{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,21]],"date-time":"2025-10-21T03:28:33Z","timestamp":1761017313994,"version":"build-2065373602"},"reference-count":54,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2020,8,29]],"date-time":"2020-08-29T00:00:00Z","timestamp":1598659200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100014440","name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","doi-asserted-by":"publisher","award":["PGC2018- 101555-B-I00E"],"award-info":[{"award-number":["PGC2018- 101555-B-I00E"]}],"id":[{"id":"10.13039\/100014440","id-type":"DOI","asserted-by":"publisher"}]},{"name":"UAL\/CECEU\/FEDER","award":["UAL18-FQM-B038-A"],"award-info":[{"award-number":["UAL18-FQM-B038-A"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>One of the main contributions of the Capital Assets Pricing Model (CAPM) to portfolio theory was to explain the correlation between assets through its relationship with the market index. According to this approach, the market index is expected to explain the co-movement between two different stocks to a great extent. In this paper, we try to verify this hypothesis using a sample of 3.000 stocks of the USA market (attending to liquidity, capitalization, and free float criteria) by using some functions inspired by cooperative dynamics in physical particle systems. We will show that all of the co-movement among the stocks is completely explained by the market, even without considering the market beta of the stocks.<\/jats:p>","DOI":"10.3390\/e22090954","type":"journal-article","created":{"date-parts":[[2020,8,30]],"date-time":"2020-08-30T06:06:22Z","timestamp":1598767582000},"page":"954","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["A New Look on Financial Markets Co-Movement through Cooperative Dynamics in Many-Body Physics"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9892-5006","authenticated-orcid":false,"given":"Mar\u00eda","family":"L\u00f3pez-Garc\u00eda","sequence":"first","affiliation":[{"name":"Department of Economics and Business, University of Almer\u00eda, 04120 Almer\u00eda, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9153-8321","authenticated-orcid":false,"given":"Miguel","family":"S\u00e1nchez-Granero","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Almer\u00eda, 04120 Almer\u00eda, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5017-2615","authenticated-orcid":false,"given":"Juan","family":"Trinidad-Segovia","sequence":"additional","affiliation":[{"name":"Department of Economics and Business, University of Almer\u00eda, 04120 Almer\u00eda, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4127-1424","authenticated-orcid":false,"given":"Antonio","family":"Puertas","sequence":"additional","affiliation":[{"name":"Department of Chemistry and Physics, University of Almer\u00eda, 04120 Almer\u00eda, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1128-6123","authenticated-orcid":false,"given":"Francisco","family":"Nieves","sequence":"additional","affiliation":[{"name":"Department of Chemistry and Physics, University of Almer\u00eda, 04120 Almer\u00eda, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2020,8,29]]},"reference":[{"key":"ref_1","first-page":"425","article-title":"Capital Asset Prices: A theory of market equilibrium under conditions of risk","volume":"19","author":"Sharpe","year":"1964","journal-title":"J. Financ."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"13","DOI":"10.2307\/1924119","article-title":"The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets","volume":"47","author":"Lintner","year":"1965","journal-title":"Rev. Econ. Stat."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"444","DOI":"10.1086\/295472","article-title":"Capital Market Equilibrium with Restricted Borrowing","volume":"45","author":"Black","year":"1972","journal-title":"J. Bus."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"8","DOI":"10.3905\/jpm.1993.409462","article-title":"Beta and returns","volume":"20","author":"Black","year":"1993","journal-title":"J. Portf. Manag. Fall"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.1540-6261.1971.tb00584.x","article-title":"On the assessment f risk","volume":"26","author":"Blume","year":"1971","journal-title":"J. Financ."},{"key":"ref_6","first-page":"79","article-title":"The capital asset pricing model: Some empirical tests","volume":"81","author":"Black","year":"1972","journal-title":"Stud. Theory Cap. Mark."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1086\/260061","article-title":"Risk, Return, and Equilibrium: Empirical Tests","volume":"81","author":"Fama","year":"1973","journal-title":"J. Political Econ."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1086\/294847","article-title":"Market and Industry Factors in Stock Price Behavior","volume":"39","author":"King","year":"1966","journal-title":"J. Bus."},{"key":"ref_9","first-page":"695","article-title":"A Re-Examination of Market and Industry Factors in Stock Price Behavior","volume":"28","author":"Meyers","year":"1973","journal-title":"J. Financ."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/0304-405X(81)90018-0","article-title":"The relationship between return and market value of common stocks","volume":"9","author":"Banz","year":"1981","journal-title":"J. Financ. Econ."},{"key":"ref_11","first-page":"541","article-title":"\u00a0R2","volume":"43","author":"Roll","year":"1988","journal-title":"J. Financ."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1111\/j.1540-6261.1988.tb03952.x","article-title":"Debt\/Equity Ratio and Expected Common Stock Returns: Empirical Evidence","volume":"43","author":"Bhandari","year":"1988","journal-title":"J. Financ."},{"key":"ref_13","first-page":"25","article-title":"Book values and stocks returns","volume":"4","author":"Stattman","year":"1980","journal-title":"Chic. MBA J. Sel. Pap."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"9","DOI":"10.3905\/jpm.1985.409007","article-title":"Persuasive Evidence of Market Inefficiency","volume":"11","author":"Rosenberg","year":"1985","journal-title":"J. Portf. Manag."},{"key":"ref_15","first-page":"427","article-title":"The Cross-Section of Expected Stock Returns","volume":"47","author":"Fama","year":"1992","journal-title":"J. Financ."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1080\/135184799337046","article-title":"Is beta still alive? Conclusive evidence from the Swiss stock market","volume":"5","author":"Isakov","year":"1999","journal-title":"Eur. J. Financ."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"101","DOI":"10.2307\/2331255","article-title":"The Conditional Relation between Beta and Returns","volume":"30","author":"Pettengill","year":"1995","journal-title":"J. Financ. Quant. Anal."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/0304-405X(93)90003-T","article-title":"Institutional trades and intraday stock price behavior","volume":"33","author":"Chan","year":"1993","journal-title":"J. Financ. Econ."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"36","DOI":"10.3905\/jpm.1996.409557","article-title":"Reports of beta\u2019s death have been greatly exaggerated","volume":"22","author":"Grundy","year":"1996","journal-title":"J. Portf. Manag."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"L\u00f3pez-Garc\u00eda, M.N., Trinidad-Segovia, J.E., S\u00e1nchez-Granero, M.A., and Pouchkarev, I. (2020). Extending the Fama and French model with a long term memory factor. Eur. J. Oper. Res., in press.","DOI":"10.1016\/j.ejor.2019.07.071"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1016\/j.finmar.2005.06.001","article-title":"Liquidity commonality and return co-movement","volume":"8","author":"Domowitz","year":"2005","journal-title":"J. Financ. Mark."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"500","DOI":"10.1016\/j.jbankfin.2019.07.018","article-title":"Decomposing global yield curve co-movement","volume":"106","author":"Byrne","year":"2019","journal-title":"J. Bank. Financ."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/S0304-405X(00)00071-4","article-title":"The information content of stock markets: Why do emerging markets have synchronous stock price movements?","volume":"58","author":"Morck","year":"2000","journal-title":"J. Financ. Econ."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.jempfin.2017.06.004","article-title":"International Stock market Comovement Time Scale Outlined A Thick Pen","volume":"43","author":"Jach","year":"2017","journal-title":"J. Empir. Financ."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/j.jbankfin.2017.09.019","article-title":"Return comovement","volume":"112","author":"Parsley","year":"2020","journal-title":"J. Bank. Financ."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1299","DOI":"10.1016\/j.jimonfin.2005.08.016","article-title":"Explaining co-movements between stock markets: The case of US and Germany","volume":"24","author":"Bonfiglioli","year":"2005","journal-title":"J. Int. Money Financ."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"632","DOI":"10.1016\/j.jempfin.2009.02.002","article-title":"International comovement of stock market returns: A wavelet analysis","volume":"16","author":"Rua","year":"2009","journal-title":"J. Empir. Financ."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1016\/j.qref.2012.07.005","article-title":"Co-movement of oil and stock prices in the GCC region: A wavelet analysis","volume":"52","author":"Akoum","year":"2012","journal-title":"Q. Rev. Econ. Financ."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1016\/j.jpolmod.2011.10.005","article-title":"Modelling oil prices and exchange rates co-movements","volume":"34","author":"Reboredo","year":"2012","journal-title":"J. Policy Model."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1002\/ijfe.448","article-title":"International stock market indices comovements: A new look","volume":"17","author":"Magdaleno","year":"2012","journal-title":"Int. J. Financ. Econ."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ribaf.2013.01.001","article-title":"Co-movement of Asia-Pacific with European and US stock market returns: A cross-time-frequency analysis","volume":"29","author":"Loh","year":"2013","journal-title":"Res. Int. Bus. Financ."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"35","DOI":"10.2469\/faj.v56.n5.2388","article-title":"The rise of sector effects in major equity markets","volume":"56","author":"Baca","year":"2000","journal-title":"Financ. Anal. J."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"41","DOI":"10.2469\/faj.v56.n5.2389","article-title":"The increasing importance of industry factors","volume":"56","author":"Cavaglia","year":"2000","journal-title":"Financ. Anal. J."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1016\/S0304-405X(98)00041-5","article-title":"Another look at the role of industrial structure of markets for international diversification strategies","volume":"50","author":"Griffin","year":"1998","journal-title":"J. Financ. Econ."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"70","DOI":"10.3905\/jpm.2002.319856","article-title":"Country, industry and risk factor loadings in portfolio management","volume":"28","author":"Sy","year":"2002","journal-title":"J. Portf. Manag."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1007\/s10679-006-6979-1","article-title":"Firm-Level Evidence on International Stock Market Comovement","volume":"10","author":"Brooks","year":"2006","journal-title":"Rev. Financ."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/j.econlet.2013.04.004","article-title":"Dynamic Co-movements of Stock Market Returns, Implied Volatility and Policy Uncertainty","volume":"120","author":"Antonakakis","year":"2013","journal-title":"Econ. Lett."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1016\/j.frl.2012.05.002","article-title":"Spatial Modeling of Stock Market Comovements","volume":"9","author":"Montero","year":"2012","journal-title":"Financ. Res. Lett."},{"key":"ref_39","first-page":"645","article-title":"Measuring Comovements by Regression Quantiles","volume":"12","author":"Cappiello","year":"2014","journal-title":"J. Financ. Econom."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1954","DOI":"10.1016\/j.jbankfin.2011.01.003","article-title":"Dependence structure and extreme comovements in international equity and bond markets","volume":"35","author":"Garcia","year":"2011","journal-title":"J. Bank. Financ."},{"key":"ref_41","first-page":"1207","article-title":"Extreme downside risk co-movement in commodity markets during distress periods: A multidimensional scaling approach","volume":"12","author":"Montero","year":"2020","journal-title":"Eur. J. Financ."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Ramos Requena, J.P., Trinidad Segovia, J.E., and S\u00e1nchez Granero, M.A. (2020). An Alternative Approach to Measure Co-Movement between Two Time Series. Mathematics, 8.","DOI":"10.3390\/math8020261"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"068301","DOI":"10.1103\/PhysRevLett.118.068301","article-title":"Diffusive and arrestedlike dynamics in currency exchange markets","volume":"118","author":"Puertas","year":"2017","journal-title":"Phys. Rev. Lett."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"S\u00e1nchez-Granero, M.A., Trinidad-Segovia, J.E., Clara-Rahola, J., Puertas, A.M., and de las Nieves, F.J. (2017). A model for foreign exchange markets based on glassy Brownian systems. PLoS ONE, 12.","DOI":"10.1371\/journal.pone.0188814"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"032307","DOI":"10.1103\/PhysRevE.101.032307","article-title":"Stock markets: A view from soft matter","volume":"101","author":"Puertas","year":"2020","journal-title":"Phys. Rev. E"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"5064","DOI":"10.1103\/PhysRevLett.82.5064","article-title":"Growing spatial correlations of particle displacements in a simulated liquid on cooling toward the glass transition","volume":"82","author":"Donati","year":"1999","journal-title":"Phys. Rev. Lett."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Cates, M.E., and Evans, M.R. (2000). Soft and Fragile Matter, Nonequilibrium Dynamics, Metastability and Flow, Institute of Physics.","DOI":"10.1887\/0750307242"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"627","DOI":"10.1126\/science.287.5453.627","article-title":"Three-dimensional direct imaging of structural relaxation near the colloidal glass transition","volume":"287","author":"Weeks","year":"2000","journal-title":"Science"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1063\/1.480541","article-title":"Time dependent, four-point density correlation function description of dynamical heterogeneity and decoupling in supercooled liquids","volume":"112","author":"Glotzer","year":"2000","journal-title":"J. Chem. Phys."},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Berthier, L., Biroli, G., Bouchad, J.-P., Cipelletti, L., and van Saarloos, W. (2011). Dynamical Heterogeneities in Glasses, Colloids and Granular Media, Oxford University Press.","DOI":"10.1093\/acprof:oso\/9780199691470.001.0001"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"R2735(R)","DOI":"10.1103\/PhysRevE.51.R2735","article-title":"\u03b2 relaxation in a highly supercooled state via molecular dynamics simulation","volume":"51","author":"Muranaka","year":"1995","journal-title":"Phys. Rev. E"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"2721","DOI":"10.1103\/PhysRevLett.82.2721","article-title":"Two-stage melting of paramagnetic colloidal crystals in two dimensions","volume":"82","author":"Zahn","year":"1999","journal-title":"Phys. Rev. Lett."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"1300","DOI":"10.1016\/j.physa.2010.12.002","article-title":"Asset returns and volatility clustering in financial time series","volume":"390","author":"Tseng","year":"2011","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"122452","DOI":"10.1016\/j.physa.2019.122452","article-title":"A novel approach to detect volatility clusters in financial time series","volume":"535","year":"2019","journal-title":"Phys. A Stat. Mech. Appl."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/9\/954\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:04:41Z","timestamp":1760177081000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/9\/954"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,29]]},"references-count":54,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2020,9]]}},"alternative-id":["e22090954"],"URL":"https:\/\/doi.org\/10.3390\/e22090954","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2020,8,29]]}}}