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 “dominates” a VaR constraint as a risk management tool.

• 저널Management Science · 50(9) · 1261–1273
• 토픽Risk and Portfolio Optimization · Management Science and Operations Research
• DOI10.1287/mnsc.1040.0201
• 저자Gordon J. Alexander, Alexandre M. Baptista