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The Generalised value at risk admissable set: constraint consistency and portfolio outcomes

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  • Bowden, Roger

Abstract

Generalised value at risk (GVaR) adds a conditional value at risk or censored mean lower bound to the standard value at risk and considers portfolio optimisation 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

  • Bowden, Roger, 2026. "The Generalised value at risk admissable set: constraint consistency and portfolio outcomes," Working Paper Series 33502, Victoria University of Wellington, School of Economics and Finance.
    • Handle: RePEc:vuw:vuwecf:33502
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    File URL: https://ir.wgtn.ac.nz/handle/123456789/33502
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    References listed on IDEAS

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    1. Roger Bowden, 2003. "The zero-capital approach to portfolio enhancement and overlay management," Quantitative Finance, Taylor & Francis Journals, vol. 3(4), pages 251-261.
    2. 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.
    3. Bowden, Roger, 2003. "The Zero Capital Approach to Portfolio Enhancement and Overlay Management," Working Paper Series 33497, Victoria University of Wellington, School of Economics and Finance.
    4. 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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