The Exact Distribution of the Hansen–Jagannathan Bound
Management Science · 2016 · Volume 62 · Issue 7
Abstract
Under the assumption of multivariate normality of asset returns, this paper presents a geometric interpretation and the finite-sample distributions of the sample Hansen–Jagannathan 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. Data, as supplemental material, are available at http://dx.doi.org/10.1287/mnsc.2015.2222 . This paper was accepted by Jerome Detemple, operations management .
Keywords
Hansen–Jagannathan bounds, finite-sample distributions, maximum likelihood estimators, in-sample arbitrage portfolios
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