portfolio management under constraints-the fractal market hypothesis

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1、Chapter9Portfoliomanagementunderconstraints9.1IntroductionWediscussedinSection(1.7.6)theexistenceofexcessreturnsandshowedthatthemarketisinefficient,thatis,sub-stantialgainisachievablebyrebalancingandpredictingmarketreturnsbasedonmarket’shistory.Asaconsequenc

2、e,weshowedinSection(2.1.1)thatmarketinefficiencyleadstoactiveequitymanagementwhereenhancedindexedport-foliosweredesignedtogenerateattractiverisk-adjustedreturnsthroughactiveweightsgivingrisetoactivereturns.Earlierresultsinthenon-parametricstatistics,informat

3、iontheoryandeconomicsliterature(suchasKelly[1956],Markowitz[1952])establishedoptimalitycriterionforlong-only,non-leveragedinvestment.WesawinSection(2.3)thatinviewofsolvingtheproblemofportfolioselectionMarkowitz[1952]introducedthemean-varianceapproachwhichis

4、asimpletrade-offbetweenreturnanduncertainty,whereoneisleftwiththechoiceofonefreeparameter,theamountofvarianceacceptabletotheindividualinvestor.Similarly,Kelly[1956]introducedaninvestmenttheorybasedongrowthbyusingtheroleoftimeinmultiplicativeprocessestosolve

5、theproblemofportfolioselection.WepresentedinSection(2.3.1.2)thecapitalassetpricingmodel(CAPM)anddescribedinAppendix(9.3.16)thegrowthoptimumtheory(GOT)asanalternativetotheexpectedutilitytheoryandthemean-varianceapproachestoassetpric-ing.Asanexample,wepresent

6、edinSection(2.3.2)thegrowthoptimalportfolio(POP)asaportfoliohavingmaximalexpectedgrowthrateoveranytimehorizon.WesawinSection(7)thatinviewoftakingadvantageofmarketexcessreturns,alargenumberofhedgefundsflourished,usingcomplexvaluationmodelstopredictmarketretur

7、ns.Specialisedquantitativestrategiesdevelopedalongwithspecificprimebrokeragestructures.WedefinedleverageinSection(7.1.2)asanymeansofincreasingexpectedreturnorvaluewithoutincreasingout-of-pocketinvestment.Wearenowgoingtointroduceportfoliocon-structioninpresenc

8、eoffinancialleverageandconstructionleveragesuchasshortsellingwhichistheprocessofborrowingassetsandsellingthemimmediately,withtheobligationtorebuythemlater.Portfoliooptimisationinthelong-shortcontextdoes