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Spanning Tests in Return and Stochastic Discount Factor Mean Variance Frontiers: A Unifying Approach

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  • Sentana, Enrique
  • Peñaranda, Francisco

Abstract

We propose new approaches to test for spanning in the return and stochastic discount factor mean-variance frontiers, which assess if either the centred or uncentred mean and cost representing portfolios are shared by the initial and extended sets of assets. We show that our proposed tests are asymptotically equivalent to the existing spanning tests under the null and sequences of local alternatives, and analyse their asymptotic relative efficiency. We also extend the theory of optimal GMM inference to deal with the singularities that arise in some spanning tests. Finally, we include an empirical application to money markets in Europe.

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  • Sentana, Enrique & Peñaranda, Francisco, 2004. "Spanning Tests in Return and Stochastic Discount Factor Mean Variance Frontiers: A Unifying Approach," CEPR Discussion Papers 4422, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:4422
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    3. 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.
    4. 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.
    5. Mayer, Walter J. & Liu, Feng & Dang, Xin, 2017. "Improving the power of the Diebold–Mariano–West test for least squares predictions," International Journal of Forecasting, Elsevier, vol. 33(3), pages 618-626.
    6. Peñaranda, Francisco & Sentana, Enrique, 2016. "Duality in mean-variance frontiers with conditioning information," Journal of Empirical Finance, Elsevier, vol. 38(PB), pages 762-785.
    7. Massimo Guidolin & Erwin Hansen & Martín Lozano-Banda, 2018. "Portfolio performance of linear SDF models: an out-of-sample assessment," Quantitative Finance, Taylor & Francis Journals, vol. 18(8), pages 1425-1436, August.
    8. Antonio Diez de Los Rios, 2015. "A New Linear Estimator for Gaussian Dynamic Term Structure Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 282-295, April.
    9. Caio Vigo Pereira & Marcio Laurini, 2020. "Portfolio Efficiency Tests with Conditioning Information - Comparing GMM and GEL Estimators," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202014, University of Kansas, Department of Economics, revised Sep 2020.
    10. Victor Chernozhukov & Emre Kocatulum & Konrad Menzel, 2015. "Inference on sets in finance," Quantitative Economics, Econometric Society, vol. 6(2), pages 309-358, July.
    11. Arvanitis, Stelios & Scaillet, Olivier & Topaloglou, Nikolas, 2020. "Spanning analysis of stock market anomalies under prospect stochastic dominance," Working Papers unige:134101, University of Geneva, Geneva School of Economics and Management.
    12. Francisco Peñaranda & Enrique Sentana, 2015. "A Unifying Approach to the Empirical Evaluation of Asset Pricing Models," The Review of Economics and Statistics, MIT Press, vol. 97(2), pages 412-435, May.
    13. Gur Huberman & Zhenyu Wang, 2005. "Arbitrage pricing theory," Staff Reports 216, Federal Reserve Bank of New York.
    14. José Cerón & Javier Suarez, 2006. "Hot and Cold Housing Markets: International Evidence," Working Papers wp2006_0603, CEMFI.
    15. Nicky Grant, 2013. "Identification Robust Inference with Singular Variance," Economics Discussion Paper Series 1315, Economics, The University of Manchester.
    16. Aleix Calveras & Juan-José Ganuza & Gerard Llobet, 2005. "Regulation and Opportunism: How Much Activism Do We Need?," Working Papers wp2005_0508, CEMFI.
    17. Fousseni Chabi-Yo & René Garcia & Eric Renault, 2005. "The Stochastic Discount Factor: Extending the Volatility Bound and a New Approach to Portfolio Selection with Higher-Order Moments," Staff Working Papers 05-2, Bank of Canada.
    18. Yoshihiko Nishiyama & Peter Robinson, 2004. "The bootstrap and the Edgeworth correction for semiparametric averaged derivatives," CeMMAP working papers 12/04, Institute for Fiscal Studies.
    19. 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.
    20. Javier Díaz-Giménez & Josep Pijoan-Mas, 2006. "Flat Tax Reforms in the U.S.: A Boon for the Income Poor," Working Papers wp2006_0611, CEMFI.
    21. 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).
    22. Diez de los Rios, Antonio, 2015. "Optimal asymptotic least squares estimation in a singular set-up," Economics Letters, Elsevier, vol. 128(C), pages 83-86.
    23. Antonio Diez de los Rios, 2017. "Optimal Estimation of Multi-Country Gaussian Dynamic Term Structure Models Using Linear Regressions," Staff Working Papers 17-33, Bank of Canada.
    24. David T. Frazier & Eric Renault, 2016. "Indirect Inference With(Out) Constraints," Papers 1607.06163, arXiv.org, revised Aug 2019.

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    More about this item

    Keywords

    Asset pricing; Asymptotic slopes; Gmm; Representing portfolios; Singular covariance; Matrix;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • 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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