Idiosyncratic volatility is the volatility of asset returns once the impact of common factors has been removed. The empirical evidence suggests the idiosyncratic volatilities are cross-sectionally correlated. This paper introduces an econometric framework for analysis of cross-sectional dependence in the idiosyncratic volatilities of assets using high frequency data. We first consider the estimation of standard measures of dependence in the idiosyncratic volatilities such as covariances and correlations. Next, we study an idiosyncratic volatility factor model, in which we decompose the variation in idiosyncratic volatilities into two parts: the variation related to the common factors such as the market volatility, and the residual variation. When using high frequency data, naive estimators of all of the above measures are biased due to the use of error-laden estimates of idiosyncratic volatilities. We provide bias-corrected estimators and establish their asymptotic properties. We apply our methodology to the 30 Dow Jones Industrial Average components, and document strong cross-sectional dependence in their idiosyncratic volatilities. We consider two different sets of idiosyncratic volatility factors, and find that neither can fully account for the cross-sectional dependence in idiosyncratic volatilities. We map out the network of dependencies in residual idiosyncratic volatilities across the stocks.
Joint work with Kokouvi Tewou