Measuring High-Frequency Causality Between Returns, Realized Volatility and Implied Volatility

In this paper, we provide evidence on two alternative mechanisms of interaction between returns and volatilities: the leverage effect and the volatility feedback effect. We stress the importance of distinguishing between realized volatility and implied volatility, and find that implied volatilities are essential for assessing 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 (2010), 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 strong dynamic leverage effect over the first three days. 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. These results can be explained by the fact that volatility feedback effect works through implied volatility which contains important information on future volatility, through its nonlinear relation with option prices which are themselves forward-looking. In addition, we study the dynamic impact of news on returns * This paper was previously circulating under the title “Measuring causality between volatility and returns with highfrequency data”. The authors thank Ryan Compton, Robert Engle, Luc Bauwens, Benoit Perron, two anonymous referees, and the Co-Editor George Tauchen for several useful comments. Earlier versions of this paper were presented at the NBER-NSF Time Series Conference inMontr ́eal (2006), the Conference on Volatility and High Frequency Data at Chicago (2007), the 47th Annual Meeting of the Société canadienne de science économique in Québec city (2007), the 41th Annual Meeting of the Canadian Economics Association at Halifax (2007), the 13th International Conference on Computing in Economics and Finance at Montréal (2007), the Tenth Annual Financial Econometrics Conference at Waterloo (2008), CORE seminar, Humboldt-Copenhagen Conference (2009), North American Summer Meeting of the Econometric Society (2009) and the 2009 European meeting of the Econometric Society (ESEM). This work was supported by theWilliam Dow Chair in Political Economy (McGill University), the Canada Research Chair Program (Chair in Econometrics, Université deMontréal), the Bank of Canada (Research Fellowship), a Guggenheim Fellowship, a Konrad-Adenauer Fellowship (Alexander-vonHumboldt Foundation, Germany), the Institut de finance mathématique de Montréal (IFM2), the Canadian Network of Centres of Excellence [program on Mathematics of Information Technology and Complex Systems (MITACS)], the Natural Sciences and Engineering Research Council of Canada, the Social Sciences and Humanities Research Council of Canada, and the Fonds de recherche sur la société et la culture (Québec). Financial support from the Spanish Ministry of Education through grants SEJ 2007-63098 is acknowledged. † William Dow Professor of Economics, McGill University, CIRANO and CIREQ. Department of Economics, McGill University, Leacock Building, Room 519, 855 Sherbrooke Street West, Montréal, Québec H3A 2T7, Canada. TEL: (1) 514 398 8879; FAX: (1) 514 398 4938; e-mail: [email protected]. Webpage: http://www.jeanmariedufour.com ‡ Edhec Business School, CIRANO and CIREQ. Edhec Business School, 393, Promenade des Anglais, BP 3116, 06202 Nice Cedex 3, France. TEL: +33(0)493187802; FAX: +33(0)493187841; e-mail: [email protected]. § Economics Department, Universidad Carlos III de Madrid, Departamento de Economía, Calle Madrid, 126 28903 Getafe (Madrid) España. TEL: +34-91 6249863; FAX: +34-91 6249329; e-mail: [email protected]. and volatility. 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. Mots-clés : Volatility asymmetry, leverage effect, volatility feedback effect, risk premium, variance risk premium, multi-horizon causality, causality measure, highfrequency data, realized volatility, bipower variation, implied volatility. JEL codes: G1, G12, G14, C1, C12, C15, C32, C51, C53.