A comparison of VaR and CVaR constraints on portfolio selection with the mean-variance model

Gordon J. Alexander, Alexandre M. Baptista

Research output: Contribution to journalArticlepeer-review

175 Scopus citations

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 "dominates" a VaR constraint as a risk management tool.

Original languageEnglish (US)
Pages (from-to)1261-1273
Number of pages13
JournalManagement Science
Volume50
Issue number9
DOIs
StatePublished - Sep 1 2004

Keywords

  • Conditional value-at-risk (CVaR)
  • Portfolio choice
  • Risk management
  • Value-at-risk (VaR)

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