0675 and variance of 00072 per day expected return is

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Unformatted text preview: 0072% per day - Expected return is higher than AT&T, Exxon and Walmart - Variance is lower than any single stocks - What is the smallest possible variance? Corporate Finance, Tri Vi Dang, Columbia University, Fall 2013 11 Review Properties of the mean Suppose 1,...., N R, und X1,...., XN random variables (M1) E[1X1]= 1E[X1] (M2) E[X1+....+XN]= E[X1]+….+E[XN] (M3) E[1X1+….+2X2]= 1E[X1]+….+NE[XN] Corporate Finance, Tri Vi Dang, Columbia University, Fall 2013 12 Covariance-Matrix V X1,....,XN are random variables, i² is varianz of Xi und ij is covariance between Xi und Xj. V is the Kovarianz-Matrix σ1 ² σ V 21 σ N1 σ12 σ1N σ2 ² σ 2N σ N2 σ N ² Note, ij=ji. Corporate Finance, Tri Vi Dang, Columbia University, Fall 2013 13 Properties of Variance Suppose 1,...., NR, =(1,...., N) a N-vector, X1,...., XN random variables and V the Covariance Matrix. (V1) Var[1X1]= 1²Var[X1] (V2) Var[1X1+….+NXN]= V Remark Formula (V2) plays a central role in portfolio theory (and asset management). Corporate Finance, Tri Vi Dang, Columbia University, Fall 2013 15 Example X1 X2 S1 S2 S3 (0.25) (0.5) (0.25) 10 20 30...
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