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Correlating random numbers seems to skew the data

First off, apologies for the cross-post from mathematics, but I found this site later and think it would be a better fit for the question (besides, there has been no comments/answers on mathematics ...
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735 views

Principle Component Analysis vs. Cholesky Decomposition for MonteCarlo

Let's assume we have a portfolio containing large number (~500) of risk factors. We want to simulate the portfolio dynamics. PCA based simulation would be faster as we can reduce the dimensionality. ...