This paper studies the cross-sectional risk–return trade-off in the stock market. A fundamental principle in finance is the positive relation between risk and expected return. However, recent empirical evidence suggests the opposite. Using several intuitive risk measures, we show that the negative risk–return relation is much more pronounced among firms in which investors face prior losses, but the risk–return relation is positive among firms in which investors face prior gains. We consider a number of possible explanations for this new empirical finding and conclude that reference-dependent preference is the most promising explanation.

We introduce uncertainty into Holmstrom and Milgrom (1987) to study optimal long-term contracting with learning. In a dynamic relationship, the agent’s shirking not only reduces current performance, but also increases the agent’s information rent due to the persistent belief manipulation effect. We characterize the optimal contract using the dynamic programming technique in which information rent is the unique state variable. In the optimal contract, the optimal effort is front-loaded and stochastically decreases over time. Furthermore, the optimal contract exhibits an option-like feature in that incentives increase after good performance. Implications about managerial incentives and asset management compensations are discussed. Received August 31, 2015; editorial decision October 20, 2016 by Editor Francesca Cornelli.