Covariance is a measure of dependence between the two variables under consideration. It is also called the amount by which the two variables change together. It is used to measure how the changes in one variable are accounted for by the changes in another variable. Particularly, it is used in finding correlation coefficients to measure the degree to which two variables are linearly related. The value of covariance would be either positive or negative. If the smaller values (or larger values) of one variable mainly match with the smaller values (or larger values) of the other variable (i.e., the variables tend to show similar behavior), then the covariance would be positive. That is, if the two variables tend to have the same behavior then the value of covariance between those variables would be positive. Similarly, if the two variables tend to have opposite behavior then the value of covariance between those variables would be negative.

It is used in various fields to find the relationship between two variables. It plays a vital role in Portfolio management, a branch of Finance theory. In finance, it is used to measure the extent to which the returns on one risky asset move together with the returns on another risky asset. In this field, the positive covariance would indicate the returns on two assets are moving together, while the negative covariance would indicate that the returns on two assets move inversely.

The mathematical formula for covariance is given by

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  • COV(X,Y) = E{ ([X − E(X)]*[Y−E(Y)] } = E(XY) – E(X) E(Y)
  • COV(X,Y) = Cor(X, Y) * S.D(X) * S.D(Y)
  • where COV (X, Y) = Covariance between X and Y
  • Cor (X, Y) = correlation between X and Y, which can also be denoted by r
  • S.D (X) = Standard deviation of X
  • S.D (Y) = Standard deviation of Y


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