Financial Entropy: The Degree of Disorder, Randomness and Unpredictability

Year 2024, Volume: 25 Issue: 54, 140 - 165, 30.06.2024

Turgay Geçer

Abstract

The notion of financial entropy refers to the degree of unpredictability, disorder, and risk in financial markets under the influence of various internal and external factors. Financial entropy possesses numerous consequences, including an elevated level of volatility, uncertainty, risk, complexity, contagion risk, and market inefficiency. Understanding the concept of financial entropy holds significant importance for financial analysts and traders as it provides valuable insights into the potential returns and risks associated with investments. The effective management of financial entropy necessitates meticulous attention to market conditions and a comprehensive comprehension of the motives and risks associated with financial markets. Numerous theories and techniques have been developed to quantify financial entropy, including random walk theory, noise, entropy index, entropy-based risk measure, Shannon entropy, Tsallis entropy, and Rényi entropy. The study explores the notion of the ‘quantum analogy of financial entropy’ and proposes a comparison between quantum mechanics and financial entropy to gain insight into the general behavior of market participants and clarify the uncertainty and unpredictability of financial markets. These principles emphasize the significance of regularly monitoring financial market conditions and adjusting strategies accordingly to effectively manage financial entropy.

Keywords

Entropy, Econophysics, Financial Entropy

Finansal Entropi: Düzensizlik, Rastgelelik ve Öngörülemezlik Ölçüsü

Abstract

Finansal entropi kavramı, çeşitli iç ve dış faktörlerin etkisi altında finansal piyasalardaki belirsizlik, düzensizlik ve risk derecesini ifade etmektedir. Finansal entropi, yüksek düzeyde oynaklık, belirsizlik, risk, karmaşıklık, bulaşma riski ve piyasa verimsizliği gibi çok sayıda sonuca sahiptir. Finansal entropi kavramının anlaşılması, yatırımlarla ilişkili potansiyel getiriler ve riskler hakkında değerli bilgiler sağladığından finansal analistler ve yatırımcılar için büyük önem taşımaktadır. Finansal entropinin etkin bir şekilde yönetilmesi, piyasa koşullarına titizlikle dikkat edilmesini ve finansal piyasalarla ilişkili getiri ve risklerin kapsamlı bir şekilde anlaşılmasını gerektirir. Finansal entropiyi ölçmek için rassal yürüyüş teorisi, gürültü, entropi endeksi, entropi tabanlı risk ölçüsü, Shannon entropisi, Tsallis entropisi ve Rényi entropisi gibi çok sayıda teori ve teknik geliştirilmiştir. Çalışma ‘finansal entropinin kuantum analojisi’ kavramını araştırmakta ve piyasa katılımcılarının genel davranışları hakkında fikir edinmek ve finansal piyasaların belirsizliğini ve öngörülemezliğini açıklığa kavuşturmak için kuantum mekaniği ile finansal entropi arasında bir karşılaştırma önermektedir. Bu ilkeler, finansal entropiyi etkin bir şekilde yönetmek için finansal piyasa koşullarını düzenli olarak izlemenin ve stratejileri buna göre ayarlamanın önemini vurgulamaktadır.

Keywords

Entropi, Ekonofizik, Finansal Entropi

References

• Ang, A. & Bekaert, G. (2001), Stock return predictability: is it there? National Bureue of Economic Research, Retrieved from https://doi.org/10.3386/w8207 .
• Baaquie, B.E. (2013), Financial modeling and quantum mathematics, Computers & Mathematics with Applications, 65 (10) pp. 1665-1673, Retrieved from https://doi.org/10.1016/j.camwa.2013.01.025.
• Bentes, S. R. & Menezes R. (2012) Entropy: A new measure of stock market volatility? Journal of Physics: Conference Series, 394, pp. 1-5, Retrieved from https://doi.org/10.1088/1742-6596/394/1/012033.
• Bouchaud, J. & Potters, M. (2003). Theory of financial risks: From statistical physics to risk management. Cambridge University Press. ISBN 9780521819169.
• Caraiani P. (2018) Modeling the Comovement of Entropy between Financial Markets, Entropy 20 (6), 417. Retrieved from https://doi.org/10.3390/e20060417.
• Chen, J. (2003) An entropy theory of psychology and its implication to behavioral finance, Financiele Studievereniging Rotterdam Forum, 6 (1), pp. 26-31 Retrieved from https://doi.org/10.2139/ssrn.465280.
• Chen, J. (2011) The entropy theory of mind and behavioral finance, ICFAI Journal of Behavioural Finance, 8(4), pp. 6-40. Retrieved from https://dx.doi.org/10.2139/ssrn.1734526.
• Çitçi, S. H. (2014), Agency and transparency in financial markets, Yönetim ve Ekonomi, 21 (2), pp. 269-279. Retrieved from https://doi.org/10.18657/yecbu.25947.
• Cockshott, R. & Zachariah, D. (2014). Conservation laws, financial entropy, and the Eurozone crisis. Economics, 8 (1), pp. 1-55. Retrieved from http://dx.doi.org/10.5018/economics-ejournal.ja.2014-5.
• Darbellay, G. A. & Wuertz, D. (2000). Entropy as a tool for analyzing statistical dependences in financial time series, Physica A: Statistical Mechanics, and its Applications, 287 (3-4), pp. 429-439. Retrieved from https://doi.org/10.1016/S0378-4371(00)00382-4.
• Deeva, G. (2017). Comparing entropy and beta as measures of risk in asset pricing. Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, 65 (6), pp. 1889-1894. Retrieved from https://doi.org/10.11118/actaun201765061889.
• Delgado-Bonal, A. (2019). Quantifying the randomness of the stock markets. Scientific Reports, 9 (12761), pp. 1-10. Retrieved from https://doi.org/10.1038/s41598-019-49320-9.
• Drummond, B. (2019) Understanding quantum mechanics: a review and synthesis in precise language. OpenPhys. 17(390–437). Retrieved from https://doi.org/10.1515/phys-2019-0045.
• Elton, E. J., Busse, J. A. & Gruber, M. J., (2002) Are investors rational? choices among index funds. NYU Working Paper, pp.1-35. Retrieved from http://dx.doi.org/10.2139/ssrn.340482.
• Fama, E. F. (1965). The behavior of stock-market prices, The Journal of Business, 38 (1), pp. 34-105. Retrieved from https://www.jstor.org/stable/2350752.
• Gârleanu, N., Panageas S. & Yu, J. (2015) Financial entanglement: a theory of incomplete integration, leverage, crashes, and contagion, American Economic Review, 105 (7), pp. 1979-2010. Retrieved from https://doi.org/10.1257/aer.20131076.
• Grant, S. & Quiggin, J. (2004), Increasing uncertainty: a definition, AgEcon Search, Research in Agricultural & Applied Economics, Working or Discussion Paper, pp. 1-33, Retrieved from https://doi.org/10.22004/ag.econ.151163.
• Heisenberg, W. (1927) Über den anschaulichen inhalt der quantentheoretischen kinematik und mechanik. Z. Physik 43, pp. 172-198. Retrieved from https://doi.org/10.1007/BF01397280.
• Hossain, T. & Siddiqua, P. (2022) Exploring the influence of behavioral aspects on stock investment decision-making: a study on Bangladeshi individual investors. PSU Research Review. Retrieved from https://doi.org/10.1108/PRR-10-2021-0054.
• Hosseini, R., Tajik, S., Koohi Lai, Z., Jamali, T., Haven, E. & Jafari, R. (2023) Quantum bohmian-inspired potential to model non–gaussian time series and its application in financial markets. Entropy 25 (7), 1061. Retrieved from https://doi.org/10.3390/e25071061.
• Jayaram, M. A. & Adavi, G. (2021) Quantum computing: some percepts and realms of applications, International Journal of Computer Applications, 183 (43), pp. 17-22. Retrieved from http://doi.org/10.5120/ijca2021921834.
• Kirilenko, A. A. & Lo, A. W. (2013) Moore’s Law vs. Murphy’s Law: Algorithmic trading and its discontents. Journal of Economic Perspectives, 27 (2), pp. 51-72. Retrieved from http://dx.doi.org/10.2139/ssrn.2235963.
• Kuhlmann, M. (2014) Explaining financial markets in terms of complex systems, Philosophy of Science 81 (5), pp. 1117-1130. Retrieved from https://doi.org/10.1086/677699.
• Kvam, P. D., Pleskac, T.J., Yu, S. & Busemeyer, J. R. (2015). Interference effects of choice on confidence: quantum characteristics of evidence accumulation, The Proceedings of the National Academy of Sciences, 112 (34), pp. 10645-10650. Retrieved from https://doi.org/10.1073/pnas.1500688112.
• Lassance, N. & Vrins, F. (2021). Minimum Rényi entropy portfolios. Annals of Operations Research, 299, pp. 3-46. Retrieved from https://doi.org/10.1007/s10479-019-03364-2.
• Liu, A., Chen, A., Yang, S. Y. & Hawkes, A. G. (2020), The flow of information in trading: an entropy approach to market regimes, Entropy 2020, 22 (9), 1064; Retrieved from https://doi.org/10.3390/e22091064.
• Lockwood, E., (2015) Predicting the unpredictable: Value-at-risk, performativity, and the politics of financial uncertainty, Review of International Political Economy, 22 (4), pp. 719-758. Retrieved from https://doi.org/10.1080/09692290.2014.957233.
• Mankiw, N. G. (2016). Principles of Macroeconomics. Cengage Learning. ISBN 1305971507.
• Meghji, S. (2021). Episode 5: The age of quantum banking FDIC Podcats Retrieved from https://www.fdic.gov/news/podcasts/transcripts/boi-podcast-ep5.pdf.
• Orrell, D. (2021). Quantum walk model of financial options. Wilmott, pp. 62-69. Retrieved from http://dx.doi.org/10.2139/ssrn.3512481.
• Orrell, D. (2022). Quantum financial entanglement: The case of strategic default, in Chakraborti A et al. (eds.), Quantum Decision Theory and Complexity Modelling in Economics and Public Policy. Cham: Springer. pp. 1-21, Retrieved from http://dx.doi.org/10.2139/ssrn.3394550.
• Özdilek, Ü. (2023) The Role of thermodynamic and informational entropy in improving real estate valuation method, Entropy 25 (907), pp.1-20. Retrieved from https://doi.org/10.3390/e25060907.
• Pilatin, A. (2023), The Impact of Political and Economic Developments on Stock Investors’ Decisions: Evidence from Türkiye, Ankara Hacı Bayram Veli Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi 25 (2) pp. 511-538. Retrieved from https://doi.org/10.26745/ahbvuibfd.1179683.
• Pinaud, N. & Boone, L. (2021) Fostering economic resilience in a world of open and integrated markets risks, vulnerabilities, and areas for policy action. OECD, Report prepared for the 2021UK presidency of the G7. Retrieved from https://www.oecd.org/newsroom/OECD-G7-Report-Fostering-Economic-Resilience-in-a-World-of-Open-and-Integrated-Markets.pdf.
• Prasad, E. S., Rogoff, K., Wie, S. V. J. & Köse, M. A. (2003) Effects of Financial Globalization on Developing Countries: Some Empirical Evidence. IMF Occasional Papers, pp.1-64. Retrieved from https://doi.org/10.5089/9781589062214.084.
• Raddant, M. & Kenett, D. (2021) Interconnectedness in the global financial market, Journal of International Money, and Finance, 110 (102280). Retrieved from https://doi.org/10.1016/j.jimonfin.2020.10228.
• Renyi, A. (1960) On Measures of Information and Entropy. Proceedings of the 4th Berkeley Symposium on Mathematics, Statistics and Probability, V. 4.I, University of California Press, Berkeley and Los Angeles, pp. 547-561. Retrieved from https://projecteuclid.org/ebook/download?urlId=bsmsp/1200512181&isFullBook=false.
• Risso, W. A. (2008) The informational efficiency and the financial crashes, Research in International Business and Finance, 22(3), pp. 396-408, Retrieved from https://doi.org/10.1016/j.ribaf.2008.02.005.
• Samuels, J. A. (2024) Understanding the dynamics of financial markets: a comprehensive analysis, Retrieved from https://doi.org/10.13140/RG.2.2.32665.60008.
• Săvoiu, G. & Iorga-Simăn, I. (2008). Some relevant Econophysics’ moments of history, definitions, methods, models and new trends, Romanian Economic Business Review, 3 (3), pp. 29-41. Retrieved from https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=161daf0695faa95b8210f426fb724655bf0aabce.
• Şengül, S. (2020). Financial regulations and risk in the context of the global recession. Journal of Business, Economics and Finance, 9(4), pp. 320-335. Retrieved from https://doi.org/10.17261/Pressacademia.2020.1313 Shannon, C. E., (1948). A mathematical theory of communication. The Bell System Technical Journal, 27 (3), pp. 379-423. Retrieved from http://dx.doi.org/10.1002/j.1538-7305.1948.tb01338.x
• Shiller, R. J. (2005). Irrational Exuberance (2. Edition). Princeton University Press. ISBN 0691123357.
• Sornette, D. (2003). Critical market crashes. Physics Reports, 378(1), pp. 1-98. Retrieved from https://doi.org/10.1016/S0370-1573(02)00634-8.
• Statman, M., (2019) Behavioral finance: the second generation, CFA Institute Research Foundation Publications, ISBN 978-1-944960-85-8.
• Tofallis, C. (2008) Investment volatility: A critique of standard beta estimation and a simple way forward, European Journal of Operational Research, 187 (3), pp. 1358-1367. Retrieved from https://doi.org/10.1016/j.ejor.2006.09.018.
• Tsallis, C. (1988). Possible generalization of Boltzmann-Gibbs statistics, Journal of Statistical Physics, 52, pp. 479-487. Retrieved from http://dx.doi.org/10.1007/BF01016429.
• Vishwanath, T. & Kaufman, D. (2001), Toward transparency: new approaches and their application to financial markets, The World Bank Research Observer, 16 (1), pp. 41–57, Retrieved from https://doi.org/10.1093/wbro/16.1.41.
• Wand, T., Hessler, M. & Kamps, O. (2023), Memory effects, multiple time scales and local stability in Langevin models of the S&P500 market correlation, Entropy 25 (1257) pp.1-21. Retrieved from https://doi.org/10.3390/e25091257.
• Yang, P. & Hou, X. (2022) Research on dynamic characteristics of stock market based on big data analysis, Hindawi Discrete Dynamics in Nature and Society, Article ID 8758976, pp.1-8, 8. Retrieved from https://doi.org/10.1155/2022/8758976.
• Ye, L. & Masato, A. (2012) Ye, Linghe; Abe, Masato (2012): The impacts of natural disasters on global supply chains, ARTNeT Working Paper Series, No. 115, Asia-Pacific Research and Training Network on Trade, Retrieved from https://hdl.handle.net/20.500.12870/1391.
• Yüzbaşioğlu, N. (2023) How does the fintech innovation wave affect financial markets, the banking industry, and customer behavior? Journal of Research in Business: 8 (2), pp. 549-574. Retrieved from https://doi.org/10.54452/jrb.1350890.
• Zheng, H. & Bai, J. (2024) Quantum leap: a price leap mechanism in financial markets, Mathematics, 12 (2), 315, pp. 1-27. Retrieved from https://doi.org/10.3390/math12020315.
• Zhou, R. & Tong, G. (2013) Applications of entropy in finance: a review, Entropy, 15 (11), pp. 4909-4931. Retrieved from https://doi.org/10.3390/e15114909.