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.

Investor preferences for holding speculative assets are likely to be more pronounced ahead of firms’ earnings announcements, probably because of lower inventory costs and immediate payoffs or because of enhanced investor attention. We show that the demand for lottery-like stocks is stronger ahead of earnings announcements, leading to a price run-up for these stocks. In sharp contrast to the standard underperformance of lottery-like stocks, lottery-like stocks outperform non-lottery stocks by about 52 basis points in the 5-day window ahead of earnings announcements. However, this return spread is reversed by 80 basis points in the 5-day window after the announcements. Moreover, this inverted-V-shaped pattern on cumulative return spreads is more pronounced among firms with a greater retail order imbalance, among firms with low institutional ownership, and in regions with a stronger gambling propensity, and it is also robust after controlling for past 12-month returns and various proxies for investor attention.

Previous research has revealed that return spreads between stocks with high and low characteristics-based factor beta remain insignificant. This study investigates the time variation in the pricing of various characteristics-based factors, uncovering a notable two-regime pattern: high-beta portfolios yield higher returns than low-beta portfolios after high-sentiment periods, while the opposite occurs after low-sentiment periods. Remarkably, this two-regime pattern is completely reversed for macro factors. Mutual fund and hedge fund returns corroborate these findings. Our results suggest that exposure to characteristics-based factors likely represents mispricing levels, particularly during high-sentiment periods, whereas exposure to macro factors likely represents risk, particularly during low-sentiment periods.

Using patent lawsuit data from 2000 to 2014, we find that a stock portfolio consisting of alleged patent infringers (i.e., firms sued for patent infringement) provides significantly higher stock returns (between 0.48% to 0.61% per month) in the following year compared to other firms with similar characteristics. In contrast, plaintiff firms’ subsequent stock returns are not significantly different from comparable firms’ returns. We examine several possible explanations for this pattern, including pessimism-driven mispricing, exposure to unknown systematic risk, cash holdings, and financial constraints. Our evidence supports the explanation based on pessimism-driven mispricing.