A note on portfolios of averages of lognormal variables

Abstract

This paper establishes conditions under which a portfolio consisting of the averages of K blocks of lognormal variables converges to a K-dimensional lognormal variable as the number of variables in each block increases. The associated block covariance matrix has to have a special structure where the correlations and variances within the block submatrices are equal. We show why the variance homogeneity assumption plays a key role in the derivation.