Optimal Portfolio Allocation Under Fractal Theory

Date

2024-8-27

Author

AÇIKGÖZ, TÜRKER

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The Efficient Market Hypothesis has been dominating the literature of finance for a long time. Meanwhile, the problematic assumptions and inappropriateness of Efficient Market Hypothesis in explaining real-life financial markets have dictated the significance of developing new theories and approaches. Up to now, among the literature on finance, the Fractal Market Hypothesis has developed as an alternative to the Efficient Market Hypothesis. The Fractal Market Hypothesis is developed based on fractal geometry and fractal Brownian motions, and their applications on financial markets. In essence, the hypothesis postulates that financial markets are structured as fractals, they exhibit statistical self-similarity, and long-term memory in their time series. On the other hand, the various portfolio applications to this hypothesis are quite limited in the literature. The present portfolio studies have a number of basic problems, including the definition of covariance, inability to propose a portfolio for more than two assets, and detrending. In this thesis, a portfolio optimization approach based on Fractal Market Hypothesis is developed which takes into account these problems of the existing models in the literature. This thesis proposes a portfolio optimization method, the Mean-MFTWXDFA (Mean-Multifractal Detrended Temporally Weighted Detrended Cross-Correlation Analysis) which is based on multifractal temporally weighted cross-correlation analysis with detrending approach by geographically weighted regression. The suggested method is also compared with those of classical portfolio applications such as the Mean-Variance, Mean-Value at Risk, and Mean-Conditional Value at Risk methods. The portfolio analysis include cryptocurrency market and three diversifying assets: oil, clean energy and equity. Applications of the fractal-based portfolio do reasonably well into out-of-sample analyses and outperform conventional ones.

Subject Keywords

Fractal Theory, Fractal Market Hypothesis, Multifractals, Portfolio Optimization, Cryptocurrencies

URI

https://hdl.handle.net/11511/110871

Collections

Graduate School of Applied Mathematics, Thesis