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Portfolio Return Distributions: Sample Statistics With Stochastic Correlations

Author

Listed:
  • DESISLAVA CHETALOVA

    (Fakultät für Physik, Universität Duisburg–Essen, 47048 Duisburg, Germany)

  • THILO A. SCHMITT

    (Fakultät für Physik, Universität Duisburg–Essen, 47048 Duisburg, Germany)

  • RUDI SCHÄFER

    (Fakultät für Physik, Universität Duisburg–Essen, 47048 Duisburg, Germany)

  • THOMAS GUHR

    (Fakultät für Physik, Universität Duisburg–Essen, 47048 Duisburg, Germany)

Abstract

We consider random vectors drawn from a multivariate normal distribution and compute the sample statistics in the presence of stochastic 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 nonstationarity by an ensemble average.

Suggested Citation

  • Desislava Chetalova & Thilo A. Schmitt & Rudi Schäfer & Thomas Guhr, 2015. "Portfolio Return Distributions: Sample Statistics With Stochastic Correlations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(02), pages 1-16.
    • Handle: RePEc:wsi:ijtafx:v:18:y:2015:i:02:n:s0219024915500120
    DOI: 10.1142/S0219024915500120
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    Citations

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    Cited by:

    1. Andreas Muhlbacher & Thomas Guhr, 2018. "Credit Risk Meets Random Matrices: Coping with Non-Stationary Asset Correlations," Papers 1803.00261, arXiv.org.
    2. Andreas Muhlbacher & Thomas Guhr, 2017. "Extreme portfolio loss correlations in credit risk," Papers 1706.09809, arXiv.org.

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