Realized Volatility Modeling of S&P 500 Index Members and the Impact of Temporal Variations in the Mean Levels

Abstract

Using a daily panel dataset including almost all the stocks in the S&P 500 dating back to 1985, we document strong similarities in the risk dynamics across stocks. The similarities in risk dynamics are exploited by implementing volatility forecasting models estimated using panel-based methods that aggregate information across stocks and force the coefficients to be the same for each stock. The models that exploit these commonalities in risk characteristics across assets produce highly competitive out-of-sample risk forecasts compared to more conventional individual asset-specific models that implicitly ignore the similarities in risk dynamics. We estimate the models on the daily range of the highest and lowest log intraday stock price, which has been shown to be a good alternative to the high-frequency-based realized volatility (RV) estimator of the integrated volatility. Further, we normalize the RV by the time-varying mean of the RV retrieved from the Kalman Filter and -Smoother as an intermediate step before model estimation. Normalizing the RV before using panel-based estimation methods produces very promising out-of-sample risk forecasts compared to the widely accepted Heterogeneous Autoregressive (HAR) model. Further, it improves the out-of-sample predictive power of the unnormalized models. An important feature of the panel-based models we present is the inclusion of a time-varying mean of each stock. Including this feature mimics introducing an asset-specific intercept for each stock and captures the differences in risk dynamics across assets, as well as the temporal variations in the mean levels.