基于分形统计测度的动量组合投资策略优化研究  

Research on the Optimization of Momentum Portfolio Investment Strategy Based on Fractal Statistical Measurement

作　　者：吴栩[1,2] 王坤 燕汝贞 张菁洋[1] WU Xu;WANG Kun;YAN Ru-zhen;ZHANG Jing-yang(Business School,Chengdu University of Technology,Chengdu 610059,China;Post-Doctoral Research Station of Management Science and Engineering,Chengdu University of Technology,Chengdu 610059,China)

机构地区：[1]成都理工大学商学院,四川成都610059 [2]成都理工大学管理科学与工程博士后流动站,四川成都610059

出　　处：《统计与信息论坛》2022年第7期75-85,共11页Journal of Statistics and Information

基　　金：国家自然科学基金青年项目“分形特征约束下基于动量生命周期的反馈交易策略研究”(71903017);国家社会科学基金一般项目“供给侧结构性改革下中国金融市场风险的大数据智能预警方法及应用研究”(17BJY188)。

摘　　要：2022年,中国A股市场投资者突破2亿,市场机构化程度稳步提升,股票和基金投资已经成为不少家庭资产配置的重要组成部分。在这一背景下,作为应用最为广泛的投资策略,动量策略受到了社会各界的广泛关注,然而,传统动量策略没有考虑权重分配方法和股票收益率的分形特征。基于此,以股票收益率的分形特征为约束将投资组合模型纳入动量策略的研究框架。首先,利用多重分形去趋势波动分析法检验发现股票收益率普遍具有分形特征;其次,借助分形统计测度构建了分形收益风险比,并以此为排序指标构建了分形风险调整动量策略;再次,在分形风险调整动量策略的基础上,构建了带约束条件的分形投资组合模型,并利用该模型给赢者和输者组合分配最优权重构建了分形动量组合投资策略(FMP策略);最后,利用回测检验对比分析了FMP策略、风险调整动量策略、分形风险调整动量策略和传统动量策略的业绩情况,从实证视角证实了FMP策略的有效性。新构建的以股票收益率的分形特征为约束,基于投资组合模型的动量策略,不仅促进了分形市场理论与投资实践的有效衔接,而且对指导投资具有重要的借鉴意义。In 2022,China’s A-share market investors exceeded 200 million,the degree of institution aliation has steadily increased,and stock and fund investments have become an important part of quite a number of families’asset allocation.In the context,as the most widely used investment strategy,momentum strategy has received wide attention from all sectors of society,however,the traditional momentum strategy does not take into account the weight allocation method and the fractal characteristics of stock return rates.On the basis,this paper introduces the portfolio model into the research framework of the momentum strategy with the fractal characteristics of stock return rates as the constraint.Firstly,with the help of multifractal detrended fluctuation analysis method,it is found that the A-share market stock return rates generally have fractal characteristics.Secondly,a fractal return-to-risk ratio is construct with the help of fractal statistical measures,which is used as the ranking index to construct a fractal risk-adjusted momentum strategy.Thirdly,on the basis of the fractal risk-adjusted momentum strategy,a fractal portfolio model with constraints is constructed by introducing fractal statistical measures and specific constraints into the portfolio model and used to assign optimal weights to the winner and loser portfolios of the fractal risk-adjusted momentum strategy to complete the construction of a fractal momentum portfolio investment strategy(FMP strategy).Finally,compare and analyze the performance of fractal momentum portfolio investment strategy,risk-adjusted momentum strategy,fractal risk-adjusted momentum strategy and traditional momentum strategy by using back-testing tests to confirm the effectiveness of FMP strategy from an empirical perspective.The main findings are:(1)Stock return rates in the A-share market generally have multiple fractal characteristics,and their tails approximately obey a power-law distribution.(2)The performance of the fractal risk-adjusted momentum strategy outperforms that

关 键 词：动量策略 分形统计测度 分形收益风险比 分形组合模型 

分 类 号：F830.91[经济管理—金融学] F224