Abstarct: This paper develops a method to describe fuzzy returns by employing‎ ‎parametric possibility distributions‎. ‎The parametric possibility distributions are‎ ‎obtained by equivalent value (EV) reduction methods‎. ‎For common type-2 triangular‎ ‎and trapezoidal fuzzy variables‎, ‎their reduced fuzzy variables are studied in the current‎ ‎development‎. ‎The parametric possibility distributions of reduced fuzzy variables are‎ ‎first derived‎, ‎then the second moment formulas for the reduced fuzzy variables are‎ ‎established‎. ‎Taking the second moment as a new risk measure‎, ‎the reward-risk and‎ ‎risk-reward models are developed to optimize fuzzy portfolio selection problems‎. ‎The‎ ‎mathematical properties of the proposed optimization models are analyzed‎, ‎including‎ ‎the analytical representations for the second moments of linear combinations of‎ ‎reduced fuzzy variables as well as the convexity of second moments with respect to‎ ‎decision vectors‎. ‎On the basis of the analytical representations for the second moments‎, ‎the reward-risk and risk-reward models can be turned into their equivalent parametric‎ ‎quadratic convex programming problems‎, ‎which can be solved by conventional‎ ‎solution methods or general-purpose software‎. ‎Finally‎, ‎some numerical experiments‎ ‎are performed to demonstrate the new modeling ideas and the efficiency of solution‎ ‎method‎.