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The generalized value at risk admissible set: constraint consistency and portfolio outcomes

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  • Roger Bowden

Abstract

Generalized value at risk (GVaR) adds a conditional value at risk or censored mean lower bound to the standard value at risk and considers portfolio optimization problems in the presence of both constraints. For normal distributions the censored mean is synonymous with the statistical hazard function, but this is not true for fat-tailed distributions. The latter turn out to imply much tighter bounds for the admissible portfolio set and indeed for the logistic, an upper bound for the portfolio variance that yields a simple portfolio choice rule. The choice theory in GVaR is in general not consistent with classic Von Neumann-Morgenstern utility functions for money. A re-specification is suggested to make it so that gives a clearer picture of the economic role of the respective constraints. This can be used analytically to explore the choice of portfolio hedges.

Suggested Citation

  • Roger Bowden, 2006. "The generalized value at risk admissible set: constraint consistency and portfolio outcomes," Quantitative Finance, Taylor & Francis Journals, vol. 6(2), pages 159-171.
    • Handle: RePEc:taf:quantf:v:6:y:2006:i:2:p:159-171
    DOI: 10.1080/14697680600580912
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    References listed on IDEAS

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    1. Roger J. Bowden, 2005. "Ordered Mean Difference Benchmarking, Utility Generators, and Capital Market Equilibrium," The Journal of Business, University of Chicago Press, vol. 78(2), pages 441-468, March.
    2. Roger Bowden, 2003. "The zero-capital approach to portfolio enhancement and overlay management," Quantitative Finance, Taylor & Francis Journals, vol. 3(4), pages 251-261.
    3. Y. Malevergne & D. Sornette, 2003. "VaR-Efficient Portfolios for a Class of Super- and Sub-Exponentially Decaying Assets Return Distributions," Papers physics/0301009, arXiv.org.
    4. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    5. Bowden, Roger J., 2000. "The ordered mean difference as a portfolio performance measure," Journal of Empirical Finance, Elsevier, vol. 7(2), pages 195-223, August.
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    Cited by:

    1. Roger Bowden, 2010. "Directional entropy and tail uncertainty, with applications to financial hazard," Quantitative Finance, Taylor & Francis Journals, vol. 11(3), pages 437-446.
    2. Juliane Proelss & Denis Schweizer, 2014. "Polynomial goal programming and the implicit higher moment preferences of US institutional investors in hedge funds," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 28(1), pages 1-28, February.
    3. Bowden, Roger J., 2009. "Lifecycle derivatives and retirement income assurance using long-term debt," Journal of Pension Economics and Finance, Cambridge University Press, vol. 8(3), pages 361-390, July.
    4. Roger Bowden & Jennifer Zhu, 2010. "Multi-scale variation, path risk and long-term portfolio management," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 783-796.

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