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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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    1. Dufour, Jean-Marie & Kiviet, Jan F., 1996. "Exact tests for structural change in first-order dynamic models," Journal of Econometrics, Elsevier, vol. 70(1), pages 39-68, January.
    2. Stephen A. Ross, 2013. "The Arbitrage Theory of Capital Asset Pricing," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 1, pages 11-30, World Scientific Publishing Co. Pte. Ltd..
    3. Zhou, Guofu, 1993. "Asset-Pricing Tests under Alternative Distributions," Journal of Finance, American Finance Association, vol. 48(5), pages 1927-1942, December.
    4. Jean-Marie Dufour, 2003. "Identification, weak instruments, and statistical inference in econometrics," Canadian Journal of Economics, Canadian Economics Association, vol. 36(4), pages 767-808, November.
    5. Dufour, Jean-Marie, 1989. "Nonlinear Hypotheses, Inequality Restrictions, and Non-nested Hypotheses: Exact Simultaneous Tests in Linear Regressions," Econometrica, Econometric Society, vol. 57(2), pages 335-355, March.
    6. 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.
    7. Peñaranda, Francisco & Sentana, Enrique, 2012. "Spanning tests in return and stochastic discount factor mean–variance frontiers: A unifying approach," Journal of Econometrics, Elsevier, vol. 170(2), pages 303-324.
    8. Beaulieu, Marie-Claude & Dufour, Jean-Marie & Khalaf, Lynda, 2010. "Asset-pricing anomalies and spanning: Multivariate and multifactor tests with heavy-tailed distributions," Journal of Empirical Finance, Elsevier, vol. 17(4), pages 763-782, September.
    9. Raymond Kan & Guofu Zhou, 2012. "Tests of Mean-Variance Spanning," Annals of Economics and Finance, Society for AEF, vol. 13(1), pages 139-187, May.
    10. Kenneth Stewart, 1997. "Exact testing in multivariate regression," Econometric Reviews, Taylor & Francis Journals, vol. 16(3), pages 321-352.
    11. Gungor, Sermin & Luger, Richard, 2009. "Exact distribution-free tests of mean-variance efficiency," Journal of Empirical Finance, Elsevier, vol. 16(5), pages 816-829, December.
    12. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
    13. Berndt, Ernst R & Savin, N Eugene, 1977. "Conflict among Criteria for Testing Hypotheses in the Multivariate Linear Regression Model," Econometrica, Econometric Society, vol. 45(5), pages 1263-1277, July.
    14. Lo, Andrew W & MacKinlay, A Craig, 1990. "Data-Snooping Biases in Tests of Financial Asset Pricing Models," The Review of Financial Studies, Society for Financial Studies, vol. 3(3), pages 431-467.
    15. Huberman, Gur & Kandel, Shmuel, 1987. "Mean-Variance Spanning," Journal of Finance, American Finance Association, vol. 42(4), pages 873-888, September.
    16. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    17. Berk, Jonathan B., 1997. "Necessary Conditions for the CAPM," Journal of Economic Theory, Elsevier, vol. 73(1), pages 245-257, March.
    18. Dufour, Jean-Marie & Khalaf, Lynda, 2002. "Simulation based finite and large sample tests in multivariate regressions," Journal of Econometrics, Elsevier, vol. 111(2), pages 303-322, December.
    19. Affleck-Graves, John & McDonald, Bill, 1990. "Multivariate Tests of Asset Pricing: The Comparative Power of Alternative Statistics," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(2), pages 163-185, June.
    20. 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.
    21. Blattberg, Robert C & Gonedes, Nicholas J, 1974. "A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices," The Journal of Business, University of Chicago Press, vol. 47(2), pages 244-280, April.
    22. Roll, Richard, 1977. "A critique of the asset pricing theory's tests Part I: On past and potential testability of the theory," Journal of Financial Economics, Elsevier, vol. 4(2), pages 129-176, March.
    23. Dufour, Jean-Marie, 2006. "Monte Carlo tests with nuisance parameters: A general approach to finite-sample inference and nonstandard asymptotics," Journal of Econometrics, Elsevier, vol. 133(2), pages 443-477, August.
    24. Enrique Sentana, 2009. "The econometrics of mean-variance efficiency tests: a survey," Econometrics Journal, Royal Economic Society, vol. 12(3), pages 65-101, November.
    25. Bing Liang, 2000. "Portfolio Formation, Measurement Errors, And Beta Shifts: A Random Sampling Approach," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 23(3), pages 261-284, September.
    26. Savin, N.E., 1984. "Multiple hypothesis testing," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 14, pages 827-879, Elsevier.
    27. Affleck-Graves, John & McDonald, Bill, 1989. " Nonnormalities and Tests of Asset Pricing Theories," Journal of Finance, American Finance Association, vol. 44(4), pages 889-908, September.
    28. Jean‐Marie Dufour, 2003. "Identification, weak instruments, and statistical inference in econometrics," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 36(4), pages 767-808, November.
    29. Jobson, J. D. & Korkie, Bob, 1989. "A Performance Interpretation of Multivariate Tests of Asset Set Intersection, Spanning, and Mean-Variance Efficiency," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(2), pages 185-204, June.
    30. Ray, Surajit & Savin, N.E. & Tiwari, Ashish, 2009. "Testing the CAPM revisited," Journal of Empirical Finance, Elsevier, vol. 16(5), pages 721-733, December.
    31. Cheung, C. Sherman & Kwan, Clarence C.Y. & Mountain, Dean C., 2009. "On the nature of mean-variance spanning," Finance Research Letters, Elsevier, vol. 6(2), pages 106-113, June.
    32. Dufour, Jean-Marie, 1990. "Exact Tests and Confidence Sets in Linear Regressions with Autocorrelated Errors," Econometrica, Econometric Society, vol. 58(2), pages 475-494, March.
    33. Nijman, T.E. & de Roon, F.A., 2001. "Testing for mean-variance spanning : A survey," Other publications TiSEM 0159f80a-c61b-4519-b004-a, Tilburg University, School of Economics and Management.
    34. Owen, Joel & Rabinovitch, Ramon, 1983. "On the Class of Elliptical Distributions and Their Applications to the Theory of Portfolio Choice," Journal of Finance, American Finance Association, vol. 38(3), pages 745-752, June.
    35. Pesaran, M. Hashem & Yamagata, Takashi, 2012. "Testing CAPM with a Large Number of Assets," IZA Discussion Papers 6469, Institute of Labor Economics (IZA).
    36. DeRoon, Frans A. & Nijman, Theo E., 2001. "Testing for mean-variance spanning: a survey," Journal of Empirical Finance, Elsevier, vol. 8(2), pages 111-155, May.
    37. Beaulieu, Marie-Claude & Dufour, Jean-Marie & Khalaf, Lynda, 2007. "Multivariate Tests of MeanVariance Efficiency With Possibly Non-Gaussian Errors: An Exact Simulation-Based Approach," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 398-410, October.
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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. 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.
    3. David Ardia & S'ebastien Laurent & Rosnel Sessinou, 2024. "High-Dimensional Mean-Variance Spanning Tests," Papers 2403.17127, arXiv.org.
    4. 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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