The exact distribution of the Hansen-Jagannathan bound - Raymond Kan; Cesare Robotti (Federal Reserve Bank of Atlanta, 2008)
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: G12; 330; Hansen-Jagannathan bound; exact distribution; no-arbitrage