Research Portfolios Based On Multifractal Theory

In1952,the famous economist Harry Markowitz proposed an analysis method on the choiceof assets,the modern portfolio theory, which established the modern finance. However,theportfolio theory proposed by Markowitz is based on the efficient market hypothesis does notmeet the actual situation of modern financial markets.Multifractal theory is considered to be a powerful tool to describe the modern financialmarkets.In this paper,according to the multifractal theory, with Stock index futures contract asthe object of the research, We use the detrended fluctuation analysis method (MF-DFA) toempirical test the multi-scale fractal characteristics of China’s financial markets. We willshow that China’s financial markets is with multi-scale fractal characteristics, and subjectto heavy-tailed distributions. Then, according to the mean-variance based on multi-scalefractal theory,we construct a new portfolio model and empirical study the new model.In theempirical study, we use gradient algorithm to calculate the numerical solution of the newmodel and give a proven model evaluation method.Finally,we will show that this portfoliomodel based on the multifractal theory is more reasonable than the classical Markowitzportfolio model by empirical study.The results of this study have theoretical and practicalsignificance.