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The exact distribution of the Hansen-Jagannathan bound

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Raymond Kan
Cesare Robotti

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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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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. 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. [Downloadable!]
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  2. Stephen G. Cecchetti & Pok-sang Lam & Nelson C. Mark, 1992. "Testing Volatility Restrictions on Intertemporal Marginal Rates of Substitution Implied by Euler Equations and Asset Returns," NBER Technical Working Papers 0124, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  3. 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. [Downloadable!] (restricted)
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  4. Gregory, Allan W. & Smith, Gregor W., 1992. "Sampling variability in Hansen-Jagannathan bounds," Economics Letters, Elsevier, vol. 38(3), pages 263-267, March. [Downloadable!] (restricted)
  5. 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. [Downloadable!] (restricted)
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  6. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March. [Downloadable!] (restricted)
  7. 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. [Downloadable!]
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  8. Jonathan Lewellen & Stefan Nagel & Jay Shanken, 2006. "A Skeptical Appraisal of Asset-Pricing Tests," NBER Working Papers 12360, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  9. 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. [Downloadable!] (restricted)
  10. 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. [Downloadable!] (restricted)
  11. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April. [Downloadable!] (restricted)
  12. Geert Bekaert & Jun Liu, 1999. "Conditioning Information and Variance Bounds on Pricing Kernels," NBER Working Papers 6880, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  13. Wayne E. Ferson & Andrew F. Siegel, 2003. "Stochastic Discount Factor Bounds with Conditioning Information," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 16(2), pages 567-595. [Downloadable!] (restricted)
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