Deterministic?!?
You would normally calculate the correlation between the two using what the experts call "data." Excel would work fine. The interesting thing is to calculate the correlation on rolling one day, one week, one month, annual bases. Or you could cheat and use
https://www.portfoliovisualizer.com/asset-correlations
Cheating is smart. Remembering that correlations are not necessarily stable isn't cheating, but is smart. I don't think the linky thing above is total return, btw.
Also, something something something about geometric vs arithmetic returns being important.
Edit: didn't really answer your question