A minimum spanning tree analysis of the Polish stock market

• Authors: Artur F. Tomeczek

Abstracts

EN

Aim/purpose - This article aims to explore the network topology of the stock market in Poland during the COVID-19 pandemic. Design/methodology/approach - Kruskal's algorithm was used to find the minimum spanning trees (MST) of three undirected correlation networks: MST1 (December 2019 - August 2021), MST2 (February 2020 - April 2020), and MST3 (June 2021 - August 2021). There were123 firms included in all three networks representing three key indexes (WIG20, mWIG40, and sWIG80). Findings - The comovements of stock prices varied between various periods of the pandemic. The most central firms in Poland were PEO, UNT, SPL, PKO, KGH, CCC, and PZU. WIG20 was the most influential stock index for all networks. During the turbulent period represented by MST2, many of Poland's largest companies have clustered around KGH at the center of the network. In contrast, MST3 is the least compact of the three networks and is characterized by the absence of a single strongly influential node. Research implications/limitations - Correlation networks are efficient at quantitatively describing the degree of interdependence of a stock. MST finding algorithms are a crucial method of analysis for correlation networks. However, a limitation of the study, inherent to undirected correlation networks, is the inability to determine the direction of influence that stocks have on each other. Originality/value/contribution - The results of the article contribute to the economic analysis of stock markets in several ways. First, it expands on Gałązka (2011) by including additional centralities and the dynamic aspect of changes in the topology during the COVID-19 pandemic. Second, it broadens the MST-based empirical research of stock markets by showing the emergence of the star topology during the period of high uncertainty in Poland. Third, it has practical applications for systemic risk assessment and portfolio diversification.

Keywords

EN

network analysis; minimum spanning tree; correlation network; stock market; COVID-19; Poland

• Publisher: Uniwersytet Ekonomiczny w Katowicach
• Journal: Journal of Economics and Management
• Year: 2022
• Volume: 44

Dates

published

2022

Contributors

author

Artur F. Tomeczek

• Szkoła Główna Handlowa w Warszawie: Kolegium Gospodarki Światowej

References

• Allen, F., Hryckiewicz, A., Kowalewski, O., & Tümer-Alkan, G. (2014). Transmission of financial shocks in loan and deposit markets: Role of interbank borrowing and market monitoring. Journal of Financial Stability, 15, 112-126. https://doi.org/ 10.1016/j.jfs.2014.09.005
• Ando, M., & Hayakawa, K. (2022). Impact of COVID-19 on trade in services. Japan and the World Economy, 62, 101131. https://doi.org/10.1016/j.japwor.2022.101131
• Ashraf, B. N. (2020). Stock markets' reaction to COVID-19: Cases or fatalities? Research in International Business and Finance, 54, 101249. https://doi.org/10. 1016/j.ribaf.2020.101249
• Balci, M. A., Akgüller, Ö., & Güzel, S. C. (2021). Hierarchies in communities of UK stock market from the perspective of Brexit. Journal of Applied Statistics, 48(13-15), 2607-2625. https://doi.org/10.1080/02664763.2020.1796942
• Battiston, S., Caldarelli, G., May, R. M., Roukny, T., & Stiglitz, J. E. (2016). The price of complexity in financial networks. Proceedings of the National Academy of Sciences, 113(36), 10031-10036. https://doi.org/10.1073/pnas.1521573113
• Billio, M., Getmansky, M., Lo, A. W., & Pelizzon, L. (2012). Econometric measures of connectedness and systemic risk in the finance and insurance sectors. Journal of Financial Economics, 104(3), 535-559. https://doi.org/10.1016/j.jfineco.2011.12.010
• Birch, J., Pantelous, A. A., & Soramäki, K. (2016). Analysis of correlation based networks representing DAX 30 stock price returns. Computational Economics, 47(4), 501-525. https://doi.org/10.1007/s10614-015-9481
• Brancaccio, E., Giammetti, R., Lopreite, M., & Puliga, M. (2018). Centralization of capital and financial crisis: A global network analysis of corporate control. Structural Change and Economic Dynamics, 45, 94-104. https://doi.org/10.1016/j.strueco. 2018.03.001
• Brandes, U. (2001). A faster algorithm for betweenness centrality. The Journal of Mathematical Sociology, 25(2), 163-177. https://doi.org/10.1080/0022250X.2001.9990249
• Brandes, U., & Erlebach, T. (Eds.). (2005). Network analysis: Methodological foundations. Springer.
• Brookfield, D., Boussabaine, H., & Su, C. (2013). Identifying reference companies using the book-to-market ratio: A minimum spanning tree approach. The European Journal of Finance, 19(6), 466-490. https://doi.org/10.1080/1351847X.2011.637571
• Brzeszczyński, J., Gajdka, J., Schabek, T., & Kutan, A. M. (2021). Central bank's communication and markets' reactions: Polish evidence. International Journal of Emerging Markets. https://doi.org/10.1108/IJOEM-09-2020-1061
• BvD. (2022). Orbis database. https://orbis.bvdinfo.com/
• Coelho, R., Gilmore, C. G., Lucey, B., Richmond, P., & Hutzler, S. (2007). The evolution of interdependence in world equity markets - evidence from minimum spanning trees. Physica A: Statistical Mechanics and Its Applications, 376, 455-466. https://doi.org/10.1016/j.physa.2006.10.045
• Danko, J., & Šoltés, V. (2018). Portfolio creation using graph characteristics. Investment Management and Financial Innovations, 15(1), 180-189. https://doi.org/10.21511/ imfi.15(1).2018.16
• Danko, J., Šoltés, V., & Bindzar, T. (2022). Portfolio creation using graph characteristics and testing its performance. Montenegrin Journal of Economics, 18(1), 7-17. https://doi.org/10.14254/1800-5845/2022.18-1.1
• Dastkhan, H., & Shams Gharneh, N. (2016). Determination of systemically important companies with cross-shareholding network analysis: A case study from an emerging market. International Journal of Financial Studies, 4(3), 13. https://doi.org/ 10.3390/ijfs4030013
• Denkowska, A., & Wanat, S. (2020). A tail dependence-based MST and their topological indicators in modeling systemic risk in the European insurance sector. Risks, 8(2), 39. https://doi.org/10.3390/risks8020039
• Diab-Bahman, R., & Al-Enzi, A. (2020). The impact of COVID-19 pandemic on conventional work settings. International Journal of Sociology and Social Policy, 40(9/10), 909-927. https://doi.org/10.1108/IJSSP-07-2020-0262
• Dias, J. (2012). Sovereign debt crisis in the European Union: A minimum spanning tree approach. Physica A: Statistical Mechanics and Its Applications, 391(5), 2046- 2055. https://doi.org/10.1016/j.physa.2011.11.004
• Dungey, M., Luciani, M., & Veredas, D. (2012). Ranking systemically important financial institutions (Discussion Paper, No. 12-115/IV/DSF44). Tinbergen Institute. http://hdl.handle.net/10419/87503
• Dwivedi, Y. K., Hughes, D. L., Coombs, C., Constantiou, I., Duan, Y., Edwards, J. S., Gupta, B., Lal, B., Misra, S., Prashant, P., Raman, R., Rana, N. P., Sharma, S. K., & Upadhyay, N. (2020). Impact of COVID-19 pandemic on information management research and practice: Transforming education, work and life. International Journal of Information Management, 55, 102211. https://doi.org/10.1016/j.ijinfo mgt.2020.102211
• Dzicher, M. (2021). Sampling methods for investment portfolio formulation procedure at increased market volatility. Journal of Economics and Management, 43, 70-89. https://doi.org/10.22367/jem.2021.43.04
• EquityRT. (2021). EquityRT database. https://www.equityrt.com/
• Euler, L. (1953). Leonhard Euler and the Koenigsberg bridges. Scientific American, 189(1), 66-70. https://doi.org/10.1038/scientificamerican0753-66
• Galanti, T., Guidetti, G., Mazzei, E., Zappalà, S., & Toscano, F. (2021). Work from home during the CODIV-19 outbreak: The impact on employees' remote work productivity, engagement and stress. Journal of Occupational & Environmental Medicine, 63(7), 426-432. https://doi.org/10.1097/JOM.0000000000002236
• Gałązka, M. (2011). Characteristics of the Polish Stock Market correlations. International Review of Financial Analysis, 20(1), 1-5. https://doi.org/10.1016/j.irfa.2010.11.002
• Gan, S. L., & Djauhari, M. A. (2015). New York Stock Exchange performance: Evidence from the forest of multidimensional minimum spanning trees. Journal of Statistical Mechanics: Theory and Experiment, 2015(12), P12005. https://doi.org/10. 1088/1742-5468/2015/12/P12005
• Garas, A., & Argyrakis, P. (2007). Correlation study of the Athens Stock Exchange. Physica A: Statistical Mechanics and Its Applications, 380, 399-410. https://doi. org/10.1016/j.physa.2007.02.097
• Giemza, D. (2021). Ranking of optimal stock portfolios determined on the basis of expected utility maximization criterion. Journal of Economics and Management, 43, 154-178. https://doi.org/10.22367/jem.2021.43.08
• Gilmore, C. G., Lucey, B. M., & Boscia, M. W. (2010). Comovements in government bond markets: A minimum spanning tree analysis. Physica A: Statistical Mechanics and Its Applications, 389(21), 4875-4886. https://doi.org/10.1016/j.physa.2010.06.057
• Goodfellow, C., Bohl, M. T., & Gebka, B. (2009). Together we invest? Individual and institutional investors' trading behaviour in Poland. International Review of Financial Analysis, 18(4), 212-221. https://doi.org/10.1016/j.irfa.2009.03.002
• GPW. (2021). List of companies. https://www.gpw.pl/list-of-companies
• Graham, R. L., & Hell, P. (1985). On the history of the minimum spanning tree problem. IEEE Annals of the History of Computing, 7(1), 43-57. https://doi.org/10.1109/ MAHC.1985.10011
• Gruszczyński, M. (2006). Corporate governance and financial performance of companies in Poland. International Advances in Economic Research, 12(2), 251-259. https:// doi.org/10.1007/s11294-006-9007-5
• Hayakawa, K., & Mukunoki, H. (2021). The impact of COVID-19 on international trade: Evidence from the first shock. Journal of the Japanese and International Economies, 60, 101135. https://doi.org/10.1016/j.jjie.2021.101135
• He, Q., Liu, J., Wang, S., & Yu, J. (2020). The impact of COVID-19 on stock markets. Economic and Political Studies, 8(3), 275-288. https://doi.org/10.1080/20954816. 2020.1757570
• Huang, W.-Q., Zhuang, X.-T., & Yao, S. (2009). A network analysis of the Chinese stock market. Physica A: Statistical Mechanics and Its Applications, 388(14), 2956-2964. https://doi.org/10.1016/j.physa.2009.03.028
• Jang, W., Lee, J., & Chang, W. (2011). Currency crises and the evolution of foreign exchange market: Evidence from minimum spanning tree. Physica A: Statistical Mechanics and Its Applications, 390(4), 707-718. https://doi.org/10.1016/j.physa. 2010.10.028
• Jung, W.-S., Chae, S., Yang, J.-S., & Moon, H.-T. (2006). Characteristics of the Korean stock market correlations. Physica A: Statistical Mechanics and Its Applications, 361(1), 263-271. https://doi.org/10.1016/j.physa.2005.06.081
• Kanno, M. (2019). Network structures and credit risk in cross-shareholdings among listed Japanese companies. Japan and the World Economy, 49, 17-31. https://doi. org/10.1016/j.japwor.2018.09.003
• Kanno, M. (2021). Risk contagion of COVID-19 in Japanese firms: A network approach. Research in International Business and Finance, 58, 101491. https://doi.org/10. 1016/j.ribaf.2021.101491
• Kazemilari, M., Mardani, A., Streimikiene, D., & Zavadskas, E. K. (2017). An overview of renewable energy companies in stock exchange: Evidence from minimal spanning tree approach. Renewable Energy, 102, 107-117. https://doi.org/10.1016/j.renene. 2016.10.029
• Konopczak, M., Sieradzki, R., & Wiernicki, M. (2010). Kryzys na światowych rynkach finansowych - wpływ na rynek finansowy w Polsce oraz implikacje dla sektora realnego. Bank i Kredyt, 41(6), 45-70. https://bankandcredit.nbp.pl/content/2010/06/ bik_06_2010_02_art.pdf
• Kruskal, J. B. (1956). On the shortest spanning subtree of a graph and the traveling salesman problem. Proceedings of the American Mathematical Society, 7(1), 48-50. https://doi.org/10.1090/S0002-9939-1956-0078686-7
• Kwon, O., & Yang, J.-S. (2008). Information flow between stock indices. Europhysics Letters, 82(6), 68003. https://doi.org/10.1209/0295-5075/82/68003
• Lee, J., Youn, J., & Chang, W. (2012). Intraday volatility and network topological properties in the Korean stock market. Physica A: Statistical Mechanics and Its Applications, 391(4), 1354-1360. https://doi.org/10.1016/j.physa.2011.09.016
• Lee, T. K., Cho, J. H., Kwon, D. S., & Sohn, S. Y. (2019). Global stock market investment strategies based on financial network indicators using machine learning techniques. Expert Systems with Applications, 117, 228-242. https://doi.org/10.1016/ j.eswa.2018.09.005
• Li, H., An, H., Gao, X., Huang, J., & Xu, Q. (2014). On the topological properties of the cross-shareholding networks of listed companies in China: Taking shareholders' cross-shareholding relationships into account. Physica A: Statistical Mechanics and Its Applications, 406, 80-88. https://doi.org/10.1016/j.physa.2014.03.041
• Li, H., & Majerowska, E. (2008). Testing stock market linkages for Poland and Hungary: A multivariate GARCH approach. Research in International Business and Finance, 22(3), 247-266. https://doi.org/10.1016/j.ribaf.2007.06.001
• Liu, H. Y., Manzoor, A., Wang, C. Y., Zhang, L., & Manzoor, Z. (2020). The COVID-19 outbreak and affected countries stock markets response. International Journal of Environmental Research and Public Health, 17(8), 2800. https://doi.org/10.3390/ ijerph17082800
• Long, H., Zhang, J., & Tang, N. (2017). Does network topology influence systemic risk contribution? A perspective from the industry indices in Chinese stock market. PLOS ONE, 12(7), e0180382. https://doi.org/10.1371/journal.pone.0180382
• Luo, Y., Xiong, J., Dong, L. G., & Tang, Y. (2015). Statistical correlation properties of the SHIBOR interbank lending market. China Finance Review International, 5(2), 91-102. https://doi.org/10.1108/CFRI-08-2014-0036
• Ma, Y., Zhuang, X., & Li, L. (2011). Research on the relationships of the domestic mutual investment of China based on the cross-shareholding networks of the listed companies. Physica A: Statistical Mechanics and Its Applications, 390(4), 749-759. https://doi.org/10.1016/j.physa.2010.10.042
• Mantegna, R. N. (1999). Hierarchical structure in financial markets. The European Physical Journal B, 11(1), 193-197. https://doi.org/10.1007/s100510050929
• Markowitz, H. M. (1952). Portfolio selection. The Journal of Finance, 7(1), 77-91. https://doi.org/10.2307/2975974
• Markowitz, H. M. (1991). Foundations of portfolio theory. The Journal of Finance, 46(2), 469-477. https://doi.org/10.1111/j.1540-6261.1991.tb02669.x
• Memon, B. A., & Yao, H. (2021). The impact of COVID-19 on the dynamic topology and network flow of world stock markets. Journal of Open Innovation: Technology, Market, and Complexity, 7(4), 241. https://doi.org/10.3390/joitmc7040241
• Memon, B. A., Yao, H., & Tahir, R. (2020). General election effect on the network topology of Pakistan's stock market: Network-based study of a political event. Financial Innovation, 6, 2. https://doi.org/10.1186/s40854-019-0165-x
• Miccichè, S., Bonanno, G., Lillo, F., & Mantegna, R. N. (2003). Degree stability of a minimum spanning tree of price return and volatility. Physica A: Statistical Mechanics and Its Applications, 324(1/2), 66-73. https://doi.org/10.1016/S0378-4371(03)00002-5
• Nešetřil, J., Milková, E., & Nešetřilová, H. (2001). Otakar Borůvka on minimum spanning tree problem. Translation of both the 1926 papers, comments, history. Discrete Mathematics, 233(1/3), 3-36. https://doi.org/10.1016/S0012-365X(00)00224-7
• Nobi, A., Maeng, S. E., Ha, G. G., & Lee, J. W. (2014). Effects of global financial crisis on network structure in a local stock market. Physica A: Statistical Mechanics and Its Applications, 407, 135-143. https://doi.org/10.1016/j.physa.2014.03.083
• Nyga-Łukaszewska, H., & Aruga, K. (2020). Energy prices and COVID-immunity: The case of crude oil and natural gas prices in the US and Japan. Energies, 13(23), 6300. https://doi.org/10.3390/en13236300
• Onnela, J.-P., Chakraborti, A., Kaski, K., & Kertész, J. (2003a). Dynamic asset trees and Black Monday. Physica A: Statistical Mechanics and Its Applications, 324(1/2), 247-252. https://doi.org/10.1016/S0378-4371(02)01882-4
• Onnela, J.-P., Chakraborti, A., Kaski, K., Kertész, J., & Kanto, A. (2003b). Dynamics of market correlations: Taxonomy and portfolio analysis. Physical Review E, 68(5), 056110. https://doi.org/10.1103/PhysRevE.68.056110
• Pang, R. K.-K., Granados, O. M., Chhajer, H., & Legara, E. F. T. (2021). An analysis of network filtering methods to sovereign bond yields during COVID-19. Physica A: Statistical Mechanics and Its Applications, 574, 125995. https://doi.org/10.1016/ j.physa.2021.125995
• Prim, R. C. (1957). Shortest connection networks and some generalizations. Bell System Technical Journal, 36(6), 1389-1401. https://doi.org/10.1002/j.1538-7305.1957.tb 01515.x
• Roy, R. B., & Sarkar, U. K. (2013). A social network approach to change detection in the interdependence structure of global stock markets. Social Network Analysis and Mining, 3, 269-283. https://doi.org/10.1007/s13278-012-0063-y
• Rutkowska-Ziarko, A., & Markowski, L. (2022). Accounting and market risk measures of Polish energy companies. Energies, 15(6), 2138. https://doi.org/10.3390/en1 5062138
• Scheicher, M. (2001). The comovements of stock markets in Hungary, Poland and the Czech Republic. International Journal of Finance & Economics, 6(1), 27-39. https://doi.org/10.1002/ijfe.141
• Sum, K. (2016). A review of individual and systemic risk measures in terms of applicability for banking regulations. Contemporary Economics, 10(1), 71-82. https:// doi.org/10.5709/ce.1897-9254.199
• Szyszka, A. (2011). The genesis of the 2008 global financial crisis and challenges to the neoclassical paradigm of finance. Global Finance Journal, 22(3), 211-216. https:// doi.org/10.1016/j.gfj.2011.10.011
• Tang, Y., Xiong, J. J., Luo, Y., & Zhang, Y.-C. (2019). How do the global stock markets influence one another? Evidence from finance big data and Granger causality directed network. International Journal of Electronic Commerce, 23(1), 85-109. https://doi.org/10.1080/10864415.2018.1512283
• Tomeczek, A. F. (2021). A financial network analysis of the equity linkages in Poland. Research Papers of Wroclaw University of Economics, 65(4), 129-143. https://doi. org/10.15611/pn.2021.4.08
• Tomeczek, A. F. (2022). The evolution of Japanese keiretsu networks: A review and text network analysis of their perceptions in economics. Japan and the World Economy, 62, 101132. https://doi.org/10.1016/j.japwor.2022.101132
• Tumminello, M., Coronnello, C., Lillo, F., Miccichè, S., & Mantegna, R. N. (2007). Spanning trees and bootstrap reliability estimation in correlation-based networks. International Journal of Bifurcation and Chaos, 17(7), 2319-2329. https://doi.org/10.1142/S0218127407018415
• Vitali, S., Glattfelder, J. B., & Battiston, S. (2011). The network of global corporate control. PLoS ONE, 6(10), e25995. https://doi.org/10.1371/journal.pone.0025995
• Wang, G.-J., Xie, C., & Chen, S. (2017). Multiscale correlation networks analysis of the US stock market: A wavelet analysis. Journal of Economic Interaction and Coordination, 12, 561-594. https://doi.org/10.1007/s11403-016-0176-x
• Wang, G.-J., Xie, C., Han, F., & Sun, B. (2012). Similarity measure and topology evolution of foreign exchange markets using dynamic time warping method: Evidence from minimal spanning tree. Physica A: Statistical Mechanics and Its Applications, 391(16), 4136-4146. https://doi.org/10.1016/j.physa.2012.03.036
• Wang, G.-J., Xie, C., & Stanley, H. E. (2018). Correlation structure and evolution of world stock markets: Evidence from Pearson and partial correlation-based networks. Computational Economics, 51, 607-635. https://doi.org/10.1007/s10614-016-9627-7
• Waszczuk, A. (2013). A risk-based explanation of return patterns - evidence from the Polish stock market. Emerging Markets Review, 15, 186-210. https://doi.org/10. 1016/j.ememar.2012.12.002
• Wiliński, M., Sienkiewicz, A., Gubiec, T., Kutner, R., & Struzik, Z. R. (2013). Structural and topological phase transitions on the German Stock Exchange. Physica A: Statistical Mechanics and Its Applications, 392(23), 5963-5973. https://doi.org/10. 1016/j.physa.2013.07.064
• Witkowska, D., Kompa, K., & Staszak, M. (2021). Indicators for the efficient portfolio construction. The case of Poland. Procedia Computer Science, 192, 2022-2031. https://doi.org/10.1016/j.procs.2021.08.208
• Wnuczak, P. (2021). Profitability of investment strategies developed on the basis of buy and sell recommendations. Journal of Economics and Management, 43, 317-338. https://doi.org/10.22367/jem.2021.43.15
• Yin, K., Liu, Z., & Liu, P. (2017). Trend analysis of global stock market linkage based on a dynamic conditional correlation network. Journal of Business Economics and Management, 18(4), 779-800. https://doi.org/10.3846/16111699.2017.1341849
• Yun, T.-S., Jeong, D., & Park, S. (2019). "Too central to fail" systemic risk measure using PageRank algorithm. Journal of Economic Behavior & Organization, 162, 251-272. https://doi.org/10.1016/j.jebo.2018.12.021
• Ziemba, E. W., & Eisenbardt, M. (2021). The effect of the Covid-19 pandemic on ICT usage by academics. Journal of Computer Information Systems, 62(6), 1154-1168. https://doi.org/10.1080/08874417.2021.1992806

Identifiers

DOI

10.22367/jem.2022.44.17

Biblioteka Nauki

2159034