Portföy seçimi ve fraktal piyasalar: Londra borsasından kanıtlar

Öz

Modern Portföy Teorisini (MPT) ve Etkin Piyasa Hipotezini (EMH) destekleyen modellerin rastgele yürüyüş teorisi çerçevesinde kurgulandığı bilinmektedir. Ancak, bu modelleri eleştiren geniş ve büyüyen bir literatür, Fraktal Piyasa Hipotezi (FMH) ile EMH'nin geçerliğini sorgulamaktadır. Bu çalışmanın motivasyonu, Peters'ın [45,46] portföy seçimini normal dağılıma uymayan çerçevede inceleyen çalışmalarına dayanmaktadır. Çalışmanın amacı, portföy seçiminin teorik çerçevesine FMH açısından yeni bir yaklaşım önermektir. Çalışmada, fraktal davranışı araştırmak için Londra Menkul Kıymetler Borsası'nda işlem gören 92 hisse senedinin günlük gözlemleri kullanılmıştır. Analizlerde, öncelikle simüle edilmiş portföyler için fraktal yapının bir göstergesi olarak Hurst üsleri hesaplanmıştır. Bulgular, Londra Menkul Kıymetler Borsası'nda MPT ve EMH'nin geçerliliğinin sorgulanabilir olduğunu göstermektedir. Getiriler ve bir risk ölçüsü olarak Hurst üsleri arasındaki ilişkiyi incelemek için 5000 simüle edilmiş portföy oluşturulmuştur. Daha sonra, simüle adilmiş portföyler üzerinde yatırımcıların getirilerini optimize etmelerini sağlayabilecek bir etkin sınırın varlığı tespit edilmiştir. Sonuçları detaylı incelemek amacıyla, simüle edilmiş etkin sınır ile Markowitz'in etkin sınır portföylerinin Hurst üsleri hesaplanmıştır ve karşılaştırmalar yapılmıştır. Sonuçta, bu iki etkin sınır arasında büyük sapmaların meydana geldiğini tespit edilmiştir. Son olarak, sapmaların davranışlarını anlamak için Lyapunov üsleri kullanılmıştır. Araştırma sonucunda, yatırımcıların getirilerini maksimize etmek için Hurst ve Lyapunov üslerine göre optimal bir çözüm hesaplamaları önerilmiştir.

Anahtar Kelimeler

• Portföy seçimi
• Etkin sınır
• Fraktal piyasa hipotezi
• Hurst üsteli
• Lyapunov üsteli

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

Abstract

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.

Keywords

• Portfolio selection
• Efficient frontier
• Fractal market hypothesis
• The hurst exponent
• The lyapunov exponent

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