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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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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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By assuming the procedure you followed in replicate the model is correct and there are not errors in data mining or quality, your findings could be affected and influenced by several reasons. I report as follows those that, according to me, could be the main ones: Data sample: the dataset you used to replicate the Fama-French model could be too little in ...


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Not sure what the question is. As John points out: the method is linear regression. For the data you could look at Kenneth French's wegpage for US stocks. In the wikipedia article you find the links to factors for other countries (UK, Germny, Switzerland) - though I have not checked these links. Note however that the Fama-French model works better for ...


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Whether or not it is flawed in practice depends on dynamic the risk exposures really are. Many factors or indices used for style analysis actually require dynamic trading to maintain - so you could potentially have a fund that trades a lot while still generating a return series that can be be modeled out of sample with static exposures. One relatively ...



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