School of Business, Chengdu University of Technology, Chengdu 610059, China.
School of Economics and Statistics, Guangzhou University, Guangzhou 510006, China.
Chaos. 2023 Jan;33(1):013130. doi: 10.1063/5.0124695.
An effective portfolio selection model is constructed on the premise of measuring accurately the risk and return on assets. According to the reality that asset returns obey the asymmetric power-law distribution, this paper first builds two fractal statistical measures, fractal expectation and fractal variance to measure the asset returns and risks, inspired by the method of measuring the curve length in the fractal theory. Then, by incorporating the fractal statistical measure into the return-risk criterion, a portfolio selection model based on the fractal statistical measure is established, namely, the fractal portfolio selection model, and the closed-form solution of the model is given. Finally, through empirical analysis, it is found that under the constraints of typical factual characteristics that the asset returns obey the asymmetric power-law distribution, the fractal portfolio is better than the traditional portfolio as a whole, which not only can improve the investment performance but also has better robustness. The validity of the fractal investment portfolio is experimentally tested.
构建有效的投资组合选择模型的前提是准确地衡量资产的风险和收益。根据资产收益服从不对称幂律分布的实际情况，本文首次利用分形理论中测量曲线长度的方法，构建了两个分形统计测度——分形期望和分形方差，用于衡量资产收益和风险。然后，通过将分形统计测度纳入收益-风险准则，建立了基于分形统计测度的投资组合选择模型，即分形投资组合选择模型，并给出了模型的封闭解。最后，通过实证分析发现，在资产收益服从不对称幂律分布的典型实际特征的约束下，分形投资组合总体上优于传统投资组合，不仅可以提高投资绩效，而且具有更好的稳健性。实验验证了分形投资组合的有效性。
