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Shiller (x62x2x15x5dx4bx57x7cx1x54x4fx1x3dx3ex4fx6bx40x7dx75x70x78x17 2000 x46x8x9
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x25x51x2dx2ex2ex10x54 -x74x78x15x60x54 -x74x73x51x78x2bx38x46x48x4x73x45x6ex72x69x4x7f
x69x54F0 = f;;?g. x10x79x41x42x73x66x49x78x2bx2bx3dx2a xdx5ex5fx51x70x2bx70x71x5fx36xf
x4xdx37x34x70x71x5ax2ex5fx36xfx78x15x2fx54 -x74x2?x54x21x51x14x69x54x51x69x78x25x18x48
x15x1fx2bx3dx5bx23x25x5fx36x78 ?x44x54x70x71x54 -x74xex5bx66x8x31x75x76x78x2exfx3cx8x48
x51x2ax69?x54x59x70x2b -x74 ?F,x5bx70x62x10x7?x54x70x64x33x34x48x4x48 ? = SIi=1 ?i,
x6cx10x66x15x1fi 6= j, ?i \?j = ;,x53x68 ?F x67x2x26x25xb?i x54x51x4x66x21x36x41
x54x78x21x22 ? x44x54x17x18x79x48x67x2x5d ? x44x54x70x2b -x74x48x10x5fx60x61x4cx42x17
x10x7x54?x44x54x33x34x78x45x31x48 ? = f1;2;3;4g. x33x34?x54x70x64x33x34x23x25x2
217
?0 = ff1;2g;f3;4gg. x58x17x10x7x54 -x74x2F0 = f;;f1;2;3;4g;f1;2g;f3;4gg.
x70x71x27x70x48x15x49?x44x54x78x2b -x74F1 x4F2,x10x3ex75x76x2ex25x77x60x2fx78
xfx2x31x32x51F1 ‰ F2, x3ax3ex67xcF2 x77F1 x2fx78x10x23x24x69x1ex1x7cx6ax69F2
x77x7cx6ax69F1 xdx51x21x2ex54x7cx6axfx78x4dx70x69x4bx48x49x62x78x2b -x74F1x4F2x48x2e
x23x10x3ex75x76x25x35x77x60x2fx48x3ax3ex51F1 \F2 x2x77x10x3ex5bx60x54x15x4ex54 -x74x48
x10x79x41x42x8x31x54xdx6ex63x7cx6axfx57x58F1 [F2 x70x71x27x70x2ex70x62x2 -x74x48xf
x2x3ax3ex23x24x5dx10x4bx1dx1x45x6ex10x54x15x16 -x74x48x51x6cx2ex74x1cx44x1F1 [F2,
x33x34x10x53x79x41x42x8x31x54xdx7cx6ax75x4xfx78x49x24x56x54x55x56x2cx48x59x2bx4fx1ex31i
x5bx51x70x2bx7cx6ax69Fi. x33x34I x2bx4fx1ex31x54xdx6ex63x7cx6axfx69x67x2TIi=1Fi,x62
x3exfx51x54xdx21x51x6ex7dx7cx6axfx69x67x2SIi=1Fi.
x25x26x54x7cx6ax69x54x25x22x17x71x3ax3ex49xbx4bx19x57xcx19x1fx78x49x8x53x33x24x5e
x21x70x71x54x2bx3dx33x54x25x22x2cx48x3ax3ex4bx57x20x19x1f -x74x59x2x70x64x7ax7bxdx7cx6a
x4bx27x4bx7bx5dxfx54x1fx6ax78x16x17x2x49x8x53x33x2cx48x31x32x51 N x2bx18x23x48x33x34x5
x54x70x71x69 ? x67x2x45x6e 2N x2bx70x71x54x69x25x78x10x54x15x2fx54 -x74FN x67x2x26
x25x2b2N x2bx38x46x54x69x25x54x21x51x14x69x21x4dx41x78x10x54x15x60x54 -x74xex2x650x2b
x18x23x26x1ex2b?x36x41x54x78x2bx38x46x54 -x74F0. x58x5bx66x8x31x75x76x54x65kx2bx18
x23x54 -x74Fk xex2x5d?x33x34x12k x2bx14x69x21x36x41x54 -x74Fk. x28x42x18x23x54
x54x4ex48x25xb -x74(x7cx6ax69)x67x4bx27x4bx2fx78
x51x61x7cx6ax69x54x25x22x24x13x48x3ax3ex67x23x3bx10x27x23x37x42x43x44x59x2bx4fx1ex31
x21x6dx6ex54x7cx6ax70x75x78x3ax3ex13x1bx19x3ax3ex24xbx57x7fx65x63x54x55x56x44x2ax17xbx4
x50x27x78x2bx18x23x48 K +1x64x2cx68x48 S x64x50x27x70x71x48 I x2bx4fx1ex31x9x9x78xfx2
x3ax3ex2ex13x0x1x17xbx70x71x2x3cx62x54x48x58x2x0x1x59x2bx4fx1ex31 i x5bx51x45x6e S
x2bx38x46x54x70x71x69?x44x54 -x74Fi x2ex1x10x54x7cx6ax69x78x2cx68k x54x17xbx4ax4b
p(xk)x5ax2ex13x2x3cx62x6cx48x58x2x70x2bx28x29x2ax6c(x4S x75x24x6c)x78x26x66x10x5ax25
x36x41?x54x70x64x33x34(x4ax4bx70x26x54x70x71x40x41?x54x70x2bx14x69)x48x39x58x10x5ax25
x36x41x10x36x57x54x7cx6ax69Fp. x25x67x2xdx4ax4bx1cx27x54x7cx6axfx78x0x1x17xbx5ax2x2e
x3cx62x54xdx15x2exfx28x69x1ex78x17x71x25x73x2x1x61x55x56x54x28x5cx78x21x25x69x54x55x56
x5ex5fx2x60x18x3ex2ax2bxbx3x2cx3ex3x2bx13x48x25x18x2cx3ex4x2bx13x5bx2x2ex3cx62x54x78x5d
x17xbx3cx2ex2bxbx4x2cx3ex54x25x41x73x2x70x2bx28x5cx55x56x78
x49x25x26x54xbx20x56x48x4fx1ex31 i x53x47x48x65x1ax51x2cx72xdx54x2cx68x14x25x15x6d
x7x8x5fx60x2ax39x2cx68x14x25 ,x53x68
8
<
:
max Ei[u(zi0;zi1)]
s:t: zi0 = !i0 ?PKk=0 kp(xk);
zi1 = !i1 +PKk=0 kxk:
(1)
x57x24xbx54x2ex10x75x73x49x66x65x8x2bx9x26x2x28x29x6cx54x9x26x48x65x70x2bx9x26x5ax2
x28x29x6cx54x9x26x78x58 Ei x2x4fx1ex31 i x54xdx74x76x25x27xfx56x54x68x4fx3ex2bx78x17x2c
x10zi1 x39x68x4fx3ex2bx57x24xbx36x51x2ex4ex48x3fx48xfx2x25x27x23x24x2x4fx1ex31ix21x7c
218
x51x54x78xfx2x10x66zi0 x54x68x4fx3ex2bx51x77xcx5ax78x25x18x1bx7cx1dx51!i0 x7x8x2x2b
Fi-x23x51x54x28x29x2ax6cx48x4x10x10x66Fi x10x7x54?x54x14x69x33x34x27x70x48x49x33x34
x54x59x70x14x69x44x10x2x7fx68x78x4dx70x69x4bx48x4ax4bp(xk)x7fx2Fp-x23x51x65x68x78x66
x2zi0 x7x8x2x2bFi [Fp-x23x51x65x68x78x4fx1ex31ix10x66zi0 x54xdx74x76x25x27xfx7
x8x10x66x25x2b -x74Fi [Fp x27x62x7ax78 3
x1ax49x61xdx51I x2bx25x26x54x4fx1ex31x48x10x3ex57xbx4bx54x70xbx61xdx70x14x40x41
x70x2bx3dx3ex42x43E(ui;!i;?). x72xdx66x24xbx54x65x63x48x3ax3ex23x24x62x7ax10x54x70x71
x72x73(ˉ i; ˉp)x1x9xax56x5cx78x38x3dx54x2cx68x14x25x64x4ax4bx14x2a
1. x10x66x15x1fi = 1;2;:::;I, ˉ i x2x17p = ˉpx18x54x5fx60(1)x54x1ex78
2. ˉ 1 + ˉ 2 +¢¢¢+ ˉ I = 0.4
x25x26x54x72x73x67xcx1x3fx59x1dx72x3dx3ex78x69x1dx1x3ex72x73x2x35x66x49x17x7ax5ax2x70
x2bx47x75x22x1x65x63x54x5fx60x78x2bx71x44x48x7ex7fx54x3dx3ex42x43x54x70x71x72x73x66x49x5f
x60x73x2x10x54x70x2bxcx45(x21x51x7cx6ax69Fi x4Fp x5bx2x15x60x54x7cx6ax69)x48x17x2c
x16x17x2x45x46x2ex7ex7fx42x43x54x54x70x71x72x73x66x49x5fx60x78x7bx7ex48x70x71x27x70x48x69
x1dx1x3ex72x73x2x2ex70x62x66x49x54x78xfx2x31x32x72x73x66x49x48x33x34x10x54x72x73x62x4a
x65x68x21x20x48x54x7cx6ax69x48x67x23x3bx27x23x37x51x3ax42x43x78
x61x62x10x66x11x42x43x54x69x1dx1x3ex72x73x4ax4b ˉpx66x49x48x25x18 ˉpx2x62x7ax49x2c
x68x54x50x27x4ax4bx44x54x28x29x2ax6cx6x65x68x78x10x66x70x2bx7cx6ax69F0 ‰F x27x70x48x68
x69E xcx1x14x4eF0 x24x14x2x5dx2ax10x66x15x1fi = 1;2;:::;I, F0 ‰ Fi [Fˉp. x25
x26x70x27x48x51x3ax42x43x54x33x72x67x23x60x54x68x21x0x68x3cx78x6ex63x7cx6ax69x23x62x7ax1T
I
i=1F
i. x10xcx62x2x42x43x51x3ax54x78x25x64x51x3ax1dx67x2x44x25x51x3ax1dx78x6ex7dx7cx6a
x69x7fx1fx62x7ax1SIi=1Fi. x7bx7ex48x25x51x3ax23x62x7ax1
8i = 1;2;:::;I;
I[
i=1
Fi ‰Fi [Fˉp:
x25x70x38x3dx2ex70x62x9xax78x31x32x10x9xax48x67x79x41x42x25x70x72x73x2x70x64x7cx6ax11
x49x4ax1bx1cx54x69x1dx1x3ex72x73x78xfx2x31x32x21x51x6ex7dx7cx6ax5bx11x7ax7bx49x4ax4bx7cx6a
x2cx48x7dx3ex67x36x51x68x69x7cx6ax54x30x43x48x24x5ex67x36x51x15x1fx6ex7dx7cx6ax78 Grossman–
Stiglitz x67x63x7fx26x7ex0x14x78x66x2x49x25x70xex4cx54x79x7ax56x48x7fx23x24x63x2cx48x7c
x6ax11x7ex7fx58x44x54x69x1dx1x3ex72x73x2ex66x49x78
3x27x44x2dxbx17x20x2dx52x2bx40x12x1ax5x7ex66x19x1ax48x3x2dx5 x7bx48x70 i x20x10x5bx30xex41x13x1x1x47
x52Fi x43x46x20x5 x56x16x17x28x47x52x10x23x30xex41x13x56x26x20x29xbx12x5xfxdx52 -x6dFi [Fp x43x46
x20x10x5bx30xex41x13x2cx32x33x55x13x5 x35x7ex47x16x17x51x52Fi x2cx36x6cx32x33x55x13x5 x1ex26x5ax52x36x6cx32
x33x55x13x2cFi x20x10x5bx30x32x33x55x13x13x29xbx17x2cx50x20x32x33x55x13x18x42x62x2cx10x5bx30x32x33x55x13x13x2b
x16x5x28x4fx47x41x42x10x63x6ax41x21x52x20x50x4bx4dx12x62x52x48x35x3ax20x24x56x13x20Bayesx1x52x29
4x18x3x4x3bx17x5x19x1ax4ex48x3x15xbx53x20x10x70x71x18x13x72x71x12xax10x6fx7dx18x13x72x71x5 x13x48x3cx4d
x5dx14x7bx48x70x60x6ex76x25x3bx43x20x72x71x25x26x5 x56x5ex11x28x2cx2cx7fx72x71x25x26x2bx62x29
219
x25x26x48x3ax3ex67x7ex1fx69x1dx1x3ex72x73x54x25x22x1x44x25x51x3ax57x25x51x3ax2ax7d
x69x63xex4cx78x25x18x3ax3ex58x23x24x3cx19x48x49x44x25x51x3ax57x25x51x3ax75x76x48x58x23x24
x51x2dx2ex2cx76x54x42x43x51x3ax78x7ax58x48x3ax3ex5ax75x1fx79x19x48x49x25x70x69x63xex4cx2c
x54x7cx6ax25x22x54xcx5ax1dx78x26x7ex37x36x54x44x25x51x3ax57x25x51x3ax57x17x6ax27x54x6fx79
x58x51xfx4ex54x48x3fx78
9.5 x15x13x48x3ax3ex13x27x3cx3c CAPM x4 APT x57x51x3ax42x43x54x3x4cx78x47
x7aCAPMx4APTx5bx51x17x3dx3ex42x43x54x70x71x57x58x72x73x55x56x48x58x7ex7fx54x70x71
x57x58x72x73x55x56x7fx2x69x1dx1x3ex72x73x55x56x54xcx45x48x33x34x44x29x54x51x3ax42x43x54
x65x63x5ax67x24x3bx66CAPMx4APT.x2fx5ex3ax3ex58x23x24x1x10x3ex2ax7dx59x2bx4fx1e
x31x5bx51x36x57x54x6ex7dx7cx6ax69x54x69x1dx1x3ex72x73x55x56x78xfx2x33x63x2CAPMx58
x2APTx48x5bx51xdx4fx1ex31x3ex2bx72x20x1dxfx54x61x62x48x5ax67x2x70x62x3ex54xdx74x76x25
x27x4x6bxfx5bx2x70x26x54x48x25x17x6cx4cx17x4ax4bx7ex7fx58x44x6ex7dx7cx6ax18x78x51x23x25x78
x25x26x70x27x48x31x32x70CAPMx4APTx5bx2x2ax7dx49x69x1dx1x3ex72x73x54x40x41x44x48
x33x34x10xcx2cx57x42x43x54x25x51x3ax61x4cx49x70x14x78x5ax67x2x70x48x31x32x42x43x25x51x3a
x1dx2ex41x7dx48x33x34CAPMx4APTx5bx2ex25x41x7dx78x58x7ax1fx27x71x2ex70x62x48x4x48
x51x23x25x42x43x25x51x3ax1dx41x7dx48x58CAPMx4APTx2ex41x7dx78x25x26x54x76x77x51x23
x25x10x5dx46x27x8x1ax54x70xbx3x66x42x43x51x3ax1dx7dx52x54xcxdx49x8x20x1ex4dx48x4x10
x3ex71x60x44x73x2x35x62x61x70x62x79x7ax56x54CAPMx4APT,x58x2ex2x51x3ax42x43x78
x1fx79x19x25xbx69x4bx51x2ex2x75x35x62xdx57x4fx3dx3ex57x58x4fxfx54x69x63x4ax6x48
x58x2x75x53x7dx3ex0x4ax19x48x3dx3ex57x58x4fxcxdx58x51x2dx2ex69x4bx47x75x22x1x78x49x57
x4fx54x69x63xex4cx2cx48x3ax3ex19x57x68x19x1ex37x62x4ax40x6fx62x69x3 Markowitz x69x63x3
CAPMx3 APT x9x9x78xfx2x31x32x13x4ex70x57x47x48x4fx1ex31x54x7cx6ax3x7cx22x58x17
x0x14x54x4fx1x24x58x3dx3ex42x43x54x1x76x31x4dx48x67x4dx5fx1ax57x4fx69x63x54x2dx2ex2exax78
x25x3bx2x17xbx3dx3ex57x58x4fx69x63xcxdx54x2dx2ex20x20x60x78
x2fx6a x25x6fx5cx5dx3cx4dx47x11x12x58x59x33x5cx4fx7x20x3bx14x9x30x31x29x27x44x2dx11x12x58x59x33x30
x31x20x7x76xcx30x47x11x12x32x33x20x43x16xcx30x5x7ex66x25x6fx5cx5dx3cx4dx74x74x47x5cx4fx30x31x20x4x2ex5
x18x28x7ex18x25x47x40x53x6x20x11x12x32x33x47x2bx48x35x37x35x43x16x20x29x1ax1ex5x79x25x2ax40x2cx20x30x31x4e
x37x3bx56x58x59x5ex11x18x5cx5dx70x6fx47x2bx16x17x20x5x7ex47x21x15x5cx5dx7axax3bx14x17x2ax28x37x5x3ex53x11
x12x67x58x36x6cx41x65x20x5cx5dx70x6fx29x27x53x25x6fx5cx5dx3cx4dx47x18xax2ax10x47x6x11x12x64x20x10x7ex5x26x13
x18x10x33x61x26x13x23x14x57x4fx29 x57x2x4dx5 x36x1ax24x2ax5x70x4fx47x2cx30x43x79x47x18x43x25x6fx5cx5dx3cx4dx60
x2bx7ex66x5bx74x29xax35x47x2cx15x6ex7ex7ax36x5ex11x7fx18x34x5cx5dx25x6fx20x5cx26x6ex7ex5x48x49xfx6ex25x20
x6ex7ex30x31x3dx61x35x1cx3fxbx17x20x2cx2cx29x31x4x52x25x6fx5cx5dx20x30x31x6ex58x63x4dx63x41x2dx29xax35x47
Lo–MacKinley [22], Shleifer [29] x33x21x2fx60x47x3x18x25x6fx5cx5dx5cx4fx3ax52x36x75x20x3bx68x2c
x2ax29xbx48x35x40x36x3bxax25x6fx5cx5dx5cx4fx6ex58x3fx12x20x70x10x29 x1ex56x5x4fx16x52x52x4fx4cx33x23x59x5a
x7cx18x43x58x1cx4cx33x3bx17x5 x10x58x1cx25x6fx5cx5dx5cx4fx13x1dx1ex25x35x0x25x20x16x13x29
x27x53x25x6fx5cx5dx3cx4dx20x30x31x9x58x77x47x7ex72x30x31x5 x56x5cx4fx11x12x58x59x33x47x15x25x6fx5cx5d
x3cx4dx7ax36x4x2ex20x29x2bx3bx5x6x2bx7x3x43x3bx56x58x59x5ex11x60x1bx20x5cx4fx11x12x58x59x33x6bx36Duffie
[4], [5], Huang–Linzenberger [13]x34Ingersoll [14]x7x60x2bx4ex4fx25x6fx5cx5dxcx30x29 Jarrow
220
[15] x2bx37x37x38x3x43x3bx56x58x59x5ex11x60x1bx5x41x3x35x20x26x3bx6bx5x6x4ex4fx47x25x6fx5cx5dx29x19x1a
xbx53x20x25x27x5cx3ax47x55x5ex11x20x5bxdx60x2exfx2fx64x53x28x29 x3cx47x5cx3ax47x55x5ex11x2ex6ex4fx47x14x9
x19x21x2cx20xexfx29x19x1ax64x3R. E. Lucas (1937–)x77x50 1995x2x6fx1x7ex58x59x33x68x62x47x2b
x37xex24x60x34x0x4ax5cx3ax47x55x3cx4dx5x41x56x12x53x47x3cx30x58x59x77x4fx3x39x20x41x47x36x1ax52x58x59x2
x79x20x5cx20x29 x3cx47x6x11x12x58x59x33x7x4ex4fx5cx3ax47x55x5ex11x2ax26x20x47Radner x33x36x20x63x36x29xb
x3bxexfx62x47Radner x2ex2cx20x11x12x5cx5dx3bx56x58x59x5ex11x7fx18x20x73x1ax29 Radner [26]x47xbx1
x11x30x31x20x28x37x5bxdx29 x56 Jordan–Radner [16]x47x5cx3ax47x55x5ex11x2cx6x36x6cx30x31x20x3bx14x58
xdx29x2bx3f Lucas [23] x4ex34x37x25x6fx5cx5dx2ex2cx3fx3bx14x3ex3fx20x5cx3ax47x55x5ex11x7fx18x29 LeRoy
[18]x28x47x3bx3dx2ax26xex41x5cx4fxfx4dx5cx20x25x6fx5cx5dx20x58xdx4fx2ex5x13x50x3bx1fx29
x4ax5cx3ax47x55x5ex11x4dx4ex4fx11x12x5cx5dx7x20x50x4bx63x5ex19x3cx36x25x2bx45x1ex20x3ex10x5xbx47x2b
x37x50x4bx27x4a -x6dx4dx43x46x16x17x18x1cx19x5cx20x20x50x4bx27x25x38x9x20x37x76x29x6fx3bxax24x16x20x4ex4f
x47x15x7bx48x70x20x5bx30xex41x7ax36x16x17x20x7ax32x5x3ex3bx4dx4ex4fx1cx3fx16x17x4bx5ex50x4bx20xcx30x29xb
x17x48x50xex41x42Green–Lucasx5ex11x20xexfx29x25x27x4ex4fx48x7cx7aLaffont [17]x5x47x2fx4ex47x50
x4bx58x59x33x1x11x20x44x6bx29
x27x53x25x6fx5cx5dx5cx4fx20x30x31x4ex4fx31x4x3dx26x29xax35x47x60x58x59x7cx37x11x12x33x20x3fx65x5xb
x1x11x20x57x4fx2ax47x28x77x51x79x29x19x1ax6x4x11x6ex58x2bx2cx47x2bx61x25x27x20x4fxdx29x1fx4x7x5x19x1a
x79x5x6x26x6dx47x3bx5a Lo–MacKinlay x20x4fxdx5x15x28x36x37x3bxax31x4x37x38x1cx18x20x30x1x66x9
x3dx73x38x29x7dx53x7cx37x11x12x33x18x25x6fx5cx5dx5cx4fx20x27x28x4fxdx5 x1fx70x48x7cx7a Shleifer [29] x7c
Shiller [30]x29
x44x30x23x41x45x23
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