Leverage effect and its causality in the Korea composite stock price index

Abstract

In this paper, we investigate the leverage effect and its causality in the time series of the Korea Composite Stock Price Index from November of 1997 to September of 2010. The leverage effect, which can be quantitatively expressed as a negative correlation between past return and future volatility, is measured by using the cross-correlation coefficient of different time lags between the two time series of the return and the volatility. We find that past return and future volatility are negatively correlated and that the cross correlation is moderate and decays over 60 trading days. We also carry out a partial correlation analysis in order to confirm that the negative correlation between past return and future volatility is neither an artifact nor influenced by the traded volume. To determine the causality of the leverage effect within the decay time, we additionally estimate the cross correlation between past volatility and future return. With the estimate, we perform a statistical hypothesis test to demonstrate that the causal relation is in favor of the return influencing the volatility rather than the other way around.