I am struggling to find a way to re write a covariance formula that includes non linear transformation of two variables. The formula is the following one:
$$\beta=\frac{\operatorname{cov}\left(r_A\cdot\frac{\mathrm{EUR}}{\mathrm{CHF}};r_I\cdot\frac{\mathrm{EUR}}{\mathrm{CHF}}\right)}{\operatorname{Var}\left(r_{I}\cdot\frac{\mathrm{EUR}}{\mathrm{CHF}}\right)}$$
I have to find a possible relation to the basic formula and the impact the transformation has:
$$\beta=\frac{\operatorname{cov}(r_A;r_I)}{\operatorname{Var}(r_{I})}$$
I tried to rewrite the covariance as expected value, but then I am stuck always with the non linear transformation.
Is there anyone who could give a hint or has any idea?
Thanks for your help