### Correlation complications

#### (Nov 25, 2012)

A basic result in probability theory is that the variance of the sum of two random variables is not necessarily the same as the sum of their variances. Mathematically, the variance of the sum of two random variables, A and B, is as follows:

Var(A+B) = Var(A) + Var(B) + 2*Cov(A,B)                (1)

where Var() denotes the variance and Cov() denotes the covariance.  The above result shows that the variance of A+B is only equal to the sum of the variances when their covariance (or correlation) is zero, i.e. when A and B are independent.  If A and B are positively correlated, for example, then ignoring the covariance term will cause the total variance to be under-estimated.  This basic result is relevant to two common scenarios…