Orthogonal Frontiers and Alternative Mean‐Variance Efficiency Tests

  • Author(s): BRUCE N. LEHMANN
  • Published: Apr 30, 2012
  • Pages: 601-619
  • DOI: 10.1111/j.1540-6261.1987.tb04571.x


This paper catalogues properties of minimum norm orthogonal portfolios: portfolios which minimize a quadratic objective function and have returns uncorrelated with those of a candidate portfolio that is not mean‐variance efficient. The analysis shows that the dollar versions of these portfolios correspond to estimators of zero beta rates based on alternative statistical criteria and grouping procedures while costless orthogonal portfolios represent candidate mean‐variance efficiency tests. It also develops inference procedures for zero and unit net investment portfolios of individual securities (instead of grouped portfolios) that have zero expected betas. The resulting mean‐variance efficiency tests are reasonably insensitive to the underlying statistical assumptions.

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