In a housing insurance market buildings have different damage probabilities. High-risk houses need investment, low-risk houses don’t. Insurers use imperfect tests to assess risks. The market is a natural monopoly: with more than one active insurer, high-risk house owners continue to apply to insurers until they are eventually assigned to the low-risk class. The natural monopoly need not be sustainable. In equilibrium the incumbent accommodates entry even when the natural monopoly is sustainable. We explain recent observations from Germany and Switzerland where damage rates and prices went up drastically after the transition from state monopolies to competitive environments.