Volatility of Volatility - The Uncertainties of Risks

Abstract: This paper is an attempt to explore the characteristics of volatility of volatility on the aggregate level and investigate its role in the pricing of equity assets. Several measures of volatility of volatility for the S&P 500 index are elaborated and investigated in this study; realized, parametrized and implied. We explain differences between the measures and the uncertainties that are tied to the volatility of volatility. The measures are used in time series regression analyses on portfolios from which cross-sectional studies are undertaken. Here, the interplay with common risk factors for equities receives special attention. It is shown that volatility of volatility has similar effects in pricing as short-term reversal and momentum. Also, there is a lag between market downturns and spikes in volatility of volatility as the latter awaits volatility to revert. Finally, the numerical and qualitative findings are exploited for stocks in a long-short trading strategy, which in its simplified form, beats a hedge fund index and the S&P 500 thanks to its good performance during market turmoil. The main findings of this paper are the nature of VVOL as a source of hedging and the special characteristics of the VVIX index, probably due its inherent variance risk premium.