How Aggregate Volatility-of-Volatility Affects Stock Returns*

Abstract

A stylized theoretical model with stochastic volatility suggests the existence of a trade-off between returns and volatility-of-volatility. Using the VVIX index as empirical measure, we confirm this prediction and detect that time-varying aggregate volatility-of-volatility commands an economically substantial and statistically significant negative risk premium. We find a two-standard deviation increase in aggregate volatility-of-volatility factor loadings to be associated with a decrease in average annual returns of about 11%. This phenomenon cannot be explained by aggregate volatility, jump risk, and several other characteristics and factor sensitivities, or by a crisis effect.

Ambiguity and Investor Behavior

“…Among the market-based measures, the volatility of volatility (examples are the VVIX or V-VSTOXX) represents second-order beliefs, which, according to many theoretical models, are appropriate to capture ambiguity (Klibanoff, Marinacci, and Mukerji (2005), Nau (2006), Segal (1987)). Therefore, it is not surprising that the volatility of volatility is regarded as a good measure for ambiguity and used as such (Baltussen, van Bekkum, and van der Grient (2018), Hollstein and Prokopczuk (2018), Huang et al (2020), Chen, Chung, and Lin (2014), Bali and Zhou (2016), Bollerslev, Tauchen, and Zhou (2009), Epstein and Ji (2013), Barndorff-Nielsen and Veraart (2012)).…”

The Memory of Stock Return Volatility: Asset Pricing Implications

“…At the same time we verify our memory estimates by showing that forecasting volatility for stocks with longer memory works better than for stocks with shorter memory. We also relate our results to existing theoretical models, which show how long 1 In recent studies, Baltussen et al (2016) and Hollstein & Prokopczuk (2017) show that volatilityof-volatility is priced in the cross-section of stock returns. Although one might think that volatility-ofvolatility is related to the degree of long memory in volatility, we empirically show that (i) it is not, and (ii) it is priced separately.…”

“…We relate higher volatility predictability to lower uncertainty regarding a stock's level of risk. In the literature, uncertainty has been measured by the volatility-of-volatility for both individual stocks and the aggregate market (Baltussen et al, 2016;Hollstein & Prokopczuk, 2017). 27 We calculate the volatility-of-volatility as the 5-year rolling window volatility of monthly realized volatility.…”

Uncertainty and the volatility forecasting power of option‐implied volatility

“…Therefore, VVIX is a similar proxy for Knightian uncertainty with a forward‐looking nature. Several studies employ the VVIX to proxy uncertainty, including those by Park (2015); Hollstein and Prokopczuk (2018); Huang, Schlag, Shaliastovich, and Thimme (2019); and Krause (2019). These studies also indicate that the VVIX is highly correlated with the VoV.…”