Forecasting VaR and ES using a joint quantile regression and its implications in portfolio allocation

In this paper we propose a multivariate quantile regression framework to forecast Value at Risk (VaR) and Expected Shortfall (ES) of multiple financial assets simultaneously, extending Taylor (2019). We generalize the Multivariate Asymmetric Laplace (MAL) joint Petrella Raponi (2019) time-varying setting, which allows us specify dynamic process for evolution both VaR ES each asset. The proposed methodology accounts dependence structure among asset returns. By exploiting properties MAL distribution, then new portfolio optimization method that minimizes risk controls well-known characteristics data. evaluate advantages approach on simulated real data, using weekly returns three major stock market indices. show our outperforms other existing models provides more accurate measure forecasts compared univariate ones.