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Expected returns are very difficult to estimate reliably without incurring estimation error as found out by Merton (1980) "On estimating the expected return on the market". This is why estimating volatility/the covariance matrix has become the default approach in the mean-variance model because volatility is easier to predict than returns. Even the global ...

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Multivariate volatility models for replacing the sample covariance matrix with in the mean-variance portfolio selection model: RiskMetrics 1996 EWMA (Exponentially weighted moving average) covariance matrix RiskMetrics 2006 EWMA covariance matrix Multivariate DCC-GARCH covariance matrix Jon Danielsson "Financial risk forecasting" has EWMA and GARCH for R ...

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For those experiencing a similar problem, here is the solution that worked for me: ## OPTIMIZE PORTFOLIO WEIGHTS UNDER THE OBJECTIVE OF MAXIMIZING THE SHARPE RATIO ## WHILE CONSTRAINING THE WEIGHTS TO SECTOR BOUNDS ## PAPER: # ACCORDING TO: http://people.stat.sc.edu/sshen/events/backtesting/reference/maximizing%20the%20sharpe%20ratio.pdf np.random.seed(101)...

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This is very simply done. It involves ensuring the constraints are presented as part of the matrix standard form. You will typically have the constraint that all assets sum to one, i.e. the matrix-vector equation: $$\delta^T x = 1$$ If you want to create an inequality constraint for assets in a sector just isolate them:  \begin{bmatrix} 1 & 1 &...

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Ledoit and Wolf have a new paper ( November 2018 ) called "Analytical Nonlinear Shrinkage of Large-Dimensional Covariance Matrices" which has MATLAB code for the procedure at the end of the paper. The paper can be downloaded at SSRN.

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If you take the average of the pair-wise correlations j-asset / housing, then it is like if you are holding an equally weighted portfolio composed by the assets. Indeed, you should first build a portfolio using the market weights you computed and then calculate the correlation with the housing. This way you get a proper average cross-sectional correlation. ...

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