This paper is the first to provide results on the finite sample properties of the Model Confidence Set (MCS) by Hansen et al. (2011) applied to the asymmetric loss functions specific to financial tail risk forecasts, such as Value-at-Risk (VaR) and Expected Shortfall (ES). In this paper, we focus on statistical loss functions that are strictly consistent in the sense of Gneiting (2011a). Our comprehensive simulation results show that, first, the MCS test keeps the best model more frequently than the confidence level 1 − α in most settings. Second, it eliminates few inferior models for out-of-sample sizes of up to four years. Third, the MCS test shows little power against models that underestimate tail risk at the extreme quantile levels p = 0.01 and p = 0.025, while the power increases with the quantile level p. Our findings imply that the MCS test may be suitable to narrow down a set of competing models, but that it is not appropriate to test if a new model beats its competitors due to the lack of power.