简介：Assetallocationisanimportantissueinfinance,andbothriskandreturnareitsfundamentalingredients.Ratherthanthereturn,themeasureoftheriskiscomplicatedandofcontroversy.Inthispaper,weproposeanappropriateriskmeasurewhichispreciselyaconvexcombinationofmeansemi-deviationandconditionalvalue-at-risk.Basedonthisriskmeasure,investorscantrade-offflexiblybetweenthevolatilityandthelosstotackletheincurringriskbychoosingdifferentconvexcoefficients.Asthepresentedriskmeasurecontainsnonsmoothterm,theassetallocationmodelbasedonitisnonsmooth.Toemploytraditionalgradientalgorithms,wedevelopauniformsmoothapproximationoftheplusfunctionandconvertthemodelintoasmoothone.Finally,anillustrativeempiricalstudyisgiven.Theresultsindicatethatinvestorscancontrolriskefficientlybyadjustingtheconvexcoefficientandtheconfidencelevelsimultaneouslyaccordingtotheirperceptions.Moreover,theeffectivenessofthesmoothingfunctionproposedinthepaperisverified.