Past Stock Returns and the MAX Effect

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.