This article presents a characterization of higher-order risk preferences such as prudence or temperance in terms of statistical moments. Our results, which are generalizations of Roger (Theory Decis, 70(1):27–44, <CitationRef CitationID="CR4">2011</CitationRef>) and Ekern (Econ Lett, 6(4), 329–333, <CitationRef CitationID="CR8">1980</CitationRef>), give a better understanding...</citationref></citationref>