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Maybe it makes sense to refer to CAPM theory: it is expected that stock return is proportional to market excess return and it beta $$ \mu_S(t) = r(t) + \beta_S\cdot(r_m(t)-r(t)).$$ Where $r_m(t)$ is market expected return and $\beta_S$ is stock beta. Thus according to CAPM it's expected that $\frac{\mu_S(t)}{r(t)} = 1+\beta_S\cdot(\frac{r_m(t)}{r(t)}-1).$

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