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It is often said that prudence and temperance play key roles in aversion to negative skewness and kurtosis, respectively. This paper puts a new perspective on these relationships and presents a characterization of higher-order risk preferences in terms of statistical moments. An implication is, for example, that prudence implies preference for distributions with higher skewness as defined by all odd moments. Moreover, we show that this preference is robust towards variation in kurtosis as defined by all even moments. We thus speak of the kurtosis robustness feature of prudence. Further, we show that all higher-order risk preferences of odd order imply skewness preference, but for different distributions than prudence. Similar results are presented for temperance and higher-order risk preferences of even order that can be related to kurtosis aversion and have a skewness robustness feature.
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