Analytical Solution for the Constrained Hansen-Jagannathan Distance Under Multivariate Ellipticity

We provide an in-depth analysis of the theoretical properties of the Hansen-Jagannathan (HJ) distance that incorporates a no-arbitrage constraint. Under a multivariate elliptical distribution assumption, we present explicit expressions for the HJ-distance with a no-arbitrage constraint, the associated Lagrange multipliers, and the SDF parameters in the case of linear SDFs. This approach allows us to analyze the benefits and costs of using the HJ-distance with a no-arbitrage constraint to rank asset pricing models.

Keywords: Hansen-Jagannathan distance, no-arbitrage, model ranking, multivariate elliptical distributions

JEL Classification: G12

Suggested Citation: Suggested Citation

Gospodinov, Nikolay and Kan, Raymond and Robotti, Cesare, Analytical Solution for the Constrained Hansen-Jagannathan Distance Under Multivariate Ellipticity (November 2012). FRB Atlanta Working Paper No. 2012-18, Rotman School of Management Working Paper No. 2479458, Available at SSRN: https://ssrn.com/abstract=2479458 or http://dx.doi.org/10.2139/ssrn.2479458