-companystocksversus,53–55,75
Lawofdiminishingreturns,76
LehmanLongBondIndex,
162Localreturn,133LongTermCapitalManagement,7
Mackay,Charles,178Malkiel,Burton,101–102,109,175
Marketcapitalization,13Marketefficiency,85–110expensesoffundsand,90–92,96,146
indexingand,94–101investmentnewslettersand,104–105
Januaryeffect,92–94market-impactcostsand,88–90,91–92,96
andpersistenceofinvestmentperformance,85–88
randomwalkand,101,106–108
rebalancingand,108–109
survivorshipbiasand,101–102
taxesand,102–103Market-impactcosts:extentof,91,92,96illustrationof,88–90
Marketmultiple(SeeP/Eratio)
Marketriskpremium,121,122
Markettiming,104–105,160
Marketvaluation,111–115,163–164,174
Markowitz,Harry,64–65,71,177–178
Maximum-returnportfolios,69
Meanreversion,70,107,109Mean-varianceanalysis,44–45,64–71,181–182
Mean-varianceoptimizers(MVOs),64–71,181–182
MemoirsofExtraordinary
PopularDelusionsandtheMadnessofCrowds(Mackay),178
Miller,Paul,115Minimum-varianceportfolios,65–69
Momentuminvesting,101,108,109,123
Moneymanagers(SeeInstitutional
investors;Mutualfunds)Moneymarket,standard
deviationofannualreturns,6
Morgan-StanleyCapitalIndexes,19–20,133,149
Morningstar:long-termreturns,21Principiadatabase,61,96–97,101–102,120,163–164,177
standarddeviationand,6,19
MSCIWorldIndex,162
Multiple(SeeP/Eratio)Multiple-assetportfolios,29–40cointossand,36correlationin,36–40diversificationand,31–36simpleportfoliosversus,31–36
Multiplechange,24Mutualfunds:asset-allocation,162–164
bond,151–152exchangetraded(ETFs),149–151
expensesof,90–92,96,146
hedging,135indexingwith,145–151,174
standarddeviationand,6supermarkets,148turnoverof,130–131
VanguardGroup,97–100,146–148,149,150,152,156,161–163
MVOPlus,65–71,181–182
NationalAssociationofRealEstateInvestmentTrusts(NAREIT),21
Negativecorrelation,31,37Neweraofinvesting:componentsof,124–127Glassman-Hassettmodel
and,127–132NewFinance:theCaseAgainstEfficientMarkets(Haugen),119,176
Newsletters,investment,104–105
Nonsystematicrisk,12–13Normaldistribution,7
OakmarkFund,88–90Optimalassetallocation,63–83
asset-allocationfundsin,162–164
assetclassesin,76–78calculationof,64–71conventionalityand,78–79correlationcoefficients,71–74
internationaldiversificationwith
smallstocks,74–75risktoleranceand,79–80,143
three-stepapproachto,75–83
Outofsample,87Overbalancing,138Overconfidence,139–140
P/Bratio(SeeBookvalue)P/Eratio:dataonrangesof,113,114earningsyieldasreverseof,119
inneweraofinvesting,
124invalueinvesting,112,119–120
PacificRimstocks,19,20,21,25,55–59,147,156
Pensionfunds,103(SeealsoInstitutionalinvestors)
Perfectlyreasonableprice(PRP),127–128
Performancemeasurement:alphain,89–90,98three-factormodelin,123–
124(SeealsoBenchmarking)
Perold,Andre,141Persistenceofperformance,85–88
Peters,Tom,118PiscataquaResearch,103Policyallocation,59Portfolioinsurance,141PortfolioSelection(Markowitz),177–178
Preciousmetalsstocks,19–20,21,48,55,57,59
Price,Michael,162Professionalinvestors(SeeInstitutionalinvestors)
Prudentmantest,60
RandomWalkDownWallStreet,A(Malkiel),101–102,175
Randomwalktheory,106–108,119
positiveautocorrelationand,106–108
randomwalkdefined,106rebalancingand,109
Raskob,JohnJ.,16–17Realestateinvestmenttrusts(REITs),38,40,100,145defined,19indexfund,148returnson,19,21,25
Realreturn,26,80,168,170
Rebalancing:frequencyof,108–109importanceof,32–33,35–36,59,63,174
andmean-varianceoptimizer(MVO),65
overbalancingin,138randomwalktheoryand,109
rebalancingbonus,74,159–160
oftax-shelteredaccounts,
159–160oftaxableaccounts,160–161
Recencyeffects,47–48,52,53,58–59,140–141
Regressionanalysis,89–90Reinvestmentrisk,23Representativeness,118Researchexpenses,92,95Residualreturn,98Retirement,165–172
assetallocationfor,153–154
durationriskand,165–167shortfallriskand,167–172(SeealsoTax-shelteredaccounts)
Return:annualized,2–3,5average,2–3cointossand,1–5companysizeand,116–117
correlationbetweenriskand,21
dividenddiscountmethod,23–24,26,127–132
efficientfrontierand,55–58
expectedinvestment,26historical,problemswith,21–27
impactofdiversificationon,31–36,63
market,168
real,26,80,168,170returnandriskplot,31–36,41–45
riskandhigh,18uncorrelated,29–31variationin,116–117
Risk:commonstock,1–5correlationbetweenreturnand,21
currency,132–137
duration,165–167efficientfrontierand,55–58
excess,12–13highreturnsand,18impactofdiversificationon,31–36,63
nonsystematic,12–13reinvestment,23returnandriskplot,31–36,41–45
shortfall,167–172sovereign,72systematic,13(SeealsoStandarddeviation)
Riskaversionmyopia,141–142
Riskdilution,45–46Risk-freeinvestments,10,15,152
Risk-freerate,121Risktimehorizon,130,131,143–144,167
Risktolerance,79–80,143RothIRA,172Rukeyser,Lou,174Ruleof72,27
Sanborn,Robert,88–90SecuritiesActof1933,92–93SecurityAnalysis(GrahamandDodd),93,118,125,176
Sellingforward,132–133Semivariance,7
Sharpe,William,141Shortfallrisk,167–172Siegel,Jeremy,19,136Simpleportfolios,31–36Sinquefield,Rex,148Small-cappremium,53,121,122
Small-companystocks,13–16,25correlationwithlarge-companystocks,53–55
efficientfrontierand,55–59
indexing,101,102,148–149
internationaldiversificationwith,74–75
Januaryeffectand,92–94large-companystocksversus,53–55,75
“lotteryticket”premiumand,127
trackingerrorof,75
Smallinvestors,institutionalinvestorsversus,59–61
Solnik,Bruno,72Sovereignrisk,72S&P500,13,38,39,55asbenchmark,60,78,79,80,86,88–89,145
efficientfrontier,56–57Spiders(SPDRS),149Spotrate,135Spread,91,92,93,96
Standarddeviation,5–8defined,6,63limitationsof,7ofmanagerreturns,96inmean-varianceanalysis,65
Standarderror(SE),87Standardnormalcumulativedistributionfunction,7
Stocks,Bonds,Bills,andInflation(IbbotsonAssociates),9–10,41–42,
178StocksfortheLongRun(Siegel),19,136
Strategicassetallocation,58–59
Survivorshipbias,101–102Systematicrisk,13
tdistributionfunction,87Tax-shelteredaccounts:assetallocationfor,153–154
rebalancing,108–109,159–160(SeealsoRetirementaccounts)
Taxableaccounts:assetallocationfor,153–154
rebalancing,160–161Taxes:inassetallocationstrategy,145
capitalgainscapture,102,108
foreigntaxcredits,161marketefficiencyand,102–103
Technologicalchange:historical,impactof,125inneweraofinvesting,125
Templeton,John,164Thaler,Richard,131,142Three-factormodel(FamaandFrench),120–124
Timehorizon,130,131,143–144,167
Trackingerror:defined,75determiningtolerancefor,83,145
ofsmall-companystocks,75
ofvariousequitymixes,79Treasurybills:1926–1998,10–11
returnson,25–26asrisk-freeinvestments,10,15,152
Treasurybonds:1926–1998,11–13,42–45ladders,152
TreasuryInflationProtectedSecurity(TIPS),80,131–132,172
Treasurynotes,11Turnover,95,102,130–131,145
Tweedy,Browne,148–149,162,176
Utilityfunctions,7
Valueaveraging,155–159ValueAveraging(Edleson),176
Valueindexfunds,145Valueinvesting,77,111–124defined,118growthinvestingversus,117,118–120
measuresusedin,112–114studieson,115–118three-factormodelof,120–124
Valuepremium,121–123VanEckGoldFund,21VanguardGroup,97–100,146–148,149,150,152,156,161–163
Variance,7,108–109mean-varianceanalysis,
44–45,64–71,181–182minimum-varianceportfolios,65–69
Variancedrag,69
Walz,DanielT.,169Websites,178–180Wilkinson,David,56,57,181–182
Williams,JohnBurr,127WilshireAssociates,120,147,162
WorldEquityBenchmarkSecurities(WEBS),149–151
zvalues,87Zerocorrelation,31
AbouttheAuthor
WilliamBernstein,Ph.D,M.D.,isapracticingneurologistinOregon.HelauncedtheWebsitewww.efficientfrontier.cominAugust1996.Knownforhisquarterlyjournalofassetallocationandportfoliotheory,EfficientFrontier,Dr.
BernsteinisalsoaprincipalinthemoneymanagementfirmEfficientFrontierAdvisors,isafrequentguestcolumnistforMorningstar,andisoftenquotedinTheWallStreetJournal.