EquityIndexing.docx

EquityIndexing.docx

《EquityIndexing.docx》由会员分享，可在线阅读，更多相关《EquityIndexing.docx（9页珍藏版）》请在冰豆网上搜索。

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.