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The problem with Ledoit-Wolf is that it's very sensitive to outliers. You should try these: DCC GARCH unfortunately, not available in Python Exponentially weighed moving average (EWMA) gives slighly worse results than DCC-GARCH Minimum Covariance Determinant suggestted by Scikit-Learn bootstrap could be used to calculate confidence interval, ...


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They are the same. The maximum growth rate is achieved when the Sharpe ratio is maximized. For the proof, see here.


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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.


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This is an interesting problem. I don't think the problem is set up correctly quite yet. I rewrote it slightly to correspond to how it's generally written as a quadratic program. The optimization problem you write down fixes betas to be a certain value. That could make sense but instead I wondered if we could simply minimize beta across the portfolio while ...



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