Volatility Risk and Volatility‐of‐Volatility Risk: State‐Dependent Correlations Between VIX and the S&P 500 Stock Index and Hedging Effectiveness

ABSTRACT Our research is one of the first to provide evidence to distinguish between two types of uncertainty: the volatility (VOL) risk and the volatility‐of‐volatility (VOV) risk. We outline a theoretical framework of state‐dependent correlations between the S&P 500 stock index and volatility index (VIX). We then develop a Buford's state‐dependent DCC model to account for various combinations of VOL and VOV risks and their nonuniform impacts on the correlations. Our empirical results show that the minimum negative correlation between the S&P 500 and VIX is observed under a high VOL but low VOV risk state, while the maximum occurs under a high VOL and high VOV risk state. The proposed state‐dependent model improves the portfolio risk reduction beyond the conventional time‐dependent models.