Before revision:  Encompassing tests generally rely on the existence of strictly consistent loss functions for the functionals under consideration, which do not exist for the ES . However, our encompassing tests are based on recently introduced loss functions and an associated regression framework which considers the ES jointly with the corresponding Value at Risk (VaR).
After revision:  Encompassing tests generally rely on the existence of strictly consistent loss functions for the pair ES and Value at Risk (VaR).