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.

中文翻译：

---

关于对数正态变量平均值投资组合的注释

本文建立了这样的条件：随着每个块中变量数量的增加，由K 个对数正态变量块的平均值组成的投资组合收敛到K维对数正态变量。关联的块协方差矩阵必须具有特殊的结构，其中块子矩阵内的相关性和方差相等。我们展示了为什么方差同质性假设在推导中起着关键作用。