基于复杂网络的投资组合优化研究

本文基于复杂网络的局部聚类系数改进了传统的全局最小方差投资组合模型。首先通过股票对数收益率的相关系数矩阵构造股票关联网络，然后计算股票关联网络的局部聚类系数，最后通过全局最小方差模型确定最佳投资组合。将改进后的模型应用于A股市场，经过夏普比率、信息比率和欧米茄比率的对比分析得出改进后的投资组合模型在样本外的表现优于传统的全局最小方差投资组合模型。

Research on Portfolio Optimization Based on Complex Network

The extentions of global minimum variance (GMV) model have received significant attention over the past decades. A vast literature focused on improved estimation of covariance and modified the risk measurement. We consider herein the extention of GMV model from a perspective of complex network in which nodes represent stocks and the edges represent the dependence structure of stock returns. Precisely, the objective function of GMV is modified by taking into account an interconnectedness matrix, consisting of the local clustering coefficients which charaterize how much an individual stock is embedded in the portfolio system. Hence, our proposed method considers not only the volatility of each stock but also the interconnection of each stock with the whole portfolio system. The main steps of our approach are summurized as follows:(1) construct the stock network via the correlation matrix (Pearson and Kendall); (2) compute the local clustering coefficients of stock network and the clustering coefficients matrix; (3) formulate the objective function of GMV model by introducing the clustering coefficients matrix; (4) model optimization. In order to evaluate our proposed method, an empirical analysis of China's stock market is performed in which portfolios obtained from our proposed model (based on Pearson and Kendall correlation matrix refer to PGMV and KGMV) will be compared with the classical GMV portfolio and the equally weighted porfolio (EW). The performance of different portfolios is examined by the Sharpe Ratio, the Information Ratio and the Omega Ratio. As a robustness check, our proposed method is applied to different rolling windows. The emperical study shows that the portfolios of PGMV and KGMV outperfom those of GMV and EW according to Sharpe, Information and Omega Ratio. Regarding the robustness check, it is observed that all the considered methods provide worse results when a shorter rolling window (60 days and 120 days) is used, but the portfolios based our approach are consistently better than the others. In all, considering the underlying structure of financial network is an effective way in improving the portfolio optimzation process and our approach gives investors a better tool for asset allocation.