A Comparison of VaR and CVaR Constraints on Portfolio Selection with the Mean-Variance Model
比较了在均值方差模型中施加VaR与CVaR约束对投资组合选择的影响，发现CVaR约束在控制轻度风险厌恶者时更有效，但在无风险资产缺失时可能迫使高度风险厌恶者选择标准差更大的组合。
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.