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Multivariate Tests of Mean-Variance Efficiency and Spanning with a Large Number of Assets and Time-Varying Covariances


  • Sermin Gungor
  • Richard Luger


We develop a finite-sample procedure to test for mean-variance efficiency and spanning without imposing any parametric assumptions on the distribution of model disturbances. In so doing, we provide an exact distribution-free method to test uniform linear restrictions in multivariate linear regression models. The framework allows for unknown forms of non-normalities, and time-varying conditional variances and covariances among the model disturbances. We derive exact bounds on the null distribution of joint F statistics in order to deal with the presence of nuisance parameters, and we show how to implement the resulting generalized non-parametric bounds tests with Monte Carlo resampling techniques. In sharp contrast to the usual tests that are not computable when the number of test assets is too large, the power of the new test procedure potentially increases along both the time and cross-sectional dimensions.

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  • Sermin Gungor & Richard Luger, 2013. "Multivariate Tests of Mean-Variance Efficiency and Spanning with a Large Number of Assets and Time-Varying Covariances," Staff Working Papers 13-16, Bank of Canada.
  • Handle: RePEc:bca:bocawp:13-16

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    References listed on IDEAS

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    Cited by:

    1. Seung C. Ahn & Alex R. Horenstein, 2017. "Asset Pricing and Excess Returns over the Market Return," Working Papers 2017-12, University of Miami, Department of Economics.

    More about this item


    Asset Pricing; Econometric and statistical methods; Financial markets;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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