Measuring causality between volatility and returns with high-frequency data

We use high-frequency data to study the dynamic relationship between volatility and equity returns. We provide evidence on two alternative mechanisms of interaction between returns and volatilities: the leverage effect and the volatility feedback effect. The leverage hypothesis asserts that return shocks lead to changes in conditional volatility, while the volatility feedback effect theory assumes that return shocks can be caused by changes in conditional volatility through a time-varying risk premium. On observing that a central difference between these alternative explanations lies in the direction of causality, we consider vector autoregressive models of returns and realized volatility and we measure these effects along with the time lags involved through short-run and long-run causality measures proposed in Dufour and Taamouti (2008), as opposed to simple correlations. We analyze 5-minute observations on S&P 500 Index futures contracts, the associated realized volatilities (before and after filtering jumps through the bispectrum) and implied volatilities. Using only returns and realized volatility, we find a weak dynamic leverage effect for the first four hours at the hourly frequency and a strong dynamic leverage effect for the first three days at the daily frequency. The volatility feedback effect appears to be negligible at all horizons. By contrast, when implied volatility is considered, a volatility feedback becomes apparent, whereas the leverage effect is almost the same. We interpret these results as evidence that implied volatility contains important information on future volatility, through its nonlinear relation with option prices which are themselves forwardlooking. In addition, we study the dynamic impact of news on returns and volatility, again through causality measures. First, to detect possible dynamic asymmetry, we separate good from bad return news and find a much stronger impact of bad return news (as opposed to good return news) on volatility. Second, we introduce a concept of news based on the difference between implied and realized volatilities (the variance risk premium) and we find that a positive variance risk premium (an anticipated increase in variance) has more impact on returns than a negative variance risk premium.