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The exact distribution of the Hansen-Jagannathan bound

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  • Raymond Kan
  • Cesare Robotti

Abstract

Under the assumption of multivariate normality of asset returns, this paper presents a geometrical interpretation and the finite-sample distributions of the sample Hansen-Jagannathan (1991) bounds on the variance of admissible stochastic discount factors, with and without the nonnegativity constraint on the stochastic discount factors. In addition, since the sample Hansen-Jagannathan bounds can be very volatile, we propose a simple method to construct confidence intervals for the population Hansen-Jagannathan bounds. Finally, we show that the analytical results in the paper are robust to departures from the normality assumption.

Suggested Citation

  • Raymond Kan & Cesare Robotti, 2008. "The exact distribution of the Hansen-Jagannathan bound," FRB Atlanta Working Paper 2008-09, Federal Reserve Bank of Atlanta.
    • Handle: RePEc:fip:fedawp:2008-09
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    File URL: https://www.frbatlanta.org/-/media/documents/research/publications/wp/2008/wp0809.pdf
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    References listed on IDEAS

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    Cited by:

    1. Xyngis, Georgios, 2017. "Business-cycle variation in macroeconomic uncertainty and the cross-section of expected returns: Evidence for scale-dependent risks," Journal of Empirical Finance, Elsevier, vol. 44(C), pages 43-65.
    2. Nikolay Gospodinov & Raymond Kan & Cesare Robotti, 2012. "Analytical solution for the constrained Hansen-Jagannathan distance under multivariate ellipticity," FRB Atlanta Working Paper 2012-18, Federal Reserve Bank of Atlanta.
    3. Wickern, Tobias, 2011. "Confidence in prior knowledge: Calibration and impact on portfolio performance," Discussion Papers in Econometrics and Statistics 7/11, University of Cologne, Institute of Econometrics and Statistics.
    4. Nikolay Gospodinov & Raymond Kan & Cesare Robotti, 2010. "On the Hansen-Jagannathan distance with a no-arbitrage constraint," FRB Atlanta Working Paper 2010-04, Federal Reserve Bank of Atlanta.

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