Abstract: It is negative risk if there is a good chance of coming out better than our reference level. This paper proposes a general risk measure: bilateral partial moment, where downside risk is supplemented with the "upside potential". Variance, mean absolute deviation, semi-variance and other downside risk definition are all incorporated in this framework. The portfolio selection problems in this general class of risk model are discussed. The portfolio optimization provides the flexibility for the selection of an appropriate target return and the weightiness of upside potentials.