PORTFOLIO RETURN DISTRIBUTIONS: SAMPLE STATISTICS WITH STOCHASTIC CORRELATIONS

Desislava Chetalova (), Thilo A. Schmitt, Rudi Schäfer and Thomas Guhr
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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

International Journal of Theoretical and Applied Finance (IJTAF), 2015, vol. 18, issue 02, 1-16

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.

Keywords: Correlation modeling; nonstationarity; market dynamics; portfolio analysis; stochastic models; non-Gaussian distributions (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S0219024915500120

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