The volatility risk premium (VRP) is the difference between implied volatility and subsequently realized volatility, and is one of the most extensively studied phenomena in options markets. We previously discussed Reference [1], which decomposes the VRP into upside and downside components and studies their dynamics separately. Reference [2] applies a similar framework to the same index, the S&P 500, but using a more recent dataset.
The author pointed out,
We examine four main points. First, we test whether investors pay a higher premium for volatility associated with equity price declines than for volatility associated with price increases. By decomposing the variance risk premium into upside and downside components using option prices and high-frequency equity return data, we find that the downside variance risk premium is statistically more pronounced than the aggregate variance risk premium.
Second, we examine whether risk premium associated with downside variance and skewness are related to the required return on equities. Empirically, these premium predict future returns, suggesting that investors view rare, large drawdowns and volatility during market declines as risk, and that compensation for bearing such risks is linked to expected equity returns.
Third, we investigate the relationship between the prediction horizon and predictive power (adjusted R2). Consistent with prior findings, predictive power for variance-related premium peaks around three to five months, while skewness-related premium exhibit relatively stronger predictive power at longer horizons.
Fourth, we evaluate whether the term structure (the difference between longer- and shorter-maturity premium) improves return forecasting. While we find limited evidence of improvement for the variance risk premium, the term structure of the skewness risk premium is statistically significant and suggests that when the longer-maturity skewness risk premium is lower (more negative) than the shorter-maturity premium, long-horizon equity returns subsequently rise, and vice versa. This is consistent with the interpretation that when investors anticipate longer-horizon tail risk, required long-run equity returns increase.
In short, the paper finds that downside VRP is substantially more pronounced than aggregate VRP. It also shows that downside variance and skewness risk premiums predict future equity returns, with variance-related predictive power strongest at medium horizons and skewness-related predictive power stronger at longer horizons. Finally, the study finds that the term structure of skewness risk premium contains forecasting information, suggesting that expectations of longer-horizon tail risk are linked to higher future required equity returns.
We believe this paper largely revisits the framework of the earlier study [1], albeit using more recent data and more extensive robustness tests, while ultimately reaching very similar conclusions.
Let us know what you think in the comments below or in the discussion forum.
References
[1] Feunou, B., Jahan-Parvar, M. R., & Okou, C. (2016), Downside Variance Risk Premium, Journal of Financial Econometrics 16 (3), 341-383
[2] Akio Ito, Variance Risk Premium, Skewness Risk Premium and Equity Expected Returns, SSRN Working Paper 6712647, 2025
Originally Published Here: Decomposing the Variance Risk Premium, Part 2
source https://harbourfronts.com/decomposing-variance-risk-premium-part-2/
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