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DEA1,2(1.,710049;2.,325035):,DEA.,DEA.:;;DEA;;;:F224.5;F830.59;O221:A:1000-5781(2005)01-0073-11MainmethodsforthemutualfundperformanceevaluationbasedonDEAmodelsCHENZhi2ping1,LINRui2yue2(1.FacultyofScience,XianJiaotongUniversity,Xian710049,China;2.TheSchoolofMathematics&InformationScience,WenzhouUniversity,Wenzhou325035,China)Abstract:Majormethodsformeasuringtheperformanceofmutualfundsarereviewedinthispaper,spe2ciallyseveralclassesofnewlyproposedmutualfundperformanceevaluationindicesbasedontheDEAmodelareintroduced.Afterdiscussingtheadvantagesandshortcomingsofvariousperformanceindicesandthe-state-of-artsofdomesticresearchinthisfield,someurgentproblemsaboutfutureresearchesontheDEAmodelanditsfurtherapplicationinthemutualfundperformanceevaluationarealsopointedout.Keywords:mutualfund;performanceevaluation;theDEAmodel;return;risk;transactioncosts0,,,.,.1868,.,..,.,;,,;,;,,.,,20120052JOURNALOFSYSTEMSENGINEERINGVol.20No.1Feb.2005:2003-12-19;:2004-12-12.:(2001SL09)..,,Morningstar,Russell.,,.,,.,,.,,..,(dataenvelopmentanalysis,DEA).1,,.,,.,,,()().,MVCAPM.1965,Treynor,Treynor[1],Ij,Treynor=E(Rj)-Rfj(1):E(Rj)j,Rf,j=Cov(Rj,Rm)/Var(Rm)j,Cov(Rj,Rm)RjRm,Var(Rm).,,Treynor,.Sharpe1966,Sharpe[2]Ij,Sharpe=E(Rj)-Rfj(2)jj.Treynor,Sharpe()j,.,.,,Sharpe.,TreynorSharpe.,AngChua[3],Ij,half-var=E(Rj)-RfHVj(3)HVj=E(Min[Rj-E(Rj),0])2,..,Jensen.Jensen[4],E(Rj)-Rf=j+j[E(Rm)-Rf](4):Rf,Rm,j,Jensen.j,j;j,j..,4720,;,;[5];MV(Sharpe)CAPM(TreynorJensen),;,,,.,.,GrinblattTitman[6],.Varian[7].SeifordThrall[8],VarianDEA.,DEA,DEA.2DEADEA[9],..,DEA,DEA.2.1DEA,DEA.,,,.DEA.CCR[9]BCC[10].nj=1,,n,tr=1,,t,mi=1,,m,jrrj,ixij,xijrj.urr,vii,jhj=tr=1urrjmi=1vixij(5)jn,urvi,hj.,j0{1,2,,n},CCRMx{vi,ur}hj0=tr=1urrj0mi=1vixij0(6)s.t.tr=1urrjmi=1vixij1,j=1,,nsur,r=1,,t,s=(mi=1vixij0)-1svi,i=1,,m:.hj0j0,1,,DEA(CCR)[11].s=(mi=1vixij0)-1,i=svi,r=sur,(6):Mxtr=1rrj0s.t.mi=1ixij0=1,mi=1ixij-tr=1rrj0,j=1,,n(7)r,r=1,,ti,i=1,,m571:DEA.(7),,BCC.Min(-tr=1s+r-mi=1s-i)(8)s.t.xij0-s-i-nj=1xijj=0,i=1,,m-s+r+nj=1rjj=rj0,r=1,,tnj=1j=1,j0j=1,,ns-i0,i=1,,ms+r0,r=1,,t:nj=1j=1.,1.(8)3j,3,s-3i,s+3r,3=1,j0DEA(BCC),;3=1,s-3i=0,1im,s+3r=0,1rt,j0DEA(BCC).(8),Mx(+tr=1s+r+mi=1s-i)(9)s.t.xij0-s-i-nj=1xijj=0,i=1,,m-s+r+nj=1rjj=rj0,r=1,,tnj=1j=1,j0j=1,,ns-i0,i=1,,ms+r0,r=1,,t,DEA:,DEA,;,DEA,;,DEA,.DEA,.2.2DEAAliSeiford[12]DEA;PastorBCC,BCC,[13].,,BCC.,,BCC.,111999,WilkensZhu[14]:j(1jn),x1j,x2j,1j,2j,3j.,i0,r0,x^ij=xij+i,i=1,2,j=1,,11^rj=rj+r,r=1,2,3,j=1,,11(10)x^ij^rj.x^ij^rjxijrj,BCC(8).,,BCC(9).,BCC,.2.3DEPI,,.,,.,.,Murthi1997DEA6720,DPEI[15].DPEI,DEA,;,,Murthi.DPEI:DPEIj=RjIi=1wixij+vj(11):Rjj(1jn,n),xijji(1iI),jj.wivxijj.DPEIjj.wiv,DPEIDEAMxDPEIj0=Rj0ni=1wixij0+vj0(12)s.t.Rjni=1wixij+vj1,j=1,,nwi,v1,j0,10,.(12),MurthiMorningstar77311993,(12)CCRDPEI..DPEIJensenSharpe,.DPEI,.[15],,,,.[15].,,DPEI;,DPEI,Sharpe.,DPEI.2.4DEA,DEA.,McMullenStrongDPEI,135,135[16].MoreyMorey[17].DEA,GalagederaSilvapulle[18][16],2571995-1999.(1235),,:,.47,GalagederaSilvapulleBCCCCR11,,,DEA.,,DEA,DEA,.,DEA,.GalagederaSilvapulleDEA771:DEA,,.,,,.2.5DEADEA,.,.,BassoFunari[19]DEA,IDEA-1IDEA-2.nRj(1jn),,E(Rj)E(Rj)-Rfoj.j{1,,n},kc1j,,ckjhq1j,,qhj,IDEA-1:Mx{u,vi,wi}uoj0hi=1viqij0+ki=1wicij0(13)s.t.uojhi=1viqij+ki=1wicij1,j=1,,nu,vi,i=1,,hwi,i=1,,kj0IDEA-1.,,(13)SharpeTreynor,IDEA-1DPEI.,BassoFunari(13).X,Y,U=U(0)C(C),nn={Un-1:(-1)nU(n)0},0.XnY,PUn,E(U(X))E(U(Y))U3nE(U3(X))E(U3(Y)).1,2,.(DARA),DARA.(prudence),3.Kimball[20]=-U(3)/U(2),(DAP).BassoFunariDAPDARA(SRA)[19].,,.,jdj=j/.,IDEA-2,Mx{u,vi,wi}u1oj0+u2dj0hi=1viqij0+ki=1wicij0(14)s.t.u1oj+u2djhi=1viqij+ki=1wicij1,j=1,,nur,r=1,2vi,i=1,,hwi,i=1,,kj0IDEA-2,djDARADAPSRA,(13).8720IDEA-1IDEA-2,BassoFunariCCR4719971999.,,DARA,dj.,.IDEA-2IDEA-1.,,,..IDEA-1IDEA-2,1,.IDEA-1IDEA-2[15,18],,DEA.,,.2.6DEA1,,.,,DEADEA?BassoFunariIDEA-2,DEA[21],DEAIDEA-gMx{ur,r,vi,wi}u1oj0+u2dj0+pr=1rIrj0hi=1viqij0+ki=1wicij0(15)s.t.u1oj+u2dj+pr=1rIrjhi=1viqij+ki=1wicij1,j=1,,nur,r=1,2r,r=1,,pvi,i=1,,hwi,i=1,,kI1j,,Ipj,(14)BassoFunari5019979200111,CCRIDEA-1IDEA-2IDEA-g.(15)SharpeTreynorJensen.,,(15)2.5.,DEA.DEA,,[21][22]DEA,.(15),.,,.,??.2.7DEA,,(ethicalfinance)..,[23].,,,,.,,,DEA.,971:DEADEA.1DEAIDEA-E,IDEA-1jej0,j0Ij0,DEA-E=u31oj0+u32ej0hi=1v3iqij0+ki=1w3icij0(16)u31,u32,v3i,w3i.Mx{u,vi,wi}u1oj0+u2ej0hi=1viqij0+ki=1wicij0(17)s.t.u1oj+u2ejhi=1viqij+ki=1wicij1,j=1,,nur,r=1,2vi,i=1,,hwi,i=1,,k:u2ej,(13).j0,Ij0,DEA-1Ij0,DEA-E;ej0=0,ej0,Ij0,DEA-1=Ij0,DEA-E.,ej,,BankerMoreyDEA[24]j0Ij0,DEA-UMx{u,vi,wi}u1oj0hi=1viqij0+ki=1wicij0-u2ej0(18)s.t.u1ojhi=1viqij+ki=1wicij-u2ej1,j=1,,nur,r=1,2vi,i=1,,hwi,i=1,,kIj0,DEA-U.,j0Ij0,DEA-UIj0,DEA-E;ej0=0ej0,Ij0,DEA-U=Ij0,DEA-E.,,..DEA,.,,,.p,,p-1,1,p-1.,1()2()3(),13d(1)j,d(2)jd(3)j.1d(1)jd(2)jd(3)j111111021003000,DEA[25]:Mx(z+hi=1s-i+ki=1s-h+i+s+1)(19)s.t.nj=1qijj+s-i=qij0,i=1,2,,hnj=1cijj+s-h+i=cij0,i=1,2,,kzoj0-nj=1ojj+s+1=0nj=1q1jq1j0d()jjd()j0,=1,2,3j0,j=1,,ns-i0,i=1,,h+ks+10.IDEA-C.DEA,nj=1q1jq1j0d()jjd()j0,=1,2,3(q1j00),q1jq1j0qijqij0(i=2,,h)0820[25].IDEA-C(19)z.ej0=0d()j=1,Ij0,DEA-C=Ij0,DEA-U=Ij0,DEA-E.,BassoFunari[25]50,2.6.,103ej.:,IDEA-1,IDEA-E,IEA-UIDEA-C;,IDEA-1IEA