Abstract
All of the commonly used utility functions exhibit mixed risk aversion. We show that the utility of downside risk diversification is maximal if and only if the decision maker is mixed risk averse. This intuitive result supports the commonly made assumption of mixed risk aversion in many areas of economics and finance and is particularly interesting for portfolio choice. The proof relies on an investigation of all moments of the proper risk apportionment lotteries of Eeckhoudt and Schlesinger (2006), thereby generalizing results of Ekern (1980) and Roger (forthcoming). These computations also give a better understanding of the relationships between proper risk apportionment, in particular, prudence and temperance, expected utility, statistical moments, preference for skewness and kurtosis aversion.
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