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A Comparison of VaR and CVaR Constraints on Portfolio Selection with the Mean-Variance Model

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  • Gordon J. Alexander

    (Department of Finance, Carlson School of Management, University of Minnesota, Minneapolis, Minnesota 55455)

  • Alexandre M. Baptista

    (Department of Finance, School of Business, The George Washington University, Washington, D.C. 20052)

Abstract

In this paper, we analyze the portfolio selection implications arising from imposing a value-at-risk (VaR) constraint on the mean-variance model, and compare them with those arising from the imposition of a conditional value-at-risk (CVaR) constraint. We show that for a given confidence level, a CVaR constraint is tighter than a VaR constraint if the CVaR and VaR bounds coincide. Consequently, a CVaR constraint is more effective than a VaR constraint as a tool to control slightly risk-averse agents, but in the absence of a risk-free security, has a perverse effect in that it is more likely to force highly risk-averse agents to select portfolios with larger standard deviations. However, when the CVaR bound is appropriately larger than the VaR bound or when a risk-free security is present, a CVaR constraint ÜdominatesÝ a VaR constraint as a risk management tool.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ormnsc:v:50:y:2004:i:9:p:1261-1273
    DOI: 10.1287/mnsc.1040.0201
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    References listed on IDEAS

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