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How Fama Went Wrong: Measures of Multivariate Kurtosis for the Identification of the Dynamics of a N-Dimensional Market

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  • Tanya Ara\'ujo
  • Jo\~ao Dias
  • Samuel Eleut\'erio
  • Francisco Lou\c{c}\~a
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    Abstract

    This paper investigates the common intuition suggesting that during crises the shape of the financial market clearly differentiates from that of random walk processes. In this sense, it challenges the analysis of the nature of financial markets proposed by Fama and his associates. For this, a geometric approach is proposed in order to define the patterns of change of the market and a measure of multivariate kurtosis is used in order to test deviations from multinormality. The emergence of crises can be measured in this framework, using all the available information about the returns of the stocks under consideration and not only the index representing the market.

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    File URL: http://arxiv.org/pdf/1207.1202
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1207.1202.

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    Date of creation: Jul 2012
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    Handle: RePEc:arx:papers:1207.1202

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    1. Jushan Bai & Serena Ng, 2001. "Tests for Skewness, Kurtosis, and Normality for Time Series Data," Boston College Working Papers in Economics, Boston College Department of Economics 501, Boston College Department of Economics.
    2. Tanya Araujo & Francisco Louçã, 2005. "The Geometry of Crashes - A Measure of the Dynamics of Stock Market Crises," Working Papers Department of Economics, ISEG - School of Economics and Management, Department of Economics, University of Lisbon 2005/15, ISEG - School of Economics and Management, Department of Economics, University of Lisbon.
    3. R. Vilela Mendes & Tanya Ara\'{u}jo & Francisco Lou\c{c}\~{a}, 2002. "Reconstructing an economic space from a market metric," Papers cond-mat/0211108, arXiv.org.
    4. Richardson, Matthew & Smith, Tom, 1993. "A Test for Multivariate Normality in Stock Returns," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 66(2), pages 295-321, April.
    5. Jean-Marie Dufour & Lynda Khalaf & Marie-Claude Beaulieu, 2003. "Exact skewness-kurtosis tests for multivariate normality and goodness-of-fit in multivariate regressions with application to asset pricing models," CIRANO Working Papers, CIRANO 2003s-33, CIRANO.
    6. Srivastava, M. S., 1984. "A measure of skewness and kurtosis and a graphical method for assessing multivariate normality," Statistics & Probability Letters, Elsevier, Elsevier, vol. 2(5), pages 263-267, October.
    7. Beaulieu, Marie-Claude & Dufour, Jean-Marie & Khalaf, Lynda, 2009. "Finite sample multivariate tests of asset pricing models with coskewness," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 53(6), pages 2008-2021, April.
    8. Henze, Norbert & Wagner, Thorsten, 1997. "A New Approach to the BHEP Tests for Multivariate Normality," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 62(1), pages 1-23, July.
    9. Javed Iqbal & Robert Brooks & Don Galagedera, 2010. "Multivariate tests of asset pricing: simulation evidence from an emerging market," Applied Financial Economics, Taylor & Francis Journals, Taylor & Francis Journals, vol. 20(5), pages 381-395.
    10. Corrado, Charles J & Su, Tie, 1996. "Skewness and Kurtosis in S&P 500 Index Returns Implied by Option Prices," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 19(2), pages 175-92, Summer.
    11. M. Hashem Pesaran & Andreas Pick & Allan Timmermann, 2010. "Variable Selection, Estimation and Inference for Multi-period Forecasting Problems," DNB Working Papers, Netherlands Central Bank, Research Department 250, Netherlands Central Bank, Research Department.
    12. V. Plerou & P. Gopikrishnan & X. Gabaix & L. A. N. Amaral & H. E. Stanley, 2001. "Price fluctuations, market activity and trading volume," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 1(2), pages 262-269.
    13. Christine A. Brown & David M. Robinson, 2002. "Skewness and Kurtosis Implied by Option Prices: A Correction," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 25(2), pages 279-282.
    14. Tanya Araujo & Francisco Louçã, 2007. "The Seismography of Crashes in Financial Markets," Working Papers Department of Economics, ISEG - School of Economics and Management, Department of Economics, University of Lisbon 2007/05, ISEG - School of Economics and Management, Department of Economics, University of Lisbon.
    15. Jarrow, Robert & Rudd, Andrew, 1982. "Approximate option valuation for arbitrary stochastic processes," Journal of Financial Economics, Elsevier, Elsevier, vol. 10(3), pages 347-369, November.
    16. Norbert Henze, 2002. "Invariant tests for multivariate normality: a critical review," Statistical Papers, Springer, Springer, vol. 43(4), pages 467-506, October.
    17. Klar, Bernhard, 2002. "A Treatment of Multivariate Skewness, Kurtosis, and Related Statistics," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 83(1), pages 141-165, October.
    18. Vilela Mendes, R. & Araújo, Tanya & Louçã, Francisco, 2003. "Reconstructing an economic space from a market metric," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 323(C), pages 635-650.
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