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.

**The Importance Of Average Skewness**

Eric Jondeau and Qunzi Zhang, authors of the November 2015 study “Average Skewness Matters!”, contribute to the literature by investigating the ability of the average variance and the average skewness of firm returns to predict future market returns.

They found that there was “a significant negative relation between the average stock skewness and future market return. This relation holds for equal-weighted and value-weighted skewness. It also holds after controlling for the usual variables known to predict market returns and after excluding firms with small price, small size, and low liquidity. Even when a measure of market illiquidity is introduced in the regression, the effect of the average stock skewness remains significant.”

Specifically, Jondeau and Zhang found that “when the lagged market return is high and average skewness is low, the model predicts a high market return for the next month. In contrast, when the market return is low and average skewness is high, the model predicts a low market return for the next month.” Continuing with the effect of one-standard-deviation changes, the authors found “the combination (high return, low skewness) predicts a market return of 3%, whereas the combination (low return, high skewness) predicts a market return of -3%.”

They concluded: “Our results all confirm that the average skewness is an important driver of subsequent market returns.” However, Jondeau and Zhang added: “We find that the value-weighted average of (standardized) stock skewness is by far the best predictor of monthly market returns. The magnitude of the effect of the monthly average skewness on the subsequent market return is sizable, as a one standard deviation increase in the average skewness implies, on average, a 1.5% decrease in the market return next month.” In other words, skewness matters.

**Definition And Example**

Skewness measures the asymmetry of a distribution. In terms of the market, the historical pattern of returns doesn’t resemble a normal distribution, and so demonstrates skewness. Negative skewness occurs when the values to the left of (less than) the mean are fewer but farther from it than values to the right of (greater than) the mean.

For example, the return series of -30%, 5%, 10% and 15% has a mean of 0%. There is only one return less than zero, and three that are higher. The single negative return is much farther from zero than the positive ones, so the return series has negative skewness. Positive skewness, on the other hand, occurs when values to the right of (greater than) the mean are fewer but farther from it than values to the left of (less than) the mean.

*Larry Swedroe is the director of research for **The BAM Alliance*, a community of more than 140 independent registered investment advisors throughout the country.