OR Spectrum

, Volume 37, Issue 3, pp 703–734 | Cite as

A general test for SSD portfolio efficiency

  • Miloš Kopa
  • Thierry Post
Regular Article


We develop and implement a Linear Programming test to analyze whether a given investment portfolio is efficient in terms of second-order stochastic dominance relative to all possible portfolios formed from a set of base assets. In case of efficiency, the primal model identifies a sub-gradient vector of a utility function that rationalizes the evaluated portfolio. In case of inefficiency, the dual model identifies a second, efficient portfolio that dominates the evaluated portfolio. The test gives a general necessary and sufficient condition, and can deal with general linear portfolio restrictions, inefficiency degree measures, and scenarios with unequal probabilities. We also develop a compact version of the test that substantially reduces computational burden at the cost of losing information about the dual dominating portfolio in case of inefficiency. An application to US investment benchmark data qualifies a broad stock market index as significantly inefficient, and suggests that no risk-averse investor would hold the market index in the face of attractive premiums offered by some more concentrated investment portfolios.


Stochastic dominance Portfolio analysis Market portfolio efficiency Linear programming 



This work was partially supported by Czech Science Foundation (Grant P402/12/G097). Financial support by Koç University Graduate School of Business is gratefully acknowledged.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Probability and Mathematical Statistics, Faculty of Mathematics and PhysicsCharles University in PraguePragueCzech Republic
  2. 2.Koç University Graduate School of BusinessSariyerTurkey

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