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On the Tail Mean-Variance optimal portfolio selection

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  • Landsman, Zinoviy
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    Abstract

    In the present paper we propose the Tail Mean-Variance (TMV) approach, based on Tail Condition Expectation (TCE) (or Expected Short Fall) and the recently introduced Tail Variance (TV) as a measure for the optimal portfolio selection. We show that, when the underlying distribution is multivariate normal, the TMV model reduces to a more complicated functional than the quadratic and represents a combination of linear, square root of quadratic and quadratic functionals. We show, however, that under general linear constraints, the solution of the optimization problem still exists and in the case where short selling is possible we provide an analytical closed form solution, which looks more "robust" than the classical MV solution. The results are extended to more general multivariate elliptical distributions of risks.

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    File URL: http://www.sciencedirect.com/science/article/B6V8N-4YCRYVM-2/2/af6877100814dc9582f22475d3f9e3f2
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    Bibliographic Info

    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 46 (2010)
    Issue (Month): 3 (June)
    Pages: 547-553

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    Handle: RePEc:eee:insuma:v:46:y:2010:i:3:p:547-553

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    Web page: http://www.elsevier.com/locate/inca/505554

    Related research

    Keywords: Tail condition expectation Tail variance Tail Mean-Variance model Optimal portfolio selection Square root of quadratic functional Elliptical family Quartic equation;

    References

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    1. Owen, Joel & Rabinovitch, Ramon, 1983. " On the Class of Elliptical Distributions and Their Applications to the Theory of Portfolio Choice," Journal of Finance, American Finance Association, vol. 38(3), pages 745-52, June.
    2. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    3. Landsman, Zinoviy, 2004. "On the generalization of Esscher and variance premiums modified for the elliptical family of distributions," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 563-579, December.
    4. Felipe Aparicio & Javier Estrada, 2001. "Empirical distributions of stock returns: European securities markets, 1990-95," The European Journal of Finance, Taylor & Francis Journals, vol. 7(1), pages 1-21.
    5. N. H. Bingham & Rudiger Kiesel, 2002. "Semi-parametric modelling in finance: theoretical foundations," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 241-250.
    6. Furman, Edward & Landsman, Zinoviy, 2005. "Risk capital decomposition for a multivariate dependent gamma portfolio," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 635-649, December.
    7. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
    8. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
    9. Merton, Robert C., 1972. "An Analytic Derivation of the Efficient Portfolio Frontier," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 7(04), pages 1851-1872, September.
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    Cited by:
    1. Owadally, Iqbal & Landsman, Zinoviy, 2013. "A characterization of optimal portfolios under the tail mean–variance criterion," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 213-221.
    2. Xu, Maochao & Mao, Tiantian, 2013. "Optimal capital allocation based on the Tail Mean–Variance model," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 533-543.

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