Both adverse selection and moral hazard models predict a positive relationship between risk and insurance; yet the most common finding in empirical studies of insurance is that of a negative correlation. In this paper we investigate the relationship between ex ante risk and private health insurance using data from the 2001 Australian National Health Survey (NHS). The Australian health system provides a setting where the relationship between risk and insurance is more transparent than many other institutional frameworks; private health insurance is not tied to employment; community rating limits the actions of insurers; and private coverage is high for a country providing free public hospital treatment. We find a strong positive association between self-assessed health and private health cover. We use the detailed information available in the NHS to investigate whether we can identify factors responsible for the negative correlation between risk (lower SAHS) and insurance cover. However this relationship persists despite the inclusion of a large set of controls for personal and socio-economic characteristics, risk-related behaviours, objective health measures and an index of mental health. The opposite effect of self-assessed health and long-term conditions on coverage suggests that SAHS is capturing factors such as personality or risk preferences.