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Tests of Mean-Variance Spanning

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  • Raymond Kan

    (University of Toronto)

  • Guofu Zhou

    (Washington University)

Abstract

In this paper, we conduct a comprehensive study of tests of mean-variance spanning. We provide both a comparison and a geometrical interpretation of three asymptotic tests (likelihood ratio, Wald, and Lagrange multiplier) of mean-variance spanning under the regression based framework of Huberman and Kandel (1987). For the case of normality, we provide the exact distributions and a comprehensive power analysis of the three tests. For the general case, we provide the GMM version of the spanning tests and evaluate their performance using simulation. In addition, we compare the performance of the spanning tests under the regression approach with those under the stochastic discount factor approach. Our results suggest that the two approaches have similar properties when returns are normally distributed but the regression approach is superior to the stochastic discount factor approach when returns follow a multivariate Student-t distribution.

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Bibliographic Info

Paper provided by China Economics and Management Academy, Central University of Finance and Economics in its series CEMA Working Papers with number 539.

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Length: 65 pages
Date of creation: Sep 2001
Date of revision:
Publication status: Published in Annals of Economics and Finance, May 2012, pages 145-193
Handle: RePEc:cuf:wpaper:539

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Web page: http://cema.cufe.edu.cn/
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  1. Ferson, Wayne E & Foerster, Stephen R & Keim, Donald B, 1993. " General Tests of Latent Variable Models and Mean-Variance Spanning," Journal of Finance, American Finance Association, vol. 48(1), pages 131-56, March.
  2. Perlman, Michael D., 1974. "On the monotonicity of the power functions of tests based on traces of multivariate beta matrices," Journal of Multivariate Analysis, Elsevier, vol. 4(1), pages 22-30, March.
  3. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
  4. Gibbons, Michael R & Ross, Stephen A & Shanken, Jay, 1989. "A Test of the Efficiency of a Given Portfolio," Econometrica, Econometric Society, vol. 57(5), pages 1121-52, September.
  5. Merton, Robert C., 1980. "On estimating the expected return on the market : An exploratory investigation," Journal of Financial Economics, Elsevier, vol. 8(4), pages 323-361, December.
  6. Enrique Sentana & Francisco Penaranda, 2004. "Spanning Tests in Return and Stochastic Discount Factor Mean-Variance Frontiers: A Unifying Approach," FMG Discussion Papers dp497, Financial Markets Group.
  7. Hansen, Lars Peter & Jagannathan, Ravi, 1991. "Implications of Security Market Data for Models of Dynamic Economies," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 225-62, April.
  8. Nijman, T.E. & Roon, F.A. de & Werker, B.J.M., 2001. "Testing for Mean-Variance spanning with short sales constraints and transaction costs: The case of emerging markets," Open Access publications from Tilburg University urn:nbn:nl:ui:12-86724, Tilburg University.
  9. Dufour, J.M. & Khalaf, L., 2000. "Simulation-Based Finite and Large Sample Tests in Multivariate Regressions," Cahiers de recherche 2000-10, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  10. Jobson, J. D. & Korkie, Bob, 1983. "Statistical Inference in Two-Parameter Portfolio Theory with Multiple Regression Software," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 18(02), pages 189-197, June.
  11. Christiansen, Charlotte & Joensen, Juanna Schroter & Nielsen, Helena Skyt, 2007. "The risk-return trade-off in human capital investment," Labour Economics, Elsevier, vol. 14(6), pages 971-986, December.
  12. Geert Bekaert & Michael S. Urias, 1995. "Diversification, Integration and Emerging Market Closed-End Funds," NBER Working Papers 4990, National Bureau of Economic Research, Inc.
  13. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  14. Nijman, T.E. & Roon, F.A. de, 2001. "Testing for mean-variance spanning: A survey," Open Access publications from Tilburg University urn:nbn:nl:ui:12-87531, Tilburg University.
  15. Dong-Hyun Ahn & Jennifer Conrad & Robert F. Dittmar, 2003. "Risk Adjustment and Trading Strategies," Review of Financial Studies, Society for Financial Studies, vol. 16(2), pages 459-485.
  16. Richardson, Matthew & Smith, Tom, 1993. "A Test for Multivariate Normality in Stock Returns," The Journal of Business, University of Chicago Press, vol. 66(2), pages 295-321, April.
  17. Huberman, Gur & Kandel, Shmuel, 1987. " Mean-Variance Spanning," Journal of Finance, American Finance Association, vol. 42(4), pages 873-88, September.
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