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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.

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Bibliographic Info

Paper provided by Federal Reserve Bank of Atlanta in its series Working Paper with number 2008-09.

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Date of creation: 2008
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Handle: RePEc:fip:fedawp:2008-09

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  1. Cecchetti, Stephen G & Lam, Pok-sang & Mark, Nelson C, 1994. " Testing Volatility Restrictions on Intertemporal Marginal Rates of Substitution Implied by Euler Equations and Asset Returns," Journal of Finance, American Finance Association, vol. 49(1), pages 123-52, March.
  2. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  3. Geert Bekaert & Robert J. Hodrick, 1991. "Characterizing Predictable Components in Excess Returns on Equity and Foreign Exchange Markets," NBER Working Papers 3790, National Bureau of Economic Research, Inc.
  4. 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.
  5. Gregory, Allan W. & Smith, Gregor W., 1992. "Sampling variability in Hansen-Jagannathan bounds," Economics Letters, Elsevier, vol. 38(3), pages 263-267, March.
  6. Burnside, Craig, 1994. "Hansen-Jagannathan Bounds as Classical Tests of Asset-Pricing Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(1), pages 57-79, January.
  7. 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.
  8. Lars Peter Hansen & Ravi Jagannathan, 1990. "Implications of security market data for models of dynamic economies," Discussion Paper / Institute for Empirical Macroeconomics 29, Federal Reserve Bank of Minneapolis.
  9. R. Mehra & E. Prescott, 2010. "The equity premium: a puzzle," Levine's Working Paper Archive 1401, David K. Levine.
  10. 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.
  11. Ferson, Wayne E & Harvey, Campbell R, 1992. " Seasonality and Consumption-Based Asset Pricing," Journal of Finance, American Finance Association, vol. 47(2), pages 511-52, June.
  12. 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.
  13. Gibbons, Michael R & Ross, Stephen A & Shanken, Jay, 1989. "A Test of the Efficiency of a Given Portfolio," Econometrica, Econometric Society, vol. 57(5), pages 1121-52, September.
  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 738-45, September.
  15. Jonathan Lewellen & Stefan Nagel & Jay Shanken, 2006. "A Skeptical Appraisal of Asset-Pricing Tests," NBER Working Papers 12360, National Bureau of Economic Research, Inc.
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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," 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 Statistics and Econometrics 7/11, University of Cologne, Department for Economic and Social Statistics.

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