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An Optimal Investment Portfolio Constructed with Fractal Analysis and Long Memory Models
The key condition for applying modern portfolio theory is the stock market efficiency. At the same time, the results of numerous studies show that markets do not always meet the efficiency criteria. The article describes the method of forming optimal investment portfolios using fractal analysis tools, which hypothetically allows one to get portfolios with a good ratio of return and risk in the fractal market. The first hypothesis of the study is as follows: the selection of assets by the criterion of the minimum value of the fractal dimension of their price series allows us to improve the characteristics of the portfolio in comparison with the index and the portfolio of random assets. The second hypothesis says that further improvement of the portfolio performance can be achieved by predicting the series of asset returns using the ARFIMA econometric models. These hypotheses were tested on the US stock market with an investment period of 1 year. To ensure the statistical reliability of the results, the techniques of a sliding window and multiple random selection of assets with averaging of the obtained indicators were used. The results do not contradict the hypotheses put forward. Namely, the use of the described techniques allowed us to obtain better portfolios in comparison with a number of other popular practical approaches. The number of assets is empirically determined whereby the portfolio formed using fractal analysis is ahead of the index and the portfolio of random assets.