This paper studies regulated health insurance markets known as exchanges, motivated by the increasingly important role they play in both public and private insurance provision. We develop a framework that combines data on health outcomes and insurance plan choices for a population of insured individuals with a model of a competitive insurance exchange to predict outcomes under different exchange designs. We apply this framework to examine the effects of regulations that govern insurers' ability to use health status information in pricing. We investigate the welfare implications of these regulations with an emphasis on two potential sources of inefficiency: (i) adverse selection and (ii) premium reclassification risk. We find substantial adverse selection leading to full unraveling of our simulated exchange, even when age can be priced. While the welfare cost of adverse selection is substantial when health status cannot be priced, that of reclassification risk is five times larger when insurers can price based on some health status information. We investigate several extensions including (i) contract design regulation, (ii) self-insurance through saving and borrowing, and (iii) insurer risk-adjustment transfers.