A Skewed GARCH-in-Mean Model: An Application to U.S. Stock Returns

In this paper we consider a GARCH-in-Mean (GARCH-M) model based on the so-called z distribution. This distribution is capable of modeling moderate skewness and kurtosis typically encountered in financial return series, and the need to allow for skewness can be readily tested. We apply the new GARCH-M model to study the relationship between risk and return in monthly postwar U.S. stock market data. Our results indicate the presence of conditional skewness in U.S. stock returns, and, in contrast to the previous literature, we show that a positive and significant relationship between return and risk can be uncovered, once an appropriate probability distribution is employed to allow for conditional skewness