Correlation

Correlation is the engine behind diversification. Two holdings that fall in the same conditions do not spread risk however different their names look, and correlation is the number that tells you which is which. It is covariance divided by the two standard deviations, and that scaling is what makes one pair's figure comparable with another pair's rather than an unreadable number in odd units.

Portfolio risk depends on these pairwise figures as much as on the volatility of each holding on its own. Adding an asset with low correlation to what you already own can shrink the whole portfolio's swings even when that asset is more volatile than anything already in it. Beta is a close relative: it is the correlation between an asset and the market, scaled by the ratio of their standard deviations.

Two things go wrong with it. The first is reading correlation as cause, when two series can move together for years because both respond to some third thing, or for no reason worth acting on. The second matters more to a portfolio: correlation is measured over a window and it is not stable. In a sharp sell-off, correlations between risky assets tend to climb toward 1, so the protection a calm-period figure implied thins out at exactly the moment it was wanted. Correlation also only captures the straight-line part of a relationship, and misses one that bends.