We relate value at risk (VaR) to mean-variance analysis and examine the economic implications of using a mean-VaR model for portfolio selection. When comparing two mean-variance efficient portfolios, the higher variance portfolio might have less VaR. Consequently, an efficient portfolio that globally minimizes VaR may not exist. Surprisingly, we show that it is plausible for certain risk-averse agents to end up selecting portfolios with larger standard deviations if they switch from using variance to VaR as a measure of risk. Therefore, regulators should be aware that VaR is not an unqualified improvement over variance as a measure of risk.
Bibliographical noteFunding Information:
We are indebted to Lawrence Benveniste, Luca Benzoni, Ravi Jagannathan, John Kareken, Dean Paxson, seminar participants at the 2000 Portuguese Finance Network Conference, University of Arizona, and University of Minnesota, and especially to Jan Werner and an anonymous referee for very helpful comments. Baptista gratefully acknowledges financial support from Sub-Programa Ciência e Tecnologia do Segundo Quadro Comunitário de Apoio. An earlier version of this paper circulated under the title ‘Value at Risk and Mean-Variance Analysis’.
- Asset pricing
- Portfolio choice
- Risk management and control