Portfolio selection in a two-regime world.

*(English)*Zbl 1341.91126Summary: 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.

##### MSC:

91G10 | Portfolio theory |

62J10 | Analysis of variance and covariance (ANOVA) |

91G70 | Statistical methods; risk measures |

62P05 | Applications of statistics to actuarial sciences and financial mathematics |

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\textit{M. Levy} and \textit{G. Kaplanski}, Eur. J. Oper. Res. 242, No. 2, 514--524 (2015; Zbl 1341.91126)

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