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

• 成果类型: Article
• 署名作者: Alexander, GJ; Baptista, AM
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities; George Washington University
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.1040.0201
• 发表日期: 2004
• 页码: 1261-1273
• 关键词: value-at-risk (VaR); conditional value-at-risk (CVaR); risk management; portfolio choice

摘要

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.