TheIntelligentAssetAllocator

TheIntelligentAssetAllocatorHowtoBuildYour

PortfoliotoMaximizeReturnsandMinimizeRisk

WilliamJ.Bernstein

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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.