Modeling the Volatility of US Excess Stock Returns: The Relationship Between Return and Variance

This paper examines the relationship between monthly US excess stock market return and its volatility using several GARCH models including the GJR GARCH-M and the Nelson’s EGARCH-M model. We find Nelson’s EGARCH-M model to fit the data the best and to pass most of the diagnostic tests. The relationship between risk and return is found to be negative but insignificant. Also there is strong evidence in favor of asymmetric respond of variance to negative and positive residuals using the EGARCH-M model. The monthly conditional volatility is shown to be not as persistence as those found in literature using daily returns.