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Unformatted text preview: FIN 275  Investment Analysis and Global Portfolio Management Quantitative Review Prof. Gergana Jostova 1 Working with Matrices Most financial applications involve working with a series of asset (stock, bond, portfolio) returns or prices over a period of time. Such a combination of crosssectional and timeseries data is called a panel and is most easily analyzed with matrices. A matrix is a rectangular array of elements arranged in horizontal rows and vertical columns , and usually enclosed in brackets. For our purposes, the elements of a matrix will always be real numbers, but in general they can also be functions or complex numbers. A matrix whose elements are numbers is called a constant matrix. 1 2 3 4 Matrices are designated by boldface uppercase letters. A general matrix A having r rows and c columns may be written A = a 11 a 12 ... a 1 c a 21 a 22 ... a 2 c ... ... ... ... a r 1 a r 2 ... a rc where the elements of the matrix are double subscripted to denote location. By convention, the row index precedes the column index, thus a 25 represents the element of A appearing the second row and fifth column, while a 31 represents the element appearing in the third row and first column. A matrix A may also be denoted as [ a ij ], where a ij denotes the general element of A appearing in the i th row and j th column. A matrix having r rows and c columns has order (or size) r c . The order of the matrix is very important for matrix multiplications. The transpose of a matrix A , denoted as A T or A , is obtained by converting the rows of A into columns of A T one at a time in sequence. If A has order m n , then A T has order n m . Be careful when multiplying matrices whether the matrix or its transpose should be used. In finance, we use matrices to combine the historic return series of several stocks into one struc ture, for example: R = r Jan,ibm r Jan,msft r Jan,lu r Feb,ibm r Feb,msft r Feb,lu r Mar,ibm r Mar,msft r Mar,lu r Apr,ibm r Apr,msft r Apr,lu r May,ibm r May,msft r May,lu r Jun,ibm r Jun,msft r Jun,lu r Jul,ibm r Jul,msft r Jul,lu Square matrices are generally used to summarize variances and covariances among multiple assets:...
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 Spring '12
 GerganaJostova

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