# Variance covariance matrix - number of periods required

Hi I am reviewing the example of Barra risk model in the following document page 23 there is the statement:

"Estimating a covariance matrix for, say, 3,000 stocks requires data for at least 3,000 periods.

Why the number of periods has to be [greater than or] equal to the number of stocks?

Covariances and variances of the stocks can be measured for any number of periods, cannot they? I don't get the point here. Can anybody please clarify?

• If you use less than 3000 periods the resulting variance covariance matrix will not be positive definite (it will be only positive semidefinite). This causes some problems when working with such a $\Sigma$ matrix (although there are also ways to get around them). For example $\Sigma^{-1}$ will not exist :(( – Alex C May 14 '18 at 0:50