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Extension of random matrix theory to the L-moments for robust portfolio allocation

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Abstract

In this paper, we propose a methodology for building an estimator of the covariance matrix. We use a robust measure of moments called L-moments (see hosking, 1986), and their extension into a multivariate framework (see Serfling and Xiao, 2007). Random matrix theory (see Edelman, 1989) allows us to extract factors which contain real information. An empirical study in the American market shows that the Global Minimum L-variance Portfolio (GMLP) obtained from our estimator well performs the Global Minimum Variance Portfolio (GMVP) that acquired from the empirical estimator of the covariance matrix.

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  • Ghislain Yanou, 2008. "Extension of random matrix theory to the L-moments for robust portfolio allocation," Documents de travail du Centre d'Economie de la Sorbonne bla08103, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  • Handle: RePEc:mse:cesdoc:bla08103
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    File URL: ftp://mse.univ-paris1.fr/pub/mse/CES2008/Bla08103.pdf
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    1. Bernard Cornet & Lionel Boisdeffre, 2009. "Elimination of arbitrage states in asymmetric information models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(2), pages 287-293, February.
    2. Lionel Boisdeffre, 2007. "No-arbitrage Equilibria with Differential Information: An Existence Proof," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(2), pages 255-269, May.
    3. Radner, Roy, 1979. "Rational Expectations Equilibrium: Generic Existence and the Information Revealed by Prices," Econometrica, Econometric Society, vol. 47(3), pages 655-678, May.
    4. Monique Florenzano, 2007. "General equilibrium," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00250167, HAL.
    5. Monique Florenzano, 1999. "General equilibrium of financial markets," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00085543, HAL.
    6. Cass, David, 2006. "Competitive equilibrium with incomplete financial markets," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 384-405, August.
    7. Cornet, Bernard & De Boisdeffre, Lionel, 2002. "Arbitrage and price revelation with asymmetric information and incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 38(4), pages 393-410, December.
    8. Duffie, Darrell & Shafer, Wayne, 1985. "Equilibrium in incomplete markets: I : A basic model of generic existence," Journal of Mathematical Economics, Elsevier, vol. 14(3), pages 285-300, June.
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    More about this item

    Keywords

    Covariance matrix; Lvariance-covariance; Lcorrelation; concomitance; random matrix theory.;

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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