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This study provides the first comprehensive analysis of individual perceptions of tail risks. It focuses not only on the probability, as has been studied by Nicholas Barberis and others, but also on anticipation of damage. We examine how those perceptions relate to experts' estimates and publicly available risk information. Behavioural factors---availability bias, threshold models of choice, worry and trust---are found to have a significant impact on risk perceptions. The probability of tail events is overestimated, which is consistent with probability weighting in prospect theory. Potential damage is underestimated, one reason why individuals do not invest in protective measures.