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Measuring financial risk and portfolio optimization with a non-Gaussian multivariate model

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  • Kim, Young Shin
  • Giacometti, Rosella
  • Rachev, Svetlozar T.
  • Fabozzi, Frank J.
  • Mignacca, Domenico
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    Abstract

    In this paper, we propose a multivariate market model with returns assumed to follow a multivariate normal tempered stable distribution. This distribution, defined by a mixture of the multivariate normal distribution and the tempered stable subordinator, is consistent with two stylized facts that have been observed for asset distributions: fat-tails and an asymmetric dependence structure. Assuming infinitely divisible distributions, we derive closed-form solutions for two important measures used by portfolio managers in portfolio construction: the marginal VaR and the marginal AVaR. We illustrate the proposed model using stocks comprising the Dow Jones Industrial Average, first statistically validating the model based on goodness-of-fit tests and then demonstrating how the marginal VaR and marginal AVaR can be used for portfolio optimization using the model. Based on the empirical evidence presented in this paper, our framework offers more realistic portfolio risk measures and a more tractable method for portfolio optimization. --

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    Bibliographic Info

    Paper provided by Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering in its series Working Paper Series in Economics with number 44.

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    Date of creation: 2012
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    Handle: RePEc:zbw:kitwps:44

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    Web page: http://www.wiwi.kit.edu/
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    Related research

    Keywords: portfolio risk; portfolio optimization; portfolio budgeting; marginal contribution; fat-tailed distribution; multivariate normal tempered stable distribution;

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    1. Christian Gourieroux & J. P. Laurent & Olivier Scaillet, 2000. "Sensitivity Analysis of Values at Risk," Econometric Society World Congress 2000 Contributed Papers 0162, Econometric Society.
    2. Eugene F. Fama, 1963. "Mandelbrot and the Stable Paretian Hypothesis," The Journal of Business, University of Chicago Press, vol. 36, pages 420.
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    Cited by:
    1. Michele Leonardo Bianchi, 2014. "Are the log-returns of Italian open-end mutual funds normally distributed? A risk assessment perspective," Temi di discussione (Economic working papers) 957, Bank of Italy, Economic Research and International Relations Area.

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