The Construction And Application Of Mean MF-X-DMA Model For Portfolio Selection In Stock Market

With the rapid development of economy and the increasing trend of economic globalization,China's securities market has become an indispensable part of the financial system through continuous development and maturity.At the same time,the market also faces greater risks.Therefore,investors hope to spread risks by means of portfolio.Since Markowitz proposed the Mean-Variance model,many scholars have proposed a variety of portfolio models.These models are basically based on the efficient market hypothesis(EMH).However,the real capital market is difficult to meet the basic hypothesis of efficient market,it's a fractal market with complex volatility.Therefore,this paper first analyzes the price fluctuation of China's securities market from the fractal perspective.And then the multifractal detrended moving-average crosscorrelation analysis(MF-X-DMA)is combined with the Mean-Variance model to establish a Mean-MF-X-DMA model.The results are shown as follows:First,the fractal correlation methods are used to test the fractal characteristics of the sample stock return series.The results of the R/S analysis show that the Hurst index of each selected stock under different scales is not equal to 0.5,indicating that each selected stock has fractal characteristics.The results of the MF-DMA show that the generalized Hurst index of each sample stock changes with the change of q,indicating that each sample has multifractal characteristics,and fluctuations of different amplitudes show different continuity characteristics.The results of the MF-X-DMA show that the correlation between the selected stocks has multifractal characteristics,the interaction between the stocks is nonlinear,and the impact of different amplitude of volatility on the correlation is also different.Therefore,it is difficult to measure the correlation between the assets with linear correlation coefficient.According to the test results,it is known that the stock market is a fractal market.Therefore,the Mean-MF-X-DMA model is tested by the sample stocks which have been proved to have fractal characteristics,and it is compared with the traditional portfolio model in multiple dimensions.The results show that,except for a few scales,the Mean-MF-X-DMA model in other scales performs better than the control group in terms of return rate,beta coefficient,Sharpe Ratio,Jensen index and Treynor index index.But the performance of standard deviation is not good.In addition,for the social and economic welfare of investors,the models based on most scales can achieve higher social and economic welfare than the control group.Because the composition of the sample stocks and the length of the prediction interval of the out-of-sample test may affect the robustness of the model,the robustness of the model are tested by changing the composition of the sample stocks and the length of the prediction interval.The results show that the performance of the model is not different from that of the previous paper,which verifies the robustness of the model to a certain extent.In order to compare the effect of the model under different scales,the effective boundary of the model under different scales are drawn,and it is found that the effective boundary is consistent with the theoretical results and the actual situation.At the same time,it is found that a smaller scale can lead to a portfolio with a lower risk.This paper has 16 figures,18 tables,and references of 91.