Three approaches have been recently proposed in the literature for backtesting Expected Shortfall, each with the advantage of being easy to implement using information readily available from a typical risk management system. The practitioner, however, is left with little information about their...

We develop a finite-sample procedure to test for mean-variance efficiency and spanning without imposing any parametric assumptions on the distribution of model disturbances. In so doing, we provide an exact distribution-free method to test uniform linear restrictions in multivariate linear...

Correlation models, such as Constant Conditional Correlation (CCC) GARCH model or Dynamic Conditional Correlation (DCC) GARCH model, play a crucial role in forecasting Value-at-Risk (VaR) or Expected Shortfall (ES). The additional inclusion of constant correlation tests into correlation models...