This study explores the relationship between the U.S. stock returns, Bitcoin returns and their uncertainties by using a multivariate GARCH model. Specifically, the study compares the reactions of Bitcoin and stock market returns in the presence of global uncertainties and changes in risk appetites. The results show that even though reactions of Bitcoin and stock returns are similar for some highly volatile or risk averse periods, the association between the two returns is not sustainable. Moreover, the U.S. stock market investors are found to be risk averse throughout the entire sample period while Bitcoin investors are not.