Past Stock Returns and the MAX Effect

Abstract

This paper investigates how past stock returns affect investors’ lottery demand. We show that the maximum daily return (MAX) effect, first documented by Bali et al. (Maxing Out: Stocks as Lotteries and the Cross-Section of Expected Returns) is predominantly concentrated among stocks that have worst returns in the recent past. In contrast, for stocks that have recorded best past returns, the MAX effect becomes much weaker or even disappears. Our findings hold in the presence of a variety of control variables including the conventional return predictors, stock mispricing, stock price proximity to its 52-week high, and capital gains overhang. We interpret it as evidence that investors’ lottery demand intensifies in the presence of investment losses, consistent with the notion of time varying and state dependent nature of investors’ lottery preference. We further show that a self-financing portfolio that goes long in stocks with the worst past returns and low MAX and short in stocks with worst past returns and high MAX yields statistically and economically significant abnormal returns after risk adjustment by standard asset pricing models.

Keywords:

• Lottery demand
• Stock price momentum
• MAX effect
• Abnormal returns

JEL CLASSIFICATION:

• G10
• G11
• G14
• G40

Notes

1 The trading-based capital gains overhang measure (CGO) is defined as the (lagged stock price – the reference price)/lagged stock price.

2 A list of studies following Bali et al. (2011) include: Fong and Toh (2014), Zhong and Gray (2016), Hung and Yang (2018), Blau et al. (2020), Byun et al. (2020). We survey this literature in the section, Literature Review.

3 We thank an anonymous referee for pointing out the need to control for the stock mispricing effect.

4 In an earlier version of the paper, we used decile sorting. We change to quintile sorting for two reasons: (1) we want to make sure the formed portfolios have enough number of stocks after the double sorting procedure. (2) Tabulated results are much less cluttered under quintile sorting than decile sorting. Nonetheless, the results using decile sorting are quantitatively similar and are available upon request.

5 We thank an anonymous referee for suggesting the reporting of such return differences under MAX and MOM sorting.

6 We thank an anonymous referee for suggesting the inclusion of the interaction terms MAX*CGO, and MAX*Near52.