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Correlation vs. Causation

Correlation
ρX,Y=Cov(X,Y)σXσY\rho_{X,Y} = \frac{\text{Cov}(X,Y)}{\sigma_X\sigma_Y}

Covariance divided by the two standard deviations, which is what makes it unitless and bounded.

Everyone knows correlation does not imply causation. Fewer people can say why it matters for a trade, which is the useful part.

Why a trader should care

If you hedge A with B because they are correlated, your hedge survives only as long as whatever produced the correlation survives.

Common cause: both respond to a third factor. The hedge works while that factor dominates and fails when something else drives one of them.

Direct causation: A genuinely drives B. Much more robust, since the mechanism persists.

Coincidence: no relationship at all. The hedge fails at an unpredictable moment, which in practice tends to be the worst one.

Same measured correlation, three completely different levels of reliability. The number cannot distinguish them; only a mechanism can.

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