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# Difference between covariance and Var(X+Y)

#### shivanin

##### Member
Can anybody tell me what is difference between Covar(X,Y) and Var(X+Y) and formulas for both of them. If different... Thanks.

#### ShaktiRathore

##### Well-Known Member
Subscriber
Hi,
Covar(X,Y) = E[(X-mean(X))(Y-mean(Y))] is the expected value of the cross products of the deviations of variables X and Y from their means.
Var(X+Y) is the variance of the portfolio with two constituents X and Y with their variances as Var(X) and Var(Y) and co-variance b/w them as Covar(X,Y).
Var(X+Y) = Var(X) +Var(Y) + 2*Covar(X,Y)

thanks

#### brian.field

##### Well-Known Member
Subscriber
They are different. Var (X + Y) is like taking the variance of 1 random variable Z which is defined as Z = X + Y. So it is a regular variance.

Covar (X,Y) describes the co-movement between X and Y, whereas X and Y are separate and distinct random variables (they are not combined in any way).

The covar(X,Y) can take any value from negative infinity to positive infinity, so it doesn't inform as much as a standardized covariance, which we call the Pearson Correlation Coefficient, rho, ,which is defined as follows: rho = Covar(X,Y) / (stdev(X)*stdev(Y)).

Rho is defined from -1 to +1. A rho = -1 means perfectly negatively correlated whereas a rho = +1 means perfectly positively correlated.