The need to ensure that central counterparties (CCPs) are robust even in crisis conditions has intensified the focus on stress testing. One question of interest is how to select a scenario that will be stressful to a given CCP. This paper is a contribution to the study of stress scenarios. We focus on historical scenarios, studying various definitions of "stress event" based on a long data set of risk factors. Our results show that both systemic and idiosyncratic stresses are important: a CCP may find itself most exposed in either a broad market disruption, such as the events around the failure of Lehman Brothers, or a more localized event in one market (or a small set of linked markets). We show that the stressed value-at-risk calculated using different stress periods varies by a factor exceeding 4. Moreover, the maximum historical loss on the risk factors studied exceeds the 99.9th percentile of fitted distributions by a factor averaging 1.38. These results highlight the importance of including the worst historical episodes in stress testing and, more broadly, the need for care in selecting the appropriate historical stresses. The paper concludes by suggesting that enhanced prudential standards for the selection of stressed historical episodes would be beneficial. These CCP-specific scenarios could be supplemented but not replaced by a requirement to conduct standardized stress testing using data from broad market disruptions.