Decomposing the Variance Risk Premium: Up and Down VRP

The variance risk premium (VRP) is a well-researched topic in quantitative finance. The VRP is the difference between the market-implied variance and the expected realized variance of an asset. Usually, the VRP is positive, reflecting the compensation investors demand for bearing volatility risks. Reference [1] extends this analysis further and breaks down the VRP into two components: an up (UVRP) and a down (DVRP) component.

The authors pointed out,

…we dissect the VRP in terms of upside (UVRP) and downside (DVRP) variance risk premia. The DVRP is the main component of the VRP, and the most important to assess, since investors tend to hedge against downward movements to avoid losing money. Conversely, investors often gravitate toward upside movements and are willing to pay to get exposure to it and the potential for higher profits.

…Thus, the DVRP should be positive (reflecting the compensation required by an agent to bear the downside risk), whereas the UVRP should be negative (viewed as the discount given by an agent to secure a positive return on an investment).

An interesting byproduct of this decomposition is the skewness risk premium, or SRP (simply defined as SRP = UVRP-DVRP), which will be negatively valued by construction. Kozhan, Neuberger, and Schneider (2014) show that compensation for variance and skewness risks are tightly linked.

In addition, this work explores the link between the DVRP and the equity risk premium, or ERP. Current asset pricing research considers that, over shorter time horizons, the VRP provides superior forecasts for the ERP; these periods are less than a year, typically one quarter, ahead (Bollerslev, Tauchen, and Zhou, 2009). To further this exploration, the study also considers the link between the SRP and the ERP at various prediction steps.

In short, the article concluded that,

• DVRP is typically positive, reflecting the premium required to bear downside risk, while the UVRP is typically negative, reflecting a discount for access to upside potential.
• The difference between UVRP and DVRP defines the skewness risk premium (SRP), which is inherently negative and reflects investor preference asymmetry.
• DVRP correlates with the equity risk premium (ERP), especially over short-term horizons such as quarterly forecasts.

This article provides further insights into volatility dynamics. Let us know what you think in the comments below or in the discussion forum.

References

[1] B Feunou, MR Jahan-Parvar, C Okou, Downside variance risk premium, Journal of Financial Econometrics 16 (3), 341-383

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