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The Exact Distribution of the Hansen–Jagannathan Bound

Author

Listed:
  • Raymond Kan

    (Rotman School of Management, University of Toronto, Toronto, Ontario M5S 3E6, Canada)

  • Cesare Robotti

    (Imperial College Business School, Imperial College London, London SW7 2AZ, United Kingdom)

Abstract

Under the assumption of multivariate normality of asset returns, this paper presents a geometric interpretation and the finite-sample distributions of the sample Hansen–Jagannathan 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.Data, as supplemental material, are available at http://dx.doi.org/10.1287/mnsc.2015.2222 . This paper was accepted by Jerome Detemple, operations management .

Suggested Citation

  • Raymond Kan & Cesare Robotti, 2016. "The Exact Distribution of the Hansen–Jagannathan Bound," Management Science, INFORMS, vol. 62(7), pages 1915-1943, July.
    • Handle: RePEc:inm:ormnsc:v:62:y:2016:i:7:p:1915-1943
    DOI: 10.1287/mnsc.2015.2222
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    References listed on IDEAS

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    3. Kan, Raymond & Wang, Xiaolu & Zheng, Xinghua, 2024. "In-sample and out-of-sample Sharpe ratios of multi-factor asset pricing models," Journal of Financial Economics, Elsevier, vol. 155(C).

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