Risk aversion and prudence: the case of mean-variance preferences

This paper studies the concepts of risk aversion and prudence in the mean-variance model and relates them to the corresponding concepts in the expected-utility-model. the concepts of risk premia and precautionary premia have their counterparts in this framework and can be represented graphically in an intuitive fashion. We show that there is an isomorphic relationship between the concept of prudence and the concept of risk aversion in the mean-variance framework. We define the conditions under which a utility function is more risk averse (more prudent) than another one and the conditions under which a utility function exhibits increasing, decreasing and constant risk aversion (prudence). In the particular case of mean-variance preference derived from expected utility and normal distributions, we show that utility is concave as a function of variance and mean if and only if it exhibits decreasing prudence

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