【摘要】 为提升投资组合的有效性,首先构建了分形期望和分形方差两个分形统计测度,给出了两个分形统计测度的运算规则;随后基于分形统计测度构建了分形投资组合模型,给出了分形投资组合模型的解析解;最后以上海证券交易所的所有行业指数为样本,实证分析了分形投资组合模型的有效性。结果发现,分形统计测度弥补了非分形统计测度难以准确测量证券收益和风险的缺陷,分形投资组合模型在确保收益的同时更好地分散了风险,更加有效。更多还原

【Abstract】 In order to improve the effectiveness of portfolio selection,we firstly construct the statistical measures of fractal expectation and fractal variance,and give the algorithm of two fractal statistical measures.Secondly,a fractal portfolio selection model is built based on the fractal statistical measures and an analytical solution for fractal portfolio selection model is calculated.Lastly,drawing the sample of all industrial indexes from Shanghai Stock Exchange,we verify the feasibility of constructing portfolio selection model using two fractal statistical measures.The empirical results demonstrate that fractal statistical measures make up the defect of the non-fractal statistical measure’s disability to measure the return and risks of stocks accurately,and the fractal portfolio model is more effective in diversifying risks while ensuring returns.更多还原