Modern portfolio theory introduced by Markowitz in 1952 is the most popular portfolio optimization framework established based on the trade-off between risk and return as an operation research model. The main shortcoming of applying Markowitz portfolio optimization in practice is that the obtained optimal weights are really sensitive to the embedded uncertainty in return series of stocks. In this paper, it is demonstrated how using a new methodology of time series clustering as a remedy can lead to a more robust and accurate portfolio in terms of the gap between mean variance efficient frontier obtained from the optimization model and the one observed in reality. In this regard, two similarity measures, the autocorrelation coefficients and the weighted dynamic time warping, are used in an innovative way to construct the desired portfolio optimization model. Moreover, the effectiveness of proposed approach is investigated in two different market conditions: semi-realistic and full-realistic. In the first one, it is assumed that the forecasted and realized stocks mean returns are the same; however, these returns are not necessarily equal in the second market conditions. Finally, a database of stock prices from the literature is utilized to show the robustness and accuracy of the proposed approach in empirical results in comparison with applied similarity measures in previous researches.

中文翻译：

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在实际市场条件下开发基于集群的有效投资组合优化模型

Markowitz在1952年提出的现代投资组合理论是最流行的投资组合优化框架，该框架基于风险和收益之间的权衡作为运筹学模型而建立。在实践中应用Markowitz投资组合优化的主要缺点是，获得的最优权重实际上对股票收益系列中嵌入的不确定性敏感。在本文中，通过从优化模型获得的平均方差有效边界与实际观察到的之间的差距，论证了使用时间序列聚类的新方法如何导致更健壮和准确的投资组合。在这方面，有两个相似性度量，即自相关系数和加权动态时间扭曲，以创新的方式来构建所需的投资组合优化模型。此外，在两种不同的市场条件下研究了所提方法的有效性：半现实和完全现实。在第一个中，假设预测和实际库存的平均收益是相同的；但是，这些收益在第二市场条件下不一定相等。最后，利用文献中的股价数据库，与以往的研究中采用的相似性度量方法相比，该方法在实证结果中显示了鲁棒性和准确性。假定预测和实际库存的平均收益是相同的；但是，这些收益在第二市场条件下不一定相等。最后，利用文献中的股价数据库，与以往的研究中采用的相似性度量方法相比，该方法在实证结果中显示了鲁棒性和准确性。假定预测和实际库存的平均收益是相同的；但是，这些收益在第二市场条件下不一定相等。最后，利用文献中的股价数据库，与以往的研究中采用的相似性度量方法相比，该方法在实证结果中显示了鲁棒性和准确性。