Worst-case analysis has increased in popularity among financial regulators in the wake of the recent financial crisis. In this paper we provide insight into this measure and provide some guidance on how to estimate it. We derive the bias for the non-parametric heavy tailed order-statistics and contrast it with the semi-parametric EVT approach. We find that if the return distribution has a heavy tail, the non-parametric worst-case analysis, i.e the minimum of the sample, is always downwards biased. Relying on semi-parametric EVT reduces the bias considerably in the case of relatively heavy tails. But for the less heavy tails this relationship is reversed. Estimates for a large sample of US stock returns indicates that this pattern in the bias is also present in financial data. With respect to risk management, this induces an overly conservative capital allocation