Recently there has been a lot of research on the question of whether higher moments of return other than volatility (specifically, the skewness of returns) helps to explain equity returns. (I’ve included a brief definition of skewness and a demonstrative example of it below.)
For instance, the role of idiosyncratic skewness has been put forward to explain why investors actually hold under-diversified portfolios. Investors with a preference for skewness may under-diversify their portfolio to invest more in assets that have positive idiosyncratic skewness. Thus, stocks with high idiosyncratic skewness will pay a premium.
The result is that, at the firm level, the expected skewness negatively affects stock returns. High idiosyncratic skewness is associated with low expected returns. Conversely, more negatively skewed stock returns are associated with higher subsequent returns. The bottom line is that assets with large upsides (positive skewness) are overpriced and thus have low expected returns, while assets with large downsides (negative skewness) are underpriced and thus have high expected returns.
Is Skewness Predictive?
As an example of the research on skewness, Diego Amaya, Peter Christoffersen, Kris Jacobs and Aurelio Vasquez, authors of the study “Does Realized Skewness Predict the Cross-Section of Equity Returns?”, which appeared in the October 2015 issue of the Journal of Financial Economics, examined the higher moments of volatility, skewness and kurtosis to determine if they have provided incremental explanatory power in the cross section of stock returns.
They reached the following conclusion: There’s “strong evidence of a negative cross-sectional relationship between realized skewness and future stock returns—stocks with negative skewness are compensated with high future returns for higher volatility. However, as skewness increases and becomes positive, the positive relation between volatility and returns turns into a negative relation. We conclude that investors may accept low returns and high volatility because they are attracted to high positive skewness.”
This is consistent with previous findings in the literature that investments with lottery-ticketlike distributions have poor returns (and are best avoided).
Additionally, a study on momentum and skewness found that “past winners are likely to outperform in the next period when they have negative skewness, whereas past losers are likely to underperform in the next period when they have positive skewness. Therefore, if the past market return is high due to winners with negative skewness, the momentum will be strong and the next-period return is likely to be high. Similarly, if the past market return is low due to losers with positive skewness, the momentum will be strong and the next-period return is likely to be low.” In other words, skewness plays a role in generating momentum.