我国证券市场分形特征研究

湖南大学硕士学位论文我国证券市场分形特征研究姓名：郭虎清申请学位级别：硕士专业：管理科学与工程指导教师：祁顺生2004102840Fama1970FamaRoberts(1967)70(1)(2)(3)(4)(5)1994420044HurstLyapunovHurstLyapunovIAbstractInthelastfortyyears,EfficientMarketHypothesishasbeenthecoreproposition.Whenwetracingitsdevelopingapproach,wefindmanyofdefinitionsofit.Inthenormal,peoplealwaysusethedefinitionbyFama,whichsays:Efficientfinancialmarketissuchmarket,inwitchitsbonds’pricesalwaysaffecttheinformationthatwecangotten.Inanotherway,FamastillputforwardsthethreetypesofefficientMarketbasedonclassifyinginformationaboutassetspricingbyRoberts,thereareweak-strongefficientmarket,semi-strongefficientmarketandstrongefficientmarket.ForthelinearessenceofEfficientMarketHypothesis,italwayshasbeenworriedbyitstest.Inthefirstinstance,empiricalresultswereabletomatchtheEfficientMarketHypothesisbyandlarge,butinthe1970s,EfficientMarketHypothesishasbeengainingmoreandmorechallengewhichnotonlyfromthetheorybutalsofromtheempiricalresearch.Thereare,especially,manyofabnormalssuchaschoastheory,catastrophetheory,behaviorfinancetheory,coherentmarkettheoryandthefractalmarkettheory,whichletresearcherstakingmoreattentionmoreabouttheuseofnon-lineartheoryinfinancialmarket.TheFractalMarketHypothesishasfivemainideas.Firstly,theFractalMarketHypothesisthinkthecapitalmarketasafeedbacksystem,whichhaslongtimecorrelationandtrend.Secondly,systemhasacriticallevel.Atthecriticallevel,thequalityofsystemshallchange,itcanbeforkedandgottennotonlyoneequilibriumstate.Inanotherway,systemmaybefromstablestatetofoul-upone,andgainedtheirregularstate.Thirdly,forbondpriceandbondreturnratearefollowingbyFractaldistribution,wecanevaluatebondmarket’svolatilityandequalcyclebyTheFractalMarketHypothesis.fourthly,capitalmarketisanmarketapartfromequilibriumcondition,itactuallyissuchamarketthatrepeatedbyrandomnoise.Fifthly,fordependedonoriginalcondition,theinputandoutputofsystemrepeatedandrepeatedcontinually,so,anydifferentoforiginalconditionshouldbemagnifiedinexponentialway,orforthesystem’srandomicity,thesystemforgettheformerdata.Inourpaper,researchingontheindexofbothshanghaiandshengzhenbondmarketfrom4th,1994to4th,2004,wefindthatourbondmarkethasobviousfractalcharacter,andworkingouttheHurstindexandLyapunovindex,whichprovethatourbondmarketcanbeentestbynon-lineartheory.Keywords:theEfficientMarketHypothesis,Fractal,Hurstindex,LyapunovindexII1______21.174.1V364.2V38III4.1354.2354.3374.4(R/S)N374.5(R/S)N38IV(EfficientMarketsHypothesis,EMH)EMH401965Fama[1][2]()EMHSharpe[3]Litner[4]Mossion[5]EMHMarkowitz[6](CapitalAssetPricingModel,CAPM)CAPMBlack&Scholes(OptionPricingModel)Ross(ArbitragePricingTheory,APT)[8]EMHEMH(206070EMHFama[1,2]Alexander[9]Hanlon&ward[10]Jensen&Benninggton[11])EMH2080,EMHEMH[12]-[14][15]-[16][17]-[20]19871019(22.6%)1998LTCM(1997ScholesMerton)EMH1(1)(2)()(3)(4),(1)(2),2(3)(4).31202050“1952HarryMarkowitz(PortfolioSelection)Markowitz(Mean-VariancePortfolioTheory)(MPTMordernPortfolioTheory)Markowitz1959RobertsOsborne(EMHEfficientMarketHypothesis)201964Markowitz(WilliamSharpe)(ASimplifiedModelofPortfolioAnalysis)MarkowitzMarkowitz(CAPMCapitalAssetPricingModel)CAPM42070(Fama1970)1976(StephenRoss)CAPM(APTArbitragePricingTheory)BlackScholesMerton(OPTOptionPricingTheory)1.11.1.1“”(randomwalk)1900(10uisbachelier)01905?“”1953Kendall1951959RobertsKendallRobertsRobertsOsborneSamuelsonEMHOsborneOsbornFama1970FamaEMHEMHEMHEMHPttt+1PttEtIt)1()/(tttIREγ+=RtPt+1PtttttPIPE=++)/(111γϕϕϕFamaFama6t-ltt-1t)\()/(11mttmttPfPf−−=ϕϕ(),,,21ntttPPPΛt1−tϕt-1t-1mt1−ϕ)/(1−ttmpfϕtt)1/(−ttpfϕ1−tϕtt-11−tϕFamaRobertsweakform(semi-strongform)(strongform)1.11.l7EMHEMH?EMH?MiltonFriedmanEMH8Friedman1.1.2()9()1976(Vanguard)5001982199715851.21.2.1(1)(2)10(3)(4)(1)(2)()()(3)()(1)(2)(3)111.2.2FamaB/M(booktomarketratios)?HawawiniKeimFama1.2.3Fama()12(smartmoney)19872020601322.1(Chaos)2070[21](1)(2)(3)(4).1980Stutzer[22],Hesieh[23]Kodres&Papell[24]PhilipatosPilarnu&Mailliaris[25]Scheinkman&Baron[26]Eldridge&Coleman[27]Abhynkar&Copeland[28]FTSE-100NpackardCrutchfieldFarmarShowTakens[29]Whitney,GrassbergerProcaccia[30]nxxx,,,21Λ,(1)m{{niix1}=niix1}=14m{{m{11}+−=mniixTmiiixxxx],,,[111−++=Λ11}+−=mniix11}+−=mniixniix1}=εmD,()−jixx||m),(εε−−||||jixxθθεεε(2){εεInmCIn,()=(2.1)∑=−=njn12||)(1εθCεθHeavisideZ0,(Z)=0Z0(Z)=1εD(ε,m)InC(,m)InεD(ε,m)(3)m(2)m,D(cmε,m)mInC(,m)InεmD=D(mc)mGrassberger&Procaccia[30]LyapunovmBroomhead&King[31]Vautard&Ghil[32]Kennel[33]Cao[34]Cao[35,36]LyapunovKolmogorovLyapunovKolmogorov.[3739]2080[40][41][42]15[43][44][45][46]26[47]-2.2(CatastropheTheory,CT)[48]1972ReneThom,30CTCTCTCTCT[4951][52]()CT[53]CT[54]CT[55]CTCT,162.3(BehaviorFinanceTheory,BFT)O.K.Burell2080(Prospecttheory,PT)BFTMarkowitzKahnemanTversky(expectedutilitytheory)(standardfinanceinvestor)(behavioralinvestor)PTPT(equitypremiumpuzzle)(optionsmile)KahnemanTverskyPTHershShfrinMeirStatman[56](BehavioralPortfolioTheory,BPT)(BehavioralAssetPricingModel,BAPM)BPTMarkowitzBPTBAPMCAPMCAPMBAPM(InformationTrader)(NoiseTrader)BSV[57]DHS[58]BSV(RepresentativeBias)(Conservatism)EMH[59](Debondt&Thaler)[60][61]DHS17(Inf