Covariance
A measure of how two assets' returns vary together, unscaled by their individual volatilities.
Formula
Covariance = Average of [(Return A - Mean A) x (Return B - Mean B)]
Unit
%
In depth
Covariance is the raw quantity that portfolio variance is built from, and correlation is simply covariance normalised by the two standard deviations so it fits between -1 and +1. Because it is unscaled, its magnitude has no interpretation on its own — only its sign is directly meaningful. It is the input to the covariance matrix that modern portfolio theory optimises over, and estimating that matrix reliably is the practical bottleneck: with 50 assets there are 1,225 distinct covariances to estimate from limited data. Estimation error in those inputs is why naive optimisers produce extreme and unstable portfolios.
Worked example
A portfolio of 50 assets requires 50 x 49 / 2 = 1,225 pairwise covariances plus 50 variances. Estimating 1,275 quantities from a few years of monthly data is why optimised weights swing wildly on small changes in input.
Illustrative figures, chosen so the arithmetic is easy to follow. Not a live price and not a valuation of any company.
Educational reference only
This entry explains what “Covariance” means. It is not investment advice and not a recommendation to buy or sell any security. Any numbers above are illustrative, not live prices, and nothing here predicts price direction or rates a stock. Consider your own circumstances and consult a SEBI-registered investment adviser before acting.