A High-Frequency Investigation of the Interaction between Volatility Changes and DAX Returns

One of the most noticeable stylized facts in nance is that stock index returns are negatively correlated with changes in volatility. The economic rationale for the e¤ect is still controversial. The competing explanations have di¤erent implications for the origin of the relationship: Are volatility changes induced by index movements, or inversely, does volatility drive index returns? To di¤erentiate between the alternative hypotheses, we analyze the lead-lag relationship of option implied volatility and index return in Germany based on Granger causality tests and impulse-response functions. Our dataset consists of all transactions in DAX options and futures over the time period from 1995 to 2005. Analyzing returns over 5-minute intervals, we nd that the relationship is return-driven in the sense that index returns Granger cause volatility changes. This causal relationship is statistically and economically signi cant and can be clearly separated from the contemporaneous correlation. The largest part of the implied volatility response occurs immediately, but we also observe a smaller retarded reaction for up to one hour. A volatility feedback e¤ect is not discernible. If it exists, the stock market appears to correctly anticipate its importance for index returns. JEL classi cation: G10; G12; G13 Keywords: Implied volatility; Granger causality; leverage e¤ect; feed-back e¤ect; asymmetric volatility. Philippe Masset, Chair of Finance and Accounting, University of Fribourg / Switzerland, Bd. de Pérolles 90, CH-1700 Fribourg, philippe.masset@unifr.ch. yProf. Dr. Martin Wallmeier, Chair of Finance and Accounting, University of Fribourg / Switzerland, Bd. de Pérolles 90, CH-1700 Fribourg, martin.wallmeier@unifr.ch (corresponding author). 1 1 Introduction 2 1 Introduction A well known stylized fact in nance is that stock index returns are negatively correlated with changes in volatility (Black (1976)). The negative relationship is typically more pronounced in falling than in rising markets (Figlewski/Wang (2000)) and is stronger for indices than for individual stocks. The distinctive cross dependence pattern between return and volatility plays an essential role in the development of volatility as an asset class, in volatility modelling and in option pricing. Nevertheless, a fully consistent economic explanation for the e¤ect has not yet been o¤ered (see Bouchaud et al. (2001), Bollerslev/Zhou (2006)). The rst attempt to nd an economic rationale for the negative return correlation relies on a corporate nance argument. Black (1976) and Christie (1982), among others, argue that a positive stock return increases the market value of the rms equity, thereby diminishing its nancial leverage ratio. The reduced leverage gear will result in a lower volatility of stock returns. The empirical observations, however, do not support this leverage hypothesis. Firstly, it is not compatible with the observed asymmetry of the e¤ect in falling and rising markets. Secondly, the leverage hypothesis predicts to nd a stronger relationship on the individual rm level than the index level. This prediction is contrary to what is empirically observed (Bouchaud et al. (2001)). 1 In a US study, Figlewski/Wang (2000) conclude that the negative correlation on the index level is far too strong to be explained by the leverage hypothesis (see also Aydemir et al. (2006)). The term leverage e¤ectis sometimes used in a broader sense for the general hypothesis that the causality runs from stock return to volatility. In this paper, we call such a directional relationship return-driven. In this terminology, the leverage e¤ect is only one possibility to explain a return-driven negative correlation. Another explanation is that bad news might have di¤erent implications for future uncertainty than good news (see, e.g., Glosten et al. (1993) and Chen/Ghysels (2007)). For instance, price drops could induce more extensive portfolio adjustments of risk-averse agents than price increases. Bouchaud et al. (2001) suggest that the apparent return-driven relationship could be due to a retarded e¤ect. In their framework, the scale for price updates does not depend on the instantaneous price but on a moving average of past prices which means that current returns lead subsequent volatility changes. The hypothesis of a volatility-driven negative relationship is known as feedback e¤ect(see, e.g., Pindyck (1984), French et al. (1987), Campbell/Hentschel (1992)). It rests on the assumption that volatility is related to systematic risk and is therefore relevant for pricing. If new information gives rise to an unanticipated increase in volatility, this will also increase risk-adjusted discount rates. As long as cash ow expectations are not a¤ected, stock prices will go down. However, the empirical evidence on the impact of volatility on expected returns is controversial. Some studies report a positive (French et al. (1987), Campbell/Hentschel (1992), Scruggs (1998), Ghysels et al. (2005), Lundblad (2007), Bae et al. (2007)), others a negative relationship (Campbell (1987), Nelson (1991)). Often, the link was found to be insigni cant and unstable over time (Glosten et al. (1993), Turner et al. (1989), Harvey (2001)). 1 This statement holds although new evidence suggests that the rm level e¤ect might be stronger than previous work has documented (see Ericsson et al. (2007), Chelley-Steeley/Steeley (2005)).