证券投资基金的管理费率设计研究

200411:100026788(2004)0120025205,,(,200052):,L,,,L,,L:;;;:F830.91:AResearchonFundManagementFeeRateDesignBasedonthePerformanceNISu2yun,XIAOHui,WUChong2feng(ManagementSchool,ShanghaiJiaotongUniversity,Shanghai200052,China)Abstract:Theinformationasymmetrybetweenfundmanagersandinvestorsaboutfundmanagers’in2vestmentabilityisthoughtofasoneofthemainreasonscausingthelowsubscriptionrateofdifferentfundsinissuance.Then,underthewayofoptionpricing,themanagementfeerateisaffiliatedwithfundreturnandmarketreturn,themanagementfeeratespreadisdesigned,andtheoption’spricesandprofitsshareholderscanobtainarecomputedthroughMonteCarlosimulation.Atlast,thedifferenceinparameterssettingsoffundmanagerswithdifferentabilityisalsoanalyzedinordertoattractshareholders’subscriptioninterest.Keywords:securityfund;fundperformance;managementfee;option:2002211225:(70025303);:(1974-),,,,:.Email:[e-mail];(1976-),,,,:;(1962-),,,,,:12002,,85L,,[1]LL,,L,L,,,,L,,L,,,©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.L,,,,L,1.5%(),,L,,,,L,,[2,3]L[4,5],,L,,,,,,L2:1)rn(t)rm(t);2)pn(t),pm(t);3)r(t)tZ,e(t)rn(t)rm(t):e(t)=e0+(rn(t)-rm(t))b(1),e0,b,rn(t)-rm(t)ZZ,,,Z,,,Z,,Z,eminZU,Z,,Z,:e(t)=emin(rn(t)-rm(t))Ue0+(rn(t)-rm(t))b(rn(t)-rm(t))EU(2),U,e0b,eminZ,Z:,,Z,Z,,Z,:e(t)=emax(rn(t)-rm(t))EUe0+(rn(t)-rm(t))b(rn(t)-rm(t))U(3),,e0b,emaxZ2.1,emax,t:62200412002,20,,7.57%;,-1.2%L,1420,1384L©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.vc(t)=E{max(0,e(t)-emax)}(4),E{}Z,t,r(t)Z,(rn(t)-rm(t))0e(t)emax,,Z,,rn(t)rm(t)ZT,,N=Tniö$tZ,ni,$t,$t=1,N=Tni,N:Vc(t)=6Ni=1E{max(0,(e(i$t)-emax)e-i$t0r(t)dt)}=6Ni=1E{max(0,(e0+b(rn(i$t)-rm(i$t))-emax)e-i$t0r(t)dt)}(5)emax,emax=emax,(5):Vc(t)=6Ni=1E{max(0,(e0+b(rn(i$t)-rm(i$t))-emax)e-i$t0r(t)dt)}(6)2.2,,,Z,,:Vp(t)=6Ni=1E{max(0,(emin-e(i$t))e-i$t0r(t)dt)}=6Ni=1E{max(0,(emin-e0-b(rn(i$t)-rm(i$t)))e-i$t0r(t)dt)}(7),Z,Z,:Vcp=6Ni=1(Vc(i$t)-Vp(i$t))=6Ni=1E{max[0,e0+b(rn(i$t)-rm(i$t))-emax]e-i$t0r(t)dt)}-6Ni=1E{max[0,emin-e0-b(rn(i$t)-rm(i$t))]e-i$t0r(t)dt)}(8)2.3,,MonteCarloZ,rn(t)rm(t)Z,pn(t)pm(t)[6],:dpn(t)=Lnpn(t)dt+Rnpn(t)dzn(t)dpm(t)=Lmpm(t)dt+Rmpm(t)dzm(t)(9),zn(t),zm(t),:dzn(t)=Endtdzm(t)=Emdt(10),EnEm,:EnN(0,1),EmN(0,1),N(0,1)0,1ZLn,Lm,Rn,RmZ721©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.:$pn(t)öpn(t)=Ln$t+RnEn$t$pm(t)öpm(t)=Lm$t+RmEm$t(11)$pn(t),$pm(t)$,(11),,Ln$t,Lm$t,Rn$t,Rm$tZ:rn(t)=$pn(t)öpn(t)N(Ln$t,Rn$t)rm(t)=$pm(t)öpm(t)N(Lm$t,Rm$t)(12)3,:1)2002.8.16,[7];2)T=15,ni=365;3)e0=1.5%ö;4)emax=2.5%ö;5)emin=0.5%ö;6)$t=1;7)10ALCSMAR2002:(Lm,Rm)=(0.1%,0.033);8),(Ln,Rn)Z,Rn,Rn=0.03,,Ln,LnZ:1VcpLn1.VcpLnb=0.05,e0=1.5%ö,(emin,emax=(0.5%,2.5%),T=15,n=365,$=1,Lm=0.1%ö,Rm=0.033,Rn=0.03,Ln-1.0%1.0%,M=100001Z,Ln,,Z(LnLm),,,,,,(CD)Z(LnLm),Ln,,,,(AB)Z,(LnLm),,,,BCZ2.Vcpbe0=1.5%ö,(emin,emax)=(0.5%,2.5%),T=15,n=365,$t=1,Lm=0.1%ö,Rm=0.033,Rn=0.03,Ln,10000,Vcp2.2,LnLm,b,LnLm,bZ,,ZLnLm,Ln,,,8220041,,,34L©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.2Vcpb,Ln,Z,Z,LnLm,b,b,Z,Z,LnLm,Z,b,,,,Z,,,Z3Vcpe03.Vcpe0b=0.10,(emin,emax)=(0.5%,2.5%),T=15,n=365,$t=1,Lm=0.1%ö,Rm=0.033,Rn=0.03,M=100003:,e0Z,,,Z,,,Z,,,,Z,,Z,,,,Z4Vcpemin(emax=2.5%)4.Vcpeminb=0.10,e0=1.5%ö,emax=2.5%ö,T=15,n=365,$t=1,Lm=0.1%ö,Rm=0.033,Rn=0.03,100004Zemax=2.5%,emin,,VcpZ,,,,Z,,,Z4,(56)921©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.Z,Zxq,ZZ:[1]MckenzieL.OptimalEconomicGrowthandturnpiketheorem[A].K.ArrowandM.Intriligator.HandbookofMathematicalEconomics[C].North2Holland,Amaterdam.[2]LaigiMontrucchio.Aturnpiketheoremforcontinuous2timeoptimal2controlmodels[J].JournalofEconomicDynam2icandControl,1989,19:599-619.[3]MakotoYano.Comparativestaticsindynamicstochasticmodels[J].JournalofMathematicalEconomics,1989,18:169-185.[4]AlainHaurie,MichelRoche.Turnpikesandcomputationofpiecewiseopen2loopequalibriainstochasticdifferentialgames[J].JournalofEconomicDynamicandControl,1994,18:317-344.[5]JiongMinYong,XunYuZhou,StochasticControls:HamiltonianSystemsandHJBEquations[M].Springer2Verlag,1999.[6],.[M].:,1988.(29)Z,,Z,,Z,,,,Z:,VcpLne0,emin,LnLmb,LnLmbZ,be0emin,Z,,,,Z:[1].[N].().2002205216.[2]ChordiaTarun.Thestructureofmutualfundcharges[J].JournalofFinancialEconomics.1996,41(1):3-39.[3]PeterTufano,MatthewSevick.Boardstructureandfee2settingintheU.S.mutualfundindustry[J].Journaloffi2nancialeconomics.1997,(46):321-355.[4]KihlstromRE.Optimalcontractsforsecurityanalystsandportfoliomanagers[J].StudiesinBankingandFinance.1988,(5):291-325.[5]KritzmanMP.Incentivefees:someproblemsandsomesolutions[J].FinancialAnalystsJournal,1987:21-26.[6]JohnC.Hull.Options,Futures,andOtherDerivativeSecurities[M].ThePrenticeHallPress,1997.[7],,.[M].:,2000.6520041©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.