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Portfolio selection based on the mean-VaR efficient frontier

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  • Chueh-Yung Tsao
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    Abstract

    Value-at-Risk (VaR) has become one of the standard measures for assessing risk not only in the financial industry but also for asset allocations of individual investors. The traditional mean-variance framework for portfolio selection should, however, be revised when the investor's concern is the VaR instead of the standard deviation. This is especially true when asset returns are not normal. In this paper, we incorporate VaR in portfolio selection, and we propose a mean-VaR efficient frontier. Due to the two-objective optimization problem that is associated with the mean-VaR framework, an evolutionary multi-objective approach is required to construct the mean-VaR efficient frontier. Specifically, we consider the elitist non-dominated sorting Genetic Algorithm (NSGA-II). From our empirical analysis, we conclude that the risk-averse investor might inefficiently allocate his/her wealth if his/her decision is based on the mean-variance framework.

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    File URL: http://www.tandfonline.com/doi/abs/10.1080/14697681003652514
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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Quantitative Finance.

    Volume (Year): 10 (2010)
    Issue (Month): 8 ()
    Pages: 931-945

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    Handle: RePEc:taf:quantf:v:10:y:2010:i:8:p:931-945

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    Web page: http://www.tandfonline.com/RQUF20

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    Related research

    Keywords: Efficient frontiers; Value at Risk; Genetic algorithms; Portfolio selection; NSGA-II;

    References

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    1. Basak, Suleyman & Shapiro, Alexander, 2001. "Value-at-Risk-Based Risk Management: Optimal Policies and Asset Prices," Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 371-405.
    2. M. A. H. dempster & C. M. Jones, 2001. "A real-time adaptive trading system using genetic programming," Quantitative Finance, Taylor & Francis Journals, vol. 1(4), pages 397-413.
    3. Andersen, Torben G., 1998. "The Econometrics Of Financial Markets," Econometric Theory, Cambridge University Press, vol. 14(05), pages 671-685, October.
    4. Allen, Franklin & Karjalainen, Risto, 1999. "Using genetic algorithms to find technical trading rules," Journal of Financial Economics, Elsevier, vol. 51(2), pages 245-271, February.
    5. Dittmar, Robert & Neely, Christopher J & Weller, Paul, 1996. "Is Technical Analysis in the Foreign Exchange Market Profitable? A Genetic Programming Approach," CEPR Discussion Papers 1480, C.E.P.R. Discussion Papers.
    6. Neely, Christopher J. & Weller, Paul A., 1999. "Technical trading rules in the European Monetary System," Journal of International Money and Finance, Elsevier, vol. 18(3), pages 429-458.
    7. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    8. Arjan Berkelaar & Phornchanok Cumperayot & Roy Kouwenberg, 2002. "The Effect of VaR Based Risk Management on Asset Prices and the Volatility Smile," European Financial Management, European Financial Management Association, vol. 8(2), pages 139-164.
    9. Campbell, John Y. & Lo, Andrew W. & MacKinlay, A. Craig & Whitelaw, Robert F., 1998. "The Econometrics Of Financial Markets," Macroeconomic Dynamics, Cambridge University Press, vol. 2(04), pages 559-562, December.
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