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Spanning tests in return and stochastic discount factor mean-variance frontiers: A unifying approach

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  • Francisco Peñaranda
  • Enrique Sentana

Abstract

We propose new spanning tests that assess if the initial and additional assets share the economically meaningful cost and mean representing portfolios. We prove their asymptotic equivalence to existing tests under local alternatives. We also show that unlike two-step or iterated procedures, single-step methods such as continuously updated GMM yield numerically identical overidentifyng restrictions tests, so there is arguably a single spanning test. To prove these results, we extend optimal GMM inference to deal with singularities in the long run second moment matrix of the influence functions. Finally, we test for spanning using size and book-to-market sorted US stock portfolios.

Suggested Citation

  • Francisco Peñaranda & Enrique Sentana, 2008. "Spanning tests in return and stochastic discount factor mean-variance frontiers: A unifying approach," Economics Working Papers 1101, Department of Economics and Business, Universitat Pompeu Fabra, revised Sep 2010.
  • Handle: RePEc:upf:upfgen:1101
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    Citations

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    Cited by:

    1. 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.
    2. repec:eee:intfor:v:33:y:2017:i:3:p:618-626 is not listed on IDEAS
    3. Peñaranda, Francisco & Sentana, Enrique, 2016. "Duality in mean-variance frontiers with conditioning information," Journal of Empirical Finance, Elsevier, vol. 38(PB), pages 762-785.
    4. 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.
    5. Gur Huberman & Zhenyu Wang, 2005. "Arbitrage pricing theory," Staff Reports 216, Federal Reserve Bank of New York.
    6. Nicky Grant, 2013. "Identification Robust Inference with Singular Variance," The School of Economics Discussion Paper Series 1315, Economics, The University of Manchester.
    7. 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.
    8. Peñaranda, Francisco & Sentana, Enrique, 2016. "Duality in mean-variance frontiers with conditioning information," Journal of Empirical Finance, Elsevier, vol. 38(PB), pages 762-785.
    9. 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.
    10. David T. Frazier & Eric Renault, 2016. "Indirect Inference With(Out) Constraints," Papers 1607.06163, arXiv.org, revised Aug 2016.
    11. 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.

    More about this item

    Keywords

    Asset Pricing; Continuously Updated GMM; Generalised Empirical Likelihood; Generalised Inverse; Representing Portfolios; Singular Covariance Matrix;

    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
    • 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

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