Second order of stochastic dominance efficiency vs mean variance efficiency

Matteo Malavasi, Sergio Ortobelli Lozza*, Stefan Trück

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In this paper, we compare two of the main paradigms of portfolio theory: mean variance analysis and expected utility. In particular, we show empirically that mean variance efficient portfolios are typically sub-optimal for non satiable and risk averse investors. We illustrate that the second order stochastic dominance (SSD) efficient set is the solution of a multi-objective optimization problem. We further show that the market portfolio is not necessarily a solution to this optimization problem. We also conduct an empirical analysis, examining the ex ante and ex post performance of SSD and mean variance efficient portfolios, using a bootstrap approach. In an ex ante analysis, we compare empirical moments, the level of diversification and set distances of mean variance and SSD efficient sets. We also show that the global minimum variance (GMV) portfolio and the part of the mean variance efficient frontier (MVEF) composed of highly diversified portfolios is second order stochastically dominated. This result also provides a possible alternative explanation for the diversification puzzle. Conducting an ex post analysis, we construct second order stochastic dominating strategies that outperform the GMV portfolio in terms of wealth and various other performance measures, producing a positive ex post opportunity cost.

Original languageEnglish
Pages (from-to)1192-1206
Number of pages15
JournalEuropean Journal of Operational Research
Issue number3
Early online date3 Sep 2020
Publication statusPublished - 1 May 2021


  • Efficient set
  • Investment analysis
  • Mean variance
  • Multiple objective programming
  • Stochastic dominance


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