Recent empirical work finds that surprisingly little variation in the demand for insurance is explained by heterogeneity in risks. I distinguish between heterogeneity in risk preferences and risk perceptions underlying the unexplained variation. Heterogeneous risk perceptions induce a systematic difference between the revealed and actual value of insurance as a function of the insurance price. Using a sufficient statistics approach that accounts for this alternative source of heterogeneity, I find that the welfare conclusions regarding adversely selected markets are substantially different. The source of heterogeneity is also essential for the evaluation of different interventions intended to correct inefficiencies due to adverse selection like insurance subsidies and mandates, risk-adjusted pricing and information policies.