Research on Asset Allocation Based on Hierarchical Clustering and Fuzzy Theory

Abstract

After Markowitz's portfolio theory was put forward in the 1950s, the optimization method of venture capital portfolio had made continuous progress in three branches. Among them, double objective function became a mainstream. On the basis of predecessors, this paper proposes an asset-weight-optimization method based on hierarchical clustering and fuzzy theory. Firstly, this paper extracts the four characteristics of stocks, uses the hierarchical clustering method to aggregate the stocks with strong correlation to form a group, and then selects two of the most representative stocks from the group (i.e. clustering the data points with the best performance in each group) to form a new stock portfolio. Then, the fuzzy programming of the expected return is carried out for the new portfolio. And finally, the optimized asset allocation weight is obtained. In the experiment, we use the data from CSMAR database for empirical analysis. For the data preprocessing process of hierarchical clustering, we choose Ward algorithm. We conduct experiments with stock pools in China with data sample sizes of 20, 35 and 45 respectively. Firstly, we use hierarchical clustering data preprocessing, then optimize to obtain the weight with fuzzy theory, and finally compare the performance of relevant indicators with different sample sizes. Experiments show that hierarchical clustering can reduce the dimension of stock correlation matrix, which breaks through the limitation of the number of stocks for experiments, realizing "large-scale stock selection". The performance of programming which uses hierarchical clustering and fuzzy theory method is better than direct linear programming, in terms of simulating the state of people's investment and meet people's expectations at the same time. The innovation of the method and the improvement of the performance of relevant index show that the method proposed in this paper has a certain reference.