34.multigroup_model

34.multigroup_model - University of California, Los Angeles...

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Unformatted text preview: University of California, Los Angeles Department of Statistics Statistics C183/C283 Instructor: Nicolas Christou Multigroup model Short sales allowed with riskless lending and borrowing- Theory From: “Simple Rules for Optimal Portfolio Selection: The Multi Group Case” Elton, E., Gruber, M., Padberg, M. (1977), Journal of Financial and Quantitative Analysis The stocks are grouped by industry. Let’s examine the simple case of two industries. The assumption here is that the correlations within the first group are the same for all the pairs in group 1 (called it ρ 11 ), similarly within the second group correlations are the same for all pairs (called it ρ 22 ), and the correlations for all pairs of stocks between the first group and second group is the same (called it ρ 12 ). For example, suppose stocks 1, 2, 3 belong to industry 1 (automobile stocks), and stocks 4, 5, 6 belong to industry 2 (chemical stocks). Then the correlations are as follows: Group 1: ρ 12 = ρ 13 = ρ 23 = ρ 11 , Group 2: ρ 45 = ρ 46 = ρ 56 = ρ 22 , Between stocks of group 1 and group 2: ρ 14 = ρ 15 = ρ 16 = ρ 24 = ρ 25 = ρ 26 = ρ 34 = ρ 35 = ρ 36 = ρ 12 . ρ = 1 ρ 11 ρ 11 ρ 12 ρ 12 ρ 12 ρ 11 1 ρ 11 ρ 12 ρ 12 ρ 12 ρ 11 ρ 11 1 ρ 12 ρ 12 ρ 12 ρ 21 ρ 21 ρ 21 1 ρ 22 ρ 22 ρ 21 ρ 21 ρ 21 ρ 22 1 ρ 22 ρ 21 ρ 21 ρ 21 ρ 22 ρ 22 1 The solution was found and it is the point of tangency to the efficient frontier. But now the stocks are grouped into industries. Assume two stocks and two industries (two per industry). The solution as alwaysgrouped into industries....
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This note was uploaded on 06/02/2011 for the course STATS 183 taught by Professor Nicolas during the Spring '11 term at UCLA.

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34.multigroup_model - University of California, Los Angeles...

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