Research on portfolio optimization under asymmetric power-law distribution of return tail

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.