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May 6th, 2013, 01:18 AM   #1
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Computing the Co-Skewness 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 co-skewness 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 co-skewness matrix M3, thus I found a alternative way to calculate the M3, that's:
The co-skewness 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!
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May 6th, 2013, 01:44 AM   #2
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Re: Computing the Co-Skewness 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.
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March 2nd, 2014, 01:58 PM   #3
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Re: Computing the Co-Skewness 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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