The VRP and the Skewness Risk Premium - A Decomposition
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The Volatility Risk Premium (VRP) is a well-documented phenomenon in financial markets, but it is not a monolithic entity. It can be decomposed into two distinct components: the symmetric volatility risk premium and the skewness risk premium. This article provides a theoretical and empirical decomposition of the VRP and explores the implications of this decomposition for option pricing and trading.
The Two Faces of Volatility Risk
The VRP arises from investors' aversion to volatility, but this aversion is not uniform. Investors are more concerned about downside volatility (crashes) than they are about upside volatility (rallies). This is due to the negative skewness of equity returns, which makes large negative returns more likely than large positive returns.
This asymmetry in risk aversion gives rise to two distinct risk premia:
- The Symmetric Volatility Risk Premium: This is the premium that investors demand for bearing the risk of symmetric, or directionally neutral, volatility. It is the compensation for the risk that volatility will be higher than expected, regardless of the direction of the market.
- The Skewness Risk Premium: This is the premium that investors demand for bearing the risk of negative skewness, or crash risk. It is the compensation for the risk of a large, sudden market decline.
Decomposing the VRP
The VRP can be decomposed into these two components by analyzing the prices of options with different strike prices. The symmetric volatility risk premium can be isolated by looking at the prices of at-the-money options, which are most sensitive to changes in overall volatility. The skewness risk premium can be isolated by looking at the prices of out-of-the-money put options, which are most sensitive to changes in skewness.
The formula for decomposing the VRP is:
VRP = Symmetric VRP + Skewness Risk Premium
Data Table: Decomposition of the VRP (S&P 500)
| Year | VRP | Symmetric VRP | Skewness Risk Premium |
|---|---|---|---|
| 2018 | 0.8 | 0.5 | 0.3 |
| 2019 | 3.2 | 1.5 | 1.7 |
| 2020 | 3.3 | 1.2 | 2.1 |
| 2021 | 4.6 | 2.0 | 2.6 |
| 2022 | 2.9 | 1.1 | 1.8 |
This table shows a hypothetical decomposition of the VRP for the S&P 500. As the table shows, both the symmetric VRP and the skewness risk premium are significant components of the overall VRP.
Actionable Examples
The decomposition of the VRP has important implications for trading. By understanding the relative contributions of the symmetric VRP and the skewness risk premium, traders can tailor their strategies to target specific sources of risk premium.
For example, a trader who wants to harvest the symmetric VRP could sell at-the-money straddles, which are most sensitive to changes in overall volatility. A trader who wants to harvest the skewness risk premium could sell out-of-the-money put options, which are most sensitive to changes in skewness.
The Term Structure of the VRP Decomposition
Just as with the VRP itself, there is a term structure to the decomposition of the VRP. The relative contributions of the symmetric VRP and the skewness risk premium can vary across different expiration dates. This can provide valuable information about the market's expectations of future volatility and skewness.
Conclusion
The decomposition of the Volatility Risk Premium into its symmetric and skewness components provides a more nuanced understanding of this important risk premium. By understanding the drivers of each component and by tailoring their strategies accordingly, traders can more effectively harvest the VRP and manage the associated risks. The key is to have a deep understanding of the option pricing models that are used to decompose the VRP and to have a disciplined and systematic approach to trading.