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Mean-Variance Portfolio Allocation with a Value at Risk Constraint

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  • Sentana, E.

Abstract

In this paper, I first provide a unifying approach to 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 within the well-known Mean-Variance allocation framework that satisfy the VaR restrictions imposed on them by regulators. 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, E., 2001. "Mean-Variance Portfolio Allocation with a Value at Risk Constraint," Papers 0105, Centro de Estudios Monetarios Y Financieros-.
    • Handle: RePEc:fth:cemfdt:0105
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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 ; MANAGERS ; INVESTMENTS;
    All these keywords.

    JEL classification:

    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G24 - Financial Economics - - Financial Institutions and Services - - - Investment Banking; Venture Capital; Brokerage
    • G20 - Financial Economics - - Financial Institutions and Services - - - General

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