We analyze asset rankings derived from state-of-the-art peak-over-threshold (POT) approaches to estimate value-at-risk (VaR). Supported by a variety of robustness checks, we gain three important insights for portfolio managers investing in equity and commodity markets. First, even though POT methods are known to yield more precise VaR estimates than classic techniques based on the normal distribution assumption or historical simulation, all techniques yield almost identical rankings. Second, even though the choice of threshold crucially influences VaR estimates, it does not significantly change asset rankings. These two results are most pronounced when the portfolio manager's focus is on identifying the best or worst assets in terms of VaR. Third, unconditional and conditional POT approaches differ considerably in the rankings they generate. Thus, neglecting the non-independent-and-identically-distributed property of returns can lead to distinctly different decisions in a risk-based asset selection process.