# Tag Info

I think what you are effectively looking at is \ \begin{align} \log(S_{AUDCAD})&=\log(S_{AUDUSD})\pm\log(S_{USDCAD})\\ \Rightarrow z&=x\pm y \end{align} Thus, $$\sigma_z^2=\mathrm{E}\left(\left(x\pm y\right)^2\right)- [\mathrm{E}(x\pm y)]^2 =\sigma_x^2+\sigma_y^2\pm 2\sigma_{xy}$$ Hence,  \tag{1} \sigma_{xy}=\frac{\sigma_z^2-\sigma_x^2-\...