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Maybe one tail test or two tail test should depend on the null hypothesis testing? H0: X=something is a two tail test while H0: X>something is a one tail test ? For backtesting the VaR model, it is more common to use H0: exception=expected no.(which is n*p)?

Yeah...I think it should be included. Let's consider another case, which is the service down due to the power cut. Obviously, there is no physical damage cost in such case. However, the expected loss due to the disruption of the service should be included and reported. If not included, the loss...