Distributionally Robust Mean-CVaR Portfolio Optimization Based On Clustering And Kernel Density Estimation

Portfolio optimization is the process of selecting the best portfolio from all portfolios,the goal of which is to strike a balance between maximizing returns and minimizing risk.As an investor,there are two decision-making goals: one is to obtain the highest possible return under the given risk;the other is to obtain the lowest possible risk under the expected return.In portfolio theory,the most typical one is Markowitz’s mean-variance model,but because it relies on a special probability distribution and is highly sensitive to parameters,slight changes in parameters may cause great changes in decision-making results.Therefore,robust optimization methods that can effectively deal with parameter uncertainty have received extensive attention.Distributionally robust optimization is one of the important robust optimization models.In this paper,based on the distribution robust optimization model,a distributionally robust mean-CVa R model based on clustering and kernel density estimation is proposed.The model considers the study of portfolio problems based on cluster analysis.The research process is mainly divided into two stages: first,the K-means clustering algorithm is used to reduce the dimension of the asset income data set,and three methods of horizontal clustering,vertical distance and cross-clustering are used to conduct comparative experiments.Horizontal clustering is the clustering of the number of assets,vertical clustering is the clustering of asset scenarios,and cross-clustering combines horizontal and vertical clustering.Aiming at the problem of selecting the initial K value in the K-means algorithm,this paper uses the improved elbow method to determine it.At the same time,we use the silhouette coefficient value combined with the upper limit of the overall error to scroll the selection of the best K value under each window,so that the model effect is the best.Then,we use the clustered asset dataset as the input of the KDE distributionally robust mean-CVa R model,and finally solve the optimal investment weights of the portfolio.In this paper,the window rolling experiment method is used,and the actual stock return data is selected for the experiment,and the model results under different clustering methods are compared and analyzed,and the optimization results under different time periods and different asset characteristics are studied.The experimental results prove that these models are effective.The results of this paper will provide more effective algorithms on the basis of existing portfolio optimization models,and at the same time help to narrow the gap between theory and practice,and better serve the practice of portfolio management.