We study the risk index of an additive gamble proposed in Aumann and Serrano (J Political Econ 116(5):810–836, <CitationRef CitationID="CR2">2008</CitationRef>). We establish a generalized duality result for this index and use it to prove Yaari (J Econ Theory 1:315–329, <CitationRef CitationID="CR19">1969</CitationRef>) alternative characterization of DARA utilities. A new...</citationref></citationref>