基于含时网络与随机矩阵理论的投资组合研究

考虑到资产收益率间复杂的线性和非线性动态相关及演化关系,基于Pearson相关系数、Kendall秩相关系数和Tail相关系数等构建含时网络并结合随机矩阵理论,研究最优投资策略问题。为了对比不同相依关系、不同中心性测度及是否降噪对投资策略的影响,构建了9个资产筛选网络模型,并基于上证180指数数据,求解最优投资策略,分析其内样本和外样本表现。研究发现:在Kendall和Tail相关系数下的模型所选资产组合可以有更低的交易成本,运用随机矩阵理论进行降噪能显著提升投资收益,含时条件中心性测度的引入有助于筛选出更优的资产组合。

Portfolio research based on temporal network and random matrix theory

Considering the complex linear and non-linear dynamic relationship and evolutional information among assets, temporal networks are constructed based on Pearson correlation coefficient, Kendall rank correlation coefficient and Tail correlation coefficient, and further deal with their noise reductions through random matrix, employ conditional centrality of temporal network as selection standard of optimal asset portfolio. Nine network models for asset screening are constructed from three aspects of dependency relationship, matrix noise reduction and central measure, and the mean-variance optimal strategy is further calculated based on SSE 180 indices. The in-sample and out-of-sample performances of investment strategies under different models are compared through indicators such as portfolio turnover and Omega ratio. The results show that the portfolio selected by the model with Kendall and Tail correlation coefficients has lower transaction costs. The application of random matrix theory can significantly improve investment returns and the introduction of temporal conditional centrality is helpful to screen out better portfolios.