Standard mean-variance analysis is based on the assumption of normal return distributions. However, a growing body of literature suggests that the market oscillates between two different regimes - one with low volatility and the other with high volatility. In such a case, even if the return distributions are normal in both regimes, the overall distribution is not - it is a mixture of normals. Mean-variance analysis is inappropriate in this framework, and one must either assume a specific utility function or, alternatively, employ the more general and distribution-free Second degree Stochastic Dominance (SSD) criterion. This paper develops the SSD rule for the case of mixed normals: the SSDMN rule. This rule is a generalization the mean-variance rule. The cost of ignoring regimes and assuming normality when the distributions are actually mixed normal can be quite substantial - it is typically equivalent to an annual rate of return of 2-3 percent.

Original languageEnglish
Pages (from-to)514-524
Number of pages11
JournalEuropean Journal of Operational Research
Issue number2
StatePublished - 16 Apr 2015


  • Mean-variance
  • Portfolio optimization
  • Regimes
  • Stochastic dominance

All Science Journal Classification (ASJC) codes

  • Computer Science(all)
  • Modelling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management


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