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

Gordon Alexander and Alexandre Baptista ()

Management Science, 2004, vol. 50, issue 9, 1261-1273

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.

Keywords: value-at-risk (VaR); conditional value-at-risk (CVaR); risk management; portfolio choice (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (126)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:50:y:2004:i:9:p:1261-1273

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