Publication: Measuring causality between volatility and returns with high-frequency data
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2008-09
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Abstract
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.
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Keywords
Volatility asymmetry, Leverage effect, Volatility feedback effect, Return risk premium, Variance risk premium, Multi-horizon causality, Causality measure, High-frequency data, Realized volatility, Bipower variation, Implied volatility