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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.

Suggested Citation

  • 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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    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.
    2. Yu, Xiufan & Yao, Jiawei & Xue, Lingzhou, 2024. "Power enhancement for testing multi-factor asset pricing models via Fisher’s method," Journal of Econometrics, Elsevier, vol. 239(2).
    3. M Hashem Pesaran & Takashi Yamagata, 2024. "Testing for Alpha in Linear Factor Pricing Models with a Large Number of Securities," Journal of Financial Econometrics, Oxford University Press, vol. 22(2), pages 407-460.
    4. Cheng, Tingting & Yan, Cheng & Yan, Yayi, 2021. "Improved inference for fund alphas using high-dimensional cross-sectional tests," Journal of Empirical Finance, Elsevier, vol. 61(C), pages 57-81.
    5. David Ardia & S'ebastien Laurent & Rosnel Sessinou, 2024. "High-Dimensional Mean-Variance Spanning Tests," Papers 2403.17127, arXiv.org.
    6. Feng, Long & Lan, Wei & Liu, Binghui & Ma, Yanyuan, 2022. "High-dimensional test for alpha in linear factor pricing models with sparse alternatives," Journal of Econometrics, Elsevier, vol. 229(1), pages 152-175.

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    More about this item

    Keywords

    Asset Pricing; Econometric and statistical methods; Financial markets;
    All these keywords.

    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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