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

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  • Sermin Gungor
  • Richard Luger

Abstract

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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Bibliographic Info

Paper provided by Bank of Canada in its series Working Papers with number 13-16.

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Length: 46 pages
Date of creation: 2013
Date of revision:
Handle: RePEc:bca:bocawp:13-16

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Keywords: Asset Pricing; Econometric and statistical methods; Financial markets;

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  16. Kenneth Stewart, 1997. "Exact testing in multivariate regression," Econometric Reviews, Taylor & Francis Journals, vol. 16(3), pages 321-352.
  17. Sermin Gungor & Richard Luger, 2013. "Testing Linear Factor Pricing Models With Large Cross Sections: A Distribution-Free Approach," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(1), pages 66-77, January.
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  23. Chamberlain, Gary, 1983. "A characterization of the distributions that imply mean--Variance utility functions," Journal of Economic Theory, Elsevier, vol. 29(1), pages 185-201, February.
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