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Abstract

This study investigates the asymmetry of the intraday return-volatility relation at different return horizons ranging from 1, 5, 10, 15, up to 60 min and compares the empirical results with results for the daily return horizon. Using data on the S&P 500 (SPX) and the VIX from September 25, 2003 to December 30, 2011 and a Quantile-Regression approach, we observe strong negative return-volatility relation over all return horizons. However, this negative relation is asymmetric in three different aspects. First, the effects of positive and negative returns on volatility are different and more pronounced for negative returns. Second, for both positive and negative returns, the effect is conditional on the distribution of volatility changes. The absolute effect is up to five times larger in the extreme tails of the distribution. Third, at the intraday level, there is evidence of both autocorrelation in volatility changes and cross-autocorrelation with returns. This lead-lag relation with returns is also very asymmetric and more pronounced in the tails of the distribution. These effects are, however, not observed at the daily return horizon.

6. Conclusions

This paper examines the intraday asymmetric relation between return and volatility by analyzing the relation at different parts of the conditional distribution of volatility changes. The S&P 500 index and the VIX index are sampled at different frequencies, ranging from 1, 5, 10, 15, 60 min, to one day, over the period September 25, 2003 to December 30, 2011. The results indicate that the relation between return and volatility is not robust across the different parts of the distribution of volatility changes. These results are consistent for all sampling frequencies considered. The effects of return shocks are more pronounced in the tails of the conditional distribution of volatility changes. Furthermore, the asymmetry between effects of positive and negative return shocks is varying over different quantiles of the distribution of volatility changes. Finally, at the intraday level, our study finds statistically significant autocorrelation and cross-autocorrelation patterns for the implied volatility changes that are not observed at the daily level.