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Exact distribution-free tests of mean-variance efficiency

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  • Gungor, Sermin
  • Luger, Richard

Abstract

This paper develops exact distribution-free tests of unconditional mean-variance efficiency. These new tests allow for unknown forms of non-normalities, conditional heteroskedasticity, and other non-linear temporal dependencies among the absolute values of the error terms in the asset pricing model. Exactness here rests on the assumption that the joint temporal error density is symmetric around zero. This still leaves open the possibility of return distribution asymmetry via coskewness with the benchmark portfolio. A simulation study shows that the new tests have very good power relative to that of many commonly used tests. The inference procedures developed are further illustrated by tests of the mean-variance efficiency of a market index using a 42-year sample of monthly returns on ten U.S. equity portfolios.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Empirical Finance.

Volume (Year): 16 (2009)
Issue (Month): 5 (December)
Pages: 816-829

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Handle: RePEc:eee:empfin:v:16:y:2009:i:5:p:816-829

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Web page: http://www.elsevier.com/locate/jempfin

Related research

Keywords: CAPM Conditional heteroskedasticity Non-parametric tests Robust inference;

References

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  1. 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, 09.
  2. Duffee, Gregory R., 1995. "Stock returns and volatility A firm-level analysis," Journal of Financial Economics, Elsevier, vol. 37(3), pages 399-420, March.
  3. DUFOUR, Jean-Marie & KHALAF, Lynda, 2000. "Simulation-Based Finite and Large Sample Tests in Multivariate Regressions," Cahiers de recherche 2000-10, Universite de Montreal, Departement de sciences economiques.
  4. Peter BOSSAERTS & Pierre HILLION, 1995. "Testing the Mean-Variance Efficiency of Well-Diversified Portfolios in Very Large Cross-Sections," Annales d'Economie et de Statistique, ENSAE, issue 40, pages 93-124.
  5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  6. Luger, Richard, 2003. "Exact non-parametric tests for a random walk with unknown drift under conditional heteroscedasticity," Journal of Econometrics, Elsevier, vol. 115(2), pages 259-276, August.
  7. 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.
  8. Chow, K. Victor & Denning, Karen C., 1993. "A simple multiple variance ratio test," Journal of Econometrics, Elsevier, vol. 58(3), pages 385-401, August.
  9. Whitney K. Newey & Kenneth D. West, 1986. "A Simple, Positive Semi-Definite, Heteroskedasticity and AutocorrelationConsistent Covariance Matrix," NBER Technical Working Papers 0055, National Bureau of Economic Research, Inc.
  10. Roll, Richard, 1979. "A reply to Mayers and Rice (1979)," Journal of Financial Economics, Elsevier, vol. 7(4), pages 391-400, December.
  11. Lo, Andrew W. (Andrew Wen-Chuan) & MacKinlay, Archie Craig, 1955-, 1989. "Data-snooping biases in tests of financial asset pricing models," Working papers 3020-89., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  12. 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 745-52, June.
  13. Jobson, J. D. & Korkie, Bob, 1982. "Potential performance and tests of portfolio efficiency," Journal of Financial Economics, Elsevier, vol. 10(4), pages 433-466, December.
  14. Breusch, T.S. & Pagan, A.R., . "The Lagrange multiplier test and its applications to model specification in econometrics," CORE Discussion Papers RP -412, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  15. 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.
  16. Berk, Jonathan B., 1997. "Necessary Conditions for the CAPM," Journal of Economic Theory, Elsevier, vol. 73(1), pages 245-257, March.
  17. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
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Citations

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Cited by:
  1. Pesaran, M. H. & Yamagata, T., 2012. "Testing CAPM with a Large Number of Assets (Updated 28th March 2012)," Cambridge Working Papers in Economics 1210, Faculty of Economics, University of Cambridge.
  2. Sermin Gungor & Richard Luger, 2013. "Multivariate Tests of Mean-Variance Efficiency and Spanning with a Large Number of Assets and Time-Varying Covariances," Working Papers 13-16, Bank of Canada.
  3. Pesaran, M. Hashem & Yamagata, Takashi, 2012. "Testing CAPM with a Large Number of Assets," IZA Discussion Papers 6469, Institute for the Study of Labor (IZA).
  4. Dufour, Jean-Marie & Khalaf, Lynda & Kichian, Maral, 2013. "Identification-robust analysis of DSGE and structural macroeconomic models," Journal of Monetary Economics, Elsevier, vol. 60(3), pages 340-350.
  5. 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.

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