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Risk, VaR, CVaR and their associated Portfolio Optimizations when Asset Returns have a Multivariate Student T Distribution

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  • William T. Shaw
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    Abstract

    We show how to reduce the problem of computing VaR and CVaR with Student T return distributions to evaluation of analytical functions of the moments. This allows an analysis of the risk properties of systems to be carefully attributed between choices of risk function (e.g. VaR vs CVaR); choice of return distribution (power law tail vs Gaussian) and choice of event frequency, for risk assessment. We exploit this to provide a simple method for portfolio optimization when the asset returns follow a standard multivariate T distribution. This may be used as a semi-analytical verification tool for more general optimizers, and for practical assessment of the impact of fat tails on asset allocation for shorter time horizons.

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    File URL: http://arxiv.org/pdf/1102.5665
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    Paper provided by arXiv.org in its series Papers with number 1102.5665.

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    Date of creation: Feb 2011
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    Handle: RePEc:arx:papers:1102.5665

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    Web page: http://arxiv.org/

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    1. W. Breymann & D. R. Lüthi & E. Platen, 2009. "Empirical behavior of a world stock index from intra-day to monthly time scales," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 71(4), pages 511-522, October.
    2. Kevin Fergusson & Eckhard Platen, 2006. "On the Distributional Characterization of Daily Log-Returns of a World Stock Index," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(1), pages 19-38.
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