We show that expectation-based loss aversion according to Koszegi and Rabin [2006, 2007] provides a natural explanation for advantageous selection in insurance markets for small and modest-scale risks. We offer plausible conditions under which the insurance provider can screen the lowest risk agents by setting a high price. Intuitively, exposure to more risk has two competing effects on the agent's willingness to pay for insurance: on one hand, because of standard adverse selection the agent is willing to pay more for insurance; on the other hand, a reference effect may decrease his willingness to pay -- particularly when reference points are "increasing" in the corresponding consumption distributions. When the reference effect dominates, advantageous selection may arise.