Relation between VIX’s Return and Volatility: A Behavioral Explanation

I investigate the relation between returns and volatility at daily to 1-min intervals for VIX ETNs (like ETFs) and futures. As VIX is the implied volatility index and also known as “fear gauge”, this study is on relation between returns of volatility and volatilities of volatility. I find that, contrary to equity markets, volatility’s return and volatility exhibit positive relation at daily basis. However, negative relation appears at the finer-grained 5-min and 1-min intervals, with the latter stronger. This paper discovers a stronger behavioral case than Hibbert, Daigler and Dupoyet (2008) and shows that behavioral explanation is the only feasible one, among the three explanations of leverage, volatility feedback and behavioral effect. First, unlike equity, VIX ETNs and futures do not involve financial leverage. Second, the chance of any event having shocks to volatility of volatility is slim. Moreover, I observe negative relation only at very short intervals (less than 15-min) and a monotonic relation change from daily positive to intraday negative, while leverage and volatility feedback models suggest longer delayed effects and no such pattern of relation change. My findings imply that there are further behavioral effects when market deals with fear, which itself has already been a behavioral outcome.