The shortcut, and why it fails
Pairwise correlation is a tidy summary number. It is also a population statistic, computed across thousands of bars where almost nothing meaningful happens. The trades that decide a portfolio's quality cluster in a few unusual weeks. In those weeks, average correlation is close to useless.
How we test independence
Before any new signal is given live capital we run a conditional dependence test against the existing book restricted to high-stress windows. A signal that looks beautifully decorrelated overall but loads on the same risk during the same five days as the rest of the portfolio is rejected.
What we mean by orthogonal
Orthogonal in our internal sense is not "uncorrelated on the long average." It is closer to "behaves differently when the rest of the portfolio is in trouble." That bar is much higher.