Covariance

To calculate covariance, find how far each value of the two variables is from its own mean, multiply the paired differences together and average the results.

Suppose two funds had monthly returns over five months that gave deviations from their means of 1.0, −2.0, 2.0, 0.0 and −1.0 for Fund X, and 0.5, −1.5, 1.5, −0.5 and 0.0 for Fund Y. Multiplying the pairs and adding them gives 6.5. Dividing by 4, one less than the number of observations, gives a sample covariance of about 1.63. The positive value shows the funds tended to move in the same direction.

Covariance is a building block of portfolio theory. When combining investments, what matters is not just how risky each one is, but how they move together. Investments with low or negative covariance can reduce a portfolio's overall risk.

The main drawback of covariance is that its size depends on the units of the data, so it is hard to interpret on its own. Is 1.63 a strong relationship or a weak one? Dividing covariance by the two standard deviations gives the correlation coefficient, which is always between −1 and +1 and much easier to interpret.