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Mean Variance Portfolio Allocation with a Value at Risk Constraint


  • Sentana, Enrique


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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    References listed on IDEAS

    1. Rogerson, Richard, 1988. "Indivisible labor, lotteries and equilibrium," Journal of Monetary Economics, Elsevier, vol. 21(1), pages 3-16, January.
    2. Chamley, Christophe & Gale, Douglas, 1994. "Information Revelation and Strategic Delay in a Model of Investment," Econometrica, Econometric Society, vol. 62(5), pages 1065-1085, September.
    3. Blanchard, Olivier Jean & Quah, Danny, 1989. "The Dynamic Effects of Aggregate Demand and Supply Disturbances," American Economic Review, American Economic Association, vol. 79(4), pages 655-673, September.
    4. Duffie, Darrell & Singleton, Kenneth J, 1993. "Simulated Moments Estimation of Markov Models of Asset Prices," Econometrica, Econometric Society, vol. 61(4), pages 929-952, July.
    5. Craig Burnside & Martin Eichenbaum & Sergio Rebelo, 1995. "Capital Utilization and Returns to Scale," NBER Chapters,in: NBER Macroeconomics Annual 1995, Volume 10, pages 67-124 National Bureau of Economic Research, Inc.
    6. Hairault, Jean-Olivier & Langot, Francois & Portier, Franck, 1997. "Time to implement and aggregate fluctuations," Journal of Economic Dynamics and Control, Elsevier, vol. 22(1), pages 109-121, November.
    7. Lucas, Robert Jr., 1972. "Expectations and the neutrality of money," Journal of Economic Theory, Elsevier, vol. 4(2), pages 103-124, April.
    8. Bikhchandani, Sushil & Hirshleifer, David & Welch, Ivo, 1992. "A Theory of Fads, Fashion, Custom, and Cultural Change in Informational Cascades," Journal of Political Economy, University of Chicago Press, vol. 100(5), pages 992-1026, October.
    9. Joseph Zeira, 1994. "Informational Cycles," Review of Economic Studies, Oxford University Press, vol. 61(1), pages 31-44.
    10. Allen, Steven G, 1985. "Why Construction Industry Productivity Is Declining," The Review of Economics and Statistics, MIT Press, vol. 67(4), pages 661-669, November.
    11. King, Robert G. & Plosser, Charles I. & Rebelo, Sergio T., 1988. "Production, growth and business cycles : II. New directions," Journal of Monetary Economics, Elsevier, vol. 21(2-3), pages 309-341.
    12. Andrew Caplin & John Leahy, 1993. "Sectoral Shocks, Learning, and Aggregate Fluctuations," Review of Economic Studies, Oxford University Press, vol. 60(4), pages 777-794.
    13. King, Robert G. & Rebelo, Sergio T., 1999. "Resuscitating real business cycles," Handbook of Macroeconomics,in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 14, pages 927-1007 Elsevier.
    14. Edmund S. Phelps, 1999. "Behind This Structural Boom: The Role of Asset Valuations," American Economic Review, American Economic Association, vol. 89(2), pages 63-68, May.
    15. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-1370, November.
    16. Abhijit V. Banerjee, 1992. "A Simple Model of Herd Behavior," The Quarterly Journal of Economics, Oxford University Press, vol. 107(3), pages 797-817.
    17. King, Robert G. & Plosser, Charles I. & Rebelo, Sergio T., 1988. "Production, growth and business cycles : I. The basic neoclassical model," Journal of Monetary Economics, Elsevier, vol. 21(2-3), pages 195-232.
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    Cited by:

    1. 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.
    2. Kaplanski, Guy, 2005. "Analytical Portfolio Value-at-Risk," MPRA Paper 80216, University Library of Munich, Germany.
    3. 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).

    More about this item


    market risk capital; portfolio frontier; risk management;

    JEL classification:

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


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