In the minimum variance model, the covariance matrix plays an important role because it measures the risk and relationship of asset returns simultaneously under the normality assumption. However, in practice, the distribution of asset returns is nonnormal and has an obvious fat‐tail nature. In addition, the risk is one‐sided. In this paper, the main objective is to propose a better tool to replace the covariance matrix. The covariance matrix can be decomposed into two parts: a diagonal variance matrix and a square matrix with its elements being the Pearson correlation coefficient. A substitution of the covariance matrix is presented by replacing the variance and Pearson correlation coefficient in the decomposition of the covariance matrix with a semivariance and distance correlation coefficient, respectively. The proposed portfolio optimization strategy is applied to empirical data, and the numerical studies show the strategy performs well.

中文翻译：

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最小方差框架下基于半方差和距离相关的投资组合选择

在最小方差模型中，协方差矩阵起着重要作用，因为它在正态性假设下同时测量资产收益的风险和关系。但是，在实践中，资产收益的分配是非正态的，并且具有明显的尾部性质。此外，风险是单方面的。本文的主要目的是提出一种更好的工具来替换协方差矩阵。协方差矩阵可分解为两部分：对角方差矩阵和方阵，其元素为皮尔逊相关系数。通过分别用半方差和距离相关系数替换协方差矩阵分解中的方差和Pearson相关系数来表示协方差矩阵的替换。