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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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    References listed on IDEAS

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    3. Wayne E. Ferson & Andrew F. Siegel, 2003. "Stochastic Discount Factor Bounds with Conditioning Information," Review of Financial Studies, Society for Financial Studies, vol. 16(2), pages 567-595.
    4. Epstein, Larry G. & Zin, Stanley E., 2001. "The independence axiom and asset returns," Journal of Empirical Finance, Elsevier, vol. 8(5), pages 537-572, December.
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    7. Christopher Otrok & B. Ravikumar & Charles H. Whiteman, 2002. "Evaluating asset-pricing models using the Hansen-Jagannathan bound: a Monte Carlo investigation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(2), pages 149-174.
    8. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
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    10. Ferson, Wayne E & Harvey, Campbell R, 1992. " Seasonality and Consumption-Based Asset Pricing," Journal of Finance, American Finance Association, vol. 47(2), pages 511-552, June.
    11. Geert Bekaert, 2004. "Conditioning Information and Variance Bounds on Pricing Kernels," Review of Financial Studies, Society for Financial Studies, vol. 17(2), pages 339-378.
    12. Bekaert, Geert & Hodrick, Robert J, 1992. " Characterizing Predictable Components in Excess Returns on Equity and Foreign Exchange Markets," Journal of Finance, American Finance Association, vol. 47(2), pages 467-509, June.
    13. Gregory, Allan W. & Smith, Gregor W., 1992. "Sampling variability in Hansen-Jagannathan bounds," Economics Letters, Elsevier, vol. 38(3), pages 263-267, March.
    14. Hagiwara, May & Herce, Miguel A, 1997. "Risk Aversion and Stock Price Sensitivity to Dividends," American Economic Review, American Economic Association, vol. 87(4), pages 738-745, September.
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    Cited by:

    1. 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.
    2. 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.
    3. 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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