Using a carefully constructed sample of euro area stock returns, the authors document that stocks with extremely high positive returns over the most recent month generate systematically lower expected returns. This finding is consistent with the work of Bali, Cakici, and Whitelaw (Journal of Financial Economics 2011), who document a similar result for the US market. The authors suggest this negative relationship exists because certain investors prefer these extremely positive return stocks that exhibit lottery-like characteristics—that is, exhibiting a low probability of experiencing a very high return and a high probability of experiencing a small loss.

The negative relationship between extremely positive returns and subsequent stock returns is found to be fairly persistent. The clear implication from the authors’ research is that investors should steer clear of those stocks with extremely large positive returns. The findings provide strong evidence that such stocks will subsequently underperform.

The authors contribute to the literature on the variation in the cross section of stock returns. Of course, the famous four-factor model (the Fama–French three factors plus the Carhart momentum factor) works very well in explaining most, but not all, of the variation. Other research has documented that such factors as liquidity are related to stock returns.

Monthly stock returns and other firm-specific data on 7,861 companies from 13 European countries are gathered from Thomson Reuters DataStream for the December 1979–June 2011 time period. The authors begin with univariate analysis by sorting stocks each month into decile portfolios by their highest daily return (their measure of extreme return) over the previous month, and decile portfolio returns (equal weighted and value weighted) are then calculated. They then form a hedge portfolio (long the high-return decile and short the low-return decile) and find negative but statistically insignificant portfolio returns and four-factor alphas.

These results reveal a very weak relationship, if any, between extremely positive returns and subsequent stock returns. The results do indicate that stocks with extremely positive returns have larger betas, smaller market caps, and higher book-to-market ratios. They also exhibit such lottery-like characteristics as lower prices, higher idiosyncratic risk, and higher skewness.

The authors then conduct bivariate analysis by double sorting stocks each month—first, into deciles on a control variable (beta, size, book-to-market ratio, and so forth) and, second, into deciles by extreme return. Decile portfolio returns are calculated again, and the high–low decile hedge portfolio is formed within each first control sort. In this case, the four-factor alphas are all negative and statistically significant for nearly all control variable groups. The authors interpret this finding as evidence of a negative relationship between extremely positive stock returns and expected returns.

Finally, they conduct multivariate regression analysis. The authors regress the cross section of monthly excess stock returns on the extreme return measure along with a host of control variables, including the Fama–French and Carhart factors. Regression results indicate that the extreme return variable is negative and statistically significant, providing strong evidence of a negative relationship between extremely positive stock returns and expected returns. In other results, the authors document that this negative relationship between extremely positive stock returns and expected returns exhibits strong persistence. Such alternative measures of extreme returns as the average return over the two (or three, four, or five) days with the highest returns during the previous month are considered. Using these different methods to measure extreme returns does not change the results.

This research is interesting and provides very compelling evidence that European stocks with extremely high positive returns will subsequently underperform. It would be interesting to see the longer-term returns of these stocks with extremely positive returns. Considering the well-documented momentum effect that persists over the short term but ultimately leads to a reversal over longer time horizons, an extension of this research might include an investigation of whether the extremely high return effect reverses itself over a longer time horizon.