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Are your 407 stocks all different? No A and B listings contained that are strongly if not perfectly correlated? The observation that the daily covariance matrix is singular makes me wonder. You can try the package corpcor for another shrinkage estimator.


This is the challenge for below-mean semivariance in optimization. Since the mean becomes a moving target, the observations that impact the min function change. Estrada proposed a heuristic method for optimization and Beach(2011) discusses the decomposition and semi covariances. Below target semivariance assumes investors do not change their target ...

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