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

One of the most noticeable stylized facts in \u85nance is that stock index returns are neg-atively 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 volatil-ity 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 transac-tions in DAX options and futures over the time period from 1995 to 2005. Analyzing returns over 5-minute intervals, we \u85nd that the relationship is return-driven in the sense that in-dex returns Granger cause volatility changes. This causal relationship is statistically and economically signi\u85cant 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