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Statistical Inference on Stochastic Dominance Efficiency. Do Omitted Risk Factors Explain the Size and Book-to-Market Effects?

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  • Post, G.T.

Abstract

This paper discusses statistical inference on the second-order stochastic dominance (SSD) efficiency of a given portfolio relative to all portfolios formed from a set of assets. We derive the asymptotic sampling distribution of the Post test statistic for SSD efficiency. Unfortunately, a test procedure based on this distribution involves low power in small samples. Bootstrapping is a more powerful approach to sampling error. We use the bootstrap to test if the Fama and French value-weighted market portfolio is SSD efficient relative to benchmark portfolios formed on market capitalization and book-tomarket equity ratio. During the late 1970s and during the 1980s, the market portfolio is significantly SSD inefficient, even if we use samples of only 60 monthly observations. This suggests that the size and book-to-market effects cannot be explained by omitted risk factors like higher-order central moments or lower partial moments.

Suggested Citation

  • Post, G.T., 2003. "Statistical Inference on Stochastic Dominance Efficiency. Do Omitted Risk Factors Explain the Size and Book-to-Market Effects?," ERIM Report Series Research in Management ERS-2003-017-F&A, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    • Handle: RePEc:ems:eureri:279
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    References listed on IDEAS

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    1. Fama, Eugene F & French, Kenneth R, 1992. "The Cross-Section of Expected Stock Returns," Journal of Finance, American Finance Association, vol. 47(2), pages 427-465, June.
    2. Valentino Dardanoni & Antonio Forcina, 1999. "Inference for Lorenz curve orderings," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 49-75.
    3. Thierry Post, 2003. "Empirical Tests for Stochastic Dominance Efficiency," Journal of Finance, American Finance Association, vol. 58(5), pages 1905-1932, October.
    4. Eric Ghysels, 1998. "On Stable Factor Structures in the Pricing of Risk: Do Time-Varying Betas Help or Hurt?," Journal of Finance, American Finance Association, vol. 53(2), pages 549-573, April.
    5. Huberman, Gur & Kandel, Shmuel, 1987. "Mean-Variance Spanning," Journal of Finance, American Finance Association, vol. 42(4), pages 873-888, September.
    6. Berk, Jonathan B., 1997. "Necessary Conditions for the CAPM," Journal of Economic Theory, Elsevier, vol. 73(1), pages 245-257, March.
    7. Thierry Post, 2003. "Empirical Tests for Stochastic Dominance Efficiency," Journal of Finance, American Finance Association, vol. 58(5), pages 1905-1931, October.
    8. Levy, Haim, 1969. "A Utility Function Depending on the First Three Moments: Comment," Journal of Finance, American Finance Association, vol. 24(4), pages 715-719, September.
    9. Russell Davidson & Jean-Yves Duclos, 2000. "Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality," Econometrica, Econometric Society, vol. 68(6), pages 1435-1464, November.
    10. Kroll, Yoram & Levy, Haim, 1980. "Sampling Errors and Portfolio Efficient Analysis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 15(3), pages 655-688, September.
    11. Haim Levy, 1992. "Stochastic Dominance and Expected Utility: Survey and Analysis," Management Science, INFORMS, vol. 38(4), pages 555-593, April.
    12. Dybvig, Philip H & Ross, Stephen A, 1982. "Portfolio Efficient Sets," Econometrica, Econometric Society, vol. 50(6), pages 1525-1546, November.
    13. Bawa, Vijay S. & Lindenberg, Eric B., 1977. "Capital market equilibrium in a mean-lower partial moment framework," Journal of Financial Economics, Elsevier, vol. 5(2), pages 189-200, November.
    14. Campbell R. Harvey & Akhtar Siddique, 2000. "Conditional Skewness in Asset Pricing Tests," Journal of Finance, American Finance Association, vol. 55(3), pages 1263-1295, June.
    15. Kraus, Alan & Litzenberger, Robert H, 1976. "Skewness Preference and the Valuation of Risk Assets," Journal of Finance, American Finance Association, vol. 31(4), pages 1085-1100, September.
    16. Levy, Haim, 1978. "Equilibrium in an Imperfect Market: A Constraint on the Number of Securities in the Portfolio," American Economic Review, American Economic Association, vol. 68(4), pages 643-658, September.
    17. Charles M. Beach & Russell Davidson, 1983. "Distribution-Free Statistical Inference with Lorenz Curves and Income Shares," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(4), pages 723-735.
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    More about this item

    Keywords

    asset pricing; market efficiency; size and book-to-market effects; statistical inference; stochastic dominance;
    All these keywords.

    JEL classification:

    • C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Other
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G3 - Financial Economics - - Corporate Finance and Governance
    • M - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics
    • M41 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Accounting - - - Accounting

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