The decisions of asset selection and allocation lie at the heart of financial portfolio management. For these challenging tasks, the mathematical programming model of the mean–variance optimization problem proposes to use the concept of diversification. The novel methodology in this article is an original, innovative and a creative representation of the accumulated knowledge of this model from the modern portfolio theory. It is a practical application for portfolio managers to help synthesize the available historical data and to infer rational decisions. The state-of-the-art backtesting methodology integrates the unsupervised machine learning method of clustering analysis into the mean–variance portfolio optimization model. The test results from the proposed novel methodology show that clustering with Euclidean distance measures outperform the results of the benchmark and other specified clustering methods for different datasets, backtesting periods, and temporal scales of major stock indices.

资产选择和分配的决定是金融投资组合管理的核心。对于这些具有挑战性的任务，均方差优化问题的数学规划模型建议使用多元化的概念。本文中的新颖方法论是对现代证券理论中该模型的累积知识的原创，创新和创造性表示。对于投资组合经理来说，这是一个实用的应用程序，可以帮助综合可用的历史数据并推断出合理的决策。最新的回测方法将聚类分析的无监督机器学习方法集成到均方差投资组合优化模型中。