The present paper combines loss attitudes and linear utility by providing an axiomatic analysis of corresponding preferences in a cumulative prospect theory (CPT) framework. In a sense we derive a two-sided variant of Yaari's dual theory, i.e., nonlinear probability weights in the presence of linear utility. The first important difference is that utility may have a kink at the status quo, which allows for the exhibition of loss aversion. Also, we may have different probability weighting functions for gains than for losses. We apply the model to both portfolio selection and insurance demand. Our results show that CPT with linear utility has more realistic implications than the dual theory since it implies only a weakened variant of plunging.