The implicit assumption of linearity is an important element in empirical finance. This study presents a hypothesis testing approach which examines the linear behaviour of the conditional mean between stock and bond returns. Conventional tests detect spurious non-linearity in the conditional mean caused by heteroskedasticity and/or autocorrelation. This study re-states these tests in a heteroskedasticity and autocorrelation consistent (HAC) framework and we find that stock and bond returns are indeed linear-in-the-mean in both univariate and bivariate settings. This study contends that previous research has detected spurious non-linearity due to size distortions caused by heteroskedasticity and autocorrelation, rather than the presence of a genuine non-linear relationship between stock and bond returns.