The (in)efficiency of emerging and developed markets: An analysis from fractal theory
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Abstract
The objective of this article is to study the behavior of the stock markets in emerging countries (BRICS) and developed countries (USA, England, Germany, and Japan), aiming to identify the evolution of their degree of efficiency between June 2007 and July 2021 based on the hypothesis of fractal markets. Using the Hurst exponent, the fractal dimension, and entropy approximation, it was built a market efficiency index. Among the main results, inconstancy of the efficiency indices over time was identified, which is consistent with previous studies within the field of econophysics. In addition, most of the inefficiency is due to the presence of deterministic elements in asset price variations, with a similarity in the efficiency level between the groups of emerging and developed countries, except for the case of China, which presented a singular behavior, which motivates new studies in this market. Finally, the results indicate the relevance of the cointegration effects of the analyzed markets, which is reflected in the inefficiencies of these markets over time.
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Abreu, D. P. A. de, Camargos, M. A. de, & Bressan, A. A. (2023). The (in)efficiency of emerging and developed markets: An analysis from fractal theory. Brazilian Administration Review, 20(1), e220051. https://doi.org/10.1590/1807-7692bar2023220051
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Research Articles
References
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Balladares, K., Ramos-Requena, J. P., Trinidad-Segovia, J. E., & Sánchez-Granero, M. A. (2021). Statistical arbitrage in emerging markets: A global test of efficiency. Mathematics, 9(2), 179. https://doi.org/10.3390/math9020179
Bhutto, S. A., Ahmed, R. R., Streimikiene, D., Shaikh, S., & Streimikis, J. (2020). Portfolio investment diversification at global stock market: A cointegration analysis of emerging BRICS(P) group. Acta Montanistica Slovaca, 25(1), 57-69. https://doi.org/10.46544/AMS.v25i1.6
Cajueiro, D. O., & Tabak, B. M. (2004). Ranking efficiency for emerging markets. Chaos, Solitons & Fractals, 22(2), 349-352. https://doi.org/10.1016/j.chaos.2004.02.005
Calvet, L. E., & Fisher, A. J. (2008). Multifractal volatility: Theory, forecasting, and pricing. Academic Press.
Caporale, G. M., Gil-Alana, L., Plastun, A., & Makarenko, I. (2016). Long memory in the Ukrainian stock market and financial crises. Journal of Economics and Finance, 40(2), 235-257. https://doi.org/10.1007/s12197-014-9299-x
Cheng, H. F., Gutierrez, M., Mahajan, A., Shachmurove, Y., & Shahrokhi, M. (2007). A future global economy to be built by BRICs. Global Finance Journal, 18(2), 143-156. https://doi.org/10.1016/j.gfj.2006.04.003
Davies, S., & Hall, P. (1999). Fractal analysis of surface roughness by using spatial data. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 61(1), 3-37. https://doi.org/10.1111/1467-9868.00160
Delgado-Bonal, A. (2019). Quantifying the randomness of the stock markets. Scientific Reports, 9(1), 12761. https://doi.org/10.1038/s41598-019-49320-9
Dima, B., Dima, Ş. M., & Ioan, R. (2021). Remarks on the behavior of financial market efficiency during the COVID-19 pandemic. The case of VIX. Finance Research Letters, 43, 101967. https://doi.org/10.1016/j.frl.2021.101967
Doorasamy, M., & Sarpong, P. K. (2018). Fractal market hypothesis and Markov regime switching model: A possible synthesis and integration. International Journal of Economics and Financial Issues, 8(1), 93-100. https://www.econjournals.com/index.php/ijefi/article/view/5738
Elliot, R. N. (1938). The wave principle. In Elliot’s masterworks (1 ed., pp. 83-150). New Classics Library.
Fama, E. F. (1970). Efficient capital markets: A review of theory and empirical work. The Journal of Finance, 25(2), 383-417. https://doi.org/10.2307/2325486
Fama, E. F. (1991). Efficient capital markets: II. The Journal of Finance, 46(5), 1575-1617. https://doi.org/10.1111/j.1540-6261.1991.tb04636.x
Genton, M. G. (1998). Highly robust variogram estimation. Mathematical Geology, 30(2), 213-221. https://doi.org/10.1023/A:1021728614555
Geweke, J., & Porter-Hudak, S. (1983). The estimation and application of long memory time series models. Journal of Time Series Analysis, 4(4), 221-238. https://doi.org/10.1111/j.1467-9892.1983.tb00371.x
Gneiting, T., Ševčíková, H., & Percival, D. B. (2012). Estimators of fractal dimension: Assessing the roughness of time series and spatial data. Statistical Science, 27(2), 247-277. http://dx.doi.org/10.1214/11-STS370
Hall, P., & Wood, A. (1993). On the performance of box-counting estimators of fractal dimension. Biometrika, 80(1), 246-252. https://doi.org/10.2307/2336774
Ikeda, T. (2017). A fractal analysis of world stock markets. Economics Bulletin, 37(3), 1514-1532. http://www.accessecon.com/Pubs/EB/2017/Volume37/EB-17-V37-I3-P137.pdf
Johansen, S. (1988). Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control, 12(2-3), 231-254. https://doi.org/10.1016/0165-1889(88)90041-3
Jovanovic, F., & Schinckus, C. (2013). The emergence of econophysics: A new approach in modern financial theory. History of Political Economy, 45(3), 443-474. https://doi.org/10.1215/00182702-2334758
Kahneman, D., & Tversky, A. (2013). Prospect theory: An analysis of decision under risk. In Handbook of the fundamentals of financial decision making (Vol. 4, Chap. 6, pp. 99-127). World Scientific. https://doi.org/10.1142/9789814417358_0006
Kapecka, A. (2013). Fractal analysis of financial time series using fractal dimension and pointwise hölder exponents. Dynamic Econometric Models, 13, 107-125. https://doi.org/10.12775/DEM.2013.006
Karp, A., & Van Vuuren, G. (2019). Investment implications of the fractal market hypothesis. Annals of Financial Economics, 14(1), 1950001. https://doi.org/10.1142/S2010495219500015
Kotyrba, M., Volna, E., Janosek, H., Habiballa, H., & Brazina, D. (2013, May). Methodology for Elliott waves pattern recognition. Proceedings of the 27th European Conference on Modelling and Simulation, Ålesund, Norway. https://www.scs-europe.net/dlib/2013/ecms13papers/is_ECMS2013_0050.pdf
Kristoufek, L., & Vosvrda, M. (2013). Measuring capital market efficiency: Global and local correlations structure. Physica A: Statistical Mechanics and Its Applications, 392(1), 184-193. https://doi.org/10.1016/j.physa.2012.08.003
Kristoufek, L., & Vosvrda, M. (2014). Measuring capital market efficiency: Long-term memory, fractal dimension and approximate entropy. The European Physical Journal B, 87(7), 162. https://doi.org/10.1140/epjb/e2014-50113-6
Lahmiri, S., & Bekiros, S. (2020). Randomness, informational entropy, and volatility interdependencies among the major world markets: The role of the COVID-19 pandemic. Entropy, 22(8), 833. https://doi.org/10.3390/e22080833
Lévy, P. (1924). Théorie des erreurs: La loi de Gauss et les lois exceptionnelles. Bulletin de la Société Mathématique de France, 52, 49-85. https://doi.org/10.24033/bsmf.1046
Mandelbrot, B. B. (1999). A multifractal walk down wall street. Scientific American, 280(2), 70-73. https://doi.org/10.1038/scientificamerican0299-70
Meng, S., Fang, H., & Yu, D. (2020). Fractal characteristics, multiple bubbles, and jump anomalies in the Chinese stock market. Complexity, 2020, 7176598. https://doi.org/10.1155/2020/7176598
Mensi, W., Hammoudeh, S., Nguyen, D. K., & Kang, S. H. (2016). Global financial crisis and spillover effects among the U.S. and BRICS stock markets. International Review of Economics & Finance, 42, 257-276.
Miloş, L. R., Haţiegan, C., Miloş, M. C., Barna, F. M., & Boțoc, C. (2020). Multifractal detrended fluctuation analysis (MF-DFA) of stock market indexes: Empirical evidence from seven central and eastern European markets. Sustainability, 12(2), 535. https://doi.org/10.3390/su12020535
Mitra, S. K. (2012). Is Hurst exponent value useful in forecasting financial time series? Asian Social Science, 8(8), 111-120. https://doi.org/10.5539/ass.v8n8p111
Nekrasova, I., Karnaukhova, O., & Sviridov, O. (2018). Fractal properties of financial assets and forecasting financial crisis. In Fractal approaches for modeling financial assets and predicting crises (pp. 23-41). IGI Global. https://doi.org/10.4018/978-1-5225-3767-0.ch002
Oprean, C., & Tănăsescu, C. (2013). Applications of chaos and fractal theory on emerging capital markets. International Journal of Academic Research in Business and Social Sciences, 3(11), 633-653. http://dx.doi.org/10.6007/IJARBSS/v3-i11/398
Peters, E. E. (1994). Fractal market analysis: Applying chaos theory to investment and economics (1 ed). Wiley.
Pincus, S. M. (1991). Approximate entropy as a measure of system complexity. Proceedings of the National Academy of Sciences, 88(6), 2297-2301. https://doi.org/10.1073/pnas.88.6.2297
Pincus, S., & Kalman, R. E. (2004). Irregularity, volatility, risk, and financial market time series. Proceedings of the National Academy of Sciences, 101(38), 13709-13714. https://doi.org/10.1073/pnas.0405168101
Rickles, D. (2011). Econophysics and the complexity of financial markets. In C. Hooker (Ed.), Philosophy of complex systems (Vol. 10, pp. 531-565). North-Holland.
Rizvi, S. A. R., & Arshad, S. (2017). Analysis of the efficiency-integration nexus of Japanese stock market. Physica A: Statistical Mechanics and Its Applications, 470(C), 296-308. https://doi.org/10.1016/j.physa.2016.11.142
Rizwanullah, M., Liang, L., Yu, X., Zhou, J., Nasrullah, M., & Ali, M. U. (2020). Exploring the cointegration relation among top eight Asian Stock Markets. Open Journal of Business and Management, 8(3), 1076-1088. https://doi.org/10.4236/ojbm.2020.83068
Robinson, P. M. (1995). Gaussian semiparametric estimation of long range dependence. The Annals of Statistics, 23(5), 1630-1661. https://www.jstor.org/stable/2242539
Sánchez-Granero, M. A., Balladares, K. A., Ramos-Requena, J. P., & Trinidad-Segovia, J. E. (2020). Testing the efficient market hypothesis in Latin American stock markets. Physica A: Statistical Mechanics and its Applications, 540(C), 123082. https://doi.org/10.1016/j.physa.2019.123082
Schinckus, C. (2010). Is econophysics a new discipline? The neopositivist argument. Physica A: Statistical Mechanics and Its Applications, 389(18), 3814-3821. https://doi.org/10.1016/j.physa.2010.05.016
Schinckus, C. (2011). What can econophysics contribute to financial economics? International Review of Economics, 58(2), 147-163. https://doi.org/10.1007/s12232-011-0115-z
Shiller, R. J. (2003). From efficient markets theory to behavioral finance. Journal of Economic Perspectives, 17(1), 83-104. https://doi.org/10.1257/089533003321164967
Siddiqui, A., Shamim, M., Asif, M., & Al-Faryan, M. A. S. (2022). Are stock markets among BRICS members integrated? A regime shift-based co-integration analysis. Economies, 10(4), 87. Are stock markets among BRICS members integrated? A regime shift-based co-integration analysis. Economies, 10(4), 87.
Wang, N., & You, W. (2022). New insights into the role of global factors in BRICS stock markets: A quantile cointegration approach. Economic Systems, 101015. https://doi.org/10.1016/j.ecosys.2022.101015
Al Nasser, O. M., & Hajilee, M. (2016). Integration of emerging stock markets with global stock markets. Research in International Business and Finance, 36, 1-12. https://doi.org/10.1016/j.ribaf.2015.09.025
Bachelier, L. (1900). Théorie de la spéculation. In Annales scientifiques de l’École Normale Supérieure (Serie 3, Volume 17, pp. 21-86). https://doi.org/10.24033/asens.476
Balladares, K., Ramos-Requena, J. P., Trinidad-Segovia, J. E., & Sánchez-Granero, M. A. (2021). Statistical arbitrage in emerging markets: A global test of efficiency. Mathematics, 9(2), 179. https://doi.org/10.3390/math9020179
Bhutto, S. A., Ahmed, R. R., Streimikiene, D., Shaikh, S., & Streimikis, J. (2020). Portfolio investment diversification at global stock market: A cointegration analysis of emerging BRICS(P) group. Acta Montanistica Slovaca, 25(1), 57-69. https://doi.org/10.46544/AMS.v25i1.6
Cajueiro, D. O., & Tabak, B. M. (2004). Ranking efficiency for emerging markets. Chaos, Solitons & Fractals, 22(2), 349-352. https://doi.org/10.1016/j.chaos.2004.02.005
Calvet, L. E., & Fisher, A. J. (2008). Multifractal volatility: Theory, forecasting, and pricing. Academic Press.
Caporale, G. M., Gil-Alana, L., Plastun, A., & Makarenko, I. (2016). Long memory in the Ukrainian stock market and financial crises. Journal of Economics and Finance, 40(2), 235-257. https://doi.org/10.1007/s12197-014-9299-x
Cheng, H. F., Gutierrez, M., Mahajan, A., Shachmurove, Y., & Shahrokhi, M. (2007). A future global economy to be built by BRICs. Global Finance Journal, 18(2), 143-156. https://doi.org/10.1016/j.gfj.2006.04.003
Davies, S., & Hall, P. (1999). Fractal analysis of surface roughness by using spatial data. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 61(1), 3-37. https://doi.org/10.1111/1467-9868.00160
Delgado-Bonal, A. (2019). Quantifying the randomness of the stock markets. Scientific Reports, 9(1), 12761. https://doi.org/10.1038/s41598-019-49320-9
Dima, B., Dima, Ş. M., & Ioan, R. (2021). Remarks on the behavior of financial market efficiency during the COVID-19 pandemic. The case of VIX. Finance Research Letters, 43, 101967. https://doi.org/10.1016/j.frl.2021.101967
Doorasamy, M., & Sarpong, P. K. (2018). Fractal market hypothesis and Markov regime switching model: A possible synthesis and integration. International Journal of Economics and Financial Issues, 8(1), 93-100. https://www.econjournals.com/index.php/ijefi/article/view/5738
Elliot, R. N. (1938). The wave principle. In Elliot’s masterworks (1 ed., pp. 83-150). New Classics Library.
Fama, E. F. (1970). Efficient capital markets: A review of theory and empirical work. The Journal of Finance, 25(2), 383-417. https://doi.org/10.2307/2325486
Fama, E. F. (1991). Efficient capital markets: II. The Journal of Finance, 46(5), 1575-1617. https://doi.org/10.1111/j.1540-6261.1991.tb04636.x
Genton, M. G. (1998). Highly robust variogram estimation. Mathematical Geology, 30(2), 213-221. https://doi.org/10.1023/A:1021728614555
Geweke, J., & Porter-Hudak, S. (1983). The estimation and application of long memory time series models. Journal of Time Series Analysis, 4(4), 221-238. https://doi.org/10.1111/j.1467-9892.1983.tb00371.x
Gneiting, T., Ševčíková, H., & Percival, D. B. (2012). Estimators of fractal dimension: Assessing the roughness of time series and spatial data. Statistical Science, 27(2), 247-277. http://dx.doi.org/10.1214/11-STS370
Hall, P., & Wood, A. (1993). On the performance of box-counting estimators of fractal dimension. Biometrika, 80(1), 246-252. https://doi.org/10.2307/2336774
Ikeda, T. (2017). A fractal analysis of world stock markets. Economics Bulletin, 37(3), 1514-1532. http://www.accessecon.com/Pubs/EB/2017/Volume37/EB-17-V37-I3-P137.pdf
Johansen, S. (1988). Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control, 12(2-3), 231-254. https://doi.org/10.1016/0165-1889(88)90041-3
Jovanovic, F., & Schinckus, C. (2013). The emergence of econophysics: A new approach in modern financial theory. History of Political Economy, 45(3), 443-474. https://doi.org/10.1215/00182702-2334758
Kahneman, D., & Tversky, A. (2013). Prospect theory: An analysis of decision under risk. In Handbook of the fundamentals of financial decision making (Vol. 4, Chap. 6, pp. 99-127). World Scientific. https://doi.org/10.1142/9789814417358_0006
Kapecka, A. (2013). Fractal analysis of financial time series using fractal dimension and pointwise hölder exponents. Dynamic Econometric Models, 13, 107-125. https://doi.org/10.12775/DEM.2013.006
Karp, A., & Van Vuuren, G. (2019). Investment implications of the fractal market hypothesis. Annals of Financial Economics, 14(1), 1950001. https://doi.org/10.1142/S2010495219500015
Kotyrba, M., Volna, E., Janosek, H., Habiballa, H., & Brazina, D. (2013, May). Methodology for Elliott waves pattern recognition. Proceedings of the 27th European Conference on Modelling and Simulation, Ålesund, Norway. https://www.scs-europe.net/dlib/2013/ecms13papers/is_ECMS2013_0050.pdf
Kristoufek, L., & Vosvrda, M. (2013). Measuring capital market efficiency: Global and local correlations structure. Physica A: Statistical Mechanics and Its Applications, 392(1), 184-193. https://doi.org/10.1016/j.physa.2012.08.003
Kristoufek, L., & Vosvrda, M. (2014). Measuring capital market efficiency: Long-term memory, fractal dimension and approximate entropy. The European Physical Journal B, 87(7), 162. https://doi.org/10.1140/epjb/e2014-50113-6
Lahmiri, S., & Bekiros, S. (2020). Randomness, informational entropy, and volatility interdependencies among the major world markets: The role of the COVID-19 pandemic. Entropy, 22(8), 833. https://doi.org/10.3390/e22080833
Lévy, P. (1924). Théorie des erreurs: La loi de Gauss et les lois exceptionnelles. Bulletin de la Société Mathématique de France, 52, 49-85. https://doi.org/10.24033/bsmf.1046
Mandelbrot, B. B. (1999). A multifractal walk down wall street. Scientific American, 280(2), 70-73. https://doi.org/10.1038/scientificamerican0299-70
Meng, S., Fang, H., & Yu, D. (2020). Fractal characteristics, multiple bubbles, and jump anomalies in the Chinese stock market. Complexity, 2020, 7176598. https://doi.org/10.1155/2020/7176598
Mensi, W., Hammoudeh, S., Nguyen, D. K., & Kang, S. H. (2016). Global financial crisis and spillover effects among the U.S. and BRICS stock markets. International Review of Economics & Finance, 42, 257-276.
Miloş, L. R., Haţiegan, C., Miloş, M. C., Barna, F. M., & Boțoc, C. (2020). Multifractal detrended fluctuation analysis (MF-DFA) of stock market indexes: Empirical evidence from seven central and eastern European markets. Sustainability, 12(2), 535. https://doi.org/10.3390/su12020535
Mitra, S. K. (2012). Is Hurst exponent value useful in forecasting financial time series? Asian Social Science, 8(8), 111-120. https://doi.org/10.5539/ass.v8n8p111
Nekrasova, I., Karnaukhova, O., & Sviridov, O. (2018). Fractal properties of financial assets and forecasting financial crisis. In Fractal approaches for modeling financial assets and predicting crises (pp. 23-41). IGI Global. https://doi.org/10.4018/978-1-5225-3767-0.ch002
Oprean, C., & Tănăsescu, C. (2013). Applications of chaos and fractal theory on emerging capital markets. International Journal of Academic Research in Business and Social Sciences, 3(11), 633-653. http://dx.doi.org/10.6007/IJARBSS/v3-i11/398
Peters, E. E. (1994). Fractal market analysis: Applying chaos theory to investment and economics (1 ed). Wiley.
Pincus, S. M. (1991). Approximate entropy as a measure of system complexity. Proceedings of the National Academy of Sciences, 88(6), 2297-2301. https://doi.org/10.1073/pnas.88.6.2297
Pincus, S., & Kalman, R. E. (2004). Irregularity, volatility, risk, and financial market time series. Proceedings of the National Academy of Sciences, 101(38), 13709-13714. https://doi.org/10.1073/pnas.0405168101
Rickles, D. (2011). Econophysics and the complexity of financial markets. In C. Hooker (Ed.), Philosophy of complex systems (Vol. 10, pp. 531-565). North-Holland.
Rizvi, S. A. R., & Arshad, S. (2017). Analysis of the efficiency-integration nexus of Japanese stock market. Physica A: Statistical Mechanics and Its Applications, 470(C), 296-308. https://doi.org/10.1016/j.physa.2016.11.142
Rizwanullah, M., Liang, L., Yu, X., Zhou, J., Nasrullah, M., & Ali, M. U. (2020). Exploring the cointegration relation among top eight Asian Stock Markets. Open Journal of Business and Management, 8(3), 1076-1088. https://doi.org/10.4236/ojbm.2020.83068
Robinson, P. M. (1995). Gaussian semiparametric estimation of long range dependence. The Annals of Statistics, 23(5), 1630-1661. https://www.jstor.org/stable/2242539
Sánchez-Granero, M. A., Balladares, K. A., Ramos-Requena, J. P., & Trinidad-Segovia, J. E. (2020). Testing the efficient market hypothesis in Latin American stock markets. Physica A: Statistical Mechanics and its Applications, 540(C), 123082. https://doi.org/10.1016/j.physa.2019.123082
Schinckus, C. (2010). Is econophysics a new discipline? The neopositivist argument. Physica A: Statistical Mechanics and Its Applications, 389(18), 3814-3821. https://doi.org/10.1016/j.physa.2010.05.016
Schinckus, C. (2011). What can econophysics contribute to financial economics? International Review of Economics, 58(2), 147-163. https://doi.org/10.1007/s12232-011-0115-z
Shiller, R. J. (2003). From efficient markets theory to behavioral finance. Journal of Economic Perspectives, 17(1), 83-104. https://doi.org/10.1257/089533003321164967
Siddiqui, A., Shamim, M., Asif, M., & Al-Faryan, M. A. S. (2022). Are stock markets among BRICS members integrated? A regime shift-based co-integration analysis. Economies, 10(4), 87. Are stock markets among BRICS members integrated? A regime shift-based co-integration analysis. Economies, 10(4), 87.
Wang, N., & You, W. (2022). New insights into the role of global factors in BRICS stock markets: A quantile cointegration approach. Economic Systems, 101015. https://doi.org/10.1016/j.ecosys.2022.101015