This article proposes a dynamic robust portfolio selection model that is based on minimizing portfolio’s worst case scenarios using the Conditional Value at Risk as relevant risk measure. Our proposed empirical model for the dynamics of portfolio constituents has three main features: i) accommodates tail dependence between assets by means of a mixture of copula functions; ii) conditional heteroscedasticity and leverage effects are considered through the implementation of a GJR-GARCH model; and iii) extreme events are taken into account by considering parametric and semiparametric hybrid models for the marginal distribution of asset returns. We illustrate the performance of this portfolio before and during the COVID-19 pandemic using statistical measures such as the Sharpe ratio, cumulative returns, and volatility. The results show the outperformance of our WCVaR portfolio during the turmoil period against benchmark portfolios commonly used by practitioners. The method also exhibits good performance during calm periods.