A Comparison of VaR and CVaR Constraints on Portfolio Selection with the Mean-Variance Model
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.
Volume (Year): 50 (2004)
Issue (Month): 9 (September)
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- Suleyman Basak & Alex Shapiro, .
"Value-at-Risk Based Risk Management: Optimal Policies and Asset Prices,"
Rodney L. White Center for Financial Research Working Papers
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