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ClassicalIssuesinFinancialEconomicsHarryMarkowitzHarryMarkowitz1*HarryMarkowitz711952377-91“——”1“”“”Hicks“”23NrittidititXiiiXi=0*CowlesCowles601J.B.WilliamsCambridgeMassHarvard193855-752J.R.HicksNewYorkOxford1939126Hicks3HarryMarkowitz2R==Ri=iR=?XiRiRiXiiXi=0?Xi=1RXiRiRRiiXi=1Rαaa=1…KR4iri1ri2…rin…i“”riR=?Xiri“”5—-E-V4r5Williams68-698?ditritt=18N??ditritXit=1i=1N8?Xi(?ditrit)i=1t=1K?Xαa=1a=1HarryMarkowitz3E-V1n342YYy1y2…yNY=y1p1Y=y2p2YE=p1y1+p2y2+….+pNyNYV=p1y1-E2+p2y2-E2+….+pNyN-E2VYVVσ=vVσ/ER1R2…RnRRiR=a1R1+a2R2+…+anRnRR11R2Rn=2a1=a2=1RR1R2…Rn6ER=a1ER1+a2ER2+…+anERn“”R1R2σ12=E{[R1-ER1][R2-ER2]}6J.V.UspenskyNewYorkMcGraw-Hill19379161-81HarryMarkowitz4R1R2RiRjσij=E{[Ri-ERi][Rj-ERj]}σijρijRiRjRiRjσij=ρijσiσjVR=RiσiVR=RiiμiRiσijRiRjσiiRiXiiR:R=?RIXiRiR7XiXi?Xi=1XiiXi=07ABABBAABNNN?a2iVXi+2??aiajσiji=1i=1jiNN??aiajσiji=1j=1HarryMarkowitz5REE=V=μiσijEVX1X2…XNEV1E-VEVVE1μiσijEVNμiσijEVEVN?Xiμii=1NN??σijXiXji=1j=1VEVEVEHarryMarkowitz6E-Vμiσij1E=2V=3=14Xi=0i=12333’X3=1–X1–X23’12EVX1X21’E=μ3+X1μ1-μ3+X2μ2-μ3V8aE=EX1X2bV=VX1X2cX1=0X2=01-X1-X2=0abc8V=X21(s11-2s13+s33)+X22s22-2s23+s33+2X1X2s12–s13–s23+s33+2X1s13–s33+2X2s23-s33+s3333??σijXiXji=1j=13?Xiμii=13?Xii=1HarryMarkowitz7c3’34X1X22acbX2X1=0X1X2=01-X1-X2=0X3=1–X1–X2=0“”“”EV92μ2?μ31’X2=a+bX11X2=E=E0-μ1-μ3/μ2-μ3E0-μ3/μ2-μ3E“”VXEVXC1C2XC1C2X4XXVXVEVEEEEEVVEEV^XEE^XEcriticallinelXEX1X2=E9μ1=μ2=μ312E-μ3μ1-μ3-X1μ2-μ3μ2-μ3HarryMarkowitz8VXlVXabdbbE3Xabbb1X2μiE3243N1010=1X4E=EX1X2X3V=VX1X2X3000001010100X4=1X3=1X2=1X1=1S123X4=0Sa1,…,aαXi=0ia1,…,aαSa1,…,aαla1,…,aαPPSa1,…,aαPEVSa1,…,aαla1,…,aαla1,…,aαEEX1X2abacE*bc4?Xii=1*Eμ1μ2μ3HarryMarkowitz94EVE=a0+a1X1+a2X2V=b0+b1X1+b2X2+b12X1X2+b11X21+b22X22115E-V-EV63-“”“”-μisijE-VEVμisijE-V118ldlaEbcHarryMarkowitz104E-VvV1277PP’=X’1X’2P’’=X1X’’2P=λP’+1-λP’’=λX’1+1-λX’2λX1+1-λX’’2PP’P’’12l124l234X1X2X3l1234HarryMarkowitz1156E-VM313EVUU=UEVdU/dE0,dU/dV014U=UEVM3dU/dM30EVE-V13RP1…Pnr1…rnEM3=14VEVEbcX1X2an?piri-E3i=1HarryMarkowitz127Xt15E-VμisijμisijμisijμisijEVEVμisijμisij15p’p’’apx-bcX1X2

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