Skewness is a measure of the asymmetry of a return distribution. In this post, I’ll discuss the skewness risk premium and how skewness can be used to forecast realized volatility.
Skewness Risk Premium in the Options Market
Skewness of returns is a statistical measure that captures the asymmetry of the distribution of an asset’s returns over a specified period. It is particularly important in risk management and option pricing, where the skewness of returns can affect the valuation of derivatives and the construction of portfolios.
Reference [1] studies the skewness risk premium in the options market. It decomposes the skewness risk premium into two components: jump skewness and leverage skewness risk premia.
Findings
-The skewness risk premium (SRP) is distinct from the variance risk premium (VRP), and both are independently priced in the options market.
-The study introduces model-free, tradable strategies to replicate realized skewness, decomposed into two components:
- Jump Skewness Risk Premium
- Leverage Skewness Risk Premium
-These strategies dynamically rebalance option and forward positions to track high-frequency realized jump skewness and leverage.
-The SRP is generally higher during overnight periods than during regular trading hours—mirroring similar behavior observed in the VRP.
-Jump skewness dominates the SRP during market hours, while overnight skewness may capture broader macro or non-U.S. investor risk.
-The SRP exhibits countercyclical behavior, becoming more pronounced during periods of market stress or left-tail events.
-The study confirms that the SRP and VRP are fundamentally different, supporting the need to treat them separately in portfolio and derivative strategies.
-This decomposition provides insights for trading and hedging strategies, offering more granular exposure to tail risk components.
-Findings are based on short-maturity S&P 500 options, analyzed both intraday and overnight to capture time-sensitive skewness behavior.
In short, the authors constructed a tradable basket of options to measure the skewness risk premium. This means that this study is model-free.
They reconfirmed that
-The skewness risk premium is different from the variance risk premium.
-The variance risk premium is compensation for bearing overnight risks.
Reference
[1] Piotr Orłowski , Paul Schneider , Fabio Trojani, On the Nature of (Jump) Skewness Risk Premia, Management Science, Vol 70, No 2
Predicting Realized Volatility Using Skewness and Kurtosis
Realized volatility refers to the actual volatility experienced by a financial asset over a specific period, typically computed using historical price data. By calculating realized volatility, investors and analysts can gain insights into the true level of price variability in the market.
Reference [2] examines whether realized volatility can be forecasted. Specifically, it studies whether realized skewness and kurtosis can be used to forecast realized volatility.
Findings
-The study investigates whether realized skewness and kurtosis can improve the prediction of realized volatility for equity assets.
-Using data from 452 listed firms on the Pakistan Stock Exchange, the research evaluates both in-sample and out-of-sample forecast performance.
-The standard Heterogeneous Autoregressive (HAR) model is extended by incorporating realized skewness and kurtosis into the volatility forecasting framework.
-The extended model predicts future realized volatility as a linear function of:
- Yesterday’s realized volatility
- Average realized volatility over the past week and month
- Yesterday’s realized kurtosis
-Realized kurtosis is found to significantly enhance forecast accuracy, particularly for short- to medium-term horizons (1, 5, and 22 days ahead).
-Realized skewness has less predictive power compared to realized kurtosis but still adds context for modeling tail risk.
-These findings suggest that higher-order moments (like kurtosis) contain valuable information beyond basic volatility measures.
-The approach supports improved asset allocation and risk-adjusted return forecasting in equity portfolios.
While the study is based on Pakistan’s equity market, the methodology can be generalized to other asset classes and global markets. The paper concluded that stocks’ own realized kurtosis carries meaningful information for stocks’ future volatilities.
Reference
[2] Seema Rehman, Role of realized skewness and kurtosis in predicting volatility, Romanian Journal of Economic Forecasting, 27(1) 2024
Closing Thoughts
Both studies show that incorporating skewness and kurtosis adds valuable insight to volatility analysis. The first study reveals that the skewness risk premium is distinct, tradable, and especially driven by jump risk during market hours. The second shows that realized kurtosis improves short-term volatility forecasts. Together, they highlight the importance of using higher-order moments for better risk management, portfolio decisions, and understanding market behavior.