Hi Jason. Thanks for your patience with me.
Consider the following arguments. The interpretation of two price series will often lead to spurious statistical conclusions. The reason these conclusions are spurious is because price series are auto-correlated, each observation within the same series being dependent on the observation before it. It is impossible to infer the strength of correlation or dependency *visually* between accumulating series for this very reason. You are 100% correct there – and kudos for point this out in a public forum.
So, you turn to statistics to prove the same point.
Using any statistical metric, say R-squared, to highlight the nature of this error only works if the assumptions of the metric are valid. Price series are auto-correlated (I think I’ve mentioned that somewhere). R^2 works on independent observations. An R^2 applied to accumulating series is equally spurious. Had you taken the log-returns of the series – in each and every example above, the R^2 would have been around zero all of the time. Had you done this, your point would have hit home beautifully. Rather, you apply R^2 to the series themselves, therefore committing the same error – not visually, but now inferentially using an assumed safer approach. But it’s not safer. It’s equally wrong, arguably more so since you are leaning on statistical architecture that commands more credos that subjective visual interpretation.
I think this dialog of yours highlights just how deep this issue goes, and how treacherous. CFA charter holders should not be making the same mistake that would fail freshman in school. But they do. Even those who are aware that something is amiss miss the mechanism. I suspect that even following this posting, most readers won’t get it. And that’s not pure arrogance – its empirical fact - that just what we see in the professional capital markets the world over.
Yours
Adam