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Portfolio return distributions: Sample statistics with non-stationary correlations

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  • Desislava Chetalova
  • Thilo A. Schmitt
  • Rudi Sch\"afer
  • Thomas Guhr
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    Abstract

    We consider random vectors drawn from a multivariate normal distribution and compute the sample statistics in the presence of non-stationary correlations. For this purpose, we construct an ensemble of random correlation matrices and average the normal distribution over this ensemble. The resulting distribution contains a modified Bessel function of the second kind whose behavior differs significantly from the multivariate normal distribution, in the central part as well as in the tails. This result is then applied to asset returns. We compare with empirical return distributions using daily data from the Nasdaq Composite Index in the period from 1992 to 2012. The comparison reveals good agreement, the average portfolio return distribution describes the data well especially in the central part of the distribution. This in turn confirms our ansatz to model the non-stationarity by an ensemble average.

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    File URL: http://arxiv.org/pdf/1308.3961
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1308.3961.

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    Date of creation: Aug 2013
    Date of revision: Jun 2014
    Handle: RePEc:arx:papers:1308.3961

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    Web page: http://arxiv.org/

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    1. Longin, Francois & Solnik, Bruno, 1995. "Is the correlation in international equity returns constant: 1960-1990?," Journal of International Money and Finance, Elsevier, vol. 14(1), pages 3-26, February.
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    5. Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May.
    6. Daniel J. Fenn & Mason A. Porter & Stacy Williams & Mark McDonald & Neil F. Johnson & Nick S. Jones, 2010. "Temporal Evolution of Financial Market Correlations," Papers 1011.3225, arXiv.org, revised May 2011.
    7. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frederic Abergel, 2011. "Econophysics review: I. Empirical facts," Quantitative Finance, Taylor & Francis Journals, vol. 11(7), pages 991-1012.
    8. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
    9. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
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