Correlation

Correlation is the arithmetic behind the diversification benefit. Two assets with correlation +1 move in lockstep; combining them gets no risk reduction, only return averaging. Two assets with correlation -1 move in perfect opposition; combining them nets to a riskless portfolio. Real-world asset pairs sit somewhere in between — usually between +0.2 and +0.8 — so the benefit is real but partial.

Several properties bite in practice. Correlation is not constant: it rises in crises ("all the correlations go to one"), which is exactly the moment diversification would matter most. It's also time-window sensitive — daily correlations look different from monthly ones, and a quarter of unusual returns can shift the long-run estimate meaningfully. Finally, correlation measures linear co-movement only; non-linear relationships can show zero correlation while still being dependent.