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Unformatted text preview: University of California, Los Angeles Department of Statistics Statistics C183/C283 Instructor: Nicolas Christou Multi-index model Short sales allowed From: Simple Rules for Optimal Portfolio Selection: The Multi Group Case Elton, E., Gruber, M., Padberg, M. (1977), Journal of Financial and Quantitative Analysis Stocks are grouped by industry. The multi-index model used here gives a diagonal form of the covariance matrix between stocks. The assumptions for this model is that stocks are linearly related to the group index (industry) and the industry is linearly related to the market index. Here is the model: R i = i + i I j + i I j = j + b j R m + c j with, E ( i k ) = 0 i = 1 ,...,n, k = 1 ,...,n, i 6 = k E ( c j c l ) = 0 j = 1 ,...,p, l = 1 ,...,p, j 6 = l E ( i c j ) = 0 i = 1 ,...,n, j = 1 ,...,p where, R i Return of stock i I j Return of index j R m Return of the market i , i Parameters associated with stock i j ,b j Parameters associated with index j i Error term with mean zero and variance 2 i c j Error term with mean zero and variance 2 c i Using these assumptions we get the following....
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- Spring '11