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Option-Implied Skewness, Realized Returns, and Skewness Risk

Article Quant Q&A · Author: KaiSqDist
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Summary

The document asks how option-implied skewness and kurtosis compare with their historical realized counterparts, and whether skewness or kurtosis risk premia show patterns similar to the volatility risk premium. The response summarizes research documenting negative daily return skewness that persists at longer horizons. It identifies outliers and the negative relationship between past returns and current stock return variance as contributors, with the latter described as especially important in the United States.

It also connects skewness to investor preferences: behavioral finance research finds demand for positively skewed, lottery-like stocks, with one cited study reporting stronger demand during crises. While standard mean-variance utility does not price skewness, cumulative prospect theory can generate pricing of idiosyncratic skewness. These points concern realized return patterns and preferences; the document does not establish a general implied-versus-realized skewness premium, its sign across market regimes, or corresponding results for kurtosis. The answer is a brief literature summary rather than a full empirical comparison.

Key ideas

  • Negative return skewness has been documented at daily and longer horizons.
  • Outliers and the relation between past returns and current variance are identified as sources of skewness.
  • Some investors prefer positively skewed stocks, and demand may rise during crises.
  • Cumulative prospect theory can price idiosyncratic skewness, unlike standard mean-variance utility.
  • The document does not settle the sign or regime behavior of a general skewness or kurtosis premium.

Tags

OptionsVolatilitySentimentStatistics
Full text
# Difference between Option-Implied Skewness/Kurtosis and Historical Realised Skewness Kurtosis


# Difference between Option-Implied Skewness/Kurtosis and Historical Realised Skewness Kurtosis












As the title states, what is the difference between option-implied skewness/kurtosis and historical realized skewness/kurtosis?

It is often the case that option-implied volatility is higher than historical realized volatility by an amount that is known as the volatility risk premium i.e. the additional compensation that is required by investors for bearing tail risk, more as a manifestation of their risk averse preferences.

Is there a similar thing for skewness and kurtosis? Skewness/Kurtosis risk premium? What are the common signs? Is it usually positive/negative in calm/crisis regimes? - similar to how the volatility risk premium is positive/negative in calm/crisis regimes.

Any peer-reviewed articles or opinions are very welcome.

## Answer by econbernardo (score 4, accepted)

https://quant.stackexchange.com/a/81328

Neuberger and Payne (2021) document a negative skewness at the daily frequency which also extrapolates to longer horizons. So even long-term investors are not exempt from the skewness risk that exists in the short term. They argue that the two main components of skewness are outliers and the negative correlation between past returns and the current variance of stock returns (the latter is the most important factor in the US).

A large literature in behavioral finance has found that investors have a preference for positively skewed stocks ("lottery-like stocks"). Kumar (2008) finds that the demand for these stocks increases in crises. According to standard mean-variance utility functions, skewness should not be priced. Barberis and Huang (2008) show that using cumulative prospect theory can generating pricing of idiosyncratic skewness.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.