IDEAS home Printed from https://ideas.repec.org/p/cuf/wpaper/539.html
   My bibliography  Save this paper

Tests of Mean-Variance Spanning

Author

Listed:
  • 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.

Suggested Citation

  • Raymond Kan & Guofu Zhou, 2001. "Tests of Mean-Variance Spanning," CEMA Working Papers 539, China Economics and Management Academy, Central University of Finance and Economics.
    • Handle: RePEc:cuf:wpaper:539
    as

    Download full text from publisher

    File URL: http://down.aefweb.net/WorkingPapers/w539.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. 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.
    3. Huberman, Gur & Kandel, Shmuel, 1987. "Mean-Variance Spanning," Journal of Finance, American Finance Association, vol. 42(4), pages 873-888, September.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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 131-156, March.
    9. Vihang Errunza & Ked Hogan & Mao‐Wei Hung, 1999. "Can the Gains from International Diversification Be Achieved without Trading Abroad?," Journal of Finance, American Finance Association, vol. 54(6), pages 2075-2107, December.
    10. Nijman, T.E. & de Roon, F.A. & Werker, B.J.M., 2001. "Testing for Mean-Variance spanning with short sales constraints and transaction costs : The case of emerging markets," Other publications TiSEM f4a3551a-d7ae-4c22-8813-b, Tilburg University, School of Economics and Management.
    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. 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.
    13. 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 1121-1152, September.
    14. 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(2), pages 189-197, June.
    15. 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 225-262, April.
    16. Bekaert, Geert & Urias, Michael S, 1996. "Diversification, Integration and Emerging Market Closed-End Funds," Journal of Finance, American Finance Association, vol. 51(3), pages 835-869, July.
    17. 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.
    18. 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.
    19. Breusch, T S, 1979. "Conflict among Criteria for Testing Hypotheses: Extensions and Comments," Econometrica, Econometric Society, vol. 47(1), pages 203-207, January.
    20. Shanken, Jay, 1992. "On the Estimation of Beta-Pricing Models," The Review of Financial Studies, Society for Financial Studies, vol. 5(1), pages 1-33.
    21. 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.
    22. 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.
    23. Frans A. De Roon & Theo E. Nijman & Bas J. M. Werker, 2001. "Testing for Mean‐Variance Spanning with Short Sales Constraints and Transaction Costs: The Case of Emerging Markets," Journal of Finance, American Finance Association, vol. 56(2), pages 721-742, April.
    24. Dong-Hyun Ahn & Jennifer Conrad & Robert F. Dittmar, 2003. "Risk Adjustment and Trading Strategies," The Review of Financial Studies, Society for Financial Studies, vol. 16(2), pages 459-485.
    25. de Roon, F.A. & Nijman, T.E. & Werker, B.J.M., 1998. "Testing for mean-variance spanning with short sales constraints and transaction costs : The case of emerging markets," Discussion Paper 1998-07, Tilburg University, Center for Economic Research.
    26. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Enrique Sentana, 2009. "The econometrics of mean-variance efficiency tests: a survey," Econometrics Journal, Royal Economic Society, vol. 12(3), pages 65-101, November.
    2. 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.
    3. Jing-zhi Huang & Zhaodong Zhong, 2013. "Time Variation in Diversification Benefits of Commodity, REITs, and TIPS," The Journal of Real Estate Finance and Economics, Springer, vol. 46(1), pages 152-192, January.
    4. Glabadanidis, Paskalis, 2009. "Measuring the economic significance of mean-variance spanning," The Quarterly Review of Economics and Finance, Elsevier, vol. 49(2), pages 596-616, May.
    5. Galvani, Valentina & Plourde, André, 2010. "Portfolio diversification in energy markets," Energy Economics, Elsevier, vol. 32(2), pages 257-268, March.
    6. Tim A. Kroencke & Felix Schindler & Andreas Schrimpf, 2014. "International Diversification Benefits with Foreign Exchange Investment Styles," Review of Finance, European Finance Association, vol. 18(5), pages 1847-1883.
    7. Galvani, Valentina & Behnamian, Aslan, 2009. "A Comparative Analysis of the Returns on Provincial and Federal Canadian Bonds," Working Papers 2009-7, University of Alberta, Department of Economics.
    8. Kroencke, Tim A. & Schindler, Felix, 2012. "International diversification with securitized real estate and the veiling glare from currency risk," Journal of International Money and Finance, Elsevier, vol. 31(7), pages 1851-1866.
    9. Galvani, Valentina & Plourde, André, 2013. "Spanning with futures contracts," The Quarterly Review of Economics and Finance, Elsevier, vol. 53(1), pages 61-72.
    10. 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.
    11. Beaulieu, Marie-Claude & Dufour, Jean-Marie & Khalaf, Lynda & Melin, Olena, 2023. "Identification-robust beta pricing, spanning, mimicking portfolios, and the benchmark neutrality of catastrophe bonds," Journal of Econometrics, Elsevier, vol. 236(1).
    12. Sermin Gungor & Richard Luger, 2016. "Multivariate Tests of Mean-Variance Efficiency and Spanning With a Large Number of Assets and Time-Varying Covariances," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(2), pages 161-175, April.
    13. Valentina Galvani & Stuart Landon, 2013. "Riding the yield curve: a spanning analysis," Review of Quantitative Finance and Accounting, Springer, vol. 40(1), pages 135-154, January.
    14. Lingfeng Li, 2003. "An Economic Measure of Diversification Benefits," Yale School of Management Working Papers ysm371, Yale School of Management, revised 01 Jul 2003.
    15. Lingfeng Li, 2003. "An Economic Measure of Diversification Benefits," Yale School of Management Working Papers ysm371, Yale School of Management, revised 01 Jul 2003.
    16. Cheol S. Eun & Sandy Lai & Frans A. de Roon & Zhe Zhang, 2010. "International Diversification with Factor Funds," Management Science, INFORMS, vol. 56(9), pages 1500-1518, September.
    17. Tim Schmitz & Ingo Hoffmann, 2020. "Re-evaluating cryptocurrencies' contribution to portfolio diversification -- A portfolio analysis with special focus on German investors," Papers 2006.06237, arXiv.org, revised Aug 2020.
    18. Cotter, John & Eyiah-Donkor, Emmanuel & Potì, Valerio, 2017. "Predictability and diversification benefits of investing in commodity and currency futures," International Review of Financial Analysis, Elsevier, vol. 50(C), pages 52-66.
    19. Fletcher, Jonathan, 2018. "An empirical examination of the diversification benefits of U.K. international equity closed-end funds," International Review of Financial Analysis, Elsevier, vol. 55(C), pages 23-34.
    20. Mensah, Jones Odei & Premaratne, Gamini, 2014. "Exploring Diversification Benefits in Asia-Pacific Equity Markets," MPRA Paper 60180, University Library of Munich, Germany.

    More about this item

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cuf:wpaper:539. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Qiang Gao (email available below). General contact details of provider: https://edirc.repec.org/data/emcufcn.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.