Diversifying crude oil price risk with crude oil volatility index: The role of volatility-of-volatility

To understand the diversification benefit of crude oil volatility, we examine the return-volatility relation in the crude oil market, given the interaction of the volatility (VOL) and the volatility-ofvolatility (VOV). We develop a novel empirical model of the crude oil price and crude oil volatility index (OVX) returns incorporating both time-varying and state-dependent variances and correlations, thus allowing us to identify distinct market regimes of VOL and VOV. We find that the behavior of the return-volatility relation is contingent on the prevailing VOV regimes. Specifically, in a low (high) VOV regime, the relation becomes less (more) negative as VOL increases. These empirical results therefore imply that the diversification benefit of crude oil volatility is far from uniform across the different market states. Finally, using our proposed empirical model, we demonstrate the economic significance of recognizing both the time-varying and state-dependent variances/correlations in portfolio risk forecasting and construction.