Portföy seçimi ve fraktal piyasalar: Londra borsasından kanıtlar

Yıl 2023, Cilt: 29 Sayı: 2, 209 - 219, 30.04.2023

Hakan Aygören Umut Uyar

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

Öz

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.

Anahtar Kelimeler

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

Kaynakça

• [1] Bachelier, L. Théorie de la Speculation. 1st ed. Paris, France, Gauthier-Villars, 1900.
• [2] Markowitz H. “Portfolio selection”. Journal of Finance, 7(1), 77-91, 1952.
• [3] Sharpe WF. “Capital asset prices: A theory of market equilibrium under conditions of risk”. The Journal of Finance, 19(3), 425-442, 1964.
• [4] Fama EF. “Efficient capital markets: A review of theory and empirical work”. The Journal of Finance, 25(2), 383-417, 1970.
• [5] Ross SA. “The arbitrage theory of capital asset pricing”. Journal of Economic Theory, 13(3), 341-360, 1976.
• [6] Fama EF. “The behavior of stock-market prices”. The Journal of Business, 38(1), 34-105, 1965.
• [7] Roll R. “Orange juice and weather”. The American Economic Review, 74(5), 861-880, 1984.
• [8] De Bondt WFM, Thaler R. “Does the stock market overreact?”. The Journal of Finance 40(3), 793-805, 1985.
• [9] Roll R. “R-squared”. Journal of Finance, 43(2), 541-566, 1988.
• [10] Michaud RO. “The Markowitz optimization enigma: Is ‘optimized’ optimal?”. Financial Analysts Journal, 45(1), 31-42, 1989.
• [11] Cutler DM, Poterba JM, Summers LH. “Speculative dynamics”. The Review of Economic Studies, 58(3), 529-546, 1991.
• [12] Jegadeesh N, Titman S. “Returns to buying winners and selling losers: Implications for stock market efficiency”. The Journal of Finance, 48(1), 65-91, 1993.
• [13] Lakonishok J, Shleifer A, Vishny RW. “Contrarian investment, extrapolation, and risk”. The Journal of Finance, 49(5), 1541-1578, 1994.
• [14] Jagannathan R, McGrattan ER.“The CAPM debate”. Federal Reserve Bank of Minneapolis Quarterly Review, 19(4), 2-17, 1995.
• [15] Elton EJ, Gruber MJ. “Estimating the dependence structure of share prices”. Journal of Finance, 28(5), 1203-32, 1973.
• [16] Siegel J. Stocks for the Long Run. 1st ed. New York, USA, McGraw-Hill, 1998.
• [17] Aygoren H. “An empirical investigation of price changes in Istanbul Stock Exchange (ISE)”. Hacettepe Universitesi IIBF Dergisi, 25(1), 109-134, 2005.
• [18] Ang A, Chen J. “CAPM over the long run: 1926– 2001”. Journal of Empirical Finance, 14(1), 1-40, 2007.
• [19] Beyhaghi M, Hawley JP. “Modern portfolio theory and risk management: assumptions and unintended consequences”. Journal of Sustainable Finance & Investment, 3(1), 17-37, 2013.
• [20] French J. “The one: A simulation of CAPM market returns”. The Journal of Wealth Management, 20(1), 126-147, 2017.
• [21] Cootner PH. The Random Character of Stock Market Prices. 1st ed. Cambridge, USA, MIT Press, 1964.
• [22] Lintner J. “The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets”. Review of Economics and Statistics, 47(1), 13-37, 1965.
• [23] Mossin J. “Equilibrium in a capital asset market”. Econometrica, 35(4), 768-783, 1966.
• [24] Black F, Scholes M. “The pricing of options and corporate liabilities”. Journal of Political Economy, 81(3), 637-654, 1973.
• [25] Grossman SJ, Stiglitz JE. “On the impossibility of informationally efficient markets”. The American Economic Review, 70(3), 393-408, 1980.
• [26] Karp A, Vuuren GV. “Investment implications of the fractal market hypothesis”. Annals of Financial Economics, 14(01), 1-27, 2019.
• [27] Jensen MC. “Some anomalous evidence regarding market efficiency”. Journal of Financial Economics, 6(2-3), 95-101, 1978.
• [28] Tversky A, Kahneman D. “Prospect theory: An analysis of decision under risk”. Econometrica, 47(2), 263-291, 1979.
• [29] Shiller R, Fischer JS, Friedman BM. (1984). “Stock prices and social dynamics”. Brookings Papers on Economic Activity, 1984(2), 457-510, 1984.
• [30] Black F. “Noise”. The Journal of Finance, 41(3), 528-543, 1986.
• [31] Benard VL, Botosan C, Phillips GD. “Challenges to the efficient market hypothesis: Limits to the applicability of fraud-on-the-market theory”. Nebraska Law Review, 73(1994), 273-781, 1994.
• [32] Kahneman D, Riepe MW. “Aspects of investor psychology”. Journal of Portfolio Management, 24(4), 52-65, 1998.
• [33] Shleifer A. Inefficient Markets: An Introduction to Behavioral Finance. 1st ed. New York, USA, Oxford University Press, 2000.
• [34] Bulkowski TN. Encyclopedia of Chart Patterns. 2nd ed. New York, USA, Wiley, 2000.
• [35] Griggs FSJr. “No stone unturned: Forecasting revisited”. AACE International Transactions, 9, 91-94, 2002.
• [36] Mandelbrot BB, Hudson RL. The misbehavior of markets: A fractal view of financial turbulence. 1st ed. New York, USA, Basic Books, 2004.
• [37] Glen PJ. “The Efficient Capital Market Hypothesis, Chaos Theory, and the Insider Filing Requirements of the Securities Exchange Act of 1934: The predictive power of Form 4 filings”. Fordham Journal of Corporate & Financial Law, 11(1), 85-114, 2005.
• [38] Jarrett JE, Kyper E. “Capital market efficiency and the predictability of daily returns”. Applied Economics, 38(6), 631-636, 2006.
• [39] Aygoren H. “Istanbul menkul kiymetler borsasinin fractal analizi”. Dokuz Eylul Universitesi Iktisadi Idari Bilimler Fakultesi Dergisi, 23(1), 125-134, 2008.
• [40] Robinson KK. Technical Analysis: Does Recent Market Data Substantiate the Efficient Market Hypothesis?. PhD Dissertation, Walden University, Minnesota, USA, 2013.
• [41] Ghazani MM, Jafari MA. “Cryptocurrencies, gold, and WTI crude oil market efficiency: A dynamic analysis based on the adaptive market hypothesis”. Financial Innovation, 7(29), 1-26, 2021.
• [42] Mandelbrot BB. “The variation of certain speculative prices”. Journal of Business, 36(3), 394-419, 1963.
• [43] Sharpe WF. Portfolio Theory and Capital Markets. 1st ed. New York, USA, McGraw-Hill, 1970.
• [44] Fama EF, Miller MH. The Theory of Finance. 1st ed. New York, USA, Holt, Rinehart & Winston, 1972.
• [45] Peters EE. Chaos and order in the capital markets, a new view of cycles, prices, and market volatility. 1st ed. New York, USA, John Wiley & Sons, 1991.
• [46] Peters EE. Fractal Market Analysis, Applying Chaos Theory to Investment and Economics. 1st ed. New York, USA, John Wiley & Sons, 1994.
• [47] Kiehling H. “Nonlinear and chaotic dynamics and its application to historical financial markets”. Historical Social Research, 21(2), 3-47, 1996.
• [48] Sharpe WF, Alexander GJ, Bailey JV. Investments. 1st ed. New York, USA, Prentice-Hall, 1999.
• [49] Osborne MFM. The Random Character of Stock Market Prices. Editor(s): Cootner P. Brownian Motion, in the Stock Market, 145-173, Cambridge, USA, MIT Press, 1964.
• [50] Turner AL, Weigel EJ. An Analysis of Stock Market Volatility. 1st ed. Tacoma, USA, Frank Russell Company, 1990.
• [51] Dillén H, Stoltz B. “The distribution of stock market returns and the market model”. Finnish Economic Papers, 12(1), 41-56, 1999.
• [52] Guan LE. “How do we Protect Ourselves Against Unpredictable Market Meltdowns?” https://www.drwealth.com/how-do-we-protectourselves-from unpredictable unforeseeable-disasterblack-swans/ (21.10.2019).
• [53] Van Der Ploeg F. “Rational expectations, risk and chaos in financial markets”. The Economic Journal, 96, 151-162, 1986.
• [54] Peters EE. “Fractal structure in the capital markets”. Financial Analysts Journal, 45(4), 32-37, 1989.
• [55] Hsieh DA. “Chaos and nonlinear dynamics: Application to financial markets”. The Journal of Finance, 46(5), 1839-1877, 1991.
• [56] Khilji NM. “Nonlinear dynamics and chaos: application to financial markets in Pakistan”. Pakistan Development Review, 33, 1417-1429, 1994.
• [57] Pandey V, Kohers T, Kohers G. “Deterministic nonlinearity in the stock returns of major European equity markets and the United States”. Financial Review, 33(1), 45-64, 1998.
• [58] Chun SH, Kim KJ, Kim SH. “Chaotic analysis of predictability versus knowledge discovery techniques: Case study of the Polish stock market”. Expert Systems, 19(5), 264-272, 2002.
• [59] Saritas H, Aygoren H. “International indexing as a means of portfolio diversification”. Applied Financial Economics, 15(18), 1299-1304, 2005.
• [60] Xu F, Lai Y, Shu X B. “Chaos in integer order and fractional order financial systems and their synchronization”. Chaos, Solitons & Fractals, 117, 125-136, 2018.
• [61] Hurst H. “Long term storage capacity of reservoirs”. Transactions of the American Society of Civil Engineers, 116(1), 770-799, 1951.
• [62] Mulligan RF. “Fractal analysis of highly volatile markets: An application to technology equities”. The Quarterly Review of Economics and Finance, 44(1), 155-179, 2004.
• [63] Litimi H, Bensaida A, Belkacem L, Abdallah O. “Chaotic behavior in financial market volatility”. Journal of Risk, 21(3), 27-53, 2019.
• [64] Akyer H, Kalayci CB, Aygoren H. “Particle swarm optimization algorithm for mean-variance portfolio optimization: A case study of Istanbul Stock Exchange”. Pamukkale University Journal of Engineering Sciences, 24(1), 124-129, 2018.
• [65] Kalayci CB, Ertenlice O, Akyer H, Aygoren H. “A review on the current applications of genetic algorithms in meanvariance portfolio optimization”. Pamukkale University Journal of Engineering Sciences, 23(4), 470-476, 2017.
• [66] Moradi, M., Jabbari Nooghabi, M., Rounaghi, M. M. “Investigation of fractal market hypothesis and forecasting time series stock returns for Tehran Stock Exchange and London Stock Exchange”. International Journal of Finance & Economics, 26(1), 662-678, 2021.
• [67] Karp, A., & Van Vuuren, G. “Investment implications of the fractal market hypothesis”. Annals of Financial Economics, 14(01), 1-27, 2019.
• [68] Tilfani, O., Ferreira, P., & El Boukfaoui, M. Y. “Building multi-scale portfolios and efficient market frontiers using fractal regressions”. Physica A: Statistical Mechanics and its Applications, 532, 1-10, 2019.
• [69] Liu, G., Yu, C. P., Shiu, S. N., & Shih, I. T. “The Efficient Market Hypothesis and the Fractal Market Hypothesis: Interfluves, Fusions, and Evolutions”. SAGE Open, 12(1), 1-8, 2022.