Individuals and/or corporations typically hold portfolios of physical, financial and human assets. Insurance on these assets would be redundant if the portfolios were completely diversified in the sense of removing unsystematic risk. For corporations, insurance would also be redundant if the ownership claims were publicly traded and investors could costlessly duplicate the risk reducing effects of insurance in the management of their personal portfolios. The widespread demand for insurance is prima facie evidence of the lack of complete diversification, perhaps because some assets such as human capital are nonmarketable. This paper examines the portfolio characteristics of rational insurance decisions and shows that some of the established results of the literature apply only when all risk facing the decision maker is insurable. The first set of results is generated under a mean-variance assumption though it is later shown that some of the results can be generalized to the entire class of risk averse utility functions.