Digging into maxing out: A re-examination of the MAX anomaly

Abstract: We re-examine the MAX anomaly, which the literature attributes to investors’ preference for lottery-like stocks. We find that, when using value-weighted portfolios, the mispricing factors introduced by Stambaugh and Yuan (2017) explain the anomaly. Also, the anomaly occurs, i.e., stocks with extremely high daily returns in the prior month (namely, high MAX stocks) generate significant negative returns over the subsequent month, only when these stocks exhibit persistence in extreme daily returns in earlier months. This contradicts with the prevalent view that high MAX stocks are lottery-like. We propose an alternative sorting order to MAX, namely MAX^β, which controls for the effect of market-wide movements on stock-level daily returns. Portfolio sorts by MAX^β have significant predictive power, and this cannot be accounted for by the mispricing factors. Moreover, the predictive power of MAX^β does not depend on whether or not stocks exhibit persistent past performance in extreme daily returns, rendering MAX^β sorts a more likely proxy for lottery-like features as compared to MAX sorts.