4 on x1 and 06 on x2 invest 40 of your wealth in

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Unformatted text preview: olio Z: invest 20% in X1 and 80% in X2. Corporate Finance, Tri Vi Dang, Columbia University, Fall 2013 20 X1 X2 Y= 0.4X1+ 0.6X2 Z= 0.2X1+ 0.8X2 S1 S2 S3 (0.25) (0.5) (0.25) 10 20 30 30 40 10 22 26 32 36 20 30 50 150 18 14 Corporate Finance, Tri Vi Dang, Columbia University, Fall 2013 21 1 1 1 E[Y] 22 32 18 26 4 2 4 E[Z] 1 1 1 26 36 14 28 4 2 4 1 1 1 (22 26)² (32 26)² (18 26)² 38 4 2 4 1 1 1 Var[Z] (26 28)² (36 28)² (14 28)² 82 4 2 4 Var[Y] Corporate Finance, Tri Vi Dang, Columbia University, Fall 2013 22 Using the formula (M3) E[1X+2X2]= 1E[X1]+2E[X2] E[Y]= 1E1+2E2=0.420+0.630=26 E[Z]= 0.220+0.830=28 (V2) Var[Y]=Var[1X1+2X2]= V Var[Y] α1 ²σ1 ² 2α1α 2 σ12 α 2 ²σ 2 ² 0.4² 50 2 0.4 0.6 (50) 0.6² 150 38 Var[Z] 0.2² 50 2 0.2 0.8 50 0.8² 150 82 Corporate Finance, Tri Vi Dang, Columbia University, Fall 2013 23 Table 2 (summary) X1 X2 Y= 0.4X1+ 0.6X2 Z= 0.2X1+ 0.8X2 S1 S2 S3 (0.25) (0.5) (0.25) 10 20 30 30 40 10 22 26 32 36 18 14 20 30 50 150 26 28 38 82 Remark - The portfolio Y has a higher mean and a lower variance than asset X1 (as in the motivating example. - Risk averse investors might prefer this. Corporate Finance, Tri Vi Dang, Columbia University, Fall 2013 24 Diversification Holdin...
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This document was uploaded on 02/16/2014 for the course ECON w4280 at Columbia.

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