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 Australian data. The institutional features of the Australian system make the effects of asymmetric information more readily identifiable than in most other countries. We find a strong positive association between self-assessed health and private health cover. By applying the Lokshin and Ravallion (J. Econ. Behav. Organ 2005; 56:141-172) technique we identify the factors responsible for this result and recover the conventional negative relationship predicted by adverse selection when using more objective indicators of health. Our results also provide support for the hypothesis that self-assessed health captures individual traits not necessarily related to risk of health expenditures, in particular, attitudes towards risk. Specifically, we find that those persons who engage in risk-taking behaviours are simultaneously less likely to be in good health and less likely to buy insurance.