The most popular and widely used measure of
multivariate dispersion is the
generalized variance. However, its computation
is quite cumbersome when the number of variables p is large and it does not work anymore when the covariance matrix is singular. The singularity of sample covariance matrix occurs, for example, when p is greater than the sample size n. This paper discusses an alternative measure called vector variance which can eliminate these obstacles and has been successfully used as the stopping rule in Fast MCD algorithm. It is known that the sample vector variance converges in distribution to a p2-variate normal distribution. The mean is quite sample, i.e. equal to the trace of the square of population covariance matrix. However, the asymptotic variance has a complicated formulation and is tedious to compute because it involves a matrix multiplication of size (p2 x p2). Using the properties of vec operator, we show that the asymptotic variance can be represented in a simple form.