This paper finds optimal portfolios for the reference-dependent preferences by Kőszegi and Rabin with piecewise linear gain–loss utility in a one-period model with a safe and a risky asset. If the return of the risky asset is highly dispersed relative to its potential gains, two personal equilibria arise, one of them including risky investments and the other one only safe holdings. In the same circumstances, the risky personal equilibrium entails market participation that decreases with loss aversion and gain–loss sensitivity, whereas the preferred personal equilibrium is sensitive to market and preference parameters. Relevant market parameters are not the expected return and standard deviation, but rather the ratio of expected gains to losses and the Gini index of the return.