Risk–return relationship in equity markets: using a robust GMM estimator for GARCH-M models

Abstract

While most asset pricing models postulate a positive relationship between excess returns and risk, there is no consensus on the nature of the relationship due to conflicting empirical evidence. The relationship is particularly ambiguous within a GARCH-M framework. This paper demonstrates that such a conflict can be attributed primarily to the downward bias of standard estimators that neglect additive outliers (AO) commonly observed in financial returns, and proposes a feasible estimation method (RGMME) for the GARCH-M model based upon a robust variant of the GMM. Monte Carlo experiments demonstrate that AOs cause more serious bias in the ML and GMM estimates of the relationship coefficient than previously expected. Therefore, in the presence of AOs, the RGMME appears superior to other standard estimators in terms of the root mean square error criterion. There is strong evidence favouring the RGMME over standard estimators based on its empirical application. In particular, it is substantially evident from the results of the RGMME that there is support for a positive relationship between excess returns and conditional volatility for all three major equity markets.