Forecasting Multiple VaR and ES Using a Dynamic Joint Quantile Regression with an Application to Portfolio Optimization

An accurate assessment of tail dependencies of financial returns is key for risk management and portfolio allocation. The use of quantitative risk measures has become an essential tool providing support for financial and asset management decisions. Extending (Taylor in J Bus Econ Stat 37(1):121–133, 2019, [10]), we propose a novel multivariate framework to simultaneously estimate Value at Risk (VaR) and Expected Shortfall (ES) of multiple financial assets, by jointly modelling their marginal quantiles taking into account for their dependence structure. We generalize the joint quantile regression approach by specifying a Conditional Autoregressive Value at Risk (CAViaR) structure in the dynamics of each marginal quantile and modelling the ES of each asset in a time-varying setting. In addition, we propose a new method for portfolio construction, based on the multivariate structure of the problem. We apply our approach to weekly stock market returns, to illustrate the practical applicability of the proposed method and its efficiency gain compared to the univariate approach.