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The Exact Distribution of the Hansen-Jagannathan Bound

Raymond Kan
University of Toronto - Joseph L. Rotman School of Management

Cesare Robotti
Federal Reserve Bank of Atlanta

February 2008

FRB Atlanta Working Paper No. 2008-9

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.

Keywords: Hansen-Jagannathan Bound, No Arbitrage, Positivity, Exact Distribution

JEL Classifications: G12

Working Paper Series

Date posted: December 21, 2007 ; Last revised: November 13, 2008

Suggested Citation

Robotti, Cesare and Kan, Raymond, The Exact Distribution of the Hansen-Jagannathan Bound (February 2008). FRB Atlanta Working Paper No. 2008-9. Available at SSRN: http://ssrn.com/abstract=1076687

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Contact Information

Raymond Kan (Contact Author) University of Toronto - Joseph L. Rotman School of Management ( email ) 105 St. George Street Toronto, Ontario M5S 3E6 Canada 416-978-4291 (Phone) 416-971-3048 (Fax)
Cesare Robotti Federal Reserve Bank of Atlanta ( email ) 1000 Peachtree Street NE Atlanta, GA 30309-4470 United States 404-498-8543 (Phone) 404-498-8810 (Fax)