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The Forbes 400, the Pareto power-law and efficient markets

  • Topical Issue on Trends in Econophysics
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Abstract.

Statistical regularities at the top end of the wealth distribution in the United States are examined using the Forbes 400 lists of richest Americans, published between 1988 and 2003. It is found that the wealths are distributed according to a power-law (Pareto) distribution. This result is explained using a simple stochastic model of multiple investors that incorporates the efficient market hypothesis as well as the multiplicative nature of financial market fluctuations.

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References

  • For the lists from recent years see www.forbes.com/lists

  • G.K. Zipf, Humen Behavior and the Principle of least Effort (Addison-Wesley Press, Cambridge, MA, 1949)

  • P.W. Anderson, Some Thoughts about Distributions in Economics, in The Economy as an Evolving Complex System II, edited by W.B. Arthur, S.N. Durlauf, D.A. Lane, SFI Studies in the Sciences of Complexity (Addison Wesley Longman, 1997)

  • V. Pareto Cours d'Économique Politique (Macmillan, Paris), Vol. 2 (1897)

  • J. Steindl, Random Processes and the Growth of Firms - A Study of the Pareto Law (Charles Griffin and Company, London, 1965)

  • A.B. Atkinson, A.J. Harrison, Distribution of Total Wealth in Britain (Cambridge University Press, Cambridge, 1978)

  • J. Persky, J. Economic Perspectives 6, 181 (1992)

    Google Scholar 

  • M. Levy, in The Economy as an Evolving Complex System III, edited by S. Durlauf, L. Blume (Oxford University Press, 2003)

  • O.S. Klass, O. Biham, M. Levy, O. Malcai, S. Solomon, Economics Lett. 90, 290 (2006)

    Article  ADS  Google Scholar 

  • D.G. Champernowne, Econometrica 63, 318 (1953)

    Google Scholar 

  • H. Wold, P. Whittle, Econometrica 25, 591 (1957)

    Article  MATH  MathSciNet  Google Scholar 

  • H.A. Simon, C.P. Bonini, Am. Econ. Rev. 48, 607 (1958)

    Google Scholar 

  • H. Kesten, Acta. Math. 131, 207 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  • M. Levy, S. Solomon, Int. J. Mod. Phys. C 7, 595 (1996)

    Article  ADS  Google Scholar 

  • D. Sornette, R. Cont, J. Phys. I France 7, 431 (1997)

    Article  MathSciNet  Google Scholar 

  • H. Takayasu, A.-H. Sato, M. Takayasu, Phys. Rev. Lett. 79, 966 (1997)

    Article  MATH  ADS  Google Scholar 

  • M. Marsili, S. Maslov, Y.-C. Zhang, Physica A 253, 403 (1998)

    Article  Google Scholar 

  • O. Malcai, O. Biham, S. Solomon, Phys. Rev. E 60, 1299 (1999)

    Article  ADS  Google Scholar 

  • J.-P. Bouchaud, M. Mézard, Physica A 282, 536 (2000)

    Article  ADS  Google Scholar 

  • J. Silver, E. Slud, K. Takamoto, J. Econ. Theory 106, 417 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  • E.F. Fama, J. Finance 25, 383 (1970)

    Article  Google Scholar 

  • E.F. Fama, J. Finance 46, 1575 (1991)

    Article  Google Scholar 

  • The results presented here were obtained using a simple bi-modal distribution in which λ can take one of two values: λ1 = 1+Δλ1 and λ2 = 1-Δλ2, where p(λ1) = p(λ2) = 1/2 and Δλ1,Δλ2 ≪1. Using other forms of p(λ) such as the Gaussian distribution, which exhibit finite values of the variance, we found that the Pareto exponent does not depend on p(λ)

  • H.E. Stanley, Introduction to Phase Transitions and Critical Phenomena (Oxford University Press, Oxford, 1971)

  • B. Gutenberg, C.F. Richter Ann. Geophys. 9, 1 (1956)

    Google Scholar 

  • M. Levy J. Economic Theory 110, 42 (2003)

  • B.B. Mandelbrot, J. Business 36, 394 (1963)

    Article  Google Scholar 

  • R.N. Mantegna, H.E. Stanley, Nature 376, 46 (1995)

    Article  ADS  Google Scholar 

  • P. Gopikrishnan, V. Plerou, L.A.N. Amaral, M. Meyer, H.E. Stanley, Phys. Rev. E 60, 5305 (1999)

    Article  ADS  Google Scholar 

  • O. Biham, Z.-F. Huang, O. Malcai, S. Solomon Phys. Rev. E 64, 026101 (2001)

    Article  ADS  Google Scholar 

  • A. Drăgulescu, V.M. Yakovenko, Physica A 299, 213 (2001)

    Article  ADS  Google Scholar 

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Klass, O., Biham, O., Levy, M. et al. The Forbes 400, the Pareto power-law and efficient markets. Eur. Phys. J. B 55, 143–147 (2007). https://doi.org/10.1140/epjb/e2006-00396-1

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  • DOI: https://doi.org/10.1140/epjb/e2006-00396-1

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