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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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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. 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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  2. 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)
  3. 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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  4. 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)
  5. 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)
  6. 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)
  7. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April. [Downloadable!] (restricted)
  8. 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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  9. 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. [Downloadable!] (restricted)
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