Common and Idiosyncratic Conditional Volatility Factors: Theory and Empirical Evidence

Abstract

We propose a multiplicative dynamic factor structure for the conditional modelling of the variances of an N-dimensional vector of financial returns. We identify common and idiosyncratic conditional volatility factors. The econometric framework is based on an observation-driven time series model that is simple and parsimonious. The common factor is modeled by a normal density and is robust to fat-tailed returns as it averages information over the cross-section of the observed N-dimensional vector of returns. The idiosyncratic factors are designed to capture the erratic shocks in returns and therefore rely on fat-tailed densities. Our model is potentially of a high-dimension, is parsimonious and it does not necessarily suffer from the curse of dimensionality. The relatively simple structure of the model leads to simple computations for the estimation of parameters and signal extraction of factors. We derive the stochastic properties of our proposed dynamic factor model, including bounded moments, stationarity, ergodicity, and filter invertibility. We further establish consistency and asymptotic normality of the maximum likelihood estimator. The finite sample properties of the estimator and the reliability of our method to track the common conditional volatility factor are investigated by means of a Monte Carlo study. Finally, we illustrate our approach with two empirical studies. The first study is for a panel of financial returns from ten stocks of the S&P100. The second study is for the panel of returns from all S&P100 stocks.