IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v630y2023ics0378437123008117.html
   My bibliography  Save this article

An exploration of the mathematical structure and behavioural biases of 21st century financial crises

Author

Listed:
  • James, Nick
  • Menzies, Max

Abstract

In this paper we contrast the dynamics of the 2022 Ukraine invasion financial crisis with notable financial crises of the 21st century — the dot-com bubble, global financial crisis and COVID-19. We study the similarity in market dynamics and associated implications for equity investors between various financial market crises and we introduce new mathematical techniques to do so. First, we study the strength of collective dynamics during different market crises, and compare suitable portfolio diversification strategies with respect to the unique number of sectors and stocks for optimal systematic risk reduction. Next, we introduce a new linear operator method to quantify distributional distance between equity returns during various crises. Our method allows us to fairly compare underlying stock and sector performance during different time periods, normalising for those collective dynamics driven by the overall market. Finally, we introduce a new combinatorial portfolio optimisation framework driven by random sampling to investigate whether particular equities and equity sectors are more effective in maximising investor risk-adjusted returns during market crises.

Suggested Citation

  • James, Nick & Menzies, Max, 2023. "An exploration of the mathematical structure and behavioural biases of 21st century financial crises," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).
    • Handle: RePEc:eee:phsmap:v:630:y:2023:i:c:s0378437123008117
    DOI: 10.1016/j.physa.2023.129256
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437123008117
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2023.129256?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Dong-Hee Kim & Hawoong Jeong, 2005. "Systematic analysis of group identification in stock markets," Papers physics/0503076, arXiv.org, revised Oct 2005.
    2. Victor DeMiguel & Lorenzo Garlappi & Raman Uppal, 2009. "Optimal Versus Naive Diversification: How Inefficient is the 1-N Portfolio Strategy?," Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 1915-1953, May.
    3. Giacomo Livan & Jun-ichi Inoue & Enrico Scalas, 2012. "On the non-stationarity of financial time series: impact on optimal portfolio selection," Papers 1205.0877, arXiv.org, revised Jul 2012.
    4. Michael C. Munnix & Takashi Shimada & Rudi Schafer & Francois Leyvraz Thomas H. Seligman & Thomas Guhr & H. E. Stanley, 2012. "Identifying States of a Financial Market," Papers 1202.1623, arXiv.org.
    5. Driessen, J.J.A.G. & Melenberg, B. & Nijman, T.E., 2003. "Common factors in international bond returns," Other publications TiSEM 06a83942-b625-4d3c-808c-a, Tilburg University, School of Economics and Management.
    6. Arjun Prakash & Nick James & Max Menzies & Gilad Francis, 2020. "Structural clustering of volatility regimes for dynamic trading strategies," Papers 2004.09963, arXiv.org, revised Nov 2021.
    7. James, Nick & Menzies, Max & Chin, Kevin, 2022. "Economic state classification and portfolio optimisation with application to stagflationary environments," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    8. Nick James & Max Menzies, 2021. "A new measure between sets of probability distributions with applications to erratic financial behavior," Papers 2106.07377, arXiv.org, revised Dec 2021.
    9. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    10. Drożdż, S & Grümmer, F & Ruf, F & Speth, J, 2001. "Towards identifying the world stock market cross-correlations: DAX versus Dow Jones," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 294(1), pages 226-234.
    11. Stanis{l}aw Dro.zd.z & Ludovico Minati & Pawe{l} O'swik{e}cimka & Marek Stanuszek & Marcin Wk{a}torek, 2019. "Competition of noise and collectivity in global cryptocurrency trading: route to a self-contained market," Papers 1911.08944, arXiv.org, revised Feb 2020.
    12. Anton J. Heckens & Sebastian M. Krause & Thomas Guhr, 2020. "Uncovering the Dynamics of Correlation Structures Relative to the Collective Market Motion," Papers 2004.12336, arXiv.org, revised Sep 2020.
    13. Muhammad Kamran Khan & Muhammad Imran Khan & Muhammad Rehan, 2020. "The relationship between energy consumption, economic growth and carbon dioxide emissions in Pakistan," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 6(1), pages 1-13, December.
    14. Baillie, Richard T. & Morana, Claudio, 2009. "Modelling long memory and structural breaks in conditional variances: An adaptive FIGARCH approach," Journal of Economic Dynamics and Control, Elsevier, vol. 33(8), pages 1577-1592, August.
    15. Marcin Wk{a}torek & Stanis{l}aw Dro.zd.z & Jaros{l}aw Kwapie'n & Ludovico Minati & Pawe{l} O'swik{e}cimka & Marek Stanuszek, 2020. "Multiscale characteristics of the emerging global cryptocurrency market," Papers 2010.15403, arXiv.org, revised Mar 2021.
    16. Marcin Wk{a}torek & Jaros{l}aw Kwapie'n & Stanis{l}aw Dro.zd.z, 2022. "Multifractal cross-correlations of bitcoin and ether trading characteristics in the post-COVID-19 time," Papers 2208.01445, arXiv.org.
    17. Lashkaripour, Mohammadhossein, 2023. "ESG tail risk: The Covid-19 market crash analysis," Finance Research Letters, Elsevier, vol. 53(C).
    18. Wilcox, Diane & Gebbie, Tim, 2007. "An analysis of cross-correlations in an emerging market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(2), pages 584-598.
    19. Higor Y. D. Sigaki & Matjaz Perc & Haroldo V. Ribeiro, 2019. "Clustering patterns in efficiency and the coming-of-age of the cryptocurrency market," Papers 1901.04967, arXiv.org.
    20. Stanis{l}aw Dro.zd.z & Robert Gk{e}barowski & Ludovico Minati & Pawe{l} O'swik{e}cimka & Marcin Wk{a}torek, 2018. "Bitcoin market route to maturity? Evidence from return fluctuations, temporal correlations and multiscaling effects," Papers 1804.05916, arXiv.org, revised Jul 2018.
    21. Lamoureux, Christopher G & Lastrapes, William D, 1990. "Persistence in Variance, Structural Change, and the GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 225-234, April.
    22. Danielsson, Jon & Jorgensen, Bjorn N. & Sarma, Mandira & de Vries, Casper G., 2006. "Comparing downside risk measures for heavy tailed distributions," Economics Letters, Elsevier, vol. 92(2), pages 202-208, August.
    23. Stanis{l}aw Dro.zd.z & Jaros{l}aw Kwapie'n & Marcin Wk{a}torek, 2023. "What is mature and what is still emerging in the cryptocurrency market?," Papers 2305.05751, arXiv.org.
    24. Nick James & Max Menzies & Georg A. Gottwald, 2022. "On financial market correlation structures and diversification benefits across and within equity sectors," Papers 2202.10623, arXiv.org, revised Jun 2022.
    25. Daniel J. Fenn & Mason A. Porter & Stacy Williams & Mark McDonald & Neil F. Johnson & Nick S. Jones, 2010. "Temporal Evolution of Financial Market Correlations," Papers 1011.3225, arXiv.org, revised May 2011.
    26. Nick James & Max Menzies & Jennifer Chan, 2023. "Semi-Metric Portfolio Optimization: A New Algorithm Reducing Simultaneous Asset Shocks," Econometrics, MDPI, vol. 11(1), pages 1-33, March.
    27. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    28. Stanis{l}aw Dro.zd.z & Ludovico Minati & Pawe{l} O'swik{e}cimka & Marek Stanuszek & Marcin Wk{a}torek, 2019. "Signatures of crypto-currency market decoupling from the Forex," Papers 1906.07834, arXiv.org, revised Jul 2019.
    29. Alexander M. Petersen & Fengzhong Wang & Shlomo Havlin & H. Eugene Stanley, 2010. "Market dynamics immediately before and after financial shocks: quantifying the Omori, productivity and Bath laws," Papers 1006.1882, arXiv.org, revised Oct 2010.
    30. Nick James & Max Menzies & Kevin Chin, 2022. "Economic state classification and portfolio optimisation with application to stagflationary environments," Papers 2203.15911, arXiv.org, revised Sep 2022.
    31. Li, Hui-Jia & Xu, Wenzhe & Song, Shenpeng & Wang, Wen-Xuan & Perc, Matjaž, 2021. "The dynamics of epidemic spreading on signed networks," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    32. Marcin Wątorek & Jarosław Kwapień & Stanisław Drożdż, 2022. "Multifractal Cross-Correlations of Bitcoin and Ether Trading Characteristics in the Post-COVID-19 Time," Future Internet, MDPI, vol. 14(7), pages 1-15, July.
    33. James, Nick & Menzies, Max, 2022. "Global and regional changes in carbon dioxide emissions: 1970–2019," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 608(P1).
    34. Fang, Yi & Shao, Zhiquan, 2022. "The Russia-Ukraine conflict and volatility risk of commodity markets," Finance Research Letters, Elsevier, vol. 50(C).
    35. Nick James & Max Menzies, 2023. "Collective dynamics, diversification and optimal portfolio construction for cryptocurrencies," Papers 2304.08902, arXiv.org, revised Jun 2023.
    36. Roy Cerqueti & Massimiliano Giacalone & Raffaele Mattera, 2020. "Skewed non-Gaussian GARCH models for cryptocurrencies volatility modelling," Papers 2004.11674, arXiv.org.
    37. Ausloos, M., 2000. "Statistical physics in foreign exchange currency and stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 285(1), pages 48-65.
    38. Raj Kumar Pan & Sitabhra Sinha, 2007. "Collective behavior of stock price movements in an emerging market," Papers 0704.0773, arXiv.org, revised Nov 2007.
    39. Fabrizio Lillo & Rosario N. Mantegna, 2001. "Power law relaxation in a complex system: Omori law after a financial market crash," Papers cond-mat/0111257, arXiv.org, revised Jun 2003.
    40. Marcin Wk{a}torek & Jaros{l}aw Kwapie'n & Stanis{l}aw Dro.zd.z, 2023. "Cryptocurrencies Are Becoming Part of the World Global Financial Market," Papers 2303.00495, arXiv.org.
    41. Adam Farago & Erik Hjalmarsson, 2023. "Small Rebalanced Portfolios Often Beat the Market over Long Horizons," The Review of Asset Pricing Studies, Society for Financial Studies, vol. 13(2), pages 307-342.
    42. Nick James & Max Menzies & Jennifer Chan, 2020. "Semi-metric portfolio optimization: a new algorithm reducing simultaneous asset shocks," Papers 2001.09404, arXiv.org, revised Mar 2023.
    43. J.-P. Onnela & K. Kaski & J. Kertész, 2004. "Clustering and information in correlation based financial networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 38(2), pages 353-362, March.
    44. James, Nick & Menzies, Max & Chok, James & Milner, Aaron & Milner, Cas, 2023. "Geometric persistence and distributional trends in worldwide terrorism," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    45. Cai, Jun, 1994. "A Markov Model of Switching-Regime ARCH," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 309-316, July.
    46. Arjun Prakash & Nick James & Max Menzies & Gilad Francis, 2021. "Structural Clustering of Volatility Regimes for Dynamic Trading Strategies," Applied Mathematical Finance, Taylor & Francis Journals, vol. 28(3), pages 236-274, May.
    47. Jaros{l}aw Kwapie'n & Marcin Wk{a}torek & Marija Bezbradica & Martin Crane & Tai Tan Mai & Stanis{l}aw Dro.zd.z, 2022. "Analysis of inter-transaction time fluctuations in the cryptocurrency market," Papers 2206.07831, arXiv.org, revised Sep 2022.
    48. Drożdż, S. & Grümmer, F. & Ruf, F. & Speth, J., 2003. "Log-periodic self-similarity: an emerging financial law?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 174-182.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Nick James & Max Menzies, 2023. "An exploration of the mathematical structure and behavioural biases of 21st century financial crises," Papers 2307.15402, arXiv.org, revised Sep 2023.
    2. Nick James & Max Menzies, 2023. "Collective dynamics, diversification and optimal portfolio construction for cryptocurrencies," Papers 2304.08902, arXiv.org, revised Jun 2023.
    3. James, Nick & Menzies, Max & Chin, Kevin, 2022. "Economic state classification and portfolio optimisation with application to stagflationary environments," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    4. James, Nick & Menzies, Max & Gottwald, Georg A., 2022. "On financial market correlation structures and diversification benefits across and within equity sectors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 604(C).
    5. Nick James & Max Menzies, 2021. "Collective correlations, dynamics, and behavioural inconsistencies of the cryptocurrency market over time," Papers 2107.13926, arXiv.org, revised Dec 2021.
    6. Nick James & Max Menzies & Kevin Chin, 2022. "Economic state classification and portfolio optimisation with application to stagflationary environments," Papers 2203.15911, arXiv.org, revised Sep 2022.
    7. James, Nick & Menzies, Max, 2023. "Collective infectivity of the pandemic over time and association with vaccine coverage and economic development," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    8. Nick James, 2021. "Evolutionary correlation, regime switching, spectral dynamics and optimal trading strategies for cryptocurrencies and equities," Papers 2112.15321, arXiv.org, revised Mar 2022.
    9. James, Nick & Chin, Kevin, 2022. "On the systemic nature of global inflation, its association with equity markets and financial portfolio implications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 593(C).
    10. Stanis{l}aw Dro.zd.z & Jaros{l}aw Kwapie'n & Marcin Wk{a}torek, 2023. "What is mature and what is still emerging in the cryptocurrency market?," Papers 2305.05751, arXiv.org.
    11. James, Nick, 2021. "Dynamics, behaviours, and anomaly persistence in cryptocurrencies and equities surrounding COVID-19," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 570(C).
    12. James, Nick & Menzies, Max & Chok, James & Milner, Aaron & Milner, Cas, 2023. "Geometric persistence and distributional trends in worldwide terrorism," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    13. Nick James, 2021. "Dynamics, behaviours, and anomaly persistence in cryptocurrencies and equities surrounding COVID-19," Papers 2101.00576, arXiv.org, revised Feb 2021.
    14. Nick James & Kevin Chin, 2021. "On the systemic nature of global inflation, its association with equity markets and financial portfolio implications," Papers 2111.11022, arXiv.org, revised Jan 2022.
    15. Nick James & Max Menzies & Georg A. Gottwald, 2022. "On financial market correlation structures and diversification benefits across and within equity sectors," Papers 2202.10623, arXiv.org, revised Jun 2022.
    16. Marcin Wk{a}torek & Jaros{l}aw Kwapie'n & Stanis{l}aw Dro.zd.z, 2023. "Cryptocurrencies Are Becoming Part of the World Global Financial Market," Papers 2303.00495, arXiv.org.
    17. BAUWENS, Luc & HAFNER, Christian & LAURENT, Sébastien, 2011. "Volatility models," LIDAM Discussion Papers CORE 2011058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
      • Bauwens, L. & Hafner, C. & Laurent, S., 2012. "Volatility Models," LIDAM Reprints ISBA 2012028, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
      • Bauwens, L. & Hafner C. & Laurent, S., 2011. "Volatility Models," LIDAM Discussion Papers ISBA 2011044, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    18. José Antonio Núñez-Mora & Roberto Joaquín Santillán-Salgado & Mario Iván Contreras-Valdez, 2022. "COVID Asymmetric Impact on the Risk Premium of Developed and Emerging Countries’ Stock Markets," Mathematics, MDPI, vol. 10(9), pages 1-36, April.
    19. Zhang, Yue-Jun & Yao, Ting & He, Ling-Yun & Ripple, Ronald, 2019. "Volatility forecasting of crude oil market: Can the regime switching GARCH model beat the single-regime GARCH models?," International Review of Economics & Finance, Elsevier, vol. 59(C), pages 302-317.
    20. Charfeddine, Lanouar, 2016. "Breaks or long range dependence in the energy futures volatility: Out-of-sample forecasting and VaR analysis," Economic Modelling, Elsevier, vol. 53(C), pages 354-374.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:630:y:2023:i:c:s0378437123008117. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.