Portfolio selection and fractal market hypothesis: Evidence from the London stock exchange

It is well known that the models supporting the Modern Portfolio Theory (MPT) and the Efficient Market Hypothesis (EMH) are constructed in the framework of random walk theory. However, a large and growing literature criticizes those models. The Fractal Market Hypothesis (FMH) was proposed as an alternative hypothesis to EMH. The motivation of this study is Peters' [45,46] works that examine the portfolio selection case based on the non-normality framework. The aim of the study is to propose a new approach to theoretical framework of portfolio selection in terms of FMH. Daily observations of 92 stocks traded in London Stock Exchange are used to investigate the fractal behavior. Thus, the Hurst exponents as a means of indicator of a fractal structure are calculated for simulated portfolios. Results of the analysis show that the validity of MPT and EMH is questionable in London Stock Exchange. To examine the relationship between Hurst exponents (as a measure of risk) and returns, scattered diagrams are constructed for 5000 simulated portfolios. Existence of a pattern with a frontier is detected that may enable investors to optimize their portfolios. Further, The Hurst exponents of efficient frontier portfolios of Markowitz are calculated in order to investigate whether there is any linkage with the frontier of simulated portfolios. The results show that major deviations occur between these two frontiers. To understand these deviations, the Lyapunov exponents are suggested for detailed information. As a conclusion, it is recommended that investors should calculate an optimal solution with regards to the Hurst and Lyapunov exponents to maximize their returns.