We compare Value at Risk (VaR) and Expected Shortfall (ES) following a Stochastic Dominance (SD) approach frequently used to order distributions in terms of welfare and in portfolio selection. Basel Committee on Banking Supervision (BCBS) recommends bank risk managers to shift the current...

An early development in testing for causality (technically, Granger non-causality) in the conditional variance (or volatility) associated with financial returns was the portmanteau statistic for non-causality in the variance of Cheng and Ng (1996). A subsequent development was the Lagrange...