Swedroe: 4 Seemingly Unrelated Factors

A recent study breaks down these market anomalies and what they mean for portfolio construction.

Reviewed by: Larry Swedroe
Edited by: Larry Swedroe

Among some of the most well-documented stock market anomalies are four apparently unrelated factors: profitability (firms with high expected profitability exhibit higher future returns), distress risk (limited liability produces skewness in returns), lotteryness (individual investors who exhibit lottery demand are willing to accept lower returns in exchange for a small chance to receive a big payoff) and idiosyncratic volatility.

Turan Bali, Luca Del Viva, Neophytos Lambertides and Lenos Trigeorgis contribute to the literature on these anomalies through their May 2017 study, “Seemingly Unrelated Stock Market Anomalies: Profitability, Distress, Lotteryness and Volatility.”

The Study

The authors explain: “Growth, distress, and lotteryness involve real options that might increase the idiosyncratic skewness of the distribution of the firm’s equity returns. If investors prefer stocks with embedded real options and have preferences for more positive idiosyncratic skewness, then high idiosyncratic skewness offered by firms with such real options might entice investors to accept lower expected returns.”

Thus, they considered a measure of growth options and related measures of profitability—controlling for asset growth in interaction with volatility—as well as distress and lotteryness, as potential drivers of idiosyncratic skewness, and examined whether their impact is priced in the cross section of equity returns.

The authors explain: “High-growth (and likely low current profitability) firms, which tend to belong in high skewness subsets, would benefit more from high convexity (being out-of-the-money options on the firm’s assets) in more volatile environments as they have more optionality to benefit and less (fixed scale) commitment to lose from demand variability.”

Their study covered 12,709 U.S. listed firms during the period 1983 to 2015. Following is a summary of their findings:


  • The part of expected idiosyncratic skewness derived from growth options is negatively related to future returns.
  • The well-known cross-sectional relationships between stock returns and profitability, distress, lotteryness and idiosyncratic volatility are linked to the positively skewed return profile of high-growth-option firms. Higher values of growth options, distress, lotteryness and idiosyncratic volatility are associated with higher future idiosyncratic skewness. Asset growth also is negatively related to skewness. In contrast, higher levels of profitability are associated with lower levels of idiosyncratic skewness. These results were all statistically significant at the 1% level and held for both value-weighted and equal-weighted portfolios.
  • The expectation of idiosyncratic skewness arising from future growth options is consistently priced in stock returns, and it helps explain the preceding anomalous phenomena.
  • Their proposed skewness factor based on growth options explains the profitability factor, but not vice versa.
  • There is an annualized risk-adjusted return spread (hedged long-short portfolio return) of about 12% between low and high expected idiosyncratic skewness decile portfolios. The idiosyncratic skewness factor due to growth options also has a substantial annualized Sharpe ratio of 0.78, higher than for all other common investment factors found in asset pricing models.
  •  The negative return premium associated with idiosyncratic skewness arising from growth options is higher for small, less-liquid stocks, and rises with higher idiosyncratic volatility, growth prospects and distress risk. It also remains significant in big and liquid stocks, and persistent over time.


What This Means For Investors

Consistent with the hypothesis that investors are willing to accept lower average returns in exchange for the positively skewed upside potential arising from corporate growth options, Bali, Del Viva, Lambertides and Trigeorgis found that “controlling for everything else, a one standard deviation increase in expected idiosyncratic skewness arising from growth options implies 5.64% per annum lower average returns.”

Thus, they reached the conclusion that expected idiosyncratic skewness driven by future growth options seems to lie behind the profitability, distress risk, lotteryness and idiosyncratic volatility anomalies.

The authors also investigated whether investors’ willingness to pay high prices and accept lower returns for stocks that in the past have exhibited high expected skewness is rational.

To answer this question, they examined whether there’s a high degree of persistence in expected skewness. If the expected skewness measure were purely random, the probability of transitioning among the five quintiles should be roughly 20%.

They found that their expected skewness measure is highly persistent, with a probability of around 80% that a stock classified in a quintile will remain in the same quintile during the next month. Furthermore, the transition probabilities remain high.

For example, a stock classified as having high expected skewness has a 51% probability of remaining in the same quintile six months later. Thus, the authors concluded “the results suggest that investors are not irrational in forming skewness expectations based on growth prospects as these expectations are persistent and they can help explain seemingly anomalous returns, in line with our growth option/skewness hypothesis.”



Bali, Del Viva, Lambertides and Trigeorgis contribute to the literature by establishing linkages among the profitability anomaly, the distress risk puzzle, lotteryness, the idiosyncratic volatility effect and the idiosyncratic skewness negative return premium. They show real growth options are positive drivers of idiosyncratic skewness, and that growth-options-induced expected idiosyncratic skewness commands a negative equity return premium.

The negative cross-sectional relationships found in prior studies between stock returns and growth options, distress risk, lotteryness and idiosyncratic volatility, as well as the positive relationship between profitability and returns, can thus be linked to the skewed distribution of returns generated by growth options.

Investors seem willing to accept lower average returns in exchange for the more favorable (positively skewed) risk/return profile resulting from future growth options. Thus, investors’ expectation of skewness arising from future growth options underlies and helps explain these anomalies.

In terms of implications for portfolio/fund construction, the authors’ findings suggest investors are better served by avoiding stocks with high idiosyncratic skewness, which includes firms with low profitability, high idiosyncratic volatility, lotteryness and firms in distress.

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


Larry Swedroe is a principal and the director of research for Buckingham Strategic Wealth, an independent member of the BAM Alliance. Previously, he was vice chairman of Prudential Home Mortgage.