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On the properties of the constrained Hansen–Jagannathan distance

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  • Gospodinov, Nikolay
  • Kan, Raymond
  • Robotti, Cesare

Abstract

We provide an in-depth analysis of the theoretical properties of the Hansen–Jagannathan (HJ) distance that incorporates a no-arbitrage constraint. Under a multivariate elliptical distribution assumption, we present explicit expressions for the HJ-distance with a no-arbitrage constraint, the associated Lagrange multipliers, and the stochastic discount factor (SDF) parameters in the case of linear SDFs. This allows us to analyze the benefits and costs of using the HJ-distance with a no-arbitrage constraint to evaluate and rank models. We also study the asymptotic and finite-sample properties of the sample constrained HJ-distance. Finally, we demonstrate the practical relevance of our theoretical findings in an empirical illustration of some popular asset-pricing models.

Suggested Citation

  • Gospodinov, Nikolay & Kan, Raymond & Robotti, Cesare, 2016. "On the properties of the constrained Hansen–Jagannathan distance," Journal of Empirical Finance, Elsevier, vol. 36(C), pages 121-150.
    • Handle: RePEc:eee:empfin:v:36:y:2016:i:c:p:121-150
    DOI: 10.1016/j.jempfin.2015.10.001
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    3. Caio Almeida & Kym Ardison & René Garcia & Jose Vicente, 2017. "Nonparametric Tail Risk, Stock Returns, and the Macroeconomy," Journal of Financial Econometrics, Oxford University Press, vol. 15(3), pages 333-376.
    4. Gospodinov, Nikolay & Maasoumi, Esfandiar, 2021. "Generalized aggregation of misspecified models: With an application to asset pricing," Journal of Econometrics, Elsevier, vol. 222(1), pages 451-467.

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    More about this item

    Keywords

    No-arbitrage; Constrained Hansen-Jagannathan distance; Asset-pricing models; Linear SDFs; Equity pricing;
    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
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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