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May 6th, 2013, 02:18 AM  #1 
Newbie Joined: May 2013 Posts: 1 Thanks: 0  Computing the CoSkewness matrix
Dear all, I want to compute the skewness of a portfolio. By reading loads of literature, I found that the formula of computing the skewness of portfolio is as following: skewness_p=?' M3 (???) where M3=E[(r?) (r?)'?(r?)']={aijk} the ? is the weight vector, the ? denote the kronecker product, M3 is the coskewness matrix, and r and u are the TxN return matrix and TxN average return matrix, respectively. However, I don't know how to decompose the expectation of the coskewness matrix M3, thus I found a alternative way to calculate the M3, that's: The coskewness matrix of M3 of dimensions (N,N*N) can be represented by N Aijk matrixes (N,N) such that: M3=[ A1jk A1jk ... ANjk ] where j,k=1,…,N as well as for an index i. The individual elements of the matrix can be obtained as: aijk=(1/T?1)?i,j,k?t [(Kt,i??i)(Kt,j??j)(Kt,k??k)]. the capital K denote the element in the TxN return matrix, T is the number of observations and N is the number of assets. But my major object is to program it in software. If I do it element by element, it will cost me several years to finish...Thus, I want to ask does anyone know how to decompose the expectation of M3 matrix? that's M3=E[(r?) (r?)'?(r?)']? I reaally reaaly appreciate your help! 
May 6th, 2013, 02:44 AM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 464 Math Focus: Calculus/ODEs  Re: Computing the CoSkewness matrix
Please post a topic only once. Otherwise, it is redundant and could possibly lead to the duplication of efforts of the part of our contributors whose time is valuable.

March 2nd, 2014, 02:58 PM  #3 
Newbie Joined: Mar 2014 Posts: 1 Thanks: 0  Re: Computing the CoSkewness matrix
For an Excel and VBA implementation with open source code see https://www.academia.edu/1873921/Por...s_matrices_VBA 

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