3
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-\...
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