Covariance

The covariance between two real random variables X and Y, is defined as the measure of how these two variables vary together. The covariance is sometimes called linear dependence between two variables.

The covariance is widely used in finance, especially in the theory of portfolios and in capital asset pricing models.

    \[COV\left ( X,Y \right )=\sum\left ( x_{i} - \bar{X} \right )*\left ( y_{i} - \bar{Y} \right ) \]

where:

xi = value of variable X
X = mean of variable X
yi = value of variable Y
Y = mean of variable Y

Covariance Properties:

1. The covariance between two independent variables is zero.

2. COV(a+bX,c+dY) = bd*COV(X,Y)

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