Fraktal-HRP: hybrid machine learning proposal in portfolio optimization

For more than half a century, investors have been using the meanvariance (MV) model developed by Markowitz (1952) to optimize their portfolios in uncertain market conditions. However, the MV model can suffer from failures, particularly under extraordinary market conditions, due to its assumption of normal distribution. In this regard, the model, which encounters significant deviations in practice, has been subject to serious criticism, particularly due to the concentration problem. The MV model, which recommends investing in limited assets within the set of investment opportunities, can cause specific assets in the market to be overvalued or undervalued. It can also lead to large losses in extreme market conditions. Many researchers have attempted to suggest solutions to these problems. Lopez de Prado proposed the "Hierarchical Risk Parity" (HRP) method based on machine learning for portfolio management in 2016. HRP reduces the concentration problem and has demonstrated outperformance in limited scenarios when compared to the MV model in different market environments. This study aims to develop a hybrid machine learning algorithm that responds to criticisms of the MV model and can provide performance improvements. To this goal, a new hybrid approach called FRAKTAL-HRP has been developed by combining the fractal market hypothesis with the HRP method. The new method proposes using the Hurst exponent instead of standard deviation as a risk measure; clustering algorithms based on machine learning instead of mathematical optimization; investing in dynamic weights instead of fixed asset weights; and finally, solving the concentration problem of the MV model. In order for FRAKTAL-HRP to demonstrate global rather than local performance superiority, tests were conducted in 18 different asset markets between 2004 and 2024. With the exception of one market, each market's unique dynamics provide investors with investment weights that can outperform the MV model. The findings demonstrate that FRAKTAL-HRP offers a powerful alternative, particularly in complex market conditions.