Return-Volatility Relationship in High Frequency Data: Multiscale Horizon Dependency

Abstract

This study investigates the relationship between the return on a stock index and its volatility using high frequency data. Two well-known hypotheses are reexamined: the leverage effect and the volatility feedback effect hypotheses. An analysis of the five-minute data of the S&P500 index reveals two distinct characteristics of the high frequency data. First, the sign of the relationship between the smallest wavelet scale components for return and volatility appears to be different from those between other scale components. Second, it was found that long memory exists in the daily realized volatility. These characteristics are incorporated in the test for the return-volatility relationship of the S&P500 index. In the study of the impact of changes in volatility on returns, we find that the leverage effect does not appear in intraday data, in contrast to the results for daily data. The difference can be attributed to the different relationships between scale components. By applying wavelet multiresolution analysis, it becomes clear that the leverage effect holds true between return and volatility components with scales equal to or larger than twenty minutes. However, these relationships are obscured in a five-minute data analysis because the smallest scale component accounts for a dominant portion of the variation of return. In testing the volatility feedback hypothesis, a modified model was used to incorporate apparent long memory in the daily realized volatility. This makes both sides of the test model balanced in integration order. No evidence of a volatility feedback effect was found under these stipulations. The results of this study reinforce the horizon dependency of the relationships. Hence, investors should be mindful of the different risk-return relationships for each horizon of interest. Additionally, the results show that the introduction of the long memory property to the proposed model is critical in the testing of risk-return relationships.