I have seen two definitions of Beta one is $$\beta = \rho\dfrac{\sigma_{asset}}{\sigma_{market}}$$ Here $\rho$ is the correlated coeffient
another one is
$$\beta = \dfrac{r_{expect} - r_{risk\ free}}{r_{market} - r_{risk\ free}}$$
I don't know which one is correct or they are equivalent? By the way, here $\sigma_{asset}$ is the volatility of historical return
or expected return
?