Covariance
Covariance measures how two random variables move together: Cov(X,Y) = E[(X−μ_x)(Y−μ_y)]. It is the off-diagonal that makes a book more than a list of variances.
Definition
Covariance refers to diagonal that makes a book more than a list of variances. Keep that definition fixed when comparing series, managers, or regimes — renaming the same tape does not create a new signal.
Why it matters
It is a named object desks use to frame risk, positioning, or process. When diagonal that makes a book more than a list of variances shifts, related hedges, limits, and narratives usually need an explicit update rather than a quiet assumption.
Case
Suppose a desk is positioned for the opposite of what covariance is saying. If diagonal that makes a book more than a list of variances moves against that book, the first question is not “is the story clever?” but whether size, hedges, and stop logic still match the observation.
How to read it
Keep the definition fixed, then challenge it with cross-checks before sizing. Prefer a short written null hypothesis for Covariance: what would falsify the current reading in the next window?