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I am currently trying to do some portfolio optimization by reproducing the methodology found in Sahamkhadam, Stephan & Östermark (2018) ("Portfolio optimization based on GARCH-EVT-Copula forecasting models"), but I am confronted with an issue in the last steps of the process...

I managed to fit an ARMA-GARCH-EVT-copula model to forecast returns, however, I am now at a point where I have 10'000 simulated returns from the copula, and I am supposed to do an asset allocation based on this (this is step 7, p. 501, in their paper).

They simply state to "Substitute the forecasts for returns in the optimization methods explained in Section 2.5 to get the optimal weights for the CET, Min-CVaR and GMV portfolios.", the optimization method being max Sharpe Ratio, GMV portoflio and min-CVaR.

I get how the min-CVaR portfolio makes sense with simulated returns, but I struggle to see how I am supposed to do the CET and GMV allocation? For the max Sharpe Ratio, I need to combine these 10'000 simulated returns for each asset into one, but I think that just taking the mean of the simulated returns would be rather weak? Same thing for the covariance matrix, should I compute it based only on the simulated returns (so compute it based on my 10'000*8 matrix, since I have 8 assets), or also take the rest of the historical returns into account?

This seems a little off to me for some reason but I can't manage to think of something better.

If anybody has a suggestion on how to proceed, I would be very grateful :)

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