Sure. If, for instance, you decide that the information you want to get from watching your investments is the value of pi, then provided you compute it in the right way (e.g., by ignoring your investments and summing a rapidly convergent series) it won't be noisy at all.

I assume you mean something distinctly less trivial than that, but I'm not sure what. I'd have thought that in a typical case the feedback you're seeking is something like "is this trading strategy I'm using a good one?" Meaning: "if I continue to use it, will I make money?". I have never worked at an investment bank or hedge fund, but my impression is that usually it takes some time before the answer to that question becomes clear, if it ever does. (The fact that the market is changing beneath your feet as you observe it doesn't make that any easier, of course.)