A general test for SSD portfolio efficiency

Miloš Kopa, Thierry Post

Research output: Contribution to journalArticlepeer-review

36 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)703-734
Number of pages32
JournalOR Spectrum
Issue number3
Publication statusPublished - 2015


  • Linear programming
  • Market portfolio efficiency
  • Portfolio analysis
  • Stochastic dominance

ASJC Scopus subject areas

  • Management Science and Operations Research


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