资产收益率分形相关性下的Mean-PDCCA组合策略研究

Research on Mean-PDCCA Portfolio Strategy Under Fractal Correlation of Asset Return

准确地测量资产之间的相关性,是构建有效投资组合模型的前提.文章针对资产收益率存在分形相关性的现实情况,首先通过消除趋势交叉相关分析(DCCA)等方法,构建了分形相关性统计测度,用于测量资产之间的相关性;随后,通过将分形相关性统计测度纳入到收益-风险准则之中,构建了多时间标度前置下的投资组合模型Mean-PDCCA,即分形投资组合模型,并给出了模型的解析解;最后,实证分析发现,在资产收益率存在分形相关性的典型事实约束下,分形投资组合整体上优于经典投资组合,不仅能够提升投资业绩,还具有更好的稳健性,为投资者提供了有效的决策参考.

Accurately measuring the correlation between assets is a prerequisite for building an effective portfolio model.In view of the reality of the fractal correlation of asset return,this paper firstly constructs the fractal correlation statistical measure by detrendeding cross correlation analysis(DCCA) and other methods to measure the correlation between assets.Then,by incorporating the fractal correlation statistical measure into the return-risk criterion,a portfolio model Mean-PDCCA(fractal portfolio model) under multi-time scale preposition is constructed,and the analytical solution of the model is given.Finally,the empirical analysis finds that under the constraint of typical facts with fractal correlation of asset return,fractal investment portfolio is superior to traditional investment portfolio on the whole,which can not only improve investment performance,but also have better robustness,providing effective decision-making reference for investors.