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We devise a novel approach to combine predictions of high-dimensional conditional covariance matrices using economic criteria based on portfolio selection. The combination scheme takes into account not only the portfolio objective function but also the portfolio characteristics in order to define the mixing weights. Three important advantages are that i) it does not require a proxy for the latent conditional covariance matrix, ii) it does not require optimization of the combination weights, and iii) can be calibrated in order to adjust the influence of the best performing models. Empirical application involving a data set with 50 assets over a 10-year time span shows that the proposed economic-based combinations of multivariate volatility forecasts leads to mean-variance portfolios with higher risk-adjusted performance in terms of Sharpe ratio as well as to minimum variance portfolios with lower risk on an out-of-sample basis with respect to a number of benchmark specifications.