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PCA gives you a decomposition of the covariance matrix of the form $$ \Sigma = V \Lambda V^T $$ where $\Lambda$ is diagonal with the eigenvalues in the diagonal. Your portfolio variance is $$ w^T \Sigma w = (V^T w )^T \Lambda (V^T w) $$ On the other hand if you take your return matrix $R$ and define $$ F = V^T R $$ then the covariance matrix of these so ...


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It is not as simple as changing a value. You need to replace the current factor loadings by feasible values. Furthermore, factor loadings have dependencies between them, that means that when you change one of them, the other factors are affected by this change. In the CCruncher Technical Document there is a proposal to do so. It propose to estimate the ...


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When I use PCA, I follow a few typical steps. First, I would apply PCA to the covariance matrix, I would then designate certain eigenvalues as dominant or significant (such as by those that contribute up to $x\%$ of variance or by RMT), and then I would identify the eigenvectors that match up with those significant eigenvalues. I think you're with me at ...


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In the chapter that deals with NMF of the book "Programming collective intelligence" , the author did NMF on several stock trading volumes and found some comovement. I googled a little. This did NMF on 40 chinese stock close prices. This developed A variant of nonnegative matrix factorization for Stock Trend Extraction. Another google found this also did ...


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If you are doing something cross-sectional (like Fama-Macbeth regressions) you can just use the ratios where you would put the factor loadings (i.e. betas from the time series regs). You probably want to do some kind of transformation on the ratio to make it well-behaved first though. If you want an actual factor based on the ratio, you can use "factor ...



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