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To account for asymmetric dependence in extreme events, we propose a dynamic generalized hyperbolic skew Student-t factor copula where the factor loadings follow generalized autoregressive score processes. Conditioning on the latent factor, the components of the return series become independent, which allows us to run Bayesian estimation in a parallel setting. Hence, Bayesian inference on different specifications of dynamic one factor copula models can be done in a few minutes. Finally, we illustrate the performance of our proposed models on the returns of 140 companies listed in the S&P500 index. We compare the prediction power of different competing models using value-at-risk (VaR), and conditional VaR (CVaR), and show how to obtain optimal portfolios in high dimensions based on minimum CVaR.