The problem of how to determine portfolio weights so that the variance of portfolio returns is minimized has been given considerable attention in the literature, and several methods have been proposed. Some properties of these estimators, however, remain unknown, and many of their relative strengths and weaknesses are therefore difficult to assess for users. This paper contributes to the field by comparing and contrasting the risk functions used to derive efficient portfolio weight estimators. It is argued that risk functions commonly used to derive and evaluate estimators may be inadequate and that alternative quality criteria should be considered instead. The theoretical discussions are supported by a Monte Carlo simulation and two empirical applications where particular focus is set on cases where the number of assets (p) is close to the number of observations (n).

中文翻译：

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估计全球最小方差投资组合的投资权重的风险观点

如何确定投资组合权重以使投资组合收益的方差最小化的问题已在文献中引起了极大的关注，并提出了几种方法。但是，这些估算器的某些属性仍然未知，因此它们的许多相对优势和劣势很难为用户评估。本文通过比较和对比用于得出有效投资组合权重估算器的风险函数，为该领域做出了贡献。有人认为，通常用于推导和评估估计量的风险函数可能不足，应考虑使用替代质量标准。理论讨论得到了蒙特卡洛模拟和两个经验应用的支持，其中特别着重于资产数量（p）接近观察数（n）。