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Going one level beyond stressed scenarios, to parameters e.g. for a VaR measure: what are the most common approaches for stressing a covariance/correlation matrix, especially taking portfolio exposure into account (so reverse testing iirc)? How many traders want e.g. to play with eigenvectors as opposed to just a concentration plus a global variance parameters? Is it common to leave full freedom of fudging the matrix subject to a later PSD correction? I'm interested in both current practice and what the leading software risk tools are offering, less in the plethora of possibilities investigated in academia.

Here's a related question with little response.

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