The Asymmetric Reverting Property of Stock Returns

Using asymmetric nonlinear smooth-transition GARCH(M) models for the period of 1926:01 - 1997:12, this paper shows that monthly excess returns on value-weighted market indexes exhibit a strong asymmetric reverting pattern; a negative return reverts more quickly, with a greater reverting magnitude, to positive returns, than do positive returns revert to negative returns. This paper also reveals that the relationship between future volatility and its risk premium is surprisingly negative when a negative return shock has been realized. The observed asymmetry in return dynamics is directly associated with a reduction in risk premium following a negative return shock. The reduction in risk premium causes not only the current stock price to rise but also the realized negative return to revert faster.