Asymmetries in the Conditional Mean and the Conditional Variance: Evidence From Nine Stock Markets

Abstract

This paper tests the hypothesis that both the conditional mean and the conditional variance of index stock returns are asymmetric functions of past information. For this purpose, an Asymmetric Autoregressive Threshold GARCH model is introduced and estimated for nine national stock markets. The empirical evidence suggests that both the conditional mean and the conditional variance respond asymmetrically to past information. In agreement with other studies, the conditional variance is an asymmetric function of past innovations rising proportionately more during market declines, the so-called leverage effect. With two exceptions, the conditional mean is also an asymmetric function of past returns. Specifically, positive past returns are twice as persistent as negative past returns of an equal magnitude. This behavior is consistent with an asymmetric partial adjustment price model where prices incorporate negative returns (bad news) faster than positive returns (good news). Furthermore, asymmetries in the conditional mean are linked to asymmetries in the conditional variance because the faster adjustment of prices to bad news causes higher volatility during down markets.