25 05 025 10 20 30 30 40 10 interpretation x1

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Unformatted text preview: 30 40 10 Interpretation X1 generates a return of 10% in state 1, 20% in state 2, 30% in state 3. X2 generates a return of 30% in state 1, 40% in state 2, 10% in state 3. Remark X1 is Apple and X2 is AT&T in the motivating example (replace state by time) Corporate Finance, Tri Vi Dang, Columbia University, Fall 2013 16 1 1 1 E[X 1 ] 10 20 30 20 4 2 4 E[X 2 ] 1 1 1 30 40 10 30 4 2 4 Var[X 1 ] 1 1 1 (10 20)² (20 20)² (30 20)² 50 4 2 4 Var[X 2 ] 1 1 1 (30 30)² (40 30)² (10 30)² 150 4 2 4 Cov[X 1 , X 2 ] ρ12 1 1 1 (10 20)(30 30) (20 20)(40 30) (30 20)(10 30) 50 4 2 4 50 50 150 50 150 1 0.57 3 Corporate Finance, Tri Vi Dang, Columbia University, Fall 2013 17 Table (summary) X1 X2 S1 S2 S3 (0.25) (0.5) (0.25) 10 20 30 30 40 10 Corporate Finance, Tri Vi Dang, Columbia University, Fall 2013 2 12 12 20 30 50 150 50 0.57 18 Remark Technically speaking, portfolio theory is about combining random variables. Example X1 X2 S1 S2 S3 (0.25) (0.5) (0.25) 10 20 30 30 40 10 Y= 0.4X1+ 0.6X2 Z= 0.2X1+ 0.8X2 Corporate Finance, Tri Vi Dang, Columbia University, Fall 2013 19 Interpretation The (new) random variable Y can be interpreted as a portfolio consisting of asset X1 and X2 with the weights 0.4 on X1 and 0.6 on X2. Invest 40% of your wealth in asset 1 and 60% in asset 2. Portf...
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This document was uploaded on 02/16/2014 for the course ECON w4280 at Columbia.

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