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Economic implications of using a mean-VaR model for portfolio selection: a comparison with mean-variance analysis. (English) Zbl 1131.91325

Summary: 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.

MSC:

91G10 Portfolio theory
91B30 Risk theory, insurance (MSC2010)
91G70 Statistical methods; risk measures
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