杨波涛-指数化投资及其在中国股市的实证研究

2003180::1718030inthesampleoutofthesample——MinMaxDMinMaxAbstractIndexinvestmentisakindofpassiveinvestmentstrategies.Itcanbedonebyinvestinginallconstituentsoftheindexproportionaltotheirshareintheindex,orbyselectingasmallersubsetoftheassetsintheindexsuchthattheresultingportfoliooptimallytrackstheperformanceofthechosenindex.Inrecentyears,passiveinvestmentstrategies(especiallyindexinvestment)havebecomeverypopular.Theemphasisofthispaperisonhowtotechnicallyconstructtheoptimalindexinvestmentportfolio.Wecanclassifythetraditionalmethodstodosointothreecategories:fullreplication,optimizationapproach,andstratifiedsampling.Becauseoftransactioncosts,itisverydifficulttoadoptfullreplicationmethodtomakeindexinvestment.Wecanonlychooseoptimizationapproachorstratifiedsampling.However,thiswillresultindifferencesbetweenportfolioreturnsandthebenchmarkindexreturns,whicharecalledTrackingError(TE).Inrealities,therearethreekindsoftechnicalmethodstoconstructindexinvestmentportfolio:meanvarianceoptimization,absolutedeviationminimization,andoptimizationalgorithms.Basedontraditionalmethods,wedesignseventeenwaystoconstructoptimalindexinvestmentportfoliobyspecifyingdifferentobjectivefunctionsandconstraintconditions.Inempiricalanalysis,wechooseShanghaiIndex180asthebenchmarkindex.Weusestratifiedsamplinginsteadoffactoranalysistoselect30representativestockstoconstructourportfolio.Wemaketheoptimalportfoliobyusinginthesampledataandthentestourportfoliobyusingoutofthesampledata.ThetestcriteriaincludeAveragereturn,Standarddeviation,Beta,Sharperatio,andTreynorratio.Wealsoconsiderratioofobjectivefunctionvaluesandtransactioncoststotesttherobustnessofourmodel.Intheend,weselecttwomostappropriatemethodsthatcanbeusedinChina’sstockmarkettomakeindexinvestment:MinMaxandDMinMax....................................................................................1..........................................................................................11meanvarianceoptimization......................................................22absolutedeviationminimization...........................................43optimizationalgorithms.....................................................................54.........................................................................................................11................................................................................................131............................................................................................................1311............................................................................................1312.....................................................................................142..................................................................................................1621Inthesample...................................................................................1622Outofthesample......................................................................1723...........................................................................18................................................................................................19........................................................................................................................21...............................................................................................................................24120011968Jensen1999Edelen200390200021meanvarianceoptimizationYYTXnX×Tnbe1Clarke(1994)MarkowitzMentalAccounting2()()EUERRgd=Δ-ΔgregretregretgMarkowitz{}2min():(()),0xERxRxPRdΔ≥∈ΔP0Rmvp≥{}2min():(()),0xERxRxPRdΔ=∈Δ(Mansini2001)3×,,,,TTnnTYXYXebbe=-∈∈∈∈¡¡¡¡min'min()'()YXYXbbeebb=--*1(')'XXXYb-=bb°°°°°min'min()'()..YXYXstRqbbeebbb=--=°**111*(')'[(')']()XXRRXXRRqbbb---=--*1(')'XXXYb-=°1Ib=I°**111*(')'[(')'](1)XXIIXXIIbbb---=--*1(')'XXXYb-=2benchmark3bCAPMb42absolutedeviationminimizationKonno&Yamazaki22T+2T+min1'(),1'(1,...,1).TXYbb-=∈¡min(max),tttXYbb-4()'()YXYXbb--()'()/YXYXTbb--T561LRiskModel1LMarkowitz5tXXttYYtKonno&Yamazaki,1991min1'(),MADTEXYbb=-min1'(),,ttMADDTEXYXYbbb=-min(max),MinMaxtttTEXYbb=-min(max),.DMinMaxtttttTEXYXYbbb=-3optimizationalgorithms7Excel61An+itpti0,...,Ain=rtI[1,]tt-1ln()ItitIrI-=tIitxtitPt{0,1,...,},titAPxin==tJt{0}titJix=≠tvt0AtntititititiiJvxpxp=∈==∑∑tt-tv-,,10.Anitittivpx--==∑7[1,]tt-,,101,1,10ln()ln().AAnititPtitntititipxvrvpx--=---===∑∑t,,,10,AntitititiCcpxx-==-∑[1,]tt-111ln()ln().PttttttvvrvvC-----==-itptI1t2t1t2t12,ttE21121,21(),tPIttttttrrEttaa=-=-∑0a12,ttR12[,]tt2112,21().tPIttttttrrRtt=-=-∑12,ttF12,ttE12,ttR121212,,,(1)ttttttFERll=--[0,1]l∈80,0,...,itAxin≥=iietPid111111,,,,tititiiititiJtpxpxiJed∈≤≤∈∑01iied≤≤K1#{}tJK≤tCtt_tvg_ttCvg≤Konno&Yamazaki,1991isiiixisiitixys=8Changtabusearchsimulatedannealingheuristics9tP{}ittyiJ∈2t{}22,titPx--=2tv-12[,]tt23[,]tt1t{}11,titPx--=1tv-12.,,,0,.....,Aititwwin--=={}11,titPx=12[,]tt12,ttF1212121,,,min(1)tttttttPFERll=--11_ttCvg≤11111_,,tititttiJpxCv∈+=∑111111,,,,tititiiititiJtpxpxiJed∈≤≤∈∑1#{}tJK≤91012[,]tt{}1