Factor Analysis for Volatility

Abstract

Factor models have become ubiquitous in finance for performing high dimensional analysis of returns and volatilities. Historical literature on the subject decomposes volatility into a factor component (systemic risk) and a remainder (idiosyncratic risk). However, recent work has suggested that a market shock to volatility may increase both systemic risk and idiosyncratic risk — specifically, that idiosyncratic volatility of US equities data has a factor structure, with the factor highly correlated with, and possibly precisely the market volatility. In this paper we attempt to characterize the underlying factor and find that it can be decomposed into a statistical (PCA) and structural (market volatility) factor. We also show that this feature is more common than expected, appearing in diverse sets of financial data. Lastly, we find that this dual- factor approach is slightly dominated in forecasting environments by a single statistical factor. Acknowledgments: For research support we thank the National Science Foundation. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.