There exists no satisfactory theory of risk in current normative decision theories. Notions based on utility curvature, loss aversion and probability weighting are derivative, cannot be applied to non-numerical consequences, and are not psychologically intuitive. I develop a Pure Risk theory which resolves these problems, is consistent with existing normative theories, and both internalises and generalises the intuitive notion of risk being related to the probability of not achieving one’s aspirations. The theory shows that existing models are misspecifed. Effects hitherto modelled as loss aversion or utility curvature may be due instead to Pure Risk.