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Mean Variance Portfolio Allocation with a Value at Risk Constraint

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  • Sentana, Enrique

Abstract

In this Paper, I first provide a simple unifying approach to static Mean-Variance analysis and Value at Risk, which highlights their similarities and differences. Then I use it to explain how fund managers can take investment decisions that satisfy the VaR restrictions imposed on them by regulators, within the well-known Mean-Variance allocation framework. I do so by introducing a new type of line to the usual mean-standard deviation diagram, called IsoVaR,which represents all the portfolios that share the same VaR for a fixed probability level. Finally, I analyse the 'shadow cost' of a VaR constraint.

Suggested Citation

  • Sentana, Enrique, 2001. "Mean Variance Portfolio Allocation with a Value at Risk Constraint," CEPR Discussion Papers 2997, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:2997
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    Cited by:

    1. Gordon J. Alexander & Alexandre M. Baptista, 2004. "A Comparison of VaR and CVaR Constraints on Portfolio Selection with the Mean-Variance Model," Management Science, INFORMS, vol. 50(9), pages 1261-1273, September.
    2. Jordi Andreu & Salvador Torra, 2009. "Optimal market indices using value-at-risk: a first empirical approach for three stock markets," Applied Financial Economics, Taylor & Francis Journals, vol. 19(14), pages 1163-1170.
    3. Josep Pijoan-Mas, 2006. "Precautionary Savings or Working Longer Hours?," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 9(2), pages 326-352, April.
    4. Francesco Paolo Natale, 2008. "Optimisation in the presence of tail-dependence and tail risk: A heuristic approach for strategic asset allocation," Journal of Asset Management, Palgrave Macmillan, vol. 8(6), pages 374-400, February.
    5. Cuoco, Domenico & Liu, Hong, 2006. "An analysis of VaR-based capital requirements," Journal of Financial Intermediation, Elsevier, vol. 15(3), pages 362-394, July.
    6. Kaplanski, Guy, 2005. "Analytical Portfolio Value-at-Risk," MPRA Paper 80216, University Library of Munich, Germany.
    7. Grau-Carles, Pilar & Sainz, Jorge & Otamendi, Javier & Doncel, Luis Miguel, 2009. "Different risk-adjusted fund performance measures: a comparison," Economics Discussion Papers 2009-54, Kiel Institute for the World Economy (IfW Kiel).

    More about this item

    Keywords

    Risk management; Portfolio frontier; Market risk capital;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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