EquityIndexing.docx
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EquityIndexing.docx
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EquityIndexing
EquityIndexing
Theterm“efficientcapitalmarket”generallyreferstopricingefficiency,orexternallyefficient.
Pricingefficiencyreferstoamarketwhereprices,atalltimes,fullyreflectallavailableinformationthatisrelevanttovaluation.
Whenamarketisprice-efficient,pursuinginvestmentstrategiesinanattempttooutperformabroad-basedindexwillnotconsistentlyproducesuperiorreturnsafteradjustingfor:
∙Risk
∙Transactionscosts
Availableinformationsets:
∙Onlypastprices
∙Allpublicinformation
∙Allpublicandprivateinformation
ActivePortfolioStrategiestrytotakeadvantageof“perceived”marketinefficiencies.
∙FundamentalAnalysis
∙TechnicalAnalysis
PassivePortfolioStrategiestrytotakeadvantageof“perceived”marketefficiencies.
∙BuyandHold
∙Indexing
OurFocushereisonIndexFundManagement,commonlycalledIndexing
Inanindexingapproach,afundmanagerdoesnottrytoidentifyunder-pricedsecuritiesorover-pricedsecurities.
Instead,the“indexer”invokesatradingstrategydesignedtocreateaportfoliothat“mimics,”“replicates,”or“tracks”theperformanceofanindex.
Thegoalhereistoshowhowanindexedportfolioisconstructedandmaintained.
Themotivationforindexingcomesfromcapitalmarkettheory,i.e.,the‘market’or‘tangency’portfolio.
∙Theportfoliois‘capturing’marketefficiency.
∙Buyandholdmaynotcapturemarketefficiency.Why?
(Later,whenwetalkmoreaboutfactorrisks,youwillseethatonecanusemuchofthismaterialthere,aswell.)
Isthemarketefficient?
∙‘Pockets’ofinefficiencyexist.
∙Difficulttooutperformthemarketconsistentlyafteraccountingforriskandtransactionscosts.
Keepinmind,manyprofessionalmoneymanagersunder-performpopularindexes,liketheS&P500.
∙Also,seeTable14.2inFabozzi.
∙BangeandMiller(WorkingPaper)
SelectingtheIndex(orBenchmark)
∙Manybroad-basedandspecialindexesexisttoday
∙‘Boutique’fundsrequireaspeciallyconstructedindex
∙ProblemswiththeS&P500asabenchmark
oStocksselectedbycommittee
oNotnecessarilybasedonfutureperformance
ConstructinganIndex-ReplicatingPortfolio
TrackingError:
Thedifferencebetweentheperformanceofthebenchmarkandthereplicatingportfolio.
Performanceisgenerallymeasuredbythetotalreturnoftheportfolioinquestion.
TrackingError=TotalReturnonReplicatingPortfolio
-TotalReturnonBenchmarkPortfolio
TrackingErrorcanbepositiveornegative.
ThegoalinIndex-Replicationistohaveatrackingerrorofzero.
Example:
TrackingErroroftheS&P500.
∙TrackingtheS&P500with50stocksresultsinatrackingerrorofabout2.5%(annualized).
∙TrackingtheS&P500with100stocksresultsinatrackingerrorofabout1.5%(annualized).
∙TrackingtheS&P500with~175stocksresultsinatrackingerrorofabout1.0%(annualized).
ANettlesomeIssue:
TransactionsCosts.
∙Thenumberofstocksincludedinthereplicatingportfolioaffectstransactionscosts.
∙Holdingfewerthanthenumberofstocksinthereplicatingportfoliogeneratestrackingerror.
SourcesofTrackingErrorOtherthantheNumberofStocks
∙Odd-LotPurchasesarecumbersome(computertradinggenerallyuses100shares).
∙Rebalancingtheportfoliogeneratestransactionscosts:
oMarketImpact,orliquidity,Risk
oBid-askspreads
oBrokeragecommissions
oTiming
Intheory,rebalancingcanbeavoidedifallstocksareheldintheindex,proportionatetotheirvalueinthebenchmark(ifthebenchmarkisvalue-weighted).
CapitalWeighted=ValueWeighted
But,becauseoftheodd-lotnatureintroducedbycapital-weighting,itisdifficulttobeginwithacapital-weightedreplicatingportfolio.
BenchmarkConstructionandtheReplicatingPortfolio
Threebasicweightingschemes:
1.Capitalization-Weighting(AKAValueWeightingorMarket-ValueWeighting):
StocksheldinproportiontotheirvalueintheBenchmarkPortfolio.
a.Large-capcompanieshavemoreinfluenceontheindex,butarethemostliquid.
b.Therefore,under/over-weightinginthelarge-capsgeneratesmoretrackingerror.
2.PriceWeighting:
Equalnumberofsharesinvestedineachstock,therefore,thepriceistheweight.
a.Thehighest-pricedstockshavethelargestweight.
b.BerkshireHathaway
3.EqualDollarWeighting:
Samedollarinvestmentineachstock.
a.Thelowest-pricedstockshavemoreinfluence.
WeightingSchemes,In-ClassExample,Datafrom3/11/94(Fabozzi,Pg.258)
Assumea$1,000,000ReplicatingPortfolio
Value-Weighting:
Shares=$1,000,000*Weight/Price
Price-Weighting
(Shares=$1,000,000/334.50=2,990)
EqualWeighting
Shares=$1,000,000*0.20/Price
Factorsthatalsoinfluenceweights(andtherefore,rebalancing):
∙Thereisamerger
∙Companymaybeaddedtoordeletedfromthebenchmark
∙Theremightbeastocksplitorastockdividend
∙Newstockmaybeissued
∙Currentstockmayberepurchased
MethodstoConstructaReplicatingPortfolio
∙ModifiedCapitalizationMethod.Assume200firmsaccountfor85%ofthevalueoftheindex.Value-weighttheseandequallyweighttheremainder.
∙StratifiedMethod.
oDefinea‘factor’bywhichthestocksmakinguptheindexmaybeclassified.Typically:
▪Anindustry
▪Beta
oSupposeindustryischosen:
▪Eachcompanyisassignedtoanindustry.
▪Attempttominimizeresidualriskbydiversifyingacrossindustrysectorsinthesameproportionasthebenchmark.
▪Selectionofstocksineach‘stratum’?
∙QuadraticOptimization
oUseaquadraticoptimizationproceduretogenerateaMarkowitzefficientset.
oThatis,minimizeriskgivenareturnlevel.Thisisknownasconstrainedoptimization.
oRecallthatinmean-variancespace,theefficientsetisaparabola,whichcanbedescribedbyaquadraticequation.
LinkstoActiveEquityManagement
∙“Enhanced”Indexing.Designawell-diversifiedportfoliothattakesadvantageof‘superior’estimatesofreturn.
o‘Tilted’Portfolio.Emphasizesaparticularindustrysector,performancefactor,oreconomicfactor:
▪Tech
▪Earningsmomemtum
▪Inflation
oUseIndexFuturestoEnhanceReturns(SeeChapter19).
▪Thisinvolvesidentifyingshort-terminstanceswhenfuturespricesare‘underpriced’relativetotheindex.
▪Insteadofbuyingmorestock,buy‘synthetic’stockusingfuturesandaninvestmentinT-bills.
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