The role of jump dynamics in the risk–return relationship

Surprisingly, a positive risk–return relationship has not been consistently observed for the traditional GARCH in the mean model in other studies. In this paper, we employ a combination of the jump diffusion and GARCH model in the mean equation to test the risk–return relationship for U.S. stock returns. The results suggest a statistically significant relationship between risk and return if the risk measure includes components of smoothly changing variance and jump events.