A Regression Based Approach to Capturing the Level Dependence in the Volatility of Stock Returns

Abstract

In this paper, we propose an alternative approach to work with the new covariance estimator Cov Ratio based on daily high-low prices that we had put forth in an earlier study (Lakshmi and Maheswaran, 2016). Using the GARCH (1, 1) and IGARCH (1, 1) models, we empirically examine four major stock indices, namely: NIFTY, S&P500, DAX and FTSE100 for the sample period ranging from 1st January 1996 to 30th March 2015. We find that the estimator is upward biased for all the indices under study. Furthermore, we find that there are no residual ARCH effects in these models. In the earlier study, we had proved that random walk behavior cannot explain this overreaction in stock returns. Therefore, we had attributed this phenomenon to the level dependence in the volatility of stock returns. In this study, we find that it is the same Constant Elasticity of Variance (CEV) effect that comes into play here that makes the estimator upward biased as seen in the data.