Lottery-Related Anomalies : The Roles of Reference-Dependent Preferences

This paper studies the role of reference-dependent preferences in explaining several anomalies related to lottery-like assets. Recent studies find that lottery-like assets significantly underperform non-lottery-like assets, probably due to investors' unconditional preference for lottery-like assets. The preference for lottery-like assets is usually attributed to investors' overweighting of small probability events, a feature of prospect theory. We document that lottery-related anomalies are significant only among stocks in which investors have lost money. Among stocks in which investors have profited, evidence for lottery-related anomalies is either very weak or even reversed. We consider several potential explanations for these empirical findings and we provide support for the reference-dependent preference under which investors are averse to losses and prefer lottery-like assets following prior losses as such assets offer a better chance to recover losses. Our findings are robust to five different measures of the lottery feature of stocks and provide a unified framework to understand lottery-related anomalies that are associated with these measures in the literature.Our findings are particularly interesting and important from a practitioner's perspective. Compared to the vanilla long-short trading strategy based on lottery-like assets, a refined strategy that focuses only on the subset of stocks with prior capital losses yields a significantly larger alpha both economically and statistically. Figure 1 compares the monthly Fama-French three-factor alphas of these two strategies for the five lottery-related measures considered in the paper – maximum daily returns (Maxret), predicted jackpot probability (Jackpotp), expected skewness (Skewexp), failure probability (Deathp), and bankruptcy probability (Oscorep). Taking Maxret as an example, a refined strategy that long low-Maxret stocks and short high-Maxret stocks among the stocks with prior losses generates a monthly alpha of 1.76%. This is an increase of over 200% in investment performance relative to an alpha of 0.52% in a plain long-short strategy. Finally, our results are robust to different subsamples, such as the exclusion of highly illiquid stocks, low price stocks, or NASDAQ stocks. This alleviates the concern about the high transaction costs related to trading such stocks and it suggests that our findings can be implemented in practice