Using Simulated ARMA-GARCH-EVT-Copula Returns for Portfolio Allocation

Summary

The document asks how to turn simulated returns from an ARMA-GARCH-EVT-copula model into allocations for three portfolio objectives: maximum Sharpe ratio, global minimum variance, and minimum CVaR. Its central practical questions are whether the simulated returns can estimate expected returns and covariance, and whether historical observations should also be included in those estimates. The setup describes 10,000 simulated return scenarios across eight assets, but presents the allocation step as unresolved rather than reporting a worked solution.

The distinction between objectives matters: CVaR can be evaluated from a simulated loss distribution, while Sharpe and variance-based optimization require estimates of return moments. The document supplies no empirical comparison, recommended estimator, or evidence that one estimation window is superior. Readers should treat it as a methodological question about matching forecast distributions to portfolio inputs, not as a validated allocation recipe. Results would depend on the simulation design, forecast horizon, and how estimates are constructed.

Key ideas

• The document considers portfolio allocation from joint returns simulated by an ARMA-GARCH-EVT-copula model.
• It asks how simulated scenarios should inform maximum-Sharpe and global-minimum-variance portfolios.
• It contrasts those moment-based objectives with minimum-CVaR optimization on a simulated loss distribution.
• It leaves unresolved whether historical returns should supplement simulated returns when estimating covariance.

Tags

# Portofolio optimization using ARMA-GARCH-EVT-Copula


# Portofolio optimization using ARMA-GARCH-EVT-Copula












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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.