What is Covariance?

What is Covariance?

This is a measure of dispersion that captures how the variables move together. Note that it is a generalization of the variance, and the covariance of a variable with itself is just the variance. This is technically a 2-by-2 matrix of values where the values along one diagonal are the variances of X1 and X2, and the terms in the other diagonal are the covariance between X1 and X2.

Examples:

For Population:
$ Cov(x,y)= \frac{\sum (x_{1}-x)*(y-y)}{N} $

For Sample:
$ Covx,y= \frac{\sum (x_{1}-x)*(y-y)}{N-1} $

What is the importance of this?

Covariance assists risk professionals in identifying the relationship between two variables. However, one of the disadvantages of it is that it doesn’t give the actual strength of the relationship between two variables, which is covered by correlation.