Long-run heterogeneity in an exchange economy with fixed-mix traders

Research Article

Abstract

We consider an exchange economy where agents have heterogeneous beliefs and assets are long-lived, and investigate the coupled dynamics of asset prices and agents’ wealth. We assume that agents hold fixed-mix portfolios and invest on each asset proportionally to its expected dividends. We prove the existence and uniqueness of a sequence of arbitrage-free market equilibrium prices and provide sufficient conditions for an agent, or a group of agents, to survive or dominate. Our main finding is that long-run coexistence of agents with heterogeneous beliefs, leading to asset prices endogenous fluctuations, is a generic outcome of the market selection process.

Keywords

Market selection hypothesis Heterogeneous beliefs Asset pricing Evolutionary finance Incomplete markets 

JEL Classification

C60 D52 D53 G11 G12 

References

  1. Alchian, A.: Uncertainty, evolution, and economic theory. J. Polit. Econ. 58, 211–221 (1950)CrossRefGoogle Scholar
  2. Beker, P.F., Chattopadhyay, S.: Consumption dynamics in general equilibrium: a characterisation when markets are incomplete. J. Econ. Theory 145, 2133–2185 (2010)CrossRefGoogle Scholar
  3. Beker, P.F., Espino, E.: The dynamics of efficient asset trading with heterogeneous beliefs. J. Econ. Theory 146, 189–229 (2011)CrossRefGoogle Scholar
  4. Bektur, Ç.: Performance of investment strategies in the absence of correct beliefs. Decis. Econ. Finance 36(1), 23–37 (2013)CrossRefGoogle Scholar
  5. Bhamra, H., Uppal, R.: Asset prices with heterogeneity in preferences and beliefs. Rev. Financ. Stud. 27, 519–580 (2014)CrossRefGoogle Scholar
  6. Blume, L., Easley, D.: Evolution and market behavior. J. Econ. Theory 58, 9–40 (1992)CrossRefGoogle Scholar
  7. Blume, L., Easley, D.: If you are so smart why aren’t you rich? Belief selection in complete and incomplete markets. Econometrica 74, 929–966 (2006)CrossRefGoogle Scholar
  8. Blume, L., Easley, D.: The market organism: Long-run survival in markets with heterogenous traders. J. Econ. Dyn. Control 33, 1023–1035 (2009)CrossRefGoogle Scholar
  9. Borovička, J.: Survival and long-run dynamics with heterogeneous beliefs under recursive preferences. Working paper, New York University (2015)Google Scholar
  10. Bottazzi, G., Dindo, P.: Evolution and market behavior with endogenous investment rules. J. Econ. Dyn. Control 48, 121–146 (2014)CrossRefGoogle Scholar
  11. Bottazzi, G., Dindo, P.: Drift criteria for persistence of discrete stochastic processes on the line. LEM Working Paper 2015-26, Sant’Anna School for Advanced Studies, Pisa (2015)Google Scholar
  12. Cao, D.: Speculation and financial wealth distribution under belief heterogeneity. Econ. J. (2017). doi:10.1111/ecoj.12519
  13. Cogley, T., Sargent, T., Tsyrennikov, V.: Wealth dynamics in a bond economy with heterogeneous beliefs. Econ. J. 124, 1–30 (2013)CrossRefGoogle Scholar
  14. Condie, S.: Living with ambiguity: prices and survival when investors have heterogeneous preferences for ambiguity. Econ. Theory 36, 81–108 (2008). doi:10.1007/s00199-007-0264-1 CrossRefGoogle Scholar
  15. Coury, T., Sciubba, E.: Belief heterogeneity and survival in incomplete markets. Econ. Theory 49, 37–58 (2012). doi:10.1007/s00199-010-0531-4 CrossRefGoogle Scholar
  16. Cvitanić, J., Jouini, E., Malamud, S., Napp, C.: Financial markets equilibrium with heterogeneous agents. Rev. Finance 16(1), 285–321 (2012)CrossRefGoogle Scholar
  17. Cvitanić, J., Malamud, S.: Price impact and portfolio impact. J. Financ. Econ. 100(1), 201–225 (2011)CrossRefGoogle Scholar
  18. Dindo, P.: Survival in speculative markets. LEM Working Paper 2015-32, Scuola Superiore Sant’Anna, Pisa (2015)Google Scholar
  19. Epstein, L., Zin, S.: Substitution, risk aversion, and the temporal behavior of consumption and asset returns: a theoretical framework. Econometrica 57, 937–969 (1989)CrossRefGoogle Scholar
  20. Evstigneev, I., Hens, T., Schenk-Hoppé, K.: Market selection of financial trading strategies: global stability. Math. Finance 12, 329–339 (2002)CrossRefGoogle Scholar
  21. Evstigneev, I., Hens, T., Schenk-Hoppé, K.: Evolutionary stable stock markets. Econ. Theory 27, 449–468 (2006)CrossRefGoogle Scholar
  22. Evstigneev, I., Hens, T., Schenk-Hoppé, K.: Globally evolutionary stable portfolio rules. J. Econ. Theory 140, 197–228 (2008)CrossRefGoogle Scholar
  23. Evstigneev, I., Hens, T., Schenk-Hoppé, K.: Evolutionary finance. In: Hens, T., Schenk-Hoppé, K. (eds.) Handbook of Financial Markets: Dynamics and Evolution. North-Holland (Handbooks in Economics Series) (2009)Google Scholar
  24. Fedyk, Y., Heyerdahl-Larsen, C., Walden, J.: Market selection and welfare in a multi-asset economy. Rev. Finance 17(3), 1179–1237 (2013)CrossRefGoogle Scholar
  25. Friedman, M.: Essays in Positive Economics. Univ. Chicago Press, Chicago (1953)Google Scholar
  26. Guerdjikova, A., Sciubba, E.: Survival with ambiguity. J. Econ. Theory 155, 50–94 (2015)CrossRefGoogle Scholar
  27. Hens, T., Schenk-Hoppé, K.: Handbook of Financial Markets: Dynamics and Evolution. North-Holland (Handbooks in Economics Series) (2009)Google Scholar
  28. Horst, U., Wenzelburger, J.: On non-ergodic asset prices. Econ. Theory 34, 207–234 (2008)CrossRefGoogle Scholar
  29. Jouini, E., Napp, C.: Heterogeneous beliefs and asset pricing in discrete time: an analysis of pessimism and doubt. J. Econ. Dyn. Control 30(7), 1233–1260 (2006)CrossRefGoogle Scholar
  30. Jouini, E., Napp, C.: Consensus consumer and intertemporal asset pricing with heterogeneous beliefs. Rev. Econ. Stud. 74(4), 1149–1174 (2007)CrossRefGoogle Scholar
  31. Jouini, E., Napp, C.: Unbiased disagreement in financial markets, waves of pessimism and the risk-return trade-off. Rev. Finance 15(3), 575–601 (2010)CrossRefGoogle Scholar
  32. Jouini, E., Napp, C.: Live fast, die young. Economic Theory 62, 265–278 (2016). doi:10.1007/s00199-015-0894-7 CrossRefGoogle Scholar
  33. Kelly, J.: A new interpretation of information rates. Bell Syst.Tech. J. 35, 917–926 (1956)CrossRefGoogle Scholar
  34. Lucas, R.: Asset prices in an exchange economy. Econometrica 46(6), 1429–1445 (1978)CrossRefGoogle Scholar
  35. Massari, F.: Markets with heterogeneous beliefs: a necessary and sufficient condition for a trader to vanish. J. Econ. Dyn. Control 78, 190–205 (2017)CrossRefGoogle Scholar
  36. Sandroni, A.: Do markets favor agents able to make accurate predictions. Econometrica 68(6), 1303–1341 (2000)CrossRefGoogle Scholar
  37. Sandroni, A.: Efficient markets and Bayes’ rule. Econ. Theory 26, 741–764 (2005). doi:10.1007/s00199-004-0567-4 CrossRefGoogle Scholar
  38. Sciubba, E.: Asymmetric information and survival in financial markets. Econ. Theory 25, 353–379 (2005). doi:10.1007/s00199-003-0434-8 CrossRefGoogle Scholar
  39. Sciubba, E.: The evolution of portfolio rules and the capital asset pricing model. Econ. Theory 29, 123–150 (2006). doi:10.1007/s00199-005-0013-2 CrossRefGoogle Scholar
  40. Taussky, O.: A recurring theorem on determinants. Am. Math. Mon. 56, 672–676 (1949)CrossRefGoogle Scholar
  41. Yan, H.: Natural selection in financial markets: Does it work? Manag. Sci. 54, 1935–1950 (2008)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Dipartimento di EconomiaUniversità Ca’ Foscari VeneziaVeneziaItaly
  2. 2.Istituto di EconomiaScuola Superiore Sant’AnnaPisaItaly

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