基于改进的聚类和核密度估计的分布鲁棒均值-CVaR投资组合优化

Robust Mean-CVaR Portfolio Optimization Based on Enhanced Clustering and Kernel Density Estimation

摘要: 在金融市场中，如何构建最优投资组合来平衡风险和回报是当今研究者所面临的主要问题之一。为了构建最优投资组合，研究者们通常使用的是VaR或CVaR模型。本研究通过综合运用聚类、核密度估计以及分布鲁棒均值-CVaR模型的方法，从而达到提升股票投资组合的构建和风险管理能力的目的。本文考虑了包含100只股票日收益数据的实验数据集，通过优化聚类方法，利用核密度估计确定了K-means算法的最佳聚类中心和k值选取。随后，将聚类后的数据输入核密度估计的分布鲁棒均值-CVaR模型中进行分析。通过窗口滚动实验，比较了在有无聚类条件下模型对投资组合收益率的影响。结果显示，应用聚类方法后的模型具有更高的投资组合收益率，有助于投资者更好地平衡风险与回报，构建最优的投资组合。

Abstract: In financial markets, how to construct an optimal investment portfolio that balances risk and return is one of the main challenges faced by researchers today. To build an optimal portfolio, researchers typically use VaR or CVaR models. This study aims to enhance the construction of stock portfolios and risk management capabilities by comprehensively utilizing methods such as clustering, kernel density estimation, and distributionally robust mean-CVaR models. The paper utilized an experimental dataset containing daily returns of 100 stocks. By optimizing clustering methods and determining the optimal clustering centers and k values of the K-means algorithm using kernel density estimation, we then input the clustered data into the robust mean-CVaR model for analysis. By rolling window experiments, we compared the impact of the model on portfolio returns with and without clustering conditions. The results show that the model with clustering methods applied has higher portfolio returns, helping investors better balance risk and return to construct optimal portfolios.